Week 6 Final Paper

12

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Scheduling

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

List the six criteria for scheduling and discuss the trade-offs involved with each. Provide an overview of the scheduling process including data requirements, order informa�on, sequencing, and dispatching. Describe how scheduling for services differs from manufacturing. Discuss issues of concern that can occur when scheduling an assembly line. Use dispatching rules to schedule jobs and discuss each rule. Discuss how priori�es are determined in MRP systems. Understand forward and backward scheduling with finite and infinite capacity. Schedule employees for service opera�ons.

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12.1 Introduction to Scheduling

Scheduling is coordina�ng work tasks, people, materials, facili�es, and equipment needed to create goods and services at a specific point in �me. Scheduling is required for making goods and for providing services successfully. There are many different approaches to scheduling; some of the most common are discussed in this chapter.

Scheduling is the last step in the process that begins with strategic planning and proceeds through increasingly detailed stages. Each successive stage of the planning process builds on its preceding stage. Proper planning in the earlier stages increases the likelihood that a schedule can be created that will meet customer demand at a reasonable cost and without delays.

Scheduling can be one of the most challenging areas of opera�ons management. As many companies have found, scheduling presents many day-to-day problems because there may be changes in customer orders, equipment breakdowns, late deliveries from suppliers, and a myriad of other disrup�ons. Techniques are very sophis�cated mathema�cally because scheduling problems are o�en very detailed, have lots of informa�on to consider, and have many possible solu�ons. This chapter focuses on scheduling rules that can lead to good solu�ons as well as some rela�vely simple applica�on techniques.

To begin the discussion of scheduling, the master schedule in Figure 12.1 calls for the produc�on of two different products during a par�cular �me period. Using material requirements planning (MRP), it has been determined that certain parts for each of those finished products must be started in the produc�on process during week 20, as shown by the circled figures in Figure 12.1.The rou�ngs for these two parts are shown in Figure 12.2. Capacity requirements planning (CRP) has been used to determine that insufficient capacity will exist in week 20 on the lathe, which is the "gateway," or first work center, for both parts. Management inves�gated both short-run and long-run solu�ons to this capacity problem, but has decided that it will follow a short-run strategy and schedule over�me to alleviate the capacity problem in the lathe department.

Figure 12.1: Produc�on plan for two products

Figure 12.2: Rou�ng for two parts

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In this example, there are two scheduling problems. One involves scheduling employees, and the other with scheduling the two parts. It is necessary to schedule employees to work during the over�me used in the lathe department. The second scheduling problem, scheduling the parts, occurs because both parts will be released to the lathe department at the same �me. This second scheduling problem is one of sequencing—determining which part to produce first.

Scheduling is a complex process that involves many different steps. This sec�on summarizes those steps before describing scheduling techniques.

Data Collection

Collec�ng the data needed for scheduling begins with orders from the customer. These orders iden�fy which product the customer wants, special features, and the product due date, among other things. When data from order entry is combined with process data, the following informa�on about the jobs, ac�vi�es, employees, equipment, and facili�es are available to prepare a schedule.

Jobs Due dates, rou�ngs, material requirements, flexibility of due dates

Ac�vi�es Expected dura�on, required ac�vi�es that precede this ac�vity, desired �me of comple�on

Employees Availability, capability, efficiency, wage rates

Equipment Machine or work center capaci�es and capabili�es, cost of opera�on, availability

Facili�es Capaci�es, possible uses, cost of use, availability

Order Entry

Order entry drives the scheduling process. Orders may originate with the customer, but they may also be generated by internal or company orders that are given to create inventory. For a make-to-order company, one that produces only to customer orders or that provides services, this occurs when a customer places an order. Given exis�ng produc�on schedules, capacity available, and the customer's desired due date, the order can be scheduled. This order scheduling will be an es�mate based on capacity requirements to produce the customer's order. Producing the order will require further scheduling of the individual parts and components for a product or the employees and facili�es for a service.

In a make-to-stock company, one that produces for inventory and meets customer orders from inventory, produc�on orders are entered by the company based on the inventory level of each item in stock, and the expected future demand of that item. In general, a make-to-stock company has a somewhat easier job of scheduling because it has some control over which products will be made. However, unlike a make-to-order company, which must produce whatever is demanded by the customers, the make-to-stock company will have excess inventory if it produces something that customers do not want. This increases costs and may lead to discoun�ng to increase sales of an item.

In an MRP environment, the MRP system will generate planned order releases based on the master schedule. This is another form of order entry—in this case, for individual parts or subassemblies.

Orders Released for Production

The planning process involves a con�nual movement from strategic plans for the distant future toward more detailed plans for the less-distant future. As �me frames diminish, plans become more precise and detailed un�l each order is released for produc�on. At that point, the schedule is implemented.

Scheduling addresses the very near future because it is the last step in produc�on planning. Plans are made to schedule a par�cular job, ac�vity, or employee, but those plans are not converted into a detailed schedule un�l the last possible moment. The earlier planning stages determine what level of resources is needed to meet the produc�on plan. Scheduling allocates those resources.

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Many car manufacturers use a make-to-stock inventory system. If a make-to-stock company produces something that customers do not want, it will have excess inventory of that item, which is one downside to this type of system.

iStockphoto/Thinkstock

When working with such minute details, such as individual machines, parts, or employees, it is always possible that changes will occur. An employee may become ill or quit, a machine may break down, or the raw materials for a part may not arrive on �me. Because of these possibili�es, scheduling must usually wait un�l the exis�ng condi�ons are known with rela�ve certainty. Even then, last minute changes must o�en be made, which is what makes scheduling so challenging.

As �me passes and the scheduled star�ng �me for a job or order is reached, that job or order is released for produc�on. That step starts the job on its way through the processing opera�ons. The final scheduling steps are the sequencing of ac�vi�es, jobs, or parts in the order they should flow through processing, and then the dispatching of those jobs. Dispatching is the assignment of priori�es and the selec�on of jobs for processing at a work center or facility. For example, a customer order for a made-to- order product must be sequenced with other orders. When the �me comes for work to begin on that order, it will be dispatched at the first work center according to its priority at that �me.

Managerial Considerations

Scheduling is an a�empt to allocate scarce resources efficiently. Machine �me may be a scarce resource that is allocated to different jobs, employee �me is allocated to different ac�vi�es, and facili�es are scheduled for a given ac�vity at a par�cular �me period. In all of these scheduling tasks, different criteria may be used when deciding which of several schedules will work best. Those criteria may relate to the amount of �me equipment may sit idle, the importance of a certain order or a certain customer, or the level at which a resource is u�lized.

The task of scheduling can be quite complex; what appears to be an op�mal schedule from one viewpoint may be far from op�mal from another. For example, a certain schedule may u�lize one machine very efficiently, but may mean idle �me for machines farther along in the processing opera�ons. Another schedule might mean that an important customer's order will not be delivered on �me. These six criteria may be used when evalua�ng possible schedules:

Provides the good or service when the customer wants it Length of �me it takes to produce that good or service (flow �me), which includes both processing and wai�ng �me Level of work-in-process (WIP) inventories Amount of �me that equipment is idle Amount of �me that employees are idle Overall costs

The rela�ve importance of each factor depends on the product or service being produced, a company's par�cular industry, and, especially, the organiza�on's compe��ve strategy. Different produc�on processes will also incur different problems, and certain criteria will, therefore, be more important. It may be impossible to sa�sfy all of the six criteria listed above at one �me. Instead, management must choose among the various trade-offs (see Table 12.1).

