MRP Inventory & Customer Service and Forecasting Methods

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Planning for Material and Resource Requirements

Learning Objec�ves A�er comple�ng this chapter, you should be able to:

Describe the rela�onships among forecas�ng, aggregate planning, master scheduling, MRP, and capacity planning. Show how a master schedule is developed from an aggregate plan. Use the method of overall factors to es�mate capacity requirements based on a master schedule. Explain the difference between independent and dependent demand, and indicate the type of demand for which MRP is appropriate. Use MRP to develop planned order releases for items at all levels of the bill of materials. Develop a load report and load profile based on MRP output, rou�ngs, and labor standards. Describe the characteris�cs of MRP II.

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9.1 Role of Planning

Planning is one of the most important, yet least understood, jobs that a manager performs. Poor planning can hinder a company's ability to handle unexpected occurrences. Good planning can place a company in an extremely strong compe��ve posi�on, one that prepares the organiza�on to deal with any event. All parts of the organiza�on—marke�ng, opera�ons, finance—must work together in the planning process to ensure that they are moving in harmony with one another.

The start of the planning ac�vity is the development of a compe��ve strategy. In today's extremely compe��ve global marketplace, organiza�ons cannot afford to go forward without a well-planned strategy, which includes the opera�ons func�on as well as every other part of the organiza�on. The strategy is then converted into a business plan—a blueprint for implemen�ng the strategic plan. Based on a forecast and the business plan, each part of an organiza�on must then develop its own plans that describe how the various parts will work to implement the business and strategic plans. Forecasts of demand and other important business factors, such as costs, are vital if an organiza�on wants to create an effec�ve plan. This series of planning stages is shown in Figure 9.1.

Figure 9.1: Opera�ons planning ac�vi�es

As part of this overall planning effort, firms develop opera�onal plans that extrapolate across different �me periods. Long-range opera�ons planning addresses facili�es and resources including the number of facili�es to build, the loca�on(s), the capacity, and the type of process technologies. Long-range planning is o�en considered to be five years, but could be longer or shorter depending on the industry, For example, if an industry such as electric power genera�on requires 10 years to build a facility, a 5-year plan would be too short. The industry must be able to plan far enough into the future so it can make the changes needed to respond to growth in demand.

Medium-range opera�ons planning develops ways to u�lize resources to meet customer demand. The �me horizon for medium-range planning is generally from 6 to 18 months in the future, but may vary outside of this range. The decisions that are usually made as part of medium-range opera�ons planning include the following:

Workforce size Opera�ng hours of the facili�es Levels of inventory that will be maintained Output rates for the processes

Medium-range opera�ons plans must be well coordinated with the marke�ng plans and the financial plans created by the organiza�on, because these help the firm to develop the aggregate plan. See Figure 9.1.

Aggregate planning is the combining of individual end items into groups or families of parts for planning purposes. For instance, an appliance manufacturer may begin medium-range planning by determining produc�on rates for each broad product family, such as refrigerators, stoves, and dishwashers. The aggregated plan is a statement of planned output by product groups on a monthly basis. It provides enough informa�on to make decisions about important opera�ng decisions such as se�ng contracts for materials, hiring and training employees, and inventory.

There must be enough flexibility in the contracts with suppliers as well as the capabili�es of the employees and facili�es so the firm can produce what the

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The planning process begins with the crea�on of a compe��ve strategy, which is then converted into a business plan—a blueprint for implemen�ng the strategic plan.

customer demands because the aggregate plan does not provide sufficient details. When actual produc�on takes place, the appliance company must specify the number of each model to be produced. For a refrigerator, the model would iden�fy the size in cubic feet, energy efficiency, and layout (side- by-side or over-under). This more detailed plan, called the master produc�on schedule, is based on the aggregate plan.

If sufficient quan��es of required resources and materials are not available when needed, customer service will suffer. When developing a master produc�on schedule, a company must ensure that the schedule is realis�c in terms of its resource and material requirements. This chapter explains how to develop a master produc�on schedule, and how an organiza�on can determine the resource and material requirements to produce the goods and services for that master produc�on schedule. This leads to a plan that will ensure the appropriate quan�ty of materials and resources available at the right �me and place.

Highlight: PC Manufacturing

An aggregate plan for a PC manufacturer will state the number of units it intends to produce, but it will not provide the number of each model or type the firm intends to produce. The aggregate plan will not iden�fy the amount of memory each unit will have or the type of video card. The aggregate plan helps the company and its suppliers to plan for produc�on over the next few weeks, months, or possibly one year. As each �me period, say one month, passes, the aggregate plan is refreshed to account for more recent informa�on about demand. A func�onal short-term aggregate plan will ensure that the firm and its suppliers have enough flexibility to respond to customer demand as it is reported in the very short term so that each PC has the features that customer wants. This final step involves scheduling so that the right material and the right employees with the right skills come together at the right place and �me with the right equipment to make the product. This is the final, essen�al step when crea�ng and execu�ng an opera�onal plan. It involves the crea�on of a master produc�on schedule.

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9.2 Master Production Schedule

The master schedule—or master produc�on schedule (MPS)—is based on the "aggregated" plan. The master produc�on schedule "disaggregates the aggregate plan" because it is a specific statement of exactly what will be produced and a specific date for produc�on. The master produc�on schedule usually states individual end items or product models. The master schedule is, therefore, a detailed extension of the medium-range opera�ons plan, or aggregate plan.

Planning Horizons

The aggregate plan is o�en developed for one year into the future. The master schedule, however, does not need to extend that far, especially because it becomes more difficult to manage as �me increases. As a general rule, companies use six months or less for their master schedule. However, an important rule is that the master scheduling horizon should be at least equal to the longest cumula�ve lead �me of any product and its component parts. In other words, enough �me must be allowed from the �me a master schedule quan�ty is entered for all parts and raw materials to be ordered from suppliers, component parts to be manufactured, and the final product to be assembled and shipped. Otherwise, the master schedule will not be able to sa�sfy the demand for those products with long cumula�ve lead �mes.

MPS Development Process

The master schedule is a statement of exactly what will be produced. It must simultaneously sa�sfy the needs of sales and marke�ng and be feasible in terms of opera�ons. Developing a master schedule that is close to the aggregate plan, yet s�ll sa�sfies marke�ng and opera�ons, is not an easy task. The aggregate plan was developed based on a strategy that maintained acceptable inventory and workforce levels. The master schedule should s�ll be based on that strategy, but must now do so for individual end items. In addi�on, the master schedule must not place more capacity demands on any machine or work center than can reasonably be met by exis�ng capacity. Due to the difficul�es involved in developing a good master produc�on schedule, the job is usually done by experienced individuals called master schedulers.

Maine Woods Company produces wooden toys using a labor-intensive produc�on process relying heavily on skilled woodworkers to make most of the parts that are used for the company's finished products. The company's aggregate produc�on plan is developed on a monthly basis for one year into the future. For planning purposes, the company's 48 different products are grouped by product characteris�cs into three product families: wheel goods, blocks, and baby toys. It is these families that are reflected in the aggregate plan. Table 9.1 shows that plan for the wheel-goods products only.

Table 9.1: Maine Woods Co. aggregate plan, wheel-goods product group

Month Demand Forecast Regular-Time Produc�on

Over�me Produc�on Beginning Inventory Ending Inventory

January 1,800 2,000 0 200

February 1,700 2,000 200 500

March 1,800 2,000 500 700

April 1,500 2,000 700 1,200

May 1,800 2,000 1,200 1,400

June 1,900 2,000 1,400 1,500

July 2,000 2,000 1,500 1,500

August 2,500 2,000 1,500 1,000

September 2,500 2,000 1,000 500

October 2,900 2,000 400 500 0

November 2,400 2,000 400 0 0

December 2,000 2,000 0 0

The company has developed an aggregate plan that emphasizes maintaining a constant workforce. Due to the high skill level required of its employees, Maine Woods does not want to hire or lay off personnel. Instead, inventory is built up in an�cipa�on of high demand during late summer and fall when the retail stores that sell Maine Woods' toys order in prepara�on for Christmas. Over�me has been planned only as a necessity in October and November when no inventory will be available.

Matching the Schedule to the Plan

Refer again to the Maine Woods aggregate plan shown in Table 9.1. Produc�on exceeds demand during the early part of the year, thus increasing inventory. During that �me period, the company's objec�ves for the master produc�on schedule will be to:

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Produce quan��es that will match the aggregate plan Produce each individual product in propor�on to its expected demand Schedule produc�on so that available capacity is not exceeded

The wheel-goods product group consists of three products: tricycles, toy wagons, and scooters. Past experience indicates that orders for these items will be divided so that approximately half are for tricycles and the remaining orders are equally divided between wagons and scooters. Thus, in January, the planned produc�on of 2,000 units should be divided so that 1,000 tricycles, 500 toy wagons, and 500 scooters are produced. The same should also be done for February and March.

Figure 9.2 shows one possible master schedule that sa�sfies the preceding requirements. No�ce that the total produc�on of all three products in each month matches the aggregate plan for that month. Further, produc�on of each individual product is distributed evenly so the produc�on facili�es will not be overloaded in some weeks and under loaded in others.

Figure 9.2: Maine Woods Co. master produc�on schedule, wheel-goods product group: Constant planned produc�on

The master schedule shown in Figure 9.2 could be extended across the first nine months of the year because planned produc�on during each of those months is the same. But, in October, planned produc�on increases to 2,400 units. To meet this increase, the difference can be spread evenly across that month, keeping each product's propor�on of the total the same as before. Figure 9.3 shows the master schedule with increased output for October.

Figure 9.3: Maine Woods Co. master produc�on schedule, wheel-goods product group

Accounting for Customer Orders

The master schedule shown in Figure 9.3 is based on the aggregate plan and historical informa�on about demand for each product. However, customer orders must become part of the process; otherwise, the company may be producing based on a plan that is no longer valid because demand has changed.

To show how a master schedule that takes demand into account can be developed, remove inventory buildup from the picture by concentra�ng on the months of November and December when inventory is not available and demand must be met from current produc�on. The example will concentrate on just one product— the toy wagon.

Suppose it is the last week of October, and the forecasts s�ll indicate that 600 toy wagons (one-fourth of 2,400) will be ordered during November and another 500 (one-fourth of 2,000) during December. We can enter this informa�on in Figure 9.4 in the "Forecast demand" row. Actual customer orders may, however, differ from the forecast. Therefore, the next row in Figure 9.4 indicates actual orders booked. No�ce how the actual number of orders received decreases farther into the future because there are fewer known orders. As the future �me periods draw closer to the present, customer orders should increase, coming closer to the forecast.Processing math: 0%

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Figure 9.4: Maine Woods Co. master produc�on schedule based on demand forecast and booked customer orders for toy wagons

Projecting On-Hand Inventory

Because Maine Woods produces toy wagons only every other week, a key to mee�ng customer orders will be inventory. For example, no�ce that the company has 100 toy wagons in inventory at the end of October. However, customer orders for the first week of November are 170. Therefore, unless more wagons are produced, demand cannot be met. To avoid this problem, Maine Woods has already scheduled another batch of 300 wagons for produc�on during the first week of November, as shown in Figure 9.4.

To plan addi�onal produc�on of toy wagons, which will be scheduled in the "Master schedule" row of Figure 9.4, it will be necessary to calculate the projected on- hand inventory. This is referred to as "projected" because it is only based on informa�on currently available. As new customer orders arrive, the actual on-hand inventory each week may change.

To determine projected inventory on hand for a specific week, execute the following steps:

1. Determine the amount available to meet demand: Add either actual inventory on hand from the preceding week or projected on-hand inventory from the preceding week to the quan�ty shown in the "Master schedule" row for the week being calculated. If the master produc�on schedule is blank, then the amount is zero.

2. Determine demand: Select the larger of forecast demand or customer orders booked. This is done for two reasons. First, actual orders may exceed the forecast. Second, addi�onal orders could be received in the future for periods in which customer orders booked are currently less than the forecast.

3. Calculate on-hand inventory: Subtract the amount determined in step 2 from the amount in step 1. The result is the projected on-hand inventory for the week.

Problem

Refer to Figure 9.4 for Maine Woods. The projected on-hand inventory for weeks 45, 46, and 47 is calculated as follows:

WEEK 45:

1. Actual on-hand inventory from the preceding week (last week of October) is 100 units. 2. The master schedule amount for week 45 is 300. 3. There are 170 customer orders booked during week 45, which is larger than the forecast for that week (150).

Projected on-hand inventory = 100 + 300 − 170 = 230

WEEK 46:

1. Projected on-hand inventory from the preceding week (week 45) is 230 units. 2. The master schedule amount in week 46 is 0. 3. There are 165 customer orders booked in week 46, which is larger than the forecast for that week (150).

Projected on-hand inventory = 230 + 0 − 165 = 65

WEEK 47:

1. Projected on-hand inventory from the preceding week (week 46) is 65 units. 2. The master schedule amount in week 47 is 0.Processing math: 0%

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A firm must be able to handle customer orders that may be received at any �me. If a customer requests 50 toy wagons to be shipped in a specified period of �me, the company must take ac�ons to ensure that the order is met.

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3. Forecast demand for week 47 is 150, which is larger than the customer orders booked for that week (140).

Projected on-hand inventory = 65 + 0 − 150 = −85

When projected on-hand inventory becomes a nega�ve number, as it has in week 47, the need for more produc�on is indicated. Thus, a master schedule quan�ty must be entered for week 47. The exact quan�ty to schedule will be determined on the basis of produc�on capacity available, expected demand, and desired batch sizes. Following its procedure of producing toy wagons every other week, Maine Woods would plan to produce enough to meet demand for the next two weeks, which would be 300, based on the demand forecast shown in Figure 9.5. No�ce that the projected on-hand inventory balance for week 47 has been recalculated, based on the new master schedule quan�ty.

Figure 9.5: Calcula�on of available-to-promise for November and December for Maine Woods Co.

Amount Available-to-Promise

In addi�on to scheduling produc�on to meet projected demand, it is essen�al to prepare for customer orders to be received at any �me. The firm must be able to respond to these requests, and that is called "available-to-promise." For example, suppose a customer has contacted Maine Woods to request 50 toy wagons to be shipped in week 46. Will the company have enough toy wagons available to meet this new order plus the exis�ng orders for weeks 45 and 46 (which are 170 and 165, respec�vely) for a total of 335 toy wagons?

Companies calculate an available-to-promise quan�ty to determine whether new orders can be accepted within a given �me period. This quan�ty represents the number of units that can be promised for comple�on any �me before the next master schedule quan�ty.

The available-to-promise quan�ty is calculated as follows:

1. In the first �me period of the planning horizon, add actual on-hand inventory from the preceding �me period to any master schedule quan�ty. Then subtract the sum of customer orders booked before the next master schedule quan�ty.

2. For subsequent weeks, calculate available-to-promise only for those weeks when a master schedule quan�ty is indicated. Subtract the sum of customer orders booked before the next master schedule quan�ty from the master schedule amount for the given week. Do not include projected on-hand inventory, as that amount could be used in preceding weeks if more orders are booked.

Problem

Referring to the Maine Woods example shown in Figure 9.5, we will determine available-to-promise quan��es for November.

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Actual on-hand inventory from the preceding week (end of October) = 100. The master schedule quan�ty for week 45 = 300. The sum of customer orders booked before the next master schedule quan�ty (week 47) = 170 + 165. The available-to-promise quan�ty = (100 + 300) − (170 + 165) = 65.

WEEK 46:

There is no master schedule quan�ty in this week, so it is skipped.

WEEK 47:

The master schedule amount = 300. The sum of customer orders booked before the next master schedule quan�ty (week 49) = 140 + 120. The available-to- promise quan�ty = 300 − (140 + 120) = 40.