Table 12.1: Factors and trade-offs

Factor Trade-off

Providing the good or service when the customer wants it

Requires flexibility. Can lead to large inventories and excess capacity during periods of low demand.

Minimizing flow �me Requires flexibility, short set-up �mes, and fast produc�on rates. Can require having excess capacity available.

Minimizing WIP inventories May require excess capacity or the use of a pull system. Can lead to high machine or employee idle �me.

Minimizing machine idle �me O�en means keeping capacity low, producing product for inventory, or accep�ng any customer orders whether the order is profitable or not. Can result in high inventories, high costs, the overloading of equipment, and late orders.

Minimizing employee idle �me O�en means keeping workforce size low, producing product for inventory, or accep�ng any orders. Can result in employee discontent, late orders, and high inventories.

Minimizing costs O�en requires compromises on the preceding criteria. All relevant costs must be properly defined and measured. Can result in poor customer service—a cost that is difficult to measure.

When determining which criteria to use, a company must carefully consider its corporate objec�ves, compe��ve strategy, and capabili�es. The company's scheduling decisions will have a great impact on facility design, the type of equipment used, and the workforce requirements. Each of these will, in turn, influence its compe��veness in terms of cost, speed, and delivery reliability.

Highlight: Tim Horton's

Tim Horton's sells coffee, pastries, breakfast, sandwiches, and other items. It responds to customer demands quickly using a combina�on of make-to-order and make-to-stock. Their coffee is pre-made, that is, made-to-stock, but it has a �me limit. If not used within a certain �me, it must be thrown out. The donuts and bagels are make-to-stock, but sandwiches are make-to-order with components including bread, meat, and cheese, and prepared for further processing and assembly. Tim Horton's relies on fast delivery, low cost, and good quality. The store managers must an�cipate demand each day, even for each por�on of the day, in order to schedule the right people at the right �me and

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without idle employees, which increases costs. They must consider the wait �me at the drive up window. Cross training is important so that if there is slack at the front counter, employees can be shi�ed to other jobs where demand exceeds the restaurant's ability to serve its customers. Managers must order the materials, such as coffee, pastries, and sliced meat, so the shop has neither too li�le (so customers cannot get what they want), nor too much (so there is waste). Long term, managers should measure equipment use and iden�fy bo�lenecks to determine if the number of coffee machines, warming ovens, and other items are sufficient for demand. Should these be increased or possibly reduced? A manager would examine the facility to see how it might be altered to be�er serve customers. Scheduling is cri�cal to Tim Horton's success.

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An ice cream company must decide which flavors it should make, in what order, and how many gallons should be produced to op�mize profit and efficiency while reducing waste.

altrendo images/Stockbyte/Thinkstoc

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12.2 Techniques for Successful Scheduling

When scheduling, two key ques�ons are:

1. When should a given job, order, or product be processed? 2. How many units should be processed at one �me?

The answers to these ques�ons impact the way a processing opera�on is run. For instance, a company that makes ice cream must decide which flavors should be made and when. If chocolate is made before vanilla, there may be extensive �me spent cleaning the equipment before switching to vanilla. Conversely, producing vanilla before vanilla-fudge marble may mean no cleanup between runs. In addi�on, the company must decide how many gallons of one flavor to make before it starts making another. The company does not want to produce so much of a given flavor that the ice cream deteriorates before it is sold. At the same �me, producing small quan��es at one �me will mean excessive �me spent cleaning and refilling the equipment between batches.

Different scheduling techniques are appropriate for different opera�on processes. Line flow, batch, and flexible manufacturing process have similari�es, and are discussed together in the next sec�on. The job shop process, which is quite different, is discussed in a later sec�on in this chapter.

Continuous Flow Processes

A con�nuous flow process is one in which materials flow in a con�nuous, or nearly con�nuous, stream from beginning to end. A good example of a con�nuous flow process is an oil refinery. Such produc�on processes are generally characterized by a few different finished products, only a few possible rou�ngs, and low work-in- process inventories.

Under such condi�ons, the relevant scheduling criteria become somewhat limited. For example, flow �me is determined by the produc�on process, rather than by a schedule because a con�nuous flow system operates with a defined sequence and that is difficult to interrupt. Generally, it is neither economical nor technically desirable to perform step one in the refining process, then place the output in inventory for a long period of �me. Work-in-process inventory is also not a major problem because it is generally quite low for con�nuous flow processes. Thus, the scheduling problem in a con�nuous flow process requires determining when to change from making one product to making another. The relevant criterion is usually minimizing cost, although minimizing the �me the facility is idle during changeover could also be important. When refining oil, a con�nuous flow process makes adjustments to make more hea�ng oil in the fall for the coming winter, and adjus�ng again to make gasoline in the late spring for the summer driving season.

Balancing an Assembly Line

An assembly-line process is similar to con�nuous flow, but instead of the products flowing con�nuously, such as a stream of gasoline or a roll of paper, the products are discrete, individual items, such as automobiles.

One of the best examples of an assembly-line process is the automobile assembly line. In this example, the product follows a fixed path. Like the con�nuous flow process, an assembly-line process usually produces a limited number of products, and the rou�ngs are the same. Work-in-process inventory is also typically small. Thus, the same basic techniques used for scheduling in con�nuous flow can also be used for assembly-line process scheduling. There are, however, two par�cular problems unique to assembly-line scheduling that are described next.

It is cri�cal to assign the same amount of work to each sta�on because assembly lines are usually a series of worksta�ons with one worker assigned to each sta�on. If the line is unbalanced, meaning that one sta�on has more work than the others, then one worker will be rushed and unable to complete the work while the others will have idle �me, thereby genera�ng waste. Successful assembly line balancing depends on having the op�mal number of appropriate worksta�ons so that idle �me is zero or close to zero. The right number of worksta�ons is also important because it helps to determine the cycle �me. The cycle �me is the amount of work assigned to the sta�on with the most work and �me. Cycle �me controls the flow of product along the line, and therefore determines the capacity of the assembly. Mathema�cally, the cycle �me for the assembly in minutes per unit of product is the inverse of the produc�on rate, which determines capacity. Assembly-line balancing provides the framework for scheduling. Assigning tasks to worksta�ons allows the material flow and job assignments to be specified by the line balance.

Assembly-line balancing is not a perfect science because people with different abili�es will be assigned to the worksta�ons. The result may be that a perfect balance was achieved theore�cally, but it will not be perfect in prac�ce. Some employees will complete their tasks in less than the average �me. Others will take longer. The end result is that a theore�cally balanced line may be unbalanced in prac�ce.

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Assembly lines are comprised of a series of worksta�ons with one or more workers assigned to each sta�on. Successful assembly lines depend on balancing the line so that idle �me is minimized.

Scheduling is one approach to overcoming this problem. A skillful supervisor will know which employees can work faster and will assign those to the sta�ons with more work. Tasks may also be shi�ed from one worksta�on to another as trouble spots appear. Thus, assigning employees to worksta�ons or tasks to employees is an integral part of fine-tuning the balance of a line through scheduling.

The details of assembly-line balancing involve complex mathema�cal problems that are beyond the scope of this book.

Sequencing

Sequencing an assembly is determining the order for making different products. In some cases, the differences are small, such as pain�ng a car red versus silver, or moun�ng 16- inch steel wheels versus 17-inch aluminum wheels. But, in other cases, the differences are very different, such as making a conver�ble versus a hardtop, or making different car models on a different pla�orm within the same produc�on line. In these cases, sequencing is very important. Assembling a conver�ble, for example, requires more �me at some worksta�ons, so it is be�er not to put those sta�ons back-to-back. This gives the workforce �me to catch up before the next conver�ble arrives.

Scheduling Batch Processes

In batch processes, the number of possible products is greater than can be produced in line-flow processes. As a result, each product is made in a group or batch. The process is stopped; the equipment is changed over, and the next product is made. The produc�on volume of each product is usually less than when made by a line-flow process. As a result, the same resources are used to produce at least several different products, producing a batch of each product at one �me. Because of this, determining the number of units to produce in one batch and the sequence of batches becomes important. The criterion of cost minimiza�on is usually used to determine produc�on quan�ty. Because each product is produced only intermi�ently, it must be produced o�en enough to avoid running out of inventory.

Note that many batch opera�ons use con�nuous flow or assembly-line processing. The difference is that a batch has a defined star�ng and ending �me with a setup or changeover between different batches. From a cost perspec�ve, it would be lower cost (lower set-up costs, less inventory, and higher equipment u�liza�on) to avoid batching by making the same or very similar product without an abrupt change. The problem with this approach is that customer demand requires a greater variety than the produc�on system can deliver without the abrupt change. The ideal, over �me, is to find a technology that can eliminate or greatly reduce the changeover so the opera�ons can make smaller batches and eventually run con�nuously.

The ice cream example described earlier is one example of a con�nuous flow process that has many op�ons and rela�vely small batches. There are hundreds of ice cream flavors available, and more are being developed every year. Determining the sequence and batch size for ice cream produc�on is cri�cal to effec�vely and efficiently schedule produc�on. Other examples of con�nuous flow process that are run in batches include paint, pharmaceu�cals, and breakfast cereals. Assembly lines can also operate in a batch mode. Appliance assembly lines that make air condi�oners and refrigerators are o�en batched to increase efficiency. Once demand is large enough for a par�cular model, or the changeover �me declines because of technology, the batch size can be greatly reduced or eliminated and the assembly lines can flow smoothly.

Run-Out Time

*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.

The ques�on of batch size only addresses how much to produce; it does not indicate which product should be produced next. One method that can be used to determine which product should be produced next is called run-out �me. This is simply a calcula�on of how long it will take for the company to run out of each product at current usage rates. Run- out �me is determined as follows:

Table 12.2 indicates current inventory and demand rates for five different products made by a process. Run-out �me calcula�ons are shown for each of the five different products. Based on those calcula�ons, product E should be produced next because it will run out first—in two weeks.

Table 12.2: Run-out �me calcula�ons

Product Current Inventory Demand Rate (Units per Week) Run-Out Time (Weeks)

A 1,000 200 1,000/200 = 5

B 500 150 500/150 = 3.3

C 2,000 500 2,000/500 = 4

D 2,500 500 2,500/500 = 5

E 600 300 600/300 = 2

Flexible Manufacturing Systems

Chapter 10 discussed the trade-off between product changeover costs (or set-up costs) and inventory carrying costs. When the cost of changeover becomes extremely small, the ques�on of how many products to produce at one �me is less important. Flexible manufacturing systems (FMS) have been able to reduce changeover costs so much that it is economical to produce just one product or part at one �me. The challenge then becomes one of sequencing to keep the changeover �me—and consequently the cost—low enough.

Group technology is an important aspect of any FMS. By grouping similar products into families, a group technology cell within a FMS only makes products that have similar characteris�cs, which tends to reduce sequencing challenges. Because computerized control is an important part of a FMS, the computer can be used to evaluate different possible sequences and determine the best one for each cell.

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Airline carriers have different boarding procedures; however, most board passengers based on some measure of customer importance, such as groups or priority status.

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12.3 Job Shop Scheduling

There are few sa�sfactory scheduling techniques for job shop processing. Unlike con�nuous flow, assembly line, or batch processes, a job shop has many different and intersec�ng rou�ngs. A job shop is fundamentally different from these con�nuous flow processes because it is arranged with similar machines in one loca�on or work center. The part being produced or the pa�ent in a hospital, moves to the various work centers as needed. Each part or pa�ent may have a different path through the factory or hospital. This is called a process layout. Con�nuous flow and assembly lines are organized around a common sequence of steps, so that the path through the facility is the same. This is called a product layout.

What makes job shop scheduling more challenging is that different jobs are vying for �me on the same machines. Deciding which job to process first on a given machine or work center can have a major impact on what happens at other machines or work centers—possibly overloading some, while leaving others idle. The flow of product and the demands on the work centers in a job shop are different and uneven, which makes scheduling a challenge.

Dispatching Rules

One of the earliest approaches to job shop scheduling focused on the criteria for sequencing the jobs that are compe�ng for �me at the work center. Those criteria could be used to generate dispatching rules to be used at a machine or work center. A rule such as "first-come, first-served" is commonly used in retail opera�ons because it is perceived as fair. A rule like first-come, first-served with priority for pa�ents with severe problems is used in emergency rooms. This is called triage, where a medical professional makes an ini�al screening to see if a pa�ent's injuries are life threatening.

An important advantage of these rules is that they are easy to use. The informa�on is readily available, and it is not necessary to know what is happening at other work centers. As with many things that are simple, the rules can some�mes lead to poor performance. Five of the most common dispatching rules are described below.

Earliest Due Date

The earliest-due-date rule focuses on the criterion of providing the product when a customer wants it. The ra�onale is that whichever job is due first should be started first. The advantage of this approach is that some jobs may meet their due dates. This rule is popular with companies that are sensi�ve to due date changes. However, finishing one job on �me may make many others late. This method also does not consider how long it will take to process a job.

Shortest Processing Time

With the shortest-processing-�me rule, the ra�onale is to get the most work done as quickly as possible in order to minimize the level of WIP inventory. Unfortunately, jobs with long processing �mes may be made quite late as they wait for shorter jobs to be finished. Otherwise, this rule o�en works best on most measures. One way this rule has been modified is to make an adjustment for long-running jobs that have been wai�ng for a long �me by moving them to the front of the line.

Having determined that there are advantages to using the shortest-processing-�me rule, it is s�ll necessary to use good judgment before applying any rule. For example, the shortest- processing-�me, including adjustment for long wai�ng jobs, works poorly in an emergency room. A pa�ent with a severe problem that requires a long �me at a work center will be delayed while other pa�ents needing less care are serviced first. For example, using this rule, pa�ents with minor fractures would move ahead of a pa�ent with a severe compound fracture.

Longest Processing Time

The longest-processing-�me rule uses a different strategy—to get the jobs that will take longest done first, leaving �me at the end to do the short-processing-�me jobs. The ra�onale behind this rule is that jobs with long processing �mes may be more likely to miss their due dates than jobs with short processing �mes are. The great disadvantage of this approach is that many short jobs may also miss their due dates because of one long job. This rule also tends to result in an increase in WIP inventory. It may be used when a cri�cal job has a long lead-�me.