This indicates that Maine Woods can promise another 65 units to its customers for comple�on in week 45 or 46. The word "or" is cri�cal because it means that there are only 65 units available across both weeks. So, Maine Woods cannot promise 65 in week 45 and 65 in week 46. The available-to-promise for week 47 or 48 is 40. Because the calcula�on is step two assumes that the 65 available-to-promise in week 45 or 46 are consumed, these 40 units are in addi�on to the 65. So, if the 65 units are used, there are s�ll 40 units available to promise in week 47 or 48. If some of the 65 available-to-promise in week 45 or 46 are not consumed, the available-to-promise in week 47 or 48 will increase by the amount that is not used.

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9.3 Master Scheduling in Practice

The discussion of master produc�on scheduling thus far provides basic informa�on. In actual prac�ce, the job is much more difficult and involved. The next sec�on discusses a few key points that are important to understand.

Integration with Other Functional Areas

Although the master schedule relates primarily to produc�on, it also has significant implica�ons for marke�ng and finance. The number of units produced during each �me period determines whether demand can be met for that �me period. Further, this produc�on will generate significant costs for labor and materials, while also determining the inflow that comes from sales. Consequently, both marke�ng and finance must not only be aware of the master schedule, but also must give it their approval.

Marke�ng and sales may have special promo�ons or other plans that must be reflected in the master schedule. If the trial MPS does not sa�sfy marke�ng's requirements, then it must be redone. Mee�ng the various internal and external demands with available resources is what makes master scheduling so difficult.

In the past, developing the MPS was o�en an itera�ve process, frequently involving only marke�ng and opera�ons. But, with today's emphasis on elimina�on of func�onal barriers, some companies have formed inter-func�onal teams with representa�ves from opera�ons, marke�ng, and finance. Such a team works together to develop a master schedule that meets all their needs. As a result, the schedule is completed more quickly. Further, through face-to-face discussions, each individual on the team can be�er understand the challenges and constraints faced by the func�onal areas other team members represent.

The first version is a "trial" MPS, not necessarily the final one. As Figure 9.6 indicates, a�er the trial master schedule is developed, a determina�on must be made as to whether sufficient capacity is available.

Figure 9.6: Itera�ve process for developing a master produc�on schedule

Approaches to Change

It is important to understand that these plans are not something a company can do only once each year. Planning is a con�nuous process that can be thought of as rolling out a scroll. As �me passes, the scroll keeps ge�ng rolled up on the end closest to the present �me and unrolled at the other end, so that a new planning horizon comes into view. This concept is called rolling through �me.

Forecasts far into the future are less accurate than nearer term forecasts. Thus, it may be necessary to make changes in planned produc�on as the planning horizon draws nearer. For instance, a company might find that demand for one of its products is far exceeding the company's forecasts. This organiza�on would be foolish not to alter its produc�on plans to meet the increased demand. Thus, both the aggregate plan and the master schedule will change as �me passes. But, too much change can be disrup�ve. For example, a company might have already hired employees and bought materials to meet its produc�on plan. Altering that plan could

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A company may find that demand for one of its products far exceeds its forecasts. This was the case for the Furby, which was the "must have" toy for the 1998 holiday season.

©Damian Dovarganes/Associated Press/AP Images

mean idle employees or inventories of unused materials. Many companies "freeze" their master schedule for a certain �me into the future to avoid such problems.

Freezing the master schedule means that no further changes can be made a�er a certain �me. For instance, a company may indicate that the master schedule will be frozen for one week into the future. Thus, no changes may be made once a plan is within one week of its execu�on date. This is depicted in Figure 9.7. The master schedule is commonly frozen for a few weeks, although longer and shorter periods are used, depending on how easily a company can change its plans.

Figure 9.7: Freezing the master schedule

Accounting for Demand

When developing a master produc�on schedule for the Maine Woods Company, two approaches were used. The first was based on producing to inventory, while the second was based on producing to customer orders. In actual prac�ce, both sources of demand must be considered. There are also other sources of demand. For example, companies that operate mul�ple plants o�en have one plant producing parts for another plant. Such orders would be iden�fied as interplant orders. Further, many companies produce replacement parts for their products, such as starter motors for automobiles or blades for lawnmowers. These service parts requirements must also be considered. Such a process is depicted in Figure 9.8.

Figure 9.8: Recognizing all sources of demand through demand management

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9.4 Rough-Cut Capacity Planning

The aggregate plan is the first step to ensure that sufficient labor, capital, and machine �me will be available to meet customer demand. But, the aggregate plan accounts for the totality of those resources, not for individual products. The technique of rough-cut capacity planning is a means of determining whether sufficient capacity exists at specific work centers to execute the master schedule, which is based on specific products.

Overall Factors

The purpose of rough-cut capacity planning is to determine whether enough capacity will be available to meet the master produc�on schedule. Many companies use the method of overall factors because of its simplicity and ease of calcula�on. This method relies primarily on historical accoun�ng informa�on to determine how many standard hours are required per unit of each product. Mul�plying this figure by the number of units planned for produc�on each week determines the overall capacity requirement. This requirement can then be broken down by individual work centers based on historical data.

Problem

Consider the produc�on plan for Maine Woods' wheel goods, which is given in Figure 9.2. An aggregate produc�on of 2,000 units has been planned for January. When developing the master schedule of Figure 9.2, Maine Woods has converted that planned produc�on into the detailed schedule for its three wheel-goods products—toy wagons, tricycles, and scooters.

Based on historical accoun�ng informa�on, each tricycle required 0.6 standard hours to produce, each toy wagon required 0.3 standard hours, and each scooter required 0.2 standard hours. This informa�on can be used, as shown in Figure 9.9, to calculate capacity requirements for each product. The total capacity requirements can be determined by the sum of the weekly capacity requirements across all products as shown at the bo�om of Figure 9.9.

Figure 9.9: Calcula�on of total capacity requirements for a master schedule

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Suppose Maine Woods is concerned about the high usage of its cu�ng and drilling opera�ons. Again, based on historical accoun�ng informa�on, 40% of all standard hours are spent on cu�ng and 35% on drilling. The other 25% of standard hours is used for noncri�cal opera�ons that are not of concern.

This historical informa�on can be used to es�mate capacity requirements at each opera�on. For example, in week 1, a total of 225 standard hours is required. Of this, 90 hours (40%) will be required for cu�ng and 78.75 hours (35%) will be required for drilling. Figure 9.10 shows the es�mated capacity requirements for each work center each week.

Figure 9.10: Calcula�on of es�mated capacity requirements for individual worksta�ons

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Insufficient Capacity

Once a company has es�mated capacity requirements at each worksta�on or opera�on, those figures can be compared to capacity available. In some cases, excess capacity may be available, which indicates the opportunity to book more orders or decrease working hours. In other cases, however, requirements may exceed capacity available.

If insufficient capacity is available to meet the master schedule, a company can either shi� some scheduled produc�on into an earlier �me period that has excess capacity, or schedule over�me, if possible. If neither of these approaches is possible, more changes may have to be made in the master schedule.

Problem

Maine Woods has 100 hours of cu�ng �me available each week and 80 hours of drilling �me. Based on Figure 9.10, sufficient capacity is available to meet the master schedule. In fact, weeks 2 and 4 have considerable excess.

However, an important customer has just asked whether an order for 75 tricycles could be completed in week 3. Although week 3 falls within the master schedule's frozen �me period, the vice-president of manufacturing has approved an override if capacity is available.

Seventy-five tricycles would require an addi�onal 45 standard hours (75 × 0.6) in week 3. Of these addi�onal hours, 18 (40%) would be used for cu�ng and 15.75 (35%) would be used for drilling. Figure 9.11 indicates the capacity requirements for cu�ng and drilling if this new order is accommodated. Unfortunately, with only 100 hours of cu�ng �me and 80 hours of drilling �me, sufficient capacity will not be available.

Figure 9.11: Proposed master schedule requiring over�me in week 3

Maine Woods has several op�ons, including turning down the order for week 3. One op�on is to schedule over�me as necessary in week 3 for cu�ng and drilling. The customer may be charged a higher price to cover the added cost.

Another op�on is shown in Figure 9.12. In this case, produc�on for the 75 tricycles has been distributed among weeks 2, 3, and 4 (35 in week 2, 5 in week 3, 35 in week 4) to u�lize available regular�me capacity. In this case, all of the customer's order could not be completed in week 3, but perhaps enough could be

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finished to sa�sfy the customer.

Figure 9.12: Proposed master schedule with changes to avoid over�me

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A bill of materials is like a recipe, lis�ng the materials needed and the quan��es of each. It also provides informa�on about how the materials combine to create the final product.

©iStockphoto/Thinkstock

9.5 Material Requirements Planning

One approach that has been used in the past for material planning is to stock all items at all �mes (some�mes called just in case inventory control). This approach requires that huge inventories be maintained, resul�ng in extensive warehouse space and a large amount of money invested in that inventory. Even then, many companies found that certain crucial items used in many of their products always seemed to run out at the wrong �me. No ma�er how much inventory is kept, a large demand for certain parts can deplete supplies quickly.

Independent Versus Dependent Demand

Inventory can also be classified according to the type of demand it intends to serve. The type of demand determines which methods are used to manage inventory. Independent demand is demand that is not controlled directly by the company, such as demand from customers. Independent demand items usually include finished products, such as the completed tricycle or replacement parts sold to customers. Demand for such items is generally independent of a company's produc�on plans. Chapter 10 will discuss procedures for managing this type of inventory.

Dependent demand is usually demand for an item that is generated by a company's produc�on process. One example would be the wheels for tricycles that a company produces. Each tricycle has three wheels; if the company plans to produce 200 tricycles in a given week, it will need 600 (200 × 3) wheels that week. Thus, the demand for wheels depends on the produc�on of tricycles. To manage inventory for dependent demand items, companies o�en use material requirements planning (MRP).

The idea behind MRP is simple; it is like planning a meal. A few days before preparing the meal, a decision is made about what to serve. The person who will prepare the meal examines the recipe to determine what ingredients are required to make the meal, checks the pantry to determine which ingredients are on hand, and makes a list of the ingredients that need to be purchased. A trip to the store is made to secure items that are not currently in stock. The same basic approach is used in material requirements planning.

The master schedule is analogous to the menu, which states what will be served for the meal. Recall that the master schedule indicates which items and how many of each item to produce. A bill of materials is like the list of ingredients in the recipe, which tells the cook the amount required of each. The bill of materials (BOM) lists the materials needed and the quan��es of each. Like the recipe, it also provides informa�on about how the materials come together. Inventory records will show how much is on hand. From this, it can be determined which parts or materials will come up short and how much more of each item is needed.

Data Files Used by MRP

For companies today, MRP is a computerized informa�on system. As such, it requires data to provide the informa�on needed for decision making. The three most important data requirements of MRP are the master produc�on schedule, bill of materials, and inventory records.

1. Master Schedule File For MRP purposes, the master schedule is what "drives" the system and generates material requirements. As men�oned earlier, this master schedule may be at the finished-products level for companies such as Maine Woods that manufacture standard products. However, for companies making customized products, the master schedule may be at the level of components or subassemblies.

2. Bill of Materials File A bill of materials serves two purposes. First, it lists all the components of a product and the quan��es needed to make the product. Second, it shows the rela�onships among those components, which indicates product structure, or how the items fit together. For example, Figure 9.13 shows an exploded view of the tricycle produced by Maine Woods. In manufacturing the tricycle, the front wheel, its supports, the axle, and the steering column are sub-assembled before the en�re tricycle is put together. Likewise, the seat and rear axle supports are sub-assembled before final assembly.

One way to indicate these subassemblies is through a product structure tree diagram, as shown in Figure 9.14. No�ce that all the parts brought together at final assembly are listed together on level 1. Any parts that are components of subassemblies are listed on level 2. Connec�ng lines indicate which parts belong to which subassembly.

Figure 9.13: Exploded view of Maine Woods' tricycle

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One way to indicate these subassemblies is through a product structure tree diagram, as shown in Figure 9.14. No�ce that all the parts brought together at final assembly are listed together on level 1. Any parts that are components of subassemblies are listed on level 2. Connec�ng lines indicate which parts belong to which subassembly.

Figure 9.14: Product structure tree for Maine Woods' tricycle

An indented bill of materials is another way to provide structure to the bill of materials. A tree diagram is visually appealing, but is difficult to use in computerized MRP systems. An indented bill of materials is used by MRP to provide informa�on about product structure. Each item is iden�fied with a level, as shown in Figure 9.14. An indented bill of materials illustrates each level indented from the one above it. Table 9.2 is the indented bill of materials for Maine Woods' tricycle.

Table 9.2: Indented bill of materials for Maine Woods' tricycle

Level Part no. Quan�ty Descrip�on

0 127 1 Tricycle

  1   3417 1 Handle

  1   2973 1 Rear axle

  1   463 1 Front assembly

    2     3987 2 Axle support (front)

    2     5917 1 Wheel

    2     2673 1 Front axle

    2     3875 1 Steering column

  1   5917 2 Wheel

  1   587 1 Seat assembly

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    2     3965 2 Axle support (rear)

3. Inventory File In order for MRP to work, accurate inventory records must be kept. For most companies, this accuracy requires con�nually upda�ng inventory records as items are withdrawn or added. To automate this func�on, many use bar codes, which are similar to the universal product codes (UPCs) you see on items at a grocery store; however, mistakes can be made despite automa�on. Cycle coun�ng is a way to reconcile inventory records and correct errors, and many companies using MRP also employ cycle coun�ng. Using this method, a physical count of each part is made at least once during its replenishment cycle, which is the period between orders to replenish inventory.

Displaying MRP Data

The objec�ve of MRP is to ensure that the correct quan��es of component parts are available at the proper �me to produce finished products according to the master produc�on schedule. This sec�on describes how that is done for items that appear immediately below the finished product in the product structure tree diagram.

The informa�on obtained from bills of materials, inventory records, and the master schedule can be shown together in the diagram of Figure 9.15, which is the table commonly used to calculate and display MRP informa�on.

Figure 9.15: Table for MRP

The table in Figure 9.15 illustrates �me periods across the top. These represent �me periods for planning purposes, or �me buckets. The �me buckets correspond to the master product schedule, which is usually set in weeks. The purpose of using these �me periods is to state the total quan�ty requirements for component parts and materials needed during each �me bucket. This process of sta�ng requirements by �me bucket is o�en called �me phasing.

The first row in Figure 9.15 is labeled gross requirements. Gross requirements represent the total quan�ty needed of a par�cular item in each �me bucket, based on the master produc�on schedule and the bill of materials, regardless of current inventory of that item. The second row, scheduled receipts, shows whether any orders for that item have been placed previously, but not yet received. Entries in this row indicate when the order should arrive and how many units should be enclosed. Projected ending inventory shows the planned number of units that should remain at the end of each �me bucket a�er all transac�ons of that period are complete. If the number of units available during a period (projected ending inventory from the previous period plus receipts) is not sufficient to cover gross requirements, then the row labeled net requirements indicates the number of units the company is short. An entry in net requirements indicates that a replenishment order will need to be placed. Thus, the last two rows show planned receipts and planned order releases. The planned receipts row shows when orders must arrive in order to avoid a shortage of necessary parts or materials, as indicated by the net requirements row. The planned order releases row indicates the �me periods in which those orders must be released (or placed) to arrive at the correct �me. The difference between scheduled receipts and planned receipts is that scheduled receipts correspond to orders that have actually been placed some�me in the past, but not yet received. Planned receipts correspond to orders planned for release, but not yet released. Both scheduled receipts and planned receipts are included as units available in the MRP record.

MRP Logic

The informa�on in Figure 9.15 may be completed for each part of raw material as follows:

1. Obtain the bill of materials for the appropriate end product. 2. Begin with a level 1 item from the bill of materials. 3. Mul�ply the number of units of the level 1 item needed per unit of finished product (from the bill of materials) by the master schedule quan�ty for each �me

bucket. Insert this as gross requirements for the appropriate �me bucket. Ordinarily, the master schedule indicates the number of units of finished product to be produced in each �me period, so the appropriate �me bucket will be that same �me period. In some cases, however, the master schedule indicates comple�on of produc�on. If so, the �me period when produc�on begins is the appropriate �me bucket for gross requirements.