First-Come, First-Served

This rule is o�en used in service facili�es because customers usually see this as the fairest method. However, it ignores due date, processing �me, or the importance of one job over the other; therefore, it does not perform well on such measures. The emergency room example is only one place where this rule performs poorly. In manufacturing, machining a part that is needed to repair a city's water supply system should have a greater priority than making a part so that an amateur stock car racer can repair her car. A few years ago (despite that seats were pre-assigned) airplanes were loaded first-come, first-served for fairness; or from back-to-front for loading efficiency so that the planes could be loaded faster. Now, most airlines board their passengers based on some measure of customer importance. Airlines use priority status and zones to let passengers know when they can board.

Cri�cal Ra�o

The cri�cal-ra�o rule is an a�empt to combine aspects of the preceding rules into one that considers both due date and processing �me. It is based on calcula�ng the cri�cal ra�o (CR), which is

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This rule is implemented by first scheduling those jobs that have the lowest cri�cal ra�o. Values of CR below one mean the job will be past due. A nega�ve value means it is already past due. Thus, an advantage is that those jobs scheduled first are the ones that have the lowest chance of missing their due dates.

It should be noted that the cri�cal-ra�o rule differs from the other dispatching rules in that it is dynamic. That is, a job's cri�cal ra�o will change over �me as the number of days un�l the due date changes and the processing �me remaining changes. Thus, the cri�cal ra�o must be updated constantly.

Highlight: Airlines Use Dispatching Rules to Load Passengers

Several years ago, most airlines boarded their airplanes by row. A�er the first-class passengers and those needing extra �me were boarded, the last few rows would be allowed to board. Next, the rows just prior to the last few rows were loaded. This boarding pa�ern was repeated from back to front of the airplane. This was done for efficiency, increasing the ability to rapidly load the airplane; if passengers in the front of the airplane load first, they would tend to block the aisles, slowing down boarding. Loading the airplane from back to front reduces this conges�on. This approach worked well. Today, airlines o�en board based on status. If passengers fly the airline o�en, they earn gold, silver, or other status, which allows them to board early. Remaining passengers use a "zone" boarding process, which is unrelated to the area of the airplane, and instead based on the passengers' frequent flier miles. This is important to passengers who want to carry on luggage for convenience, or to avoid checked baggage fees.

Problem

The Hillside Machine Corpora�on has four jobs wai�ng to be run on its lathe. Figure 12.3 shows the days un�l due date and the processing �me remaining for each job. Hillside wants to see which sequences will be generated by using each of the five dispatching rules. Figure 12.3 shows these sequences. It is interes�ng to note that in this example, the longest-processing-�me and cri�cal-ra�o rules produce the same sequence of jobs—although that result will not always occur.

Figure 12.3: Comparison of dispatching rules

Sequencing Jobs on One Machine

Flow �me is the amount of �me it takes to produce a product. If the product spends a large amount of �me wai�ng to be processed, then its flow �me will be long. Average flow �me will be minimized by processing as many jobs as possible during a given period of �me. The way to achieve this result is by using the shortest-processing-�me rule, which has been proven to always minimize average flow �me.

Problem

Refer to the Hillside Machine Corpora�on data in the previous example. Suppose the company tracks the number of days each job requires un�l comple�on, using the cri�cal- ra�o and shortest-processing- �me rules. As the results in Figure 12.4 indicate, all four jobs are finished within 20 days, regardless of which rule is used. However, with the cri�cal-ra�o rule, the average �me each job spends before comple�on is 15.75 days. With the shortest-processing-�me rule, the average �me is only 9.25 days.

Figure 12.4: Comparison of average flow �mes for two sequencing rules

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Johnson's Rule

When there are two successive machines or work centers through which a group of jobs must all be sequenced, Johnson's Rule can be used to minimize total processing �me for the group of jobs, which is called the makespan �me. The method u�lizes the following steps:

1. List the jobs and the �me each job requires at each work center. 2. From the list, select the job with the shortest �me at either work center (if two or more jobs in the list have the same �me, one is selected at random). If the �me is for the first work

center, proceed to step 2a. If it is for the second work center, proceed to step 2b. a. Place the job as close to the beginning of the sequence as possible without replacing other jobs. Go to step 3. b. Place the job as close to the end of the sequence as possible without replacing other jobs. Go to step 3.

3. Eliminate the job just scheduled from your list. Return to step 2.

Note that this rule requires all jobs to follow the same sequence through both work centers. The sequence cannot change at the second work center.

Problem

University Data Services has five computer payroll jobs wai�ng to be processed before Friday a�ernoon. Each job requires compu�ng and then prin�ng, in that order. Based on past experience, the company es�mates each job will take the following �me:

Processing Time (Hours)

Job Compu�ng Prin�ng

A 1.5 1.0

B 1.0 0.75

C 0.5 1.25

D 2.0 1.5

E 0.75 0.5

Using Johnson's Rule, proceed as follows.

Two jobs, C and E, have the shortest processing �mes, 0.5 hours. Job C is selected arbitrarily. Because its shortest �me is for the first opera�on, Job C is scheduled at the beginning of the sequence.

Job C is eliminated from further considera�on, and the process returns to step 2. Now Job E has the shortest processing �me. Because that �me is for the second opera�on (prin�ng), Job E is scheduled at the end of the sequence.

Job E is now eliminated from the list. Therefore, Job B has the shortest processing �me, which is for the second opera�on. Job B is scheduled as close to the end of the sequence as possible.

A�er elimina�ng Job B, of the remaining two jobs, A has the shortest processing �me. Because that �me is for the second process, job A is scheduled as close to the end as possible, which, in this example, is the third posi�on.

The last remaining job, job D, is placed in the remaining slot in the schedule, producing the following sequence:

This sequence of jobs produces the processing sequence for each opera�on shown in Figure 12.5. This method completes all jobs within 6.25 hours and leaves only 0.5 hour of idle �me for the printer at the beginning of the sequence and 0.75 hour between Jobs C and D.

Figure 12.5: Processing of computer jobs based on sequencing by Johnson's Rule

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12.4 Dispatching in MRP

The rules men�oned above are limited because they only consider the condi�ons that exist for a given point in �me and a given work center. By and large, they ignore that a given part may be part of a subassembly that must be complete before the final product can be assembled.

MRP takes into account lead �mes. As long as the planning lead �mes used in MRP are valid, then the priority of each item should be based on the MRP lead �mes. Therefore, in an MRP system, priori�es are determined by referring to the planned order releases and lead �mes. Thus, the dispatching rules are irrelevant to MRP systems. Instead, MRP works from the order due dates, scheduling order releases far enough ahead of �me that the due dates should be met. Unfortunately, there s�ll may be conflicts at machines and work centers that need to be addressed.

Machine Loading

The dispatching rules previously described a�empt to determine a schedule based on the a�ributes, such as due date or processing �me, of each job. However, the �me it takes for a job to be processed consists of the following five components:

1. Wait �me 2. Move �me 3. Queue �me 4. Set-up �me 5. Run �me

Wait �me is the �me a job spends wai�ng before it is moved to the next work center. Move �me is the material-handling �me between work centers. Queue �me is the �me a job spends wai�ng to be processed at a work center. Set-up �me is the �me to prepare a machine to process that job, and run �me is actual processing �me.