4. Enter any scheduled receipts of the item, based on lead �me and orders previously released, in the appropriate �me buckets.Processing math: 0%

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5. Determine how many units should be in inventory at the start of the first �me bucket. Enter this number in the square to the le� of the first �me bucket. 6. Perform the following steps for each �me bucket, beginning with the first, un�l the end of the planning horizon is reached. Add projected ending inventory from

the preceding �me bucket to scheduled receipts for the present period. If this total equals or exceeds gross requirements for the present period, go to step a. If not, go to step b.

a. If gross requirements in the �me bucket being planned are less than or equal to the sum of projected ending inventory from the preceding �me bucket and scheduled receipts for the current �me bucket, enter the difference as projected ending inventory in the current period. Leave net requirement blank, and repeat this step for the next �me bucket.

b. If gross requirements are greater than the sum of projected ending inventory from the preceding �me bucket and scheduled receipts for the current �me bucket, enter the difference as net requirements. Leave projected ending inventory blank for the present �me period un�l the following sub-steps have been performed.

i. For any period in which net requirements appear, plan an order release and corresponding receipt to cover the net requirement. (This ordering approach is termed lot-for-lot. Net requirements from several periods may be combined into one planned order release using other lot sizing methods.)

ii. Subtract net requirements from planned receipts, and enter the total as projected ending inventory for the current �me bucket. Proceed to step a for the next �me bucket.

Problem

Consider the Maine Woods Company. The bill of materials for tricycles, shown in Table 9.2, indicates the front assembly (part #463) is a level 1 item. The inventory file for this item shows 100 units are expected to be in inventory at the end of December. Produc�on lead �me, the �me it takes to receive front assemblies a�er more are ordered into produc�on, is two weeks. An order for 500 front assemblies was released earlier and is scheduled for receipt during week 1 of January. Using the master schedule for tricycles of Figure 9.12, determine planned order releases for front assemblies. The produc�on for weeks 5 and 6 is set at 250 units each.

Step 1. The bill of materials (Table 9.2) indicates one front assembly is needed for each tricycle.

Step 2. Front assemblies are a level 1 item, so begin planning with them.

Step 3. The master produc�on schedule during weeks 1 through 6 is shown at the top of Figure 9.16. Because one front assembly is needed for each tricycle, and the master schedule shows units to be produced during each week, the gross requirements for front assemblies in each week will be the same as the master schedule quan��es of tricycles.

Step 4. The scheduled receipt of 500 units is entered for week 1.

Step 5. The 100 front assemblies projected to be in inventory at the end of December are entered in the projected ending inventory box to the le� of week 1.

Step 6. Week 1: Gross requirements in week 1 are less than projected ending inventory from the previous week, plus scheduled receipts for week 1. The difference is entered as projected ending inventory for week 1, as shown in Figure 9.16.

(100 + 500) − 250 = 350

Week 2: Gross requirements in week 2 are less than projected ending inventory from week 1. Projected ending inventory for week 2 is:

350 − 285 = 65,

as shown in Figure 9.17.

Figure 9.16: MRP for front assemblies

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Figure 9.17: Par�ally completed MRP: Front assemblies

Week 3: Gross requirements in week 3 are greater than projected ending inventory from week 2 by 190 units. This difference is entered as net requirements for week 3.

1. An order for week 3 net requirements must be planned for receipt in week 3. Because the lead �me is two weeks, the order must be planned for release in week 1 (week 3 minus 2 weeks lead �me = week 1).

2. The planned receipts for week 3 are 190 units, and net requirements are 190 units. Therefore, the projected ending inventory for week 3 will be zero.

Weeks 4 through 6 are completed in the same way, producing the results shown in Figure 9.18.

Figure 9.18: Completed MRP: Front assemblies

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In this example, the planned order releases were determined for front assemblies, which are a level 1 item. The gross requirements for all level 1 items will be determined from the master produc�on schedule. But items that are level 2 in the bill of materials will be used in making level 1 items. Thus, their gross requirements will be determined from planned order releases for level 1 items, not from the master schedule. For example, the front assemblies that were just planned using MRP are a level 1 item. However, the front axle supports used in that assembly are level 2. Therefore, the gross requirements for front axle supports will be determined by the planned order releases for front assemblies, as shown in Figure 9.19.

Figure 9.19: MRP for a level 2 item: Front axle supports

Coordinating Purchasing

Many �mes, one par�cular part or subassembly will be used in more than one product. In such cases, the gross requirements for that part must take into account all planned produc�on of products or subassemblies that use that part.

Problem

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The front wheel in the Maine Woods tricycle is exactly the same as the two rear wheels. However, the front wheel is part of a subassembly, while the rear wheels are not. Furthermore, the wheels on Maine Woods' scooter are also the same as the wheels used on its tricycle. Therefore, gross requirements for wheels (part #5917) will be the sum of planned order releases for tricycle front assemblies (Figure 9.18) plus the master schedule quan��es for tricycles (Figure 9.12), mul�plied by two, and scooters (Figure 9.12), also mul�plied by two, as shown in Figure 9.20.

Figure 9.20: Combining demand from mul�ple sources and levels

MRP Coordinates Purchasing and Operations

The output from MRP is a schedule of planned order releases. There are two types of orders. A shop order authorizes produc�on to make certain component parts or subassemblies. A purchase order is an authoriza�on for a vendor to supply parts or materials. If the orders request component parts or subassemblies made by the company itself, then a shop order will be released. If the planned order release is for a part or raw material that is purchased from an outside vendor, then a purchase order will be released.

The opera�ons part of a company is usually the department responsible for running MRP. Thus, opera�ons are aware that the release of a shop order means that a certain part or component should be started in produc�on because a need will exist for it some�me in the near future. Because opera�ons generated the shop order release, they will be aware that it is a valid order and that it should be produced in the quan�ty indicated. Purchase orders are usually handled by a purchasing or procurement department. If the order releases generated by MRP are to be carried out, then the purchasing department must be aware of what the MRP system is doing and trust in the output it generates. Close coordina�on between the opera�ons and purchasing departments is essen�al.

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9.6 Extensions of MRP

The discussion of MRP thus far has focused on the basics, o�en referred to as "li�le MRP." It is important to understand how MRP can be extended to make it more useful and applicable to areas of the business beyond opera�ons.

Capacity Requirements Planning

As men�oned previously, the master schedule is developed from the aggregate plan. Thus, the master schedule can provide much more exact measures of the capacity requirements than the aggregate plan can. As the master schedule is developed, rough-cut capacity planning is used to check capacity requirements against capacity availability. Rough-cut capacity planning does not take into account lead-�me offse�ng, or the amount ahead of �me that component parts must be made to meet the master schedule for end items. MRP can form the basis for much more detailed capacity calcula�ons because MRP performs lead-�me offse�ng when it generates planned order releases. For parts made in-house, the planned order releases generated by MRP indicate exactly when certain parts must be made and in what quan�ty. Those planned order releases will ini�ate a series of produc�on requirements on the machines and equipment used to produce those parts and subassemblies. These demands consume a por�on of capacity of the machines and equipment. Using a rou�ng sheet, which indicates the sequence of machines or work centers through which a part must pass during processing and the labor standards, it is possible to determine capacity requirements at each opera�on.

Figure 9.21 shows planned order releases for tricycle axle supports, along with informa�on contained in the rou�ng sheet for that part. In each week, the run �me on each machine is mul�plied by the order quan�ty for that week and then added to set-up �me to get capacity requirements. This procedure is done for each work center and each week.

Figure 9.21: Capacity requirements planning for tricycle axle supports

The informa�on generated in Figure 9.21 is only for one part. Many other parts would also generate capacity requirements at the same work centers. By adding together all the capacity requirements for each work center in each week, a total figure for capacity requirements will be generated. The total capacity requirements placed on a work center during a given �me period are called the load. The output of capacity requirements planning (CRP) is usually in the form of a load report, or load profile, which is a graphical representa�on of the load on each work center by �me period. An example of a load report is shown in Figure 9.22.

Figure 9.22: Drill work center load report

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Closed-Loop MRP

Capacity requirements planning is of significant benefit in ensuring that a company's plans are realis�c and can be implemented. However, MRP can only project what should happen if demand is as forecasted on the master produc�on schedule. In reality, machines may break down, deliveries from suppliers may be delayed, or some other calamity may occur. If these events are not reflected back in the MRP plan, then that plan will be invalid.

Closed-loop MRP provides feedback about the execu�on of produc�on plans. By tracking what actually happens on the shop floor and then reflec�ng that informa�on in the MRP record, plans can be kept valid. Instead of "launching" orders with no informa�on about comple�on, closed-loop MRP provides the feedback loop necessary to keep informa�on up to date.

Manufacturing Resource Planning (MRP II)

Many companies have found that material requirements planning can greatly improve their opera�ons through be�er planning. MRP also forces companies to be�er coordinate the ac�vi�es of opera�ons, marke�ng, and purchasing. The master schedule will have implica�ons for finance, personnel, workforce requirements, and purchases of materials. A company must be sure that its opera�ons plan fits appropriately with the business plan. All func�onal areas must base their ac�vi�es on the plan. To do that, an extension of MRP has been developed called manufacturing resource planning.

Manufacturing resource planning, or MRP II, as it is commonly called to differen�ate it from material requirements planning (MRP), is a way of tying all parts of an organiza�on together to build on the strategic plan. The strategic plan is an overall blueprint that specifies the company's objec�ves and how it plans to reach them. The opera�ons func�on will develop its own goals and plans to help achieve the corporate objec�ve, as will the marke�ng, finance, and all other departments of the organiza�on. The ac�ons of one func�onal area, however, will have an impact on the other areas. For instance, if marke�ng plans a promo�onal effort that will greatly increase sales, then opera�ons must be ready and able to produce enough product to meet that increased demand. Hiring more employees or buying addi�onal equipment, which will, in turn, have a major impact on the financial area, may be necessary. Because the opera�ons ac�vity is such an integral part of any organiza�on, it can be especially vulnerable to the ac�ons taken by other departments, and will have a large influence on other areas of the company through its ac�ons.

Planned orders can also provide informa�on about expected expenditures. Purchase order releases can be used to es�mate future payments to suppliers. Shop order releases will generate needs for machine �me and labor, so that they can also be used to es�mate future expenses. Before the development of MRP II, companies used cost accoun�ng primarily as a way to determine success a�er the fact. It was a way to find out what it had cost to do what was already done.

MRP II can change the way companies operate. By genera�ng cost projec�ons, it is possible to plan for produc�on costs ahead of �me and then compare actual costs to these projec�ons. Any major devia�ons can be spo�ed and inves�gated. A related advantage with MRP II is that it can be used to answer what-if types of ques�ons. Using MRP II, a company can es�mate the effect of a supplier cost increase and develop strategies to address it, instead of trying to respond a�er the fact. Figure 9.23 shows how MRP II connects all parts of the organiza�on.

Figure 9.23: MRP II

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When airlines create a master schedule they also compile a list of materials needed to provide that service such as fuel for the airplanes and snacks for the passengers.

©iStockphoto/Thinkstock

MRP in Service Organizations

Although MRP was originally developed for manufacturing companies, it can also be applied to service organiza�ons. Instead of the master schedule represen�ng goods to be produced, it can represent services to be provided.

For example, an airline's master schedule could show the number of flights from different ci�es each week. In this case, the materials required to provide that service include fuel for the airplanes, meals for the passengers, and other related items. Likewise, hospitals can develop a master schedule showing the number of different types of surgeries each week.

Materials required include various surgical supplies. This is a variant of MRP, known as hospital requirements planning (HRP).

Although some surgeries are emergencies, many others are scheduled in advance. Historical informa�on about emergency surgeries can be combined with those that are scheduled to develop a master schedule. MRP can then be used to convert the master schedule into requirements for medical equipment, instruments, supplies, opera�ng rooms, and staff. Houston's Park Plaza Hospital has used this approach to improve management of expensive inventory.

Distribution Requirements Planning (DRP)

In the retail se�ng, the MRP approach has been applied so widely that a variant of MRP, called distribu�on requirements planning (DRP), has been developed. In this way, the MRP planning logic is applied to requirements for retail outlets or warehouses.

Distribu�on networks o�en consist of local outlets or service centers that are supplied from local distribu�on centers. In turn, these distribu�on centers may be fed by a regional or na�onal warehouse. By thinking of each level in the distribu�on network as a level in a bill of materials, it is possible to see that orders placed by the service centers will generate gross requirements at the regional warehouses. Figure 9.24 shows an example of distribu�on requirements planning.

Giant Food Company, a supermarket chain, uses DRP as part of its ECR (efficient consumer response) approach to supply chain management. DRP allows the company to connect its POS (point-of-sale) informa�on from stores to inventory levels throughout the supply chain, making that informa�on available to all supply chain partners. DRP then "pulls" items through the system based on customer demand, facilita�ng one of the basic ideas behind ECR.

Figure 9.24: Distribu�on requirements planning

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Role of Management Information Systems in Planning

MRP is usually calculated on a computer because of the large volume of computa�ons that must be performed and because much of the informa�on, such as bills of material and inventory records, is stored on computerized databases. MRP II, by including more organiza�onal func�ons within its scope, further increases the need for computerized informa�on. As a result, companies very o�en use computerized informa�on systems for opera�ons planning and control ac�vi�es. One such system and the data files that it works with are shown in Figure 9.25. Enterprise resource planning (ERP) uses a single integrated database for the en�re organiza�on. In this way, each part of the organiza�on is connected, and efforts to break down barriers within the organiza�on are facilitated.

Figure 9.25: Informa�on system for managing and controlling opera�ons

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Chapter Summary

The produc�on planning process leads from an aggregate plan to a master schedule to MRP. The master schedule is a more detailed version of the aggregate plan that includes produc�on for individual end products and the specific week in which the produc�on will take place. The method of overall factors uses historical informa�on to make a rough-cut capacity requirements es�mate from the master schedule. Material requirements planning (MRP) uses the master schedule, bills of materials, and inventory records to plan orders for subassemblies and parts. Capacity requirements planning uses rou�ng sheets and labor standards to develop �me-phased es�mates of capacity requirements based on planned order releases. Manufacturing resource planning (MRP II) provides cost informa�on and other data that can be shared throughout the organiza�on.

Case Studies

Able Electronics Company

Mike Lanier, produc�on manager for the Able Electronics Company, has just sat through another frustra�ng mee�ng with the company's marke�ng manager, Pam Brandt. Pam has been receiving complaints from customers that their orders are not being delivered on �me. Mike had to admit that the company's on-�me delivery record of 53% was not very good. But Mike felt that it was partly the fault of Able's salespeople. In their efforts to make a sale, the company's salespeople o�en promised delivery within a period of �me that they knew would be difficult, if not impossible, for produc�on to meet. Many �mes, these orders were for special, customized products that required different parts or different processes than Able used on its standard products.

Able Electronics produces printed circuit boards and other electronic components that are sold to companies that use them to make a range of products from computer hardware to televisions and radios. In the past, the company has produced some 2,000 fairly standard products. However, the compe��ve electronics business has increasingly required that Able be willing to customize its products to customer needs as foreign compe��on has picked up the business in standardized products by offering much lower prices than Able. Able now makes a total of approximately 3,600 different products, although only about 300 different components are used.

To meet this increased demand for customized products, Able has started increasing its levels of component-parts inventory. This has helped somewhat, but the company's inventory investment has increased dras�cally from $824,000 to $1,243,000 during the past year. This has also been partly due to efforts to increase the finished-goods inventory for standard products, which would allow the company to meet standard orders from inventory, freeing up more �me to make special orders. Unfortunately, that has not worked. In fact, the on-�me record for special orders has worsened.

At one �me, the company had considered using MRP, but that idea was abandoned because Able thought that, with the large number of different products it made, developing a master schedule would be next to impossible. Now Mike Lanier wonders if he shouldn't reconsider.