In general, all of these components—except queue �me—will be nearly fixed. Queue �me really depends to a large extent on the workload that has been scheduled for each work center. If a machine's capacity is being used extensively, then it is more likely that many jobs will be wai�ng for processing at that machine. When the capacity of a work center is exceeded, lines of work (queues) will build up in front of that work center.

Loading is an approach to scheduling that a�empts to take capacity u�liza�on into account. There are several different approaches to loading, but loading begins with scheduling.

Forward Scheduling

Suppose scheduling begins immediately so that each job starts at the earliest possible moment. This is called forward scheduling. As jobs progress through a produc�on facility, each work center will have a certain workload placed on it from the jobs assigned to that work center. Figure 12.6 illustrates the schedule that could be generated by forward scheduling four jobs (A, B, C, and D) through three work centers (lathe, mill, and drill). This schedule assumes six hours for wait and move �me between machines. Note that the jobs use the same three work centers, but use them in different orders, so Opera�on l for Job A uses the lathe, but Opera�on l for Job D uses is the drill. Also note that Job B and Job D do not use the lathe and the mill, respec�vely.

Figure 12.6: Forward schedule for four jobs with finite loading

Work Center Sequence and Processing Time

(Number Is Sum of Set-up and Run Times in Hours)

Job Opera�on I Opera�on II Opera�on III

A Lathe 3 Drill 2 Mill 4

B Mill 4 Drill 3

C Lathe 2 Mill 3 Drill 4

D Drill 5 Lathe 4

In a forward schedule shown in Figure 12.6, each job begins as close to �me zero as possible, and each job is scheduled similarly through the successive opera�on, allowing six hours for wait and move �me between machines. Some jobs have been delayed (queue �me) at certain work centers because another job had already started at that work center.Processing math: 0%

For example, Job C had to wait three hours before it could start on the lathe because Job A was s�ll being processed on that machine. This approach of making one job wait if another has been scheduled on the same machine is called finite loading because it takes into considera�on the limited capacity on each machine. Another approach uses infinite loading, which does not take capacity considera�ons into account. Infinite loading assumes that there is unlimited or infinite capacity.

Backward Scheduling

Backward scheduling starts from a desired due date and works backward. The informa�on for the four jobs and three work centers previously presented is used again, but the following due dates are added:

Job Due Date

A Hour 24

B Hour 16

C Hour 24

D Hour 16

In this case, infinite loading will be used, elimina�ng the problem of more than one job at the same work center at the same �me. The resul�ng schedule is shown in Figure 12.7. Backward scheduling begins by scheduling the last opera�on for each job so that it would end at the �me due, and then works backward through each opera�on. As a result of infinite loading, some work centers have been scheduled to do more than one job at one �me. This may not be a problem if more than one machine is available. Actually, either finite or infinite loading can be used with either forward or backward scheduling.

Figure 12.7: Backward schedule for four jobs with infinite loading

Either of the preceding schedules can also be used to generate a load profile for each work center. A load profile indicates the workload being placed on that work center. Figure 12.8 shows the load profiles for the backward schedule of Figure 12.7 at an hourly rate. These load profiles were obtained by adding up the number of jobs scheduled during each hour for each machine. No�ce that any hour in which more than one hour of machine �me is scheduled could present a problem if only one of each machine is available.

Figure 12.8: Load profiles for backward schedule

Forward and backward scheduling are both widely used—and many companies use both. Forward scheduling is useful for jobs that need to start immediately. Backward scheduling works well when a desired due date is specified. Both finite and infinite loading can be used with forward and backward scheduling. Finite loading requires much more effort for companies to keep track of which jobs are scheduled for which machines and at what �me. Unforeseen problems, varia�ons in processing �me, and other factors can combine to make this a wasted effort. Therefore, most companies use infinite loading and then address over-loaded work centers a�er examining the load profile.

This approach to scheduling helps to point out the importance of capacity requirements planning and its �e-in with both the medium-range produc�on plan and the master schedule. While capacity requirements planning is only a rough es�ma�on, it s�ll helps to ensure that sufficient capacity will be available. If the master schedule indicates a realis�c capacity, then infinite loading does not o�en produce too many problems.

Sequencing

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When using a forward schedule with finite loading, two jobs are not allowed to be in the same work center at the same �me. Thus, if Job 1 had been started at work center A, Job 3 had to wait. But, would it have been be�er to start Job 3 on work center A first and make Job 1 wait? To answer that ques�on, it is possible to use a tool to schedule each work center— the Gan� load chart.

Each work center can be indicated by one bar on the Gan� load chart. The job being processed at each work center and its processing �me can also be indicated. Figure 12.9 shows the Gan� load chart that corresponds to the forward finite load schedule of Figure 12.6. The primary difference between the forward schedule shown in Figure 12.6 and the Gan� load chart in Figure 12.9 is that the former is organized by job and �me, and the la�er is organized by opera�on and �me. The Gan� load chart is very useful for finite scheduling because it allows only one job to be run on each machine or work center at one �me. Any conflicts will immediately become apparent.

Figure 12.9: Gan� load chart for forward schedule

Input/Output Control

Input/output control is a simple method for managing work flow and queue lengths. If work is put into a work center faster than it comes out, a queue will build up. If work is put in at a slower rate than it comes out, the work center may run out of work.

Figure 12.10 shows the input/output report for a work center. The cumula�ve devia�on of actual input from planned input, and cumula�ve devia�on of actual output from planned output are recorded each week. Further, the cumula�ve change in backlog is determined each week by comparing actual input to actual output. For example, in week 43, actual output exceeds actual input by 30 hours. Therefore, the cumula�ve backlog decreases by that amount. In week 45, actual input exceeds actual output by 20 hours, therefore, backlog increases by 20 hours.

Figure 12.10: Input/output report in standard hours

Simulation in Developing Schedules

Scheduling and sequencing can be rather difficult in some situa�ons. This is especially true in job shops where many different end products require different opera�ons. Unfortunately, manually developing schedules in such situa�ons can be extremely �me consuming and difficult because there are too many combina�ons to consider.

Computers help to address this difficulty. Using simula�on techniques, it is possible to develop a trial schedule on the computer and then test that schedule without actually processing the jobs. Through this simula�on, poten�al problems can be iden�fied and an improved schedule can be developed. Today, more companies are developing computer simula�on programs to help solve their scheduling problems.

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12.5 Special Problems in Scheduling Services

One major difference between scheduling the produc�on of goods and scheduling the produc�on of services is that a service cannot be inventoried. For example, a company that manufactures air condi�oners can build up its inventory during the winter months in prepara�on for peak summer demand. But a hospital cannot build up an inventory of emergency room services in advance. Unlike goods, services can be produced only at the �me of demand, which means that the strategies for mee�ng that demand are more limited than for goods. When scheduling some services, such as phone service or public transporta�on, there is less concern with sequencing and more concern with capacity and service delays or wai�ng �me. Because most service opera�ons cannot store finished goods, they try to resolve excess demand problems with extra capacity or by ra�oning capacity. These firms provide incen�ves for people to use services in off-peak �mes, such as traveling to Hawaii in the summer or offering discounts to seniors for shopping at non-peak �mes. These efforts to shi� demand are tools that service industries use to manage capacity.