1. How might MRP help Able deal with some of its problems? 2. What approach could Able use to overcome the problem of master scheduling for customized products? 3. How would master scheduling improve the salespeople's ability to give customers more realis�c delivery dates? 4. What aspects of MRP would be most useful to Able?

Space Age Furniture Company

The Space Age Furniture Company manufactures tables and cabinets to hold microwave ovens and portable televisions. These products are made in various sizes and with various features, but all follow basically the same produc�on and assembly opera�ons. However, two of these products—the Saturn microwave stand and the Gemini TV stand—have a part (no. 3079) that requires machining on a special lathe used only for making that part. At present the machine is run by Ed Szewczak, a machinist who also operates other machines in Space Age's shop. Once set up and started, the lathe can run nearly una�ended. However, the machinist must be present (even if not actually a�ending the machine) any �me one of the machines, including the lathe, is in opera�on. At present, Ed works a regular 40-hour week. However, due to the workload for producing part 3079, it has been necessary to schedule frequent over�me for him in order to finish the necessary parts on �me.

Coral Snodgrass, opera�ons manager for Space Age, has just heard from Ed's foremen that Ed is becoming unhappy about so much over�me. As Coral knows, Ed has been with the company a long �me and is an excellent, reliable employee. Skilled machinists with Ed's experience and employment record are extremely difficult to find. Coral wonders what can be done to alleviate this problem.

Recently, Space Age began using an MRP system that has helped reduce inventories greatly and improve on-�me deliveries. In fact, Space Age carries no finished- goods inventory. Instead, everything in the master schedule is being produced for customer orders, so all products are shipped almost immediately. Previously Space Age had es�mated that it cost $1.25 per week to store each Gemini and $1.50 per week to store each Saturn that wasn't shipped immediately. The master schedule for producing these two items for the next six weeks is shown below.

Master Schedule

Week

1 2 3 4 5 6Processing math: 0%

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Gemini 600 400 700 500 400 600

Saturn 300 400 400 600 300 300

The part in ques�on, 3079, is used in two different subassemblies: no. 435, which is used in the Gemini TV stand, and no. 257, which is used in the Saturn microwave stand. One of part 3079 is used in each subassembly, and one of each subassembly is used in each of the final products.

Part 3079 may be produced in any quan�ty since the lathe that makes it is not used for anything else. However, both of the subassemblies are produced using the same equipment. To minimize change over �me, Space Age has decided that these subassemblies should be made in minimum quan��es of 1,000 at a �me, although there is no problem with capacity on the equipment that makes them. In fact, an order for 1,000 of subassembly 435 is due to be received in week 1, as is an order for 1,000 of subassembly 257. Lead �me for both these subassemblies is one week, and no inventory is expected to be on hand for either part at the beginning of week 1. There is not any on-hand inventory of part 3079, and there are no orders in process.

Ed Szewczak earns $22 per hour and gets a 50% premium for any over�me work. Whenever part 3079 is made, there is no set-up �me, but processing takes 0.03 hour per unit. It costs $0.25 per week to hold any of these parts over from one week to the next. The cost of holding each subassembly in inventory is $0.75 per unit per week.

1. What op�ons are open to Coral to address this problem? 2. How would reducing the minimum quan�ty of subassemblies help? 3. What are the costs of carrying excess items in inventory at each stage? 4. What is the trade-off between over�me costs and inventory costs?

Discussion Ques�ons

Click on each ques�on to reveal the answer.

1. Define the following terms: a. Rough-cut capacity planning b. Time bucket c. Lead-�me offse�ng d. Freezing the master schedule e. Available-to-promise (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

a. Rough-Cut Capacity Planning – used to es�mate whether sufficient produc�on capacity will exist at individual work centers to meet the master schedule.

b. Time bucket – Time periods for planning purposes, which correspond with the master schedule and are usually stated in terms of weeks. Their purpose is to state requirements for component parts and materials in terms of the total quan�ty needed during each �me bucket.

c. Lead-�me offse�ng – the process of taking net requirements for component parts or raw materials and conver�ng the requirements into planned order releases by taking produc�on or procurement lead �me into considera�on.

d. Freezing the master schedule – means that no further changes can be made a�er a certain point in �me (i.e., a month into the future). Though it is important to make changes in planned produc�on as the planning horizon draws nearer, too much change can be disrup�ve. A company will freeze its master schedule to avoid idle employees or unused inventory which would result from changes in the master schedule a�er the employees are hired or materials are purchased.

e. Available-to-promise – the number of planned produc�on units in a master schedule that are not yet commi�ed to customer orders before the next produc�on period.

2. Explain how a restaurant could use MRP. In what ways would its use in a restaurant differ from its use in a manufacturing organiza�on? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Based on inventory, bills of material (recipes) and projected sales, the restaurant would order goods within an appropriate �me frame so they will have enough inventory on hand to meet projected customer demand. The restaurant will differ from a manufacturing organiza�on in that the majority of its orders could be for perishable goods. The restaurant is unable, therefore, to store inventory for very long periods of �me, thus making MRP a�rac�ve by tying ordering with expected demand. However, a restaurant cannot control what customers order. Thus, actual orders may differ from the produc�on plan.

3. Describe the informa�on generated by MRP II and how it could be used by the following departments in a company: a. Personnel b. Finance c. Marke�ng d. Engineering (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

MRP II is a way of tying all parts of an organiza�on together with the opera�ons ac�vity to build on the business plan. MRP II generates cost projec�ons through planned order releases and provides informa�on on workforce and financial requirements. Each department might use MRP II informa�on in the following ways.

a. Personnel may use MRP II to determine the number of employees (human capacity) required to meet produc�on each month. Processing math: 0%

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b. Finance could use MRP II to obtain informa�on on capital and cash requirements resul�ng from labor costs and inventory expenditures.

c. Marke�ng would find MRP II useful to determine the availability of resources. They must know how much product is available to sell and if any addi�onal capacity is available for special orders or large accounts.

d. Engineering would be concerned about which parts and products the company is planning to make. Issues such as the following must be addressed by engineering: is the current design sa�sfactory? are any changes in the design of parts being planned? are there new parts being considered that must be designed? The effect of any design changes on the company's plan must also be looked at.

4. Explain how MRP can decrease a company's inventory while improving its customer service level. (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Through the use of MRP, a company can place orders for goods and materials to arrive as they are needed to meet the projec�ons of the master schedule. The company, therefore, does not have to accumulate large inventories. The customer service level is also improved with the use of MRP. The company is planning ahead, ordering components it will need to meet product demand, and therefore decreasing back orders to its customers.

5. Discuss the rela�onship between MRP and MRP II. (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Material Requirements Planning (MRP) facilitates be�er planning and forces companies to be�er coordinate the ac�vi�es of opera�ons, marke�ng, and purchasing. Manufacturing Resource Planning (MRP II), is a way of tying all parts of an organiza�on together with the opera�ons ac�vity to build on the business plan. The results of MRP II are stated in financial terms that can be used by the en�re organiza�on.

6. Why is it important for an organiza�on to plan and allocate resources? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Any organiza�on needs to know where it wants to go and how it intends to get there. Addi�onally, an organiza�on must be sure that its plans are coordinated with the organiza�on's objec�ves and that resources are allocated appropriately to achieve those objec�ves. With limited resources, an organiza�on must be sure to make resource alloca�ons in ways that will assure achievement of the organiza�on's objec�ves.

7. Define the following terms: a. Bill of materials b. Net requirements c. Gross requirements d. Scheduled receipts e. Planned receipts (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

a. Bill of materials – a lis�ng of exactly what's needed and in what amounts to produce a par�cular product.

b. Net requirements – In the table commonly used to calculate and display MRP informa�on, the row labeled as net requirements indicates the number of units short for the �me period a�er scheduled receipts and inventory have been accounted for.

c. Gross requirements – In the table for MRP, gross requirements represents the total quan�ty needed of a par�cular item in each �me bucket, based on the master schedule and bill of materials, regardless of current inventory of that item.

d. Scheduled receipts – is the number of units, indicated on the Table for MRP, that have been previously ordered and are expected to be received during the �me period.

e. Planned receipts – is the number of units that are expected to be received that correspond to orders planned for release but not yet released.

8. Why are there separate lines for planned receipts and scheduled receipts in the MRP table? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

There are separate lines for planned receipts and scheduled receipts in the MRP table because they correspond to different orders. Scheduled Receipts correspond to orders that have actually been released some �me in the past, but not yet received. Planned Receipts correspond to orders planned for release but not yet released.

9. Describe how capacity requirements planning differs from rough-cut capacity planning. (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Rough-cut capacity planning is used to es�mate whether sufficient capacity will exist at individual work centers to meet the master schedule. However, it is based on the master schedule and historical informa�on. Capacity requirements planning (CRP) is the process of es�ma�ng total capacity that will be required at each work center or machine, based on the master schedule and material requirements planning (MRP). Because CRP includes the lead �me offse�ng of MRP it gives more accurate es�mates.

10. What informa�on is needed for capacity requirements planning, and how is that informa�on obtained? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Informa�on that is needed for capacity requirements planning, obtained from management, includes planned order releases, which would usually be generated by the MRP system, informa�on about the processing sequence and set up �mes of each component, usually obtained from the rou�ng sheets, and informa�on about the availability of resources, which would be based on planned opera�ng hours.

11. The �me you have available for studying is a limited resource. For the next week, develop a load profile that compares the �me you have available (capacity) with the �me you should devote to studying for all your courses. What are your op�ons if capacity is exceeded?Processing math: 0%

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Week

1 2 3 4 5 6 7 8 9

300 400 375 325 300 280 300 250 200

April Week

1 2 3 4 5

900 875 850 745 720

Product A Week

1 2 3 4 5 6 7 8

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The answer to this ques�on will be unique for each student. The "load profile" will show to the �me each student should study, which is usually two hours for each hour spent in class, compared to studying �me available each day.

Op�ons available when capacity is exceeded include:

– Eliminate some ac�vi�es of lower importance (such as watching TV).

– "Offload" by ge�ng others to do some of your non-study ac�vi�es (such as doing your laundry).

– Reschedule some study �me to earlier or later in the week when extra capacity exists.

– Add capacity by pu�ng in an "all-nighter" (not recommended).

12. In what units might the capacity of a hotel be expressed, and what op�ons are available if it is expected that capacity will be exceeded? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Capacity for a hotel could be expressed as either number of rooms or number of beds available per night. If it is expected that capacity will be exceeded, the op�ons are somewhat limited. The most common op�ons are to either turn people away or find them rooms at other hotels.

13. What are some things a company can do when rough-cut capacity planning indicates insufficient capacity to meet the master schedule? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

The following are some things a company can do when rough-cut capacity planning indicates insufficient capacity to meet the master schedule:

1. Revise the master schedule by shi�ing planned produc�on to periods when capacity is available.

2. Schedule over�me or plan to add another shi�.

3. Do nothing and hope everything works out (not a recommended approach).

14. How is the master produc�on schedule modified for computerized MRP? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

There is really no major change made in the master produc�on schedule for computerized MRP, except that it is set up as a computer file. Of course this computer file must be established in a way that will interface with the other MRP files such as BOM and inventory.

15. How does closed-loop MRP maintain the validity of a produc�on plan? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Closed-loop MRP maintains the validity of a produc�on plan by feeding back execu�on informa�on to the MRP system. In this way informa�on can be updated and changes made accordingly so the plan remains valid.

Problems

1. The aggregate plan for Brookline Clothing Company indicates 3,750 men's pants are to be produced during March. Of these, 20% are style 493. Assuming there are five weeks of produc�on in March, develop a master schedule for style 493 men's pants if they are produced in a batch of 250.

2. A certain company has forecast demand during the first nine weeks of the year as 350 units per week for product A. Projected inventory of product A at the end of December is 800 units. If product A is produced in batches of 1,000, determine the master schedule and the available-to-promise quan��es, based on the following

customer orders booked:

3. The Evans Spor�ng Goods Company has developed an aggregate plan to produce 5,000 units of its wood-products group during April. Baseball bats make up 80% of this product group, based on past sales. At the end of March, the company expects to have 800 bats available in inventory. Customer orders booked in the five

weeks of April are as follows:

If bats are produced in batches of 2,000, develop a master schedule, assuming forecast demand is expected to be uniformly distributed throughout the month.

4. A company has the following master schedules for two of its products:

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240 300 350 350 400 300 300 400

Product B Week

1 2 3 4 5 6 7 8

500 450 400 400 300 350 500 500

Week 1 2 3 4

Number of audits requested

5 8 10 9

Number of tax prepara�ons requested

10 8 9 7

Week 1 2 3 4

Surgeries Scheduled 30 60 55 60

Master Schedule—Coffee Tables

Week

32 33 34 35 36 37

500 400 450 300 450 400

Master Schedule—12 oz. Vegetable Beef Soup

Week

12 13 14 15 16 17

1,200 1,500 600 900 2,000 1,500

Both products must be processed on the same cri�cal machine. Product A requires 0.2 hour of �me on this machine per unit, and product B requires 0.1 hour per unit. The machine is available 120 hours per week. Use rough-cut capacity planning to determine whether sufficient capacity will be available on the machine. Suggest possible ways that any capacity shortage may be solved.

5. The Ernie and Winnie Public Accoun�ng Company has only two employees (Ernie and Winnie). Ernie is available 30 hours per week for audi�ng and 20 hours per week for tax prepara�on. Winnie is available 10 hours per week for audi�ng and 30 hours per week for tax prepara�on. Each audit requires five hours, and each tax prepara�on requires two hours. The company has received requests to perform the following audits and tax prepara�ons each week during the next month.

Iden�fy possible problems that may occur if each employee's audi�ng and tax prepara�on �mes are fixed. Can excess �me for one ac�vity be used for another ac�vity? Why or why not?

6. Referring to your answer in Problem 3, historical informa�on shows that two standard hours are required to produce each baseball bat. Further, 60% of all standard hours for wood products have been for lathe �me and 40% for finishing. Es�mate the standard hours required in each opera�on to produce the bats scheduled in Problem 3.

7. Referring to Problem 6, suppose 2,000 standard hours of lathe �me and 1,500 standard hours of finishing �me are available each week. Determine whether sufficient capacity will be available each week. If not, suggest ways to meet demand with available capacity.

8. Central Eye Hospital has scheduled the following number of cataract surgeries during each of the next four weeks. Each cataract surgery requires the use of five pairs of surgical gloves. These gloves are ordered from a supplier in quan��es of 1,000 pairs at a �me. Ordering lead �me is two weeks. Inventory records indicate that there will be 200 pairs of gloves in inventory at the start of week 1. An order for 1,000 more is expected to arrive during week 1.

Use MRP to schedule planned order releases for gloves.

9. A company that manufactures furniture produces a par�cular type of coffee table. As you may guess, each coffee table has four legs. The produc�on lead �me for these legs is two weeks. Inventory records show that 2,500 of these legs will be available as on-hand inventory at the beginning of week 32. An order for 2,500 legs has already been released and is scheduled to arrive in week 33. These legs may be produced in any quan�ty. Use MRP to schedule planned order releases.

10. A company that makes canned soups has developed the following master schedule for its 12-ounce cans of vegetable beef soup:

Each 12-ounce can of vegetable beef soup requires seven ounces of beef broth. The company currently has 9,000 ounces of beef broth that will be available in week 12. Produc�on lead �me for beef broth is one week. Each ounce of beef broth requires three ounces of beef bones. These bones are ordered from a supplier in mul�ples of 32,000 ounces (2,000 pounds) and have a lead �me of two weeks. There will be 30,000 ounces on hand at the beginning of week 12, and another 32,000 ounces are scheduled for receipt during week 13. Develop planned order releases for beef bones.

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Item Lead Time (Weeks)

On-Hand Week 42

Scheduled Receipts

Quan�ty Week

A38 2 3,000 3,000 44

B493 1 3,000

1438 1 3,000

1297 1 4,500

1395 3 4,000 10,000 44

4217 2 60,000

6438 1 5,000

Master Schedule—5400s

Week

43 44 45 46 47

2,000 2,400 3,000 2,300 2,300

Week

Planned order releases 1 2 3 4 5 6

Part A 100 50 300 50 100

Part B 200 200 100 200 100

Setup (Hrs./Batch) Run (Hrs./Unit)

Part A 1 0.3

Part B 2 0.2

Transmission Repairs Scheduled

Monday Tuesday Wednesday Thursday Friday

11. Referring to Problem 10, suppose that the supplier of beef bones has called to indicate that the delivery of 32,000 ounces for week 13 has been delayed un�l week 14. How do you need to alter the master schedule for produc�on of vegetable beef soup to compensate for this change if it is uneconomical to produce less than 100 cans of soup at a �me?

12. An electronics manufacturer makes a product designated as 5400. Each 5400 is assembled from one of each of two subassemblies, A38 and B493.    Subassembly A38 requires two of part 1438 and two of component 1297. Component 1297 in turn is made from one of part 6438 and five fasteners numbered 4217. Subassembly B493 consists only of two units of part 1395 and four fasteners numbered 4217.

a. Draw a tree diagram indica�ng the structure of product 5400. b. Using low-level coding, at what level would fastener 4217 be coded in the BOM? c. Develop an indented bill of materials for product 5400.

13. Referring to Problem 12, the master schedule for product 5400 is as shown below.

a. Determine gross requirements for A38 and B493 in each week. b. Suppose that in addi�on to the informa�on provided, the MRP system's item master file indicates the following lead �mes, and the inventory data file indicates

the current amounts on hand and the scheduled receipts shown below. Develop planned order releases for parts 1438 and 1395.

c. Using the preceding informa�on, develop planned order releases for all parts and fasteners.

14. Referring to Problem 9, suppose the master schedule for coffee tables is altered, so that 500 tables are planned for produc�on in week 33. Change the planned order releases for table legs accordingly.

15. The Skillful Machining Company makes two different parts, and both require milling. The planned order releases for these parts are shown below, alongside the mill �me required by each. If the milling machine is available 60 hours per week, develop a load profile for the milling machine in each week.

16. The Davis Auto Center has scheduled the following numbers of transmission repairs on each day for the coming week. Each transmission repair requires two hours of transmission specialist �me and four hours of general mechanic �me. The company has one transmission specialist who works eight hours per day and two general mechanics who each work eight hours per day. Develop load profiles for the transmission specialist and the general mechanics.

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1 3 2 2 3

Click here to see solu�ons to the odd-numbered problems. (h�ps://media.thuze.com/MediaService/MediaService.svc/constella�on/book/AUBUS644.13.2/{pdf}bus644_ch09_odd_problem_solu�ons.pdf)

Key Terms

Click on each key term to see the defini�on.

aggregate planning (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Medium-range opera�ons planning. A first rough-cut approxima�on at determining how exis�ng resources of people and facili�es should be used to meet projected demand.

available-to-promise (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The number of units in a master schedule not yet commi�ed to customer orders.

bill of materials (BOM) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The document that describes the type and quan�ty of each component part needed to build one unit of a product.

capacity requirements planning (CRP) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A process for es�ma�ng total capacity that will be required at each work center or machine, based on the master schedule and MRP.

closed-loop MRP (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A varia�on of MRP in which feedback about execu�on of produc�on plans is provided so MRP can be updated to reflect reality.

cycle coun�ng (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A procedure in which inventory of an item is counted at least once during an order cycle.

dependent demand (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The demand (usually for components or raw materials) that depends on produc�on of a finished product.

distribu�on requirements planning (DRP) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A system for determining the quan�ty of products needed within the distribu�on system. DRP uses forecasts of customers' orders to es�mate the quan�ty of materials to have available at the distribu�on centers.

freezing the master schedule (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A policy that prevents changes in the master schedule within a certain �me period from the present.

gross requirements (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

In MRP, the total demand for an item during a �me bucket.

indented bill of materials (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A bill of materials in which components are indented from the item in which they belong.

independent demand (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The demand (usually from the consumer) for a part or product that is not dependent upon a produc�on plan. Processing math: 0%

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load (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The total capacity requirements placed on a machine or work center during a specified period of �me.

load profile (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A graphical representa�on of the load on a machine or work center over �me; also known as load report.

long-range opera�ons planning (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Ac�vi�es that are planned to occur five years or more in the future. It involves resources such as facili�es, people, and equipment that are needed to produce the goods and services.

load report (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

See load profile.

lot-for-lot (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An order release and corresponding receipt that covers the net requirement.

lot sizing methods (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Net requirements from several periods that are combined into one planned order release.

manufacturing resource planning (MRP II) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An integrated decision support system that connects departments such as engineering, finance, personnel, manufacturing and marke�ng via a computer-based dynamic simula�on model. MRP II works within the limits of an organiza�on's present produc�on system and with known orders and demand forecasts.

master produc�on schedule (MPS) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A specific statement of exactly what, usually individual end items or product models, will be produced in each �me period. Usually these �me periods are weeks, although they may be days or even hours.

medium-range opera�onal planning (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Ac�vi�es planned between six months and 18 months ahead. It involves how exis�ng facili�es are used to sa�sfy demand.

method of overall factors (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A procedure for rough-cut capacity planning that uses historical accoun�ng data to es�mate the number of standard hours required per unit.

net requirements (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The addi�onal number of units required in MRP during a �me bucket a�er inventory and scheduled receipts have been considered.

planned order release (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An order to either the shop or a supplier, planned to be released for a given amount during a �me bucket in MRP.

planned receipts (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

In MRP, a quan�ty expected to be received in a given �me bucket based on an order that is planned, but not yet released.

product structure (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The way in which the component parts and subassemblies are used to build the product.Processing math: 0%

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purchase order (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An authoriza�on for a vendor to supply parts or materials.

rolling through �me (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A planning analogy that conceptualizes �me as a scroll. As �me passes, the scroll is rolled up on the end at the right and unrolled at the other end.

rough-cut capacity planning (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Used to determine whether sufficient overall produc�on capacity will exist to meet the master produc�on schedule.

rou�ng sheet (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A document used in manufacturing to indicate the sequence of opera�ons, machines, or work centers that a part or product must follow.

scheduled receipts (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

In MRP, a quan�ty for which an order has already been released and which is planned for receipt during a given �me bucket.

shop order (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An order for more parts to be produced in a company's own fabrica�on facili�es.

�me bucket (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A period of �me, usually one week, in which demand and requirements are grouped for master scheduling and material requirements planning.

�me phasing (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The process used in material requirements planning for determining requirements by �me period.

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10

©iStockphoto/Thinkstock

Inventory Management

Learning Objec�ves A�er comple�ng this chapter, you should be able to:

List the purposes that inventory serves. Describe the different types of inventory. Explain the differences between perpetual and periodic inventory systems. Use the EOQ model to calculate order size. Calculate economic order quan��es with quan�ty discounts. Determine the reorder point. Calculate safety stock.

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For manufacturing companies, wholesale and retail organiza�ons, and food service providers, inventory represents a significant investment in working capital and a substan�al cost to store and manage.

©John McBride & Company Inc./The Image Bank/Ge�y Images

10.1 Inventory

Inventory represents a significant investment of working capital for manufacturing companies such as Sony, wholesale and retail organiza�ons such as Walmart, and food service providers such as Red Lobster. Firms like these should carefully consider the costs and benefits of holding inventory. When firms hold large amounts of inventory, they increase the costs associated with holding inventory including working capital, storage, and inventory management. Conversely, when firms hold small amounts of inventory, they must make frequent orders and accept the risk of being unable to sa�sfy customer demand. Making small and frequent orders tends to increase transac�on, transporta�on, and equipment set-up costs. This is a fundamental trade-off in managing inventory.

Mul�ple elements that impact this trade-off are discussed throughout the chapter and are relevant in the following chapters. This chapter also discusses methods for controlling independent demand inventory. The previous chapter addressed dependent demand items. Different systems for controlling and monitoring independent demand inventory are discussed and several mathema�cal models are described in this chapter. These systems help companies determine how much inventory should be ordered to minimize costs and also when to order inventory so that the desired level of customer service can be provided. Determining how much inventory to order and when is key to managing inventory.

Purpose of Inventory

Inventory can help businesses meet demand and work more efficiently. For many items, it does not make sense to produce them only when there is demand. When a customer walks into a retail store to buy groceries or cosme�cs, they expect to walk out of the store with the item. When customers walk into a dealer's showroom to buy a car, they do not want to wait un�l the car is produced; they want to drive it away. There are also advantages to maintaining a stable level of produc�on. Employment levels must be changed and equipment must be ac�vated or shut down to allow produc�on rates to fluctuate. These changes incur cost. In some cases, there simply is not enough capacity to meet the high level of demand, therefore, an alterna�ve must be found. During low-demand �mes, firms can produce more product than they can currently sell with the unused por�on going to inventory. The inventory can be used when demand accelerates and increasing the produc�on level is not possible or is not economically feasible.

Many firms keep a cushion or "safety stock" of inventory to protect against unexpected demand. In this way, they can con�nue to meet customer demand without delays. Keeping a safety stock of inventory is also useful when shipments from suppliers are delayed. This allows the firm to meet customer demand even though the supplier cannot meet its lead �me commitment.

When producing goods, it is o�en important to separate steps in the produc�on process that operate at different speeds. For example, a manufacturing part may be machined at one rate—one part in five minutes. The next step is to heat treat the machined parts in a furnace that operates in a batch mode—the furnace can hold up to 100 parts and take eight hours for heat trea�ng. Therefore, an inventory of up to 100 parts should be accumulated before heat treatment.

In many situa�ons, discounts are available to purchase a certain quan�ty. These can be quan�ty discounts or transporta�on discounts. A firm may need a certain amount of parts, but it may decide to buy more because a supplier is offering a discount for purchasing the larger amount. This is similar to buying a larger box of laundry detergent because it cost less per unit than the smaller box. Shipping in a certain amount may substan�ally reduce transporta�on costs. The best known transporta�on discount involves shipping in full truck load quan��es rather than less than truck load amounts. The same can be said for shipping a full rail car versus less than a full rail car.

A company may try to hedge against possible price increases. When an increase in the purchase price is an�cipated by the company or announced by the supplier, the company may order addi�onal materials prior to the increase. This is similar to the quan�ty discount. Other �mes, firms may want to hedge against uncertainty in supply. A supplier may announce down �me for its opera�ons, or a supplier may have an upcoming contract nego�a�on with its labor union. Maintaining some extra inventory on hand may be prudent.

Types of Inventory

Several common types of inventory are:

1. Raw materials: These parts and materials are obtained from suppliers and are used in the produc�on process. 2. Work-in-process (WIP): These are partly finished parts, components, subassemblies, or modules. 3. Finished goods: Items are ready to ship to the customer. No more work is required. 4. Replacement parts: These are maintained to replace other parts in machinery or equipment as those parts wear out. 5. Supplies: Parts or materials are used to support the produc�on process, but not usually a component of the product. These items, such as lubricant and cu�ng

tools, are consumed in the produc�on process. 6. Transporta�on (pipeline): The por�on of inventory that is in the process of being shipped through the distribu�on system. Processing math: 0%

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10.2 Information Systems for Inventory Management

The purpose of inventory management systems is to provide informa�on so that sufficient inventory will exist to meet the company's objec�ves. Of course, too much inventory can mean extra costs. Thus, the inventory management system is designed to ensure that inventory levels are maintained within a desired range for each item.

Today's computer systems and the widespread use of bar codes (as shown in Figure 10.1), have made inventory control more automated. It is not always be possible, or even desirable, to computerize all inventory control. This sec�on describes different systems and how they can be used, either with or without computers. All these systems focus on helping companies determine what, when, and how much to order.

Figure 10.1: Bar codes used for inventory management

Real World Scenarios: Toys "R" Us—Dealing with Fads in the Toy Business

A major problem in the toy industry is iden�fying when fads begin and end. There is a long history of fads including GI Joes, Smurfs, Furbies, and Transformers, which have recently made a comeback. In many cases, these items are hot one year and gone the next. Toys "R" Us carries more than 20,000 different items. To maximize profits, the company must be sure it maintains just the right amount of each item. One way it does this is by using computers to monitor sales data and to order (or stop ordering) as point-of-sale (POS) demand informa�on indicates. This informa�on is transmi�ed each day to the company's headquarters where it is automa�cally monitored. Thus, when demand for scooters picks up, the computers can catch the trend and began placing larger orders. Likewise, drops in sales when a fad has ended can be caught and replenishment orders halted.

Perpetual Inventory Systems

A perpetual inventory system con�nuously monitors inventory levels. It is also known as a con�nuous review system. Under such a system, inventory transac�ons are recorded as they occur. If the number of transac�ons is small, this recording can be done by hand, which is how inventory was recorded before computerized systems. This non-computerized approach makes sense if there are only a handful of items to inventory. Computers, however, have made the process much easier and faster for a larger number of items. For example, grocery stores and retailers such as Walmart use point-of-sale systems that record the transac�on as each item is read by the bar code scanner. As at Toys "R" Us, this informa�on is passed along to the supplier, so replenishment can take place. An ATM is anotherProcessing math: 0%

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To keep track of inventory, retailers use a point-of-sale (POS) system that records each transac�on as the items are read by a bar code scanner.

Digital Vision/Photodisc/Thinkstock

example of a perpetual inventory system; this system updates the balance in a patron's bank account as withdrawals are made. Debit cards are one way for the bank to move the money from the user's account at the �me of transac�on. These cards also allow the bank to determine if there is sufficient money to cover the transac�on, which is good for the bank and the retailer.

Companies use bar codes for raw material and work-in-process inventories as a way to computerize these inventory records. The bar codes shown in Figure 10.1 are used on a component part ordered from a supplier. Using bar codes or other similar technologies allow the firm to be constantly aware of inventory levels. When inventory drops to a predetermined level (the order point) an order for more can be generated. O�en, this ordering is completed automa�cally by the same computer system that maintains the inventory records. The quan�ty ordered is usually a fixed amount, o�en the economic order quan�ty, which is discussed later in this chapter.

Periodic Inventory Systems

For the con�nuous review system to work, it is necessary to know the inventory level constantly, and to have a supplier who will replenish inventory at any �me. In this way, when the order point in the con�nuous review system is reached, an order can be sent and delivery can take place.

When a company does not know the level of inventory or the supplier will only deliver at a specific interval such as monthly or weekly, the periodic review system can be used. A meaningful order cannot be placed if the on-hand level of inventory is unknown. Also, ordering a�er the supplier's order window has closed will not generate an immediate response. The supplier will not process and deliver the order un�l the order window is open.

To be effec�ve, the periodic review system is designed to place an order only when onhand inventory informa�on is available and the supplier is willing to deliver, in other words, when the order window is open. The local concrete plant uses cement, which it stores in large tanks. It takes a physical inventory only on Monday because it is �me consuming, so it does not know if or how much it needs to order except on Monday. The storage tanks at most gasoline service sta�ons are refilled on a preset schedule, for example, once each week on Friday. Monitoring inventory con�nuously and placing an order on Saturday does not help because the delivery will not be made un�l the following Friday.

In these cases, the order point must be set at a level that will allow the company to meet expected demand un�l the next order window occurs plus demand during the lead �me. If the on-hand inventory is less than this order point, an order is generated that will push on-hand inventory back to a predetermined level. The periodic review system, also called the fixed order interval system, can be run without a computerized system to monitor inventory levels, but it is more likely to run out of stock because the system is unable to react quickly to changes in demand because inventory level is not con�nually monitored. If the firm wishes to keep the chance of stockouts low, it must increase the level of safety stock inventory.

Aggregate Performance Measures

Inventory represents a tremendous capital investment. In general, the companies that can operate with less inventory are the companies that operate more efficiently. Aggregate performance measures can be used to judge how well a company is u�lizing its inventory resources. One of the most common measures is average inventory investment—the dollar value of a company's average level of inventory. The primary disadvantage of this measure is that it makes comparisons between companies difficult. For example, larger companies will generally have more inventory than smaller companies. Thus, a large mul�na�onal company may have a larger average inventory investment than a small business, but the larger company may be using its inventory more efficiently.