Sequencing rules are usually applied to situa�ons in which parts or products are wai�ng to be processed. In the service industry it may be customers who are wai�ng. In general, companies o�en apply the first-come, first-served rule in such situa�ons. Of course, that can be frustra�ng for those of us who, for example, simply want to just cash a check at the bank and must wait for someone with a �me-consuming transac�on. Banks have adjusted by crea�ng a single wai�ng line to serve mul�ple tellers rather than a line for each teller; one person with a very long transac�on does not impact everyone wai�ng in line because that person is free to go to any of the other available tellers. ATMs are widely available so that a simple transac�on can be handled many places outside of the bank branch. Some banks have found ways to assuage those callers who must wait to speak with an employee. For example, frequent messages alert wai�ng customers that their calls will be answered shortly.

Services offer some unique challenges for scheduling. The following sec�ons discuss some of the more common approaches to scheduling for services.

Schedule for Peak Demand

One possible approach to scheduling for services is to schedule for peak demand. That means that sufficient capacity will be available at any �me to meet the peak expected demand. The advantage of this approach is that it allows for demand to be met at all �mes under normal condi�ons. Its greatest disadvantage is that a large por�on of capacity may be idle a large percentage of the �me.

U�lity companies like electricity providers face this problem because they are required by government regula�on to meet the demand of its consumers. Electrical power genera�on systems are very expensive, so idle equipment becomes very expensive. In response, some u�li�es have offered homeowners a free programmable thermostat with the caveat that the u�lity can turn up the thermostat by a couple of degrees on days when demand for air condi�oning is high in order to reduce usage during a power peak. The u�lity companies offer discounts to manufacturing companies who use power during low-demand �mes, like at night. Electric u�li�es can also buy power from another u�lity that is nearby when extra power is needed.

Chase Demand

There are two methods that companies can use to adjust produc�on rates to match demand—varying the workforce and using over�me. Either of these strategies can be very useful for service companies if they can es�mate expected demand with reasonable accuracy. For example, Burger King fast-food restaurants maintain extensive records of historical demand during various days of the week and hours of the day. Each restaurant uses this informa�on to determine how many employees it will need to schedule during each hour.

This approach works best if the employees are willing to work on a part-�me basis. Fast food is one industry that is able to schedule its employees in this way. The primary advantage of this approach is that it costs less than scheduling for peak demand, while it enables the organiza�on to meet its an�cipated demand. The disadvantages are that it requires an extremely flexible workforce, and demand forecasts must be accurate.

Other Approaches

Other methods for coping with uneven demand include scheduling appointments or reserva�ons for service, increasing consumer self-service, crea�ng adjustable capacity, sharing capacity, and cross-training employees.

The reserva�on strategy is commonly used by restaurants, hotels, and airlines. Reserva�ons allow an organiza�on to determine the advance demand for its service while also limi�ng access to that service. Airlines, in par�cular, have used reserva�ons to control access to their lowest fares. Those travelers who are willing to book their flights far in advance and sa�sfy certain length-of-stay criteria receive the best fares; those who book only hours before the flight, when space may be limited, must pay the highest fares. Conversely, when demand for a par�cular flight is light, late booking may pay dividends with a low-cost fare.

Fast-food restaurants have successfully used consumer par�cipa�on, such as allowing customers to serve themselves from the salad bar or pour their own drinks, as a way to reduce staffing requirements. This strategy considerably reduces workforce scheduling problems because fewer people are needed. Self-service gas sta�ons also use this technique. The single employee who takes the customers' money can usually handle any level of demand because the most labor-intensive part—pumping the gas—is done by the customers.

Adjustable capacity involves the ability to use only part of the facili�es or available employees at any given �me. For example, restaurants can close off sec�ons when demand is low. The wait staff who serve those sec�ons can fill saltshakers and perform other ac�vi�es to prepare for peak demand. As demand increases, those waiters and waitresses can be moved to wait on tables as sec�ons are opened.

Cross-training employees also provides similar advantages. If employees are trained to perform more than one ac�vity, then they can be shi�ed from one to another as demand changes, as when employees in a supermarket stock shelves when not working as checkers or baggers. Sharing capacity is a way that different organiza�ons, or different parts of the same organiza�on, with different demand pa�erns can use the same facili�es, and, possibly, the same employees. For example, many churches have found that their Sunday school facili�es, which are idle during the week, can be put to good use as day-care centers. On the weekend, when day care is not in session, the church will use those facili�es for other ac�vi�es. Airlines share gates, check-in facili�es, and even ground crews.

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Reserva�ons allow an organiza�on to determine the advance demand for its service, while also limi�ng access to that service.

Tetra Images/Ge�y Images

Chapter Summary

There are a wide variety of criteria considered for scheduling, including due date, flow �me, WIP inventory, equipment idle �me, employee idle �me, and costs. Performing well on some criteria can mean performing poorly on others. Scheduling involves obtaining the right data about orders (jobs), ac�vi�es, employees, equipment, and facili�es. Scheduling a con�nuous flow process and an assembly line are based on knowing how that facility is organized and what work is assigned to each worksta�on or department. Scheduling a batch process, where different products with similar processing requirements share the same equipment, involves determining the load on the equipment and the sequence that provides the best outcome. Some of the most commonly used dispatching rules for scheduling job shops and some service opera�ons are the earliest due date; shortest processing �me; longest processing �me; first-come, first-served; and cri�cal ra�o. Johnson's rule is a way to schedule a set of jobs across two departments. This provides an op�mal result based on flow through �me. Forward and backward scheduling allows organiza�ons to assign tasks to machines to finish as early as possible to give maximum assurance that due dates will be met (forward scheduling), or as late as possible to avoid holding extra inventory (backward scheduling). These can be done with finite loading, which assumes limited capacity, or infinite loading, which assumes unlimited capacity. Priori�es are set in an MRP system by considering the due dates and lead �mes of jobs.

Case Study

Central Electronics Company

The Central Electronics Company makes electronic chassis that are used to hold the components of electronics such as televisions and microcomputers. Central has just received an order from a large microcomputer manufacturer with whom Central would like to develop a long-term rela�onship. If this order can be completed by the due date, such a rela�onship is almost assured. However, the chances of mee�ng that due date do not look good.

Each chassis in this order consists of four parts. Each part has the rou�ng and the run �mes given below. In addi�on, there is a one-hour set-up �me on each machine whenever it is changed from making one part to another, or from performing one opera�on to another on the same part. The following table shows the run �me in minutes per unit for each part.

Rail Bracket A Press—2 mins. Shear—1 min. Drill—1 min. Press—1 min. Press—2 mins. Press—3 mins. Shear—1 min. Drill—5 mins.

Bracket B Shield Shear—1 min. Shear—6 mins. Press—2 mins. Press—1 min. Drill—1 min. Drill—1 min.

Shear—2 mins. Drill—4 mins.