Inventory turnover ra�o is a measure that allows for be�er comparison among companies. This ra�o is calculated by comparing a company's sales to its average inventory investment, as follows:

Inventory turnover = annual cost of goods sold/average inventory investment

The inventory turnover ra�o indicates how many �mes the inventory turns over or is sold during one year. Because this ra�o is a rela�ve measure, companies of different sizes can be more easily compared. In general, a company with a higher turnover ra�o will be using its inventory more efficiently. For example, automobile companies using just-in-�me (JIT) o�en have very high inventory turnover ra�os of 30 or more, while those not using JIT may be in the range of 6 to 12. JIT is providing only the items that are needed at the �me they are needed. One disadvantage of this ra�o is that figures among industries may not be comparable.

A measure closely related to inventory turnover is days of inventory. The calcula�on procedure is as follows:

Days of Inventory = average inventory investment/(annual cost of goods sold/days per year)

The days of inventory indicate approximately how many days of sales can be supplied solely from inventory. The lower this value, the more efficiently inventory is being used. In general, inventory turnover can be converted to days of inventory by using the following calcula�on:

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ABC analysis is used to determine which inventory items should receive the highest level of control. This method focuses efforts where the payoff is highest.

©Stockbyte/Thinkstock

Days of inventory = days per year/inventory turnover rate

ABC Classification

Interes�ngly, companies do not need to keep accurate track of all inventory items. For instance, certain parts may have a rela�vely low value and be used infrequently; those items can o�en be monitored very loosely. On the other hand, high-value and high-usage items must be tracked carefully and con�nuously. ABC analysis has been developed to determine which inventory items should receive the highest level of control. By mul�plying the dollar value of each item by its annual usage, a dollar usage value can be obtained. Dollar usage follows the Pareto Principle (see Chapter 4) in that typically, only 20% of all the items account for 80% of the total dollar usage, while the remaining items typically account for only 20% of the dollar usage. This principle leads to the ABC classifica�on, which is based on focusing efforts where the payoff is highest.

A�er calcula�ng the dollar usage for each inventory item, the items are ranked by dollar usage, from highest to lowest. The first 20% of the items are assigned to class A, as shown in Table 10.1. These are the items that warrant closest control and monitoring through a perpetual inventory system. Accurate inventory records are important, and there is a high poten�al for cu�ng costs through careful buying and close scru�ny of safety stocks.

Table 10.1: ABC classifica�on of inventory items

Item Annual Demand Unit Cost Annual Dollar Usage % Annual Dollar Usage Cumula�ve % Annual Dollar Usage Classifica�on

1 5,000 $30 $150,000 48.91 48.91 A

2 200 450 90,000 29.34 78.25 A

3 2,000 10 20,000 6.52 84.77 B

4 800 20 16,000 5.22 89.99 B

5 1,000 10 10,000 3.26 93.25 B

6 1,200 5 6,000 1.96 95.21 C

7 1,300 4 5,200 1.69 96.90 C

8 2,500 2 5,000 1.63 98.53 C

9 3,500 1 3,500 1.14 99.67 C

10 500 2 1,000 0.33 100.00 C

306,700

The next 30% of the items are classified as B items. These deserve less a�en�on than A items. Finally, the last 50% of stocked items are C items. These have the lowest dollar usage and can be monitored loosely, with larger safety stocks maintained to avoid stockouts.

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10.3 Economic Order Quantity Model

Inventory decisions involve trade-offs: Keeping more inventory may decrease the amount of stockouts as well as reduce the ordering and set-up costs, but keeping more inventory requires more investment, storage, and management costs. One model that seeks to minimize these costs is the economic order quan�ty (EOQ). The EOQ model is concerned primarily with the cost of ordering and the cost of holding inventory, but the basic model can be expanded to address several issues.

Costs of Ordering and Holding

One major component of cost associated with inventory is the cost of replenishing it, usually called ordering cost. If a part or raw material is ordered from outside suppliers, an ordering cost is incurred. Conversely, parts, subassemblies, or finished products may be produced in-house. In that case, ordering cost is represented by the costs associated with changing over equipment from producing one item to producing another, and is referred to as set-up cost. To simplify, this text will refer to both ordering costs and set-up costs as ordering costs.

Ordering costs may include many different items. Some of these will be rela�vely fixed, and others may vary. It will be important to differen�ate between the ordering costs that do not change much and those that are incurred each �me an order is placed. For example, suppose a company currently places orders for a given part with its supplier five �mes per year. If, instead, the company ordered six �mes per year, which costs would probably change (variable costs), and which would probably not (fixed costs)? The general breakdown between fixed and variable ordering costs is listed in Table 10.2.

Table 10.2: Fixed costs and variable costs

Fixed Costs Variable Costs

Staffing costs (payroll, benefits, etc.) Office furniture and equipment

Shipping costs Cost of placing an order (phone, postage, order forms) Cost of lost produc�on during set-up Cost of materials used during set-up Receiving and inspec�on costs

Although it costs money to replenish inventory, it also costs money to hold that inventory. Such inventory holding costs, also called carrying costs, may include costs paid for storage space, interest paid on borrowed money to finance the inventory, and any losses incurred due to damage or obsolescence. Once again, it is important to differen�ate between fixed and variable costs of holding inventory. To understand this difference, consider this ques�on: What happens if an inventory level is increased by one unit? Which costs would not change (fixed costs), and which costs would change (variable costs)? The general breakdown for inventory holding is shown in Table 10.3.

Table 10.3: Inventory holding

Fixed Costs Variable Costs

Capital costs of warehouse Taxes on warehouse and property Costs of opera�ng warehouse Personnel costs

Cost of capital in inventory Insurance on inventory value Losses due to obsolescence, the�, spoilage Taxes on inventory value Cost of ren�ng warehouse space

In the next sec�on, the most basic approach to determining order quan�ty, called the economic order quan�ty (EOQ) model, is discussed. The goal of firms using the EOQ model is to minimize the total annual costs of ordering and holding inventory by varying the order quan�ty. Only variable costs are considered because fixed costs are not affected by shor�erm varia�on in order quan�ty. To understand EOQ, it is important to understand the differences between the fixed and variable costs that are listed above. Also, it is important to realize that the division between fixed and variable costs may change depending on the context. If addi�onal personnel must be hired, staffing costs may be considered variable.

Ordering cost and holding cost can be described with the analogy of two children si�ng on a seesaw. When one goes up, the other goes down, and vice versa. This trade-off appears to present somewhat of a quandary: If an effort is made to decrease total annual variable holding costs, total annual variable ordering costs will increase—and vice versa. A solu�on to this dilemma is to combine the two costs as total annual variable costs and minimize only that cost. As Figure 10.2 indicates, there is just one point at which total costs are minimized. The order quan�ty associated with that point is called the economic order quan�ty (EOQ).

Figure 10.2: Total annual variable costs

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Assumptions of the EOQ

Figure 10.2 indicates the economic order quan�ty point. A set of simplifying assump�ons can be made because the EOQ model is a simplifica�on of real ordering processes. Those assump�ons are described here. Later, varia�ons of the EOQ model will be considered when some of these assump�ons are not necessary.

1. Constant known demand: The first assump�on is that demand is fairly stable, or constant, and reasonably known. 2. Cost per unit is not dependent on order quan�ty: Most things can be purchased at a lower cost per unit if they are purchased in larger quan��es. For instance, large

sizes of laundry detergent usually cost less per ounce than smaller sizes. This example, however, makes purchase cost a variable cost—something for which the EOQ model does not account. Thus, the assump�on is that purchase cost per unit remains the same, regardless of whether the amount is one, 100, or 1,000 units each �me.

3. En�re order delivered at once: This assump�on relates to how inventory is replenished. Gradually building up inventory, as would happen in a clothing factory, is one possibility. As a par�cular model of jacket is produced, the inventory of that jacket builds up gradually. Another possibility is for all units in an order to arrive at one �me, which is what happens when a retail store orders from a factory. The factory ships an en�re order of the jacket at one �me and the store's inventory is replenished all at once. It is this la�er, instantaneous replenishment that is assumed by the EOQ. This assump�on, combined with the assump�on of constant demand, results in the inventory pa�ern depicted in Figure 10.3.

4. Ordering and carrying costs known and independent: The final assump�on is that the variable costs of ordering and carrying inventory are known. In many cases, such costs can be determined from company records or from the accoun�ng department; however, they are some�mes not readily available and must be es�mated. Also, the assump�on is made that these two costs are not related in any way, and that only variable costs are effected by the order quan�ty.

These assump�ons may seem restric�ve, and possibly unrealis�c. Recall, however, that the EOQ model is the basic star�ng point. This model may be altered to relax some of these assump�ons—and more closely match reality.

Figure 10.3: Basic EOQ inventory pa�ern

Mathematics of EOQ

Sta�ng the EOQ formula in mathema�cal terms requires the use of variables to represent the parameters. The variables are:

D = demand rate (units/year)

Q = order quan�ty or lot size (units) Processing math: 0%

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Co = variable ordering cost ($/order)

Ch = variable holding cost ($/unit/year)

Once again, please note that these are the variable costs and that the variable ordering costs will represent addi�onal costs incurred when another order is placed. Holding costs also include only the variable costs associated with keeping one more unit in inventory. These variables are stated as cost per unit per year because the model is illustra�ng annual costs.

Another way of sta�ng inventory holding costs is to divide Ch into two components. The elements that make up variable holding costs depend on the number of

units in inventory and the value of each unit. In most instances, it is possible to state inventory holding cost, Ch, as a percentage of unit cost per year ($/year). The

greatest part of this percentage is accounted for by capital �ed up in the inventory. Because capital cost is usually stated as a percentage, it is especially convenient to state holding cost in this form. To do so, the following variables are used:

v = cost or value of item ($/unit)

r = holding-cost percentage of unit value ($/$/year)

Then Ch = vr.

Regardless of how many units are ordered at a �me, the number of orders can be determined by dividing annual demand, D, by the order quan�ty, Q. Thus,

Since the cost per order is Co, annual variable ordering costs can be easily calculated as follows:

*Throughout this text, to enlarge the size of the math equa�ons, please right click on the equa�on and choose "se�ngs" then "scale all math" to increase the viewing percentage.

Annual Variable Holding Costs

No�ce in Figure 10.3 that if the order quan�ty is set equal to the EOQ, the theore�cal inventory pa�ern is a straight line between the EOQ and zero. Remember the assump�on is that demand is constant over �me, which makes the drawdown of inventory a straight line. Suppose, instead, that the variable Q represents the quan�ty ordered each �me. In that case, the maximum inventory level would be Q, assuming inventory is replenished just as it reaches zero. Minimum inventory would s�ll be zero. This fluctua�on in the inventory level makes the calcula�on of annual holding costs somewhat difficult because there will be a different number of units in inventory at any one �me. To make ma�ers worse, each unit will be in inventory for a different length of �me—some for a very short period, others longer. There is also an easier, but equivalent, way to determine annual holding costs.

The method used to determine annual holding costs is based on average inventory level. Because inventory follows a uniform pa�ern, with a maximum of Q and a minimum of zero, the average level will be halfway between the maximum and minimum values, or Q/2. In terms of the number of units in inventory, and the �me each unit spends there, the fluctua�ng system shown in Figure 10.3 is actually equivalent to maintaining Q/2 units at all �mes, as shown in Figure 10.4. This simplifies the calcula�on of annual variable holding costs to:

Figure 10.4: Average inventory

Economic Order Quan�ty Formula

Total annual variable costs will be the sum of holding costs and ordering costs. Using the formulas noted above, this will be:

The economic order quan�ty will be the point at which the total cost func�on is minimized. An easy way to find this point is by iden�fying that the EOQ occurs where annual holding costs and annual ordering costs are equal, as shown in Figure 10.2. In mathema�cal terms, this is

Note that Q* has been used to designate the op�mal value of Q, which is the economic order quan�ty. Solving the above equa�on for Q* we obtain

and by taking the square root of each side,

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Problem

Bill Green, general manager for Poolco, a company that provides home pool maintenance services in the Los Angeles area, is responsible for developing inventory policies regarding all items the company stocks. One item that he is expected to monitor is a clarifying agent that is added to pool water to improve its clarity. This item costs $5/gallon. Variable costs of storing it in inventory amount to 25% of unit cost per year. Paperwork and shipping costs for placing an order are $10 per order. Each year the company uses an average of 500 gallons, a rate that is not expected to change. How many gallons should be ordered each �me to minimize total annual variable costs?

Ch = vr Ch = 5(0.25) = $1.25 (per unit/year)

EOQ = EOQ = 89.44 gallons

Because an order must be placed for whole gallons, Bill would round this down to 89 gallons per order.

Sensitivity of the EOQ Value

The EOQ in the preceding example did not result in an even value; rounding down to the nearest whole number s�ll provided a result that was somewhat unusual. It would be far more likely that Bill Green could order 90 gallons at a �me than 89. But, suppose this clarifying agent is only available in 55-gallon drums. In that case, the closest order quan�ty would be two drums, or 110 gallons. What impact will this have on total annual variable costs if Poolco must order 110 gallons of clarifying agent at a �me?

The total annual variable cost func�on is rather "flat" around the EOQ, as shown in Figure 10.5. That is, order quan��es can be varied considerably from the EOQ, especially above it, without greatly increasing costs.

Figure 10.5: Total annual cost curve near the EOQ

Problem

Suppose Bill Green of Poolco wants to determine how much higher costs will be if he orders in lots of 110 gallons instead of the 89.44 gallons determined by the EOQ formula.

The total annual variable costs for the EOQ of the preceding example will be

Total annual variable costs = = = $55.90 + $55.90 = $111.80

However, by changing Q to 110, the total annual variable costs will become

Total annual variable costs = = = $68.75 + $45.45 = $ 114.20

Thus, the cost increase incurred by ordering in quan��es of 110 gallons at a �me is only $2.40, or 2.15% more than the total annual variable costs of ordering EOQ quan��es.

As this example indicates, the cost consequences of varying from the EOQ are not very great. The EOQ value should be an es�mate that indicates approximate minimum-cost order quan��es, not a value that must be used exactly.Processing math: 0%

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Items usually cost less, per unit, when purchased in bulk. Therefore, the order quan�ty directly influences the purchase price of an item.

Gene J. Puskar/Associated Press/AP Images

Holding and ordering cost figures for the EOQ formula are usually obtained from accoun�ng when opera�ons does not have the informa�on available. In some companies, accoun�ng is responsible for determining inventory holding and ordering costs. Such costs are o�en buried as part of overhead expenses and are not readily available for use in calcula�ng the EOQ. Determining these figures o�en requires that departments work together to calculate numbers that are realis�c.

Quantity Discounts: An EOQ Model Variation

Star�ng with the basic EOQ model, it is possible to develop other models that have less restric�ve assump�ons, or are appropriate for other situa�ons. One assump�on from the example is that purchase price remained the same regardless of how many units were purchased. In reality, this is usually not true. For example, things usually cost less per unit, when purchased by the case rather than individually. An en�re truckload generally will cost less than each case. Order quan��es directly influence the purchase price of an item.

Incorpora�ng quan�ty discounts into the order quan�ty calcula�ons requires modifica�on of the total-cost calcula�on to include purchase cost—which had not been included in the previous example because it was a fixed cost. The total annual cost of purchasing an item may vary due to quan�ty discounts. The op�mal answer cannot be found by subs�tu�ng numbers into a formula, as in the example for the EOQ. This situa�on occurs because quan�ty discounts occur in a stepwise manner, as shown in Figure 10.6. When this pa�ern of purchase costs is used to calculate total annual purchase cost and then combined with ordering and holding costs, the total-cost curve appears (also shown in Figure 10.6) A step-by-step procedure is required to determine the order quan�ty that generates the lowest total annual costs.

Figure 10.6: Total annual cost with quan�ty discounts

The procedure for calcula�ng lot sizes when a quan�ty discount is available is based on using the unit cost, v, and holding-cost percentage, r, to calculate holding cost. In other words, Ch = vr.

No�ce that as the unit purchase cost varies, so does the holding cost.

Step 1. Start with the lowest unit price. Calculate the holding cost, Ch, for this price, and then determine the EOQ. If this EOQ is "feasible"—in other words, if it

falls in the range of order quan��es required for that unit price—this is the op�mal order quan�ty. Stop here.

If the EOQ is not feasible, determine the minimum order quan�ty required for that unit price, and calculate the total annual variable costs (holding cost, ordering cost, and purchase cost) associated with that minimum order quan�ty. Proceed to step 2.

Step 2. For the next higher unit price, calculate holding cost, and determine EOQ. If the EOQ is feasible, then calculate its total annual variable costs, and compare this with the total annual variable costs for order quan��es calculated previously. That order quan�ty with the lowest total annual variable costs will be op�mal. Stop here.

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Gallons Ordered Unit Price

54 or less $5.00

55–274 4.80

275–549 4.60

550 or more 4.50

If the EOQ is not feasible, repeat this step un�l a feasible EOQ is found; then calculate its associated total annual costs, and compare these costs with all total annual costs previously calculated. The order quan�ty with the lowest associated total annual variable costs will be op�mal.

Problem

Bill Green of Poolco has learned that the supplier of the clarifying agent will begin offering quan�ty discounts according to the following schedule:

Bill wonders whether he should change his lot size for ordering the clarifying agent. To answer his ques�on, he proceeds through the steps described previously.

Step 1. Calculate the holding cost and EOQ corresponding to the lowest unit price. This unit price will be $4.50, and its associated holding cost is (0.25)($4.50) = $1.125/gallon/year.

EOQ = = 94 gallons (rounding to the nearest whole number)

However, this is not feasible because at least 550 gallons must be the ordered quan�ty each �me an order is placed with the supplier to obtain the $4.50 unit price. Recall that Bill's supplier requires an order of at least 550 gallons to have the price be $4.50. Because this solu�on is not feasible, the second part of Step 1 is implemented. The minimum order quan�ty required to obtain the unit price of $4.50 is used to calculate the total annual variable costs (holding cost, ordering cost, and purchase cost). In this case, that minimum order quan�ty is 550 gallons.

Total annual variable costs = = = $309.38 + $9.09 + $2,250.00 = $2,568.47

Step 2. For the next higher unit price, calculate holding cost, and determine EOQ. This next higher unit price will be $4.60, obtained by ordering between and including 275 and 549 gallons each �me.

Holding cost will be (0.25)($4.60) = $1.15/gallon/year and

EOQ = = 93 gallons

This also is not feasible because 93 is not between or including 275 to 549 gallons required for the $4.60 unit price. Thus, taking the minimum value in that range of 275, the associated total annual variable cost is calculated.

Total annual variable costs= = = $158.13 + $18.18 + $2,300.00 = $2,476.31

Because the EOQ for this unit price was not feasible, the process moves to the next higher price of $4.80/gallon. Its holding cost will be $1.20/gallon/year, and the EOQ is 91 gallons.

This EOQ is feasible, so the total annual variable costs are calculated.

Total annual variable costs= = = $54.60 + $54.95 + $2,400.00 = $2,509.55

Total annual variable costs calculated are compared in the following table:

Order Quan�ty (Gallons) Total Annual Variable Costs

550 $2,568.47

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91 2,509.55

The lowest-cost order quan�ty will be 275 gallons, and Poolco should change its lot size for the clarifying agent accordingly.

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Apple experienced a stockout when the iPhone 4 was released. A stockout occurs when an organiza�on underes�mates demand or has delays in produc�on which lead to late delivery of the product.

Weng lei/Imaginechina/AP Images

10.4 Stockouts and Safety Stock

In the EOQ model, it is assumed that demand is constant and known, however, in prac�ce this is rarely true for independent demand items. This sec�on discusses ways to ensure that uncertainty about actual demand does not result in lost sales. The process begins by determining the point at which inventory must be replenished.

Order-Point Determination

In the calcula�ons thus far, it was assumed that inventory would be replenished just as the inventory level hit zero. Thus, the minimum inventory level was treated as zero. In most situa�ons, the replenishment of inventory requires some advance no�ce. For example, a company that orders materials from a supplier must account for (1) the �me it takes that order to reach the supplier's offices, (2) the �me to fill the order, and (3) the shipping �me. This is called lead �me. Failing to account for lead �me can cause an organiza�on to run out of inventory. This situa�on is known as a stockout. Any �me a stockout occurs, a disrup�on in produc�on, idle employees, and unhappy customers will likely be the result. Most companies try to avoid stockouts if possible.

The easiest way to account for lead �me is to use what is called an order point. An order point is simply a level of inventory at which an order should be placed, accoun�ng for lead �me and safety stock, so that the order will arrive before a stockout occurs. Figure 10.7 shows how the order point is determined.

Figure 10.7: Order-point determina�on

The graph depicted in Figure 10.7 indicates that the order point should be a level of inventory that will be sufficient to last throughout the lead �me, with inventory reaching zero just as the order arrives. Mathema�cally, the order point can be determined as follows.

d = daily demand rate (units/day)

L = lead �me (days)

Then the order point, OP, can be determined by using the formula given below.

OP = dL

Problem

Suppose that Poolco wants to determine the order point for its clarifying agent. Daily demand is two gallons per day (500 gallons per year/250 working days per year). Suppose that the lead �me for ordering the clarifying agent is 10 working days. The order point is:

OP = dL = 2(10) = 20 gallons

Therefore, when only 20 gallons are le� in inventory, an order for more should be placed. That order should arrive just as inventory reaches zero.

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Safety Stock

The order-point determina�on described in the prior sec�on works well when demand rate and lead �me are known. It is much more common to find that demand and lead �me are both variables. If either lead �me or demand (or both) is less than expected, there will be no problem when the order arrives; some inventory will remain. But if either demand or lead �me (or both) exceed our expected values, then a stockout will occur because inventory will hit zero before the order arrives, as shown in Figure 10.8. There is no margin of safety in the preceding order-point calcula�on.

Figure 10.8: Stockout occurrence

To avoid stockouts, most companies add a safety stock, which is an extra amount of inventory, to the order-point calcula�on so that

OP = dL + s

where

s = safety stock

This adds a buffer of inventory that can be expected to remain when an order is received. Instead of allowing inventory be depleted before an order comes in, it only decreases to s, the amount of safety stock, as shown in Figure 10.9. Due to demand and lead-�me variability, more or less stock may remain at any given �me. The expecta�on is that this buffer of safety stock will be sufficient to prevent most stockouts.

Figure 10.9: Inventory level with safety stock

Service Level

No ma�er how much safety stock a company carries, there is always some chance that a stockout will occur due to unusually high demand or an unexpected long lead �me. It is not possible for a company to avoid stockouts altogether. The trade-off is easy to understand. If a company adds more safety stock its inventory holding cost will increase, but the probability of a stockout and lost sales decline. What is the "right" amount of safety stock to balance these two possibili�es? Many companies choose to address this trade-off by selec�ng a level of stockouts that they are willing to accept, which is commonly called the service level. Service level is the percentage of replenishment orders that are received before a stockout occurs. For instance, a 95% service level would indicate that 95% of all orders placed to replenish inventory are received before a stockout occurs. But in 5% of the cases, inventory will hit zero before the order is received.

Inventory levels can greatly influence a company's ability to fulfill customer orders. For companies such as Lands' End, rapid delivery of customer orders can be so important that the extra cost incurred by carrying higher inventory is worthwhile. In other organiza�ons, though, customers may not always expect the item they want to be in stock.Processing math: 0%

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Because service level is so important, its determina�on must involve not only opera�ons but also marke�ng, and some�mes finance. Considering the role of rapid delivery in the organiza�on's compe��ve strategy, and balancing this role against the added costs of carrying extra inventory, can allow an organiza�on to determine the service level that will best meet its needs.

Determina�on of service level is a managerial decision that must be based on many factors. A company that competes for quality of service may choose a service level of 99% or higher. Another company may be in an industry where mee�ng customer demand from inventory is not important. For the la�er, a service level of 80% or lower may be acceptable. Once the service level has been determined, a company may proceed to calculate its safety stock.

With the rapid expansion of online shopping, an organiza�on does not need to have the item on hand because the customer will not leave the store with the item. These companies can ship goods directly from the producer or the producer's distribu�on center.

Calculating the Safety Stock

The assump�on will be made that demand during the lead �me follows the normal probability distribu�on, which is o�en realis�c and allows the use of the commonly available normal probability tables. The normal probability distribu�on is described by a mean and a standard devia�on. For this problem, these values are

DL = average demand during lead �me

σL = standard devia�on of demand during lead �me

The safety stock necessary to obtain a desired service level can be calculated as

Safety stock = zσL

where

z = number of standard devia�ons from the mean required to obtain desired service level

The order point is then

OP = DL + safety stock

= DL + zσL

As Figure 10.10 indicates, the service level—or probability of no stockout—will be equal to the area under the normal curve up to DL + zσL. The value of z is

determined by the desired service level.

Figure 10.10: Normal probability distribu�on

Problem

A company has average demand during the ordering lead �me that is normally distributed with a mean of 35 and a standard devia�on of six. What safety stock and order point are necessary to obtain approximately a 90% service level?

Referring to the normal distribu�on table in Table 10.4, the probability closest to 0.90 is 0.8997, which is in the 1.2 row and 0.08 column. Thus, a z value of 1.28 is needed to obtain a 90% service level.

Safety stock = zσL = 1.28(6) = 7.692 or 8

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Order point = DL + safety stock

= 35 + 8 = 43

Table 10.4: Areas under the standardized normal curve from – ∞ to + z

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.512 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

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10.5 Fixed-Order-Interval Model

The EOQ model is most o�en used when a company can con�nuously monitor its inventory level to determine when the order point is reached. Con�nuous monitoring may not be reasonable or necessary. In such cases, orders are o�en placed at a fixed interval of �me, which is when the inventory is reviewed. In spite of this difference, the EOQ model can be used to determine an op�mum interval for reviewing and replenishing inventory. From any given review interval, a policy can be developed to determine how much to order.

Review Interval

Refer to the EOQ model and Figure 10.3. The �me that elapses between replenishments depends on the order quan�ty, or lot size. The model can be used to determine the number of replenishment orders placed per year. In a periodic review system, the opposite will occur. That is, the �me between reviews, or the review interval (R), will determine average order quan�ty because the annual demand must be met during one year. If orders are placed frequently, then each order will be smaller. Infrequent ordering means larger lot sizes.

Recall, though, that there is s�ll a trade-off between variable ordering costs and variable inventory holding costs. Thus, the review interval that is chosen can directly affect total annual variable costs.

Fortunately, most of what is needed to calculate that op�mal interval, R, was learned when the EOQ was calculated. This is because the rela�onship between order size and order interval means that an economic order quan�ty will also produce an economic order interval. In other words, the op�mal review interval is simply the interval that results in ordering an EOQ quan�ty each �me. This order interval is the EOQ divided by demand rate, D.

Problem

The Hunziker Hardware Store carries many different items, ranging from nails and screws to appliances and hot-water heaters. While the firm has a point-of- sales data collec�on system, it doesn't make sense for them to order different items at different �mes, especially when the items are rela�vely low cost and are provided by the same supplier. Instead, the company would like to determine a review interval at which all items ordered from one regular supplier can be checked and ordered at one �me.

One group consists of brass items, such as screws, hinges, and cupboard handles. Because all such items are similar in cost and demand level, they have been grouped together. The annual demand rate for these items is 10,000 units per year. Ordering cost is $25 per order, and holding cost is $0.02 per unit per year. Using the above data, the EOQ is determined as follows:

EOQ = = 5,000 units

Based on this, the review interval is:

R = = 5,000/10,000 =

The Hunziker Hardware Store should review the inventory levels of these small hardware items twice per year and order the required quan�ty of each.

Order-Up-to Level

The next value to be determined in a periodic review system is how much to order. Under con�nuous review, a replenishment order is always placed when inventory reached the order point. However, in a periodic review system, the inventory level at the �me of review will vary, as depicted in Figure 10.11.

Figure 10.11: Order-up-to level in a periodic review system

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If a constant amount were ordered each �me, it would be very difficult to recover from a low inventory level. Instead, the quan�ty ordered must increase inventory to a level sufficient to cover an�cipated demand before the next order is received. This is called the order-up-to level, or M. A diagram of an order-up-to level is shown in Figure 10.11.

Another difference between con�nuous and periodic review systems relates to the period of �me that must be covered by an order. Inventory levels are monitored con�nuously and an order is placed whenever the inventory reaches the order point if stock is con�nuously reviewed. A periodic review system only reviews inventory at the review point; once an order has been placed the inventory will not be checked again un�l the next review point. Each order must contain a sufficient amount to cover expected demand during the review interval plus demand during the lead �me, as shown in Figure 10.12, or a stockout will occur. If the review interval, R, and the lead �me, L, are stated for one year, then the order-up-to level to cover demand during the review interval plus the lead �me must be:

M = D(R + L)

Figure 10.12: Period of �me an order must cover

Problem

It was determined in the previous example that the review interval for the common group of brass hardware items will be one-half of one year for all items in that group. One of the hardware items in that group is a brass gate hinge that has a demand of 1,000 units per year. Lead-�me is one-tenth of one year. What should the order-up-to level be for this hardware item? We can use the preceding formula to calculate this level as follows:

M = D(R + L) = 1,000(0.5 + 0.1) = 600 units

This means that when the hardware store reviews inventory for this group of items, it should order enough of the brass gate hinges to bring on-hand plus on- order inventory up to 600 units. For example, suppose that during the semi-annual inventory review, 100 brass gate hinges are in inventory. In that case, 500 brass gate hinges (600 – 100) should be ordered.

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Safety Stock for the Fixed-Order Interval Model

The order-up-to level described above is similar to the order point in a con�nuous review system. As with the basic order-point calcula�on, the preceding order-up- to formula does not include safety stock. Because of the nature of periodic review systems, safety stock is probably more important and necessary than in con�nuous review systems. It will also be larger. Under a con�nuous review system, the lead �me following an order was the period of �me when a stockout could occur. Therefore, safety stock was calculated using the standard devia�on of demand during the lead �me. However, with a periodic review system, a stockout could theore�cally occur at any �me between review periods and during the lead �me. Thus, safety stock for a periodic review system must be calculated based on the standard devia�on of demand during the review interval plus the lead �me. Except for this modifica�on, the calcula�on is the same as for a con�nuous review system; safety stock will now be added to the order-up-to level.

Problem

The brass gate hinge discussed in the previous example had an order-up-to level of 600 with no safety stock. Suppose that demand during the review interval plus the lead �me has a standard devia�on of 100 units. What must the order-up-to level be set at to obtain a 95% service level if demand is equally distributed?

From the normal probability tables (Table 10.4), a probability of 95% corresponds to a z value of 1.645. Therefore, the safety stock will be:

Safety stock = zσR+L = 1.645(100) = 164.5 or 165 hinges

Adding this to the expected demand during the review interval plus the lead �me (the M calculated in the preceding example), the new order-up-to level becomes:

M = D(R+L) + safety stock = 1,000(0.5 + 0.1) + 165 = 765

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Chapter Summary

The purposes served by inventory include mee�ng expected demand, absorbing demand and lead �me fluctua�ons, decoupling produc�on processes, hedging against price increases, and protec�ng against delivery disrup�ons. The economic order quan�ty model is based on the assump�ons that demand is constant and known. Cost per unit does not depend on order quan�ty, and an en�re order is delivered at one �me. Quan�ty discounts mean that the total-cost curve is discon�nuous, requiring a stepwise procedure to find the minimum cost point. The order point is determined from expected demand during the lead �me. If demand during the lead �me is variable, then a safety stock may be added to the order point, based on a probability distribu�on. In a perpetual inventory system, inventory level is constantly monitored, and orders are placed whenever necessary. In a periodic system, inventory is checked at regular intervals, and enough is ordered to bring inventory up to a desired level.