Central has only one press, one drill, and one shear, and each is available only eight hours per day. The order for 150 units must be completed within five days. Each machine must be set up at the start of processing, and again each �me a different opera�on or part is processed on it. There is no assembly �me, as the individual parts are shipped to the customer, which assembles them. However, 150 units of each part must be completed within five days for the order to be filled.

1. If the parts are made in batches of 150, will it be possible to meet the deadline? (Hint: Develop a Gan� load chart for each machine.) 2. Can you iden�fy one machine that has the heaviest load (the bo�leneck machine)? 3. What should your strategies be for scheduling produc�on on that bo�leneck machine? 4. How can you schedule other machines to be sure that the bo�leneck is not idle?

Discussion Ques�ons

Click on each ques�on to reveal the answer.Processing math: 0%

1. Discuss the ways in which flexible manufacturing systems may alter the ac�vi�es of produc�on scheduling. (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/books/AUBUS644

A flexible manufacturing system allows for a greater flexibility in scheduling because of the system's ability to change easily. In an FMS there is no backlog of parts wai�ng to be processed. The flow of materials in the flexible manufacturing system operates on an instantaneous movement basis, for example, through the use of conveyor belts. Thus, there may be less concern about sequencing in an FMS. At the same �me, there is also less flexibility in sequencing because a large backlog of jobs does not exist.

2. List the six criteria that can be used for scheduling. (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/books/AUBUS644

The six criteria that can be used for scheduling are: 1) Providing the good or service when the customer wants it 2) Minimizing the length of �me it takes to produce that good or service (called flow �me) 3) Minimizing the level of work-in-process inventories 4) Minimizing the amount of �me that equipment is idle 5) Minimizing the amount of �me that employees are idle 6) Minimizing costs

3. Which scheduling criterion do you think is most relevant for a fast-food restaurant? For a physician's office? For a hospital emergency room? (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/books/AUBUS644

In a fast-food restaurant the most relevant scheduling criteria is that which will minimize the �me it takes to prepare a customer's order (flow �me). A physician's office will use scheduling criteria that will result in minimal idle �me for the doctor, keeping a steady stream of pa�ents throughout the day. An emergency room, however, is most concerned with scheduling so that those pa�ents with the most severe problems are seen first.

4. Which of the dispatching rules do you use to decide which homework assignment to do first? (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/books/AUBUS644

The answer to this may be unique for each student. However, the more likely choices will be either shortest processing �me, longest processing �me, or earliest due date.

5. Explain why scheduling a con�nuous flow produc�on process involves different methods than those used for scheduling a job shop process. (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/books/AUBUS644

In a high volume produc�on process there are a small number of products and usually only one or two possible rou�ngs. Thus, the scheduling problems in this process include when to change from making one product to another and assembly line balancing for smooth materials flow.

A job shop on the other hand has a large number of products with varying produc�on sequences. The scheduling problems become more complex with so many products vying for �me on the same machines. A decision on which job to process first will impact other machines or work centers with possible overload or idle �me.

6. Which service opera�ons may use the scheduling methods tradi�onally used for job shops? (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/books/AUBUS644

Service opera�ons that might use job shop scheduling methods include: physicians, accoun�ng firms, hospitals, and print shops.

7. For each of the dispatching rules, indicate which scheduling criteria will be sa�sfied, as well as the advantages and disadvantages of that rule. (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/books/AUBUS644

Click here to reveal the answer (h�ps://media.thuze.com/MediaService/MediaService.svc/constella�on/book/AUBUS644.13.2/{pdf}ch_12_ques�on_7.pdf)

8. List the data needed for scheduling, and indicate the usual sources. (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/books/AUBUS644

Click here to reveal the answer (h�ps://media.thuze.com/MediaService/MediaService.svc/constella�on/book/AUBUS644.13.2/{pdf}ch_12_ques�on_8.pdf)

9. How does dispatching differ from sequencing? (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/books/AUBUS644

Sequencing is determining the order in which jobs should be processed beforehand. Dispatching is the selec�on of jobs in real �me. This o�en involved a priority rule such as earliest due date.

10. How are priori�es set for jobs in an MRP 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/books/AUBUS644

Priori�es in MRP are based ini�ally on the planned order releases and lead �mes. Thus, an order that is released earlier will have higher priority than one released later. If jobs get behind schedule then priori�es can be set again by referring to due dates and lead �mes.

However, there may s�ll be conflicts. In that case, either backward or forward scheduling can be used to determine job priori�es so due dates can be met.

11. Explain the purpose of using input/output control. (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/books/AUBUS644

The purpose of input/output control is to ensure that work centers are neither overloaded nor starved for work. The idea is simply to balance input and output so that work backlog does not become excessively long if input exceeds output or disappear if output exceeds input.

12. How can computer simula�on be used for scheduling? (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/books/AUBUS644

Computer simula�on can be used to simulate various schedules. Thus, it is possible to es�mate rapidly the outcomes of many possible schedules and determine the one that best meets the company's objec�ves.

13. Discuss different scheduling procedures that might be used for various types of service opera�ons, such as a restaurant, a hospital, or an airline. (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/books/AUBUS644

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For service opera�ons there may be several different aspects that o�en must be scheduled. These may include scheduling the employees, scheduling the use of resources, and scheduling the customers. For example, in a restaurant, the restaurant's opera�ng hours will determine the availability of facili�es to customers. The pa�ern of demand at different �mes during the day and on different days of the week will determine the requirements for employees, who must be scheduled for their working �mes. If the restaurant takes reserva�ons, then customers are also scheduled into various �me periods. For a hospital, some parts of its services may resemble those of a restaurant. For example, elec�ve surgeries can be scheduled in advance when the facili�es are available, with each pa�ent having a reserved �me. However, emergencies may resemble a restaurant that does not accept reserva�ons, but must serve anyone who shows up. Airlines probably have the most fixed scheduling systems as flights are scheduled well in advance and each flight has a predetermined passenger limit. Flight crews are scheduled to match the flights.

Problems

1. A company produces four types of paper in batches. Based on the following informa�on, which product should be produced next according to the run-out �me criterion?

Product Demand Rate (1,000 �. per Month)

Current Inventory (1,000 �.)

Kra� paper 30,000 80,000 Duplicator bond 20,000 40,000 Regular bond 60,000 150,000 Carbon �ssue 10,000 40,000

2. The David-Harleyston Bicycle Company produces its two models of bicycles, the Avenger and the Hawk, in batches. Based on the following informa�on, which model should be produced next?

Model EOQ Current Inventory Monthly Sales Avenger 2,000 10,000 30,000 Hawk 5,000 6,000 20,000

3. A consultant must complete four reports. She es�mates that report A will take four hours, report B will take three hours, report C will take six hours, and report D will take two hours. In what sequence should she complete the reports, using the shortest-processing-�me rule?

4. A job shop has four jobs wai�ng to be processed on its computer numerically controlled (CNC) lathe. Determine the sequence of these jobs by using each of the five dispatching rules. Assume today is day 107, jobs arrived for processing in the order listed, and the following informa�on is given:

Job Due (Day) Process Time on CNC Lathe (Hours)

Total Processing Time Remaining (Days)

A 120 4 12 B 113 8 5 C 125 2 7 D 115 10 10

5. Late Wednesday a�ernoon, Data Processing Associates had four jobs wai�ng to be processed the next day. Each of these jobs requires keying in the data and then processing it on the company's computer. The DPNs data entry clerks, who work from 8:00 a.m. to 5:00 p.m., with an hour for lunch at noon, complete the data entry. The computer will be available con�nuously beginning at 9:00 a.m. on Thursday. Jobs may be processed immediately a�er being entered, or held for processing later.