Case Studies

Alliance Supermarkets

Alliance Supermarkets has been using a point-of-sale (POS) system for some �me to track its inventory. The system uses a laser scanner to read the universal product code (UPC) on each item at the checkout container. The UPC is a number that uniquely iden�fies the product on which it appears. Currently, Alliance is using the UPC informa�on to update inventory records for each item. Although the system has greatly improved the company's ability to replenish inventory promptly, the company s�ll has some problems. For example, sudden changes in demand for a par�cular item can catch the company by surprise as it bases inventory replenishment on historical demand pa�erns. Further, demand pa�erns and preferences may vary from one store to another depending on the customers served by each, but the inventory system groups all demand informa�on together and treats each store equally. Finally, the manufacturers that make the products stocked by Alliance Supermarkets are always pressuring Alliance to help them target appropriate customers for special promo�ons and sales.

The chief informa�on officer (CIO) of Alliance realizes that much more could probably be done with the data collected from its POS system. For example, the company could analyze the rela�onship between each product's sales and weather pa�erns. It is even possible to analyze an individual customer's buying habits and iden�fy instances when a customer may be persuaded to try a different brand of a certain product.

Suppose you have been asked to study this situa�on and suggest possible new and innova�ve uses for the informa�on generated by the POS system. Ideally, these ideas should help Alliance be�er serve its customers by ensuring that adequate quan��es of each item are available, that costs are kept low, and that customers are made aware of new products that may interest them.

1. What informa�on may help Alliance reduce costs while providing be�er service? 2. If purchase informa�on can be obtained on individual customers, what new approach could be used by Alliance?

Discussion Ques�ons

Click on each ques�on to reveal the answer.

1. Describe the reasons why an organiza�on would keep inventory. (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Inventory can help businesses meet demand and work more efficiently as well as help companies meet expected demand. When a customer walks into a retail store to buy groceries or cosme�cs, they expect to walk out of the store with the item. They do not want to wait. With inventory, firms are able to maintain a stable level of produc�on even when customer demand varies from day to day or week to week. If produc�on varies, employment levels must be changed and equipment must be ac�vated or shut down to allow produc�on rates to fluctuate. These changes incur cost. In some cases, there simply is not enough capacity to meet the high level of demand, so an alterna�ve must be found.

Also some firms keep a cushion or "safety stock" of inventory to protect against unexpected demand. In this way, they can con�nue to meet customer demand without delays. In the produc�on of goods it is o�en important to separate steps in the produc�on process that operate at different speeds. For example, in manufacturing a part may be machined at one rate—one part in five minutes. The next step is to heat treat the machined parts in a furnace that operates in a batch mode—the furnace can hold up to 100 parts and take eight hours for heat trea�ng. An inventory of up to 100 parts should be accumulated before heat treatment.

In many situa�ons, discounts are available to purchase a certain quan�ty. These can be either quan�ty discounts or transporta�on discounts. Even though a firm may need a certain amount, it may decide to buy more because the supplier is offering a discount for purchasing the larger amount. A company may try to hedge against possible price increases. When an increase in the purchase price is an�cipated by the company or announced by the supplier, the company may order addi�onal materials prior. This is similar in effect to the quan�ty discount. Other �mes, firms may want to hedge against uncertainty in supply.

2. What are the different types of inventory, and what are the uses of these types? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

There are several types of inventory.

• Raw materials: These parts and precursors are used in the produc�on process.

• Work-in-process (WIP): These partly-finished parts, components, subassemblies, or modules are not yet finished. Processing math: 0%

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• Finished goods: Items are ready to ship to the customer. No more work is required.

• Replacement parts: These are maintained to replace other parts in machinery or equipment as those parts wear out.

• Supplies: Parts or materials are used to support the produc�on process, but not usually a component of the product. These items, such as lubricant and cu�ng tools, are consumed in the produc�on process.

• Transporta�on (pipeline): The por�on of inventory that is in the process of being shipped through the distribu�on system.

3. Describe the perpetual and the periodic inventory systems. How are they different? Are there circumstances in which one system be�er than the other? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

A perpetual inventory system monitors inventory levels on a con�nuous basis. It is also o�en known as a con�nuous review system. Under such a system, inventory transac�ons are recorded as they occur. With point of sales technology, computerized systems can pass along sales informa�on to the supplier as it occurs. When inventory drops to a predetermined level (the order point) an order for more can be generated. O�en, this ordering is done automa�cally by the same computer system that maintains the inventory records. The quan�ty ordered is usually a fixed amount, o�en the economic order quan�ty.

The periodic review system is designed to place an order only when on-hand inventory informa�on is available and the supplier is willing to deliver, in other words, when the order window is open. For example, the storage tanks at most gasoline service sta�on are refilled on a preset schedule, for example, once a week on Friday. Monitoring inventory con�nuous and placing an order on Saturday does not help because the delivery will not be made un�l the following Friday. In these cases, the reorder point must be set at a level that will allow the company to meet expected demand un�l the next order window occurs plus demand during the lead �me. If the on-hand inventory is less than this reorder point an order is generated that will push on-hand inventory back to a predetermined level. The periodic review system, also called the fixed order interval system, can be run without a computerized system to monitor inventory levels, but it is more likely to run out of stock because the system is unable to react quickly to changes in demand because inventory level is not con�nually monitored.

4. How does the ABC classifica�on system work, and how does it help to control costs? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

ABC inventory classifica�on has been developed to determine which inventory items should receive the highest level of control. Some parts may have a rela�vely low value and be used infrequently; those items can o�en be monitored very loosely. On the other hand, high-value and high-usage items should be tracked carefully and con�nuously. By mul�plying the dollar value of each item by its annual usage, a dollar usage value is obtained for each item. Dollar usage usually follows the Pareto Principle in that only 20 percent of all the items account for 80 percent of the total dollar usage. The remaining items typically account for only 20 percent of the dollar usage. This truth leads to the ABC classifica�on, which is based on focusing efforts where the payoff is highest.

A�er calcula�ng the dollar usage for each inventory item, the items are ranked by dollar usage, from highest to lowest. The first 20 percent of the items are assigned to class A. These are the items that warrant closest control and monitoring through a perpetual inventory system. Accurate inventory records are important, and there is a high poten�al for cu�ng costs through careful buying and close scru�ny of safety stocks. The next 30 percent of the items are classified as B items. These deserve less a�en�on than A items. Finally, the last 50 percent of items are C items. These have the lowest dollar usage and can be monitored loosely.

5. The economic order model is based on the trade-off between holding and ordering costs. Describe these two different types of costs and how each depends on order size. (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

Ordering costs may include many different elements, some of these are fixed while others may vary. Ordering costs may also include the cost setup produc�on when the order is placed to an in-house source of supply. Fixed costs can include staffing costs, furniture, and equipment such as informa�on systems that place the order. Variable ordering costs can include shipping costs, receiving and inspec�on costs, the cost to place the order, the cost of lost produc�on during the setup, and the cost of labor and materials during the setup.

Inventory holding costs, also called carrying costs, include costs paid for storage space, interest paid on borrowed money to finance the inventory, and any losses incurred due to damage or obsolescence. Once again, it is important to differen�ate between fixed and variable costs of holding inventory. To understand this difference, consider the ques�on, What if the inventory level is increased by one unit? Which costs would not change (fixed costs), and which would change (variable costs)? The general breakdown for inventory holding follows:

Fixed Costs:             Variable Costs:                  Capital costs of warehouse      Cost of capital in inventory Taxes on warehouse 7 property     Insurance on inventory value Costs of opera�ng warehouse     Losses due to obsolescence, the�, spoilage Personnel costs           Taxes on inventory value; Cost of ren�ng warehouse space

To understand how ordering cost and holding cost vary with order size, it is necessary to look at the annual cost of ordering and the annual cost of holding inventory. It a company make very few orders each year, its annual ordering cost will be very small, but because it makes few orders, the orders must be very large to meet demand for the year. On the other hand, many small orders to meet the same level of demand will lead to higher ordering costs but a much lower inventory level and therefore to lower inventory holding cost. When one goes up, the other goes down.

6. How do quan�ty discounts impact the decision about amounts ordered? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

The basic EOQ model assumes that the purchase price remained the same regardless of how many units were purchased. In many cases, suppliers provide a discount if a certain quan�ty is ordered. This has two impacts on the amount that should be ordered. Because, the cost of the inventory is less because the purchase price is less, the annual inventory holding costs declines slightly. This �ps the balance between ordering and holding cost in favor of making slightly larger orders. The second impact can be much larger. When the quality discount is available and the firm chooses to take advantage of the discount, this amount is saved on each unit ordered during the year. This usually pushes the order quan�ty higher.

7. What is safety stock, and what is the basis for determining the amount of inventory to hold as safety stock? (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cove

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Safety stock is an extra amount added to the order point as a buffer against stockout possibili�es. The amount of safety stock depends upon the amount of varia�on in the system. The first type of varia�on is lead �me varia�on. If the lead �me is a week on the average, that means that it could be 8, 9, 10 days or more. Second, the demand during the lead �me is also variable, so it could be more than expected. These two elements determine safety stock.

Problems

1. Fast-Mart is a discount retailer that uses a POS system to maintain con�nuous inventory records. A par�cular item has an average annual demand of 40,000 units. It costs $25 to replenish inventory of that item, which has a value of $10 per unit. If the inventory carrying cost is 20% of the unit value, how many units should be ordered each �me to minimize total annual variable costs?

2. Suppose Fast-Mart has found that the item described in Problem 1 has a lead �me of two working days. If the company operates 250 days per year, determine the order point for that item.

3. The Fill-er-Up gas sta�on has found that demand for its unleaded gasoline is fairly constant and uniform at the rate of 100,000 gallons per year. Fill-er-Up must pay $100 for shipping per order of gasoline, which it currently buys for $3.75/gallon. Inventory carrying cost is 10% of unit cost per year. How many gallons should be ordered at a �me?

4. Suppose that in Problem 3, Fill-er-Up's underground storage tanks can hold only 10,000 gallons of unleaded gasoline. What is the extra cost incurred by ordering this quan�ty each �me instead of the EOQ?

5. The Slick Oil Company buys crude oil from a supplier that has recently offered the following quan�ty discounts:

Barrels Ordered Price per barrel

1–999 $110

1,000–2999 $105

3,000 or more $102

If inventory holding cost is 25% of the unit price and it costs $100 for each order, regardless of order size, how many barrels should Slick order each �me to sa�sfy its annual demand of 10,000 barrels?

6. Burger-Farm is a fast-food restaurant that buys hamburger buns from a local bakery. Those buns are used at the rate of 50,000 per year. The baker has just offered Burger-Farm the following quan�ty discounts:

Buns Ordered Price per bun

1–999 $.030

1,000–1,999 $.028

2,000 or more $.027

If it costs Burger-Farm $1 for each order placed and the inventory holding cost is 25% of the unit cost, determine how much should be ordered each �me to minimize total annual variable costs.

7. Referring to Problem 6, suppose Burger-Farm is limited to ordering only one week's worth of buns at a �me due to storage space limita�ons and spoilage problems. What impact will this have on total annual variable cost?

8. The Young Professionelle Shoppe is a bou�que for professional women. A periodic system is used to control inventory. Suppose that a certain blazer has an average annual demand of 1,000 units. The ordering cost is $5, and the inventory carrying cost is $10 per unit per year. What should the review interval be for this blazer?

9. Suppose that the Young Professionelle Shoppe in Problem 8 prefers to review its inventory weekly. Es�mate the effect on total annual variable costs of following this procedure.

10. A discount retail store uses a periodic inventory system through which each item's inventory level is reviewed twice monthly. Suppose it has been determined that a par�cular item has an average annual demand of 6,000 units, with a standard devia�on of 100 units per month. If lead �me is one-half month and the store wants a service level of 85%, determine the order-up-to level for this item.

11. The Goodstone Tire Store has been using a periodic review system to control its inventory. For one �re model, the annual demand averages 5,000 units. In the past, inventory was reviewed so that the review interval plus lead �me was one month. The standard devia�on of demand during this period was 50 units. The company is now planning to use a con�nuous review system. Suppose lead �me is one week and the standard devia�on of demand during lead �me is 10 units. Compare the safety stock necessary under periodic review with what would be necessary for con�nuous review at a 90% service level.

12. An inventory clerk at the Fargo Machine Tool Company has just calculated the EOQ for one of the steel alloys used by this company as 500 pounds. However, the lead �me for ordering this steel is four months, and the company uses 150 pounds per month—an order point of 600 pounds—which is greater than the EOQ. Can you help this inventory clerk figure out how to handle this case, in which order point exceeds the EOQ?

13. West Coast Furniture Distributors is a company that buys large quan��es of furniture from manufacturers at low prices, and then sells to the public at prices below what most furniture stores charge. To minimize costs, West Coast Furniture uses EOQ for ordering. For one par�cular model of sofa, the manufacturer has now agreed to cover part of the shipping costs, reducing the ordering cost from $50 per order to $40. At the same �me, West Coast Furniture has been able to obtain lower interest rates on borrowed money, reducing its inventory carrying cost from 25% of unit cost to 20%. The company expects to sell 1,225 of these sofas per year and pays $100 to purchase each one.

a. What effect will the preceding changes have on the EOQ? b. What effect will the preceding changes have on the total annual costs of ordering and carrying inventory?Processing math: 0%

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14. Referring to Problem 13, how many days' worth of demand will be covered by each order of sofas? 15. A company maintains inventories of the following nine items. Based on this informa�on, determine which are A items, B items, and C items.

Item # Value Annual Usage

209 $14.76 2,000

4914 5.98 15,000

37 1.15 297,000

387 6.48 6,000

3290 2.17 6,000

235 75.00 300

48 23.95 7,000

576 4.32 5,000

14 932.00 1,000

Click here to see solu�ons to the odd-numbered problems. (h�ps://media.thuze.com/MediaService/MediaService.svc/constella�on/book/AUBUS644.13.2/{pdf}bus644_ch10_odd_problem_solu�ons.pdf)

Key Terms

Click on each key term to see the defini�on.

ABC analysis (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A classifica�on system for inventory items so that 20% of items (A items) that account for the top 80% of dollar usage receive the most a�en�on.

average inventory investment (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The dollar value of a company's average level of inventory.

carrying costs (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The variable costs associated with keeping inventory.

days of inventory (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Indicates approximately how many days of sales can be supplied solely from inventory.

economic order quan�ty (EOQ) (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An amount to order at one �me that minimizes total annual cost of ordering and holding inventory.

inventory turnover ra�o (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

Indicates how many �mes during one year the inventory turns over, or is sold.

lead �me (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The difference between the �me the order is placed and the delivery of the product.

order point (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A level of inventory at which an order should be placed.

ordering cost (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/booProcessing math: 0%

1/14/2020 Print

https://content.ashford.edu/print/AUBUS644.13.2?sections=cover,ch09,sec9.1,sec9.2,sec9.3,sec9.4,sec9.5,sec9.6,ch09summary,ch10,sec10.1,sec… 61/61

The variable costs associated with replenishing inventory.

order-up-to level (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The level to which a replenishment order should bring on-hand plus on-order inventory within a periodic review inventory control system.

perpetual inventory system (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A system in which inventory level is con�nuously monitored and a replenishment order placed when inventory reaches a predetermined level.

review interval (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The �me between one review of inventory and the next in a periodic review inventory control system.

safety stock (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

An extra amount added to the order point as a buffer against stockout possibili�es.

service level (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The percentage of inventory replenishment orders that are received before a stockout occurs.

set-up cost (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

The costs associated with changing over equipment from producing one item to producing another.

stockout (h�p://content.thuzelearning.com/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/books/AUBUS644.13.2/sec�ons/cover/boo

A condi�on that occurs when no more inventory of an item is available.

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