Job Data Entry Time (Hours) Processing Times (Hours) Time Due A 1 1 3:00 p.m. B 1 2 12:00 noon C 2 0.5 2:00 p.m. D 2 2 5:00 p.m.

a. Develop schedules using the shortest-processing-�me, longest-processing-�me, and earliest-due-date rules, and draw Gan� load charts for data entry and processing, based on each rule.

b. Evaluate each of the schedules in part a to accommodate for customer service by calcula�ng average past due hours per job for each scheduling rule. 6. Bill Berry, the heat trea�ng department's second shi� foreman at Ace Machine Tool Company, wants to become foreman on the first shi�. To look good, Bill wants to keep queues in

his department to a minimum, so he has been using the shortest-processing-�me rule to schedule work. The assembly department, which usually receives jobs a�er they have been processed in Berry's department, is complaining they o�en do not get jobs early enough to meet the due dates.

The following jobs are currently in queue at the heat trea�ng department and must all be processed through the heat trea�ng department and then through the assembly department. Develop a schedule based on the shortest-processing-�me rule, and draw a Gan� chart for each department.

Processing Time (Days)

Job Heat Trea�ng Assembly Days Un�l Due 317 3 1 12 318 1 3 4 324 2 3 10 326 4 2 8

a. Determine whether there is a schedule that can meet all the due dates. b. Comment on the implica�ons of allowing each machine or work center to schedule its own work.

7. Dr. Houseworth, an orthopedic surgeon, likes to be kept busy during his office hours. All pa�ents scheduled must first have X-rays before they see the doctor. On a certain Monday morning, Dr. Houseworth arrives at his office, and the following three pa�ents are wai�ng to be X-rayed before seeing him. Determine the sequence in which the pa�ents should be X-rayed to minimize the �me Dr. Houseworth is idle.

Pa�ent Time to X-Ray (Min.) Time with Doctor (Min.) Mrs. Green 5 10 Mr. White 15 20Processing math: 0%

Ms. Gray 10 20

8. The following jobs are wai�ng to be processed on one machine. Determine the sequence that will minimize average flow �me.

Job Processing Time (Days) A 4 B 2 C 6 D 3 E 5

9. The following jobs are wai�ng to be processed through two work centers. a. Use Johnson's Rule to determine a sequence. b. Draw a Gan� load chart for each work center.

Processing Time (Hours)

Job Work Center 1

Work Center 2

A 3.0 2.0 B 2.4 3.2 C 1.8 4.0 D 2.2 3.5

10. A printer has six prin�ng jobs. Each job requires typese�ng and prin�ng. a. Use Johnson's Rule to sequence the jobs based on the following expected processing �mes. b. Draw Gan� load charts for prin�ng and typese�ng.

Processing Time (Hours)

Job Typese�ng Prin�ng 1 2.00 3.00 2 3.00 4.00 3 2.50 1.75 4 1.25 2.00 5 3.50 2.50 6 2.25 3.00

11. A city government requires that all new construc�on projects be reviewed by an architect, a city planner, and an environmental engineer (in that order). Four different construc�on projects are wai�ng to be reviewed, and the review �me of each has been es�mated as shown in the following.

Project Architect City Planner Environmental Engineer

A 3 hrs. 2 hrs. 4 hrs. B 2 hrs. 3 hrs. 2 hrs. C 4 hrs. 1 hr. 3 hrs. D 2 hrs. 1 hr. 3 hrs.

If the four projects must be processed in the order A, B, C, D by each person, use forward scheduling with finite loading to develop a Gan� load chart for each person.

12. Five parts must be processed through the following opera�ons, and each has the due date shown. The following table shows the �me required for each processing opera�on:

Part A Part B Part C Part D Part E Lathe (2 days) Lathe (1 day) Mill (1 day) Mill (3 days) Drill (1 day) Mill (3 days) Grind (1 day) Drill (1 day) Grind (1 day) Mill (3 days) Drill (1 day) Mill (2 days) Lathe (2 days) Grind (1 day)

Drill (1 day) Drill (1 day) Due at end of day 8 Due at end of day 6 Due at end of day 5 Due at end of day 10 Due at end of day 6

Use backward scheduling with infinite loading to develop a schedule for each part.

13. Develop a load profile for the city planner in Problem 11. 14. Develop a load profile for the milling opera�on in Problem 12.

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_ch12_odd_problem_solu�ons.pdf)

Key Terms

Click on each key term to see the defini�on

backward scheduling (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/books/AUBUS644.13.2/

An approach to scheduling that starts from a desired due date and works backward.

Processing math: 0%

cri�cal-ra�o rule (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/books/AUBUS644.13.2/

A measure of the ra�o between �me un�l an order is due and the processing �me remaining.

dispatching (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/books/AUBUS644.13.2/

Assigning priori�es and selec�on of jobs for processing at a work center.

dispatching rules (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/books/AUBUS644.13.2/

Rules used for assigning processing priori�es to jobs for scheduling.

finite loading (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/books/AUBUS644.13.2/

An approach to machine loading that considers available capacity.

forward scheduling (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/books/AUBUS644.13.2/

An approach to scheduling that starts from the present �me and schedules each job to start at the earliest possible moment.

Gan� load chart (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/books/AUBUS644.13.2/

A graphic device for indica�ng the schedule of jobs on equipment or facili�es.

infinite loading (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/books/AUBUS644.13.2/

An approach to machine loading that does not take capacity considera�ons into account.

input/output control (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/books/AUBUS644.13.2/

A method for managing work flow and queue lengths by comparing input to a machine with output from it.

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/books/AUBUS644.13.2/

A diagram that indicates the work load being placed on each work center.

loading (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/books/AUBUS644.13.2/

An approach to scheduling that tries to take capacity u�liza�on into account.

makespan �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/books/AUBUS644.13.2/

The total �me required to complete a set of jobs.

make-to-order company (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/books/AUBUS644.13.2/

A company that produces only to customer orders.

make-to-stock company (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/books/AUBUS644.13.2/

A company that produces for inventory and meets customer orders from inventory.

move �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/books/AUBUS644.13.2/

The material handling �me between work centers.

peak 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/books/AUBUS644.13.2/

The highest level of demand that can be expected during a specific �me period.

queue �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/books/AUBUS644.13.2/

The �me a job spends wai�ng to be processed at a work center. Processing math: 0%

run-out �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/books/AUBUS644.13.2/

The period of �me before a company will run out of a par�cular product.

run �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/books/AUBUS644.13.2/

The actual processing �me for a job.

scheduling (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/books/AUBUS644.13.2/

A final, detailed determina�on of the �mes employees will work, the sequence in which goods or services will be provided, and the opera�ng �mes for machines.

sequencing (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/books/AUBUS644.13.2/

A step in the scheduling process in which the ordering of jobs or work is determined.

wait �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/books/AUBUS644.13.2/

The �me a job spends wai�ng before being moved to the next work center.

Processing math: 0%