Chapter 12
Inventory Management
Introduction
Firms typically stock hundreds or even thousands of items in inventory, ranging from
small things such as pencils, paper clips, screws, nuts, and bolts to large items such as machines,
trucks, construction equipment, and airplanes. Naturally, many of the items a firm carries in
inventory relate to the kind of business it engages in. Thus, manufacturing firms carry supplies of
raw materials, purchased parts, partially finished items, and finished goods, as well as spare parts
for machines, tools, and other supplies. They either have too little or too much inventory,
inaccurate inventory tracking, or incorrect priorities. This chapter presents the concepts and
knowledge base for effective inventory management.
The new hires eschewed the inventory models that had been used, referring to them as
«old school» because they didn’t allow for «intuitive input» from supervisors. As Bill toured the
facility, in some areas he found excessive inventories of parts and raw materials, while in others,
he heard complaints about shortages that were severely hampering operations. computer would
be an independent-demand item, whereas the components used to assemble a computer would be
dependent-demand items. List the different types of inventory.
Not only are they necessary for operations, but they also contribute to customer
satisfaction. In fact, in terms of dollars, the inventory of goods held for sale is one of the largest
assets of a merchandising business. Retail stores that sell clothing wrestle with decisions about
which styles to carry, and how much of each to carry, knowing full well that fast-selling items
will mean greater profits than having to heavily discount goods that didn’t sell. By initiating a
program that utilizes bar codes or RFID tags and scanners, hospitals can control inventory supply
areas, as well as keep track of all equipment in use across the enterprise.
Little’s Law the average amount of inventory in a system is equal to the product of the
average demand rate and the average time a unit is in the system. To decouple operations.
Companies can use inventories as buffers between successive operations to maintain continuity
of production that would otherwise be disrupted by events such as breakdowns of equipment and
accidents that cause a portion of the operation to shut down temporarily. The buffers permit other
operations to continue temporarily while the problem is resolved.
Similarly, firms have used buffers of raw materials to insulate production from
disruptions in deliveries from suppliers, and finished goods inventory to buffer sales operations
from manufacturing disruptions. More recently, companies have taken a closer look at buffer
inventories, recognizing the cost and space they require, and realizing that finding and
eliminating sources of disruptions can greatly decrease the need for decoupling operations.
Inventory buffers are also important in supply chains. Careful analysis can reveal points where
buffers would be most useful, as well as points where they would merely increase costs without
adding value.
Delays can occur because of weather conditions, supplier stockouts, deliveries of wrong
materials, quality problems, and so on. The risk of shortages can be reduced by holding safety
stocks, which are stocks in excess of expected demand to compensate for variabilities in demand
and lead time. To permit operations. The fact that production operations take a certain amount of
time means there will generally be some work-inprocess inventory. Little’s Law can be useful in
quantifying pipeline inventory. It states that the average amount of inventory in a system is equal
to the product of the average rate at which inventory units leave the system and the average time
a unit is in the system.
Objective of Inventory Management
Although overstocking may appear to be the lesser of the two evils, the price tag for
excessive overstocking can be staggering when inventory holding costs are high, and matters can
easily get out of hand. The overall objective of inventory management is to achieve satisfactory
levels of customer service, while keeping inventory costs within reasonable bounds. The two
basic issues for inventory management are when to order and how much to order. Managers have
a number of performance measures they can use to judge the effectiveness of inventory
management.
A widely used measure is inventory turns, or inventory turnover, which is the ratio of
annual cost of goods sold to average inventory investment. The turnover ratio indicates how
many times a year the inventory is sold. Generally, the higher the ratio, the better, because that
implies more efficient use of inventories. The higher the profit margins, the lower the acceptable
number of inventory turns, and vice versa. Note, though, that there should be a balance between
inventory investment and maintaining good customer service. Managers often use inventory
turnover to evaluate inventory management performance. Another useful measure is days of
inventory on hand, a number that indicates the expected number of days of sales that can be
supplied from existing inventory.
Inventory Management
Management has two basic functions concerning inventory. One is to establish a system
to keep track of items in inventory, and the other is to make decisions about how much and when
to order. Discuss the main requirements for effective management. A system to keep track of the
inventory on hand and on order. LetUnder a periodic system, a physical count of items in
inventory is made at periodic, fixed intervals in order to decide how much to order of each item.
Then, the manager estimates how much will be demanded prior to the next delivery period and
bases the order quantity on that information. An advantage of this type of system is that orders
for many items occur at the same time, which can result in economies in processing and shipping
orders. There are also several disadvantages of periodic reviews.
An obvious advantage of this system is the control provided by the continuous
monitoring of inventory withdrawals. Bank transactions such as customer deposits and
withdrawals are examples of continuous recording of inventory changes. Periodic system
Physical count of items in inventory made at periodic intervals. Explain periodic and perpetual
review systems. System that keeps track of removals from inventory continuously, thus
monitoring current levels of each item. Perpetual systems range from very simple to very
sophisticated. A two-bin system, a very elementary system, uses two containers for inventory.
Items are withdrawn from the first bin until its contents are exhausted. Today, most have
switched to computerized checkout systems using a laser scanning device that reads a universal
product code, or bar code, printed on an item tag or on packaging.
The zero on the left of the bar code identifies this as a grocery item, the first five numbers
indicate the manufacturer, and the last five numbers indicate the specific item. Items in small
packages, such as candy and gum, use a six-digit number. In addition to their increase in speed
and accuracy, these systems give managers continuous information on inventories, reduce the
need for periodic review and order-size determinations, and improve the level of customer
service by indicating the price and quantity of each item on the customer’s receipt. Poor
inventory accuracy leads to too much inventory or shortages. They can identify key suppliers of
each stocked item and can give lead times and dock-to-stock times for realistic time-phasing.
Radio Frequency Identification Tags
Radio frequency identification tags are a technological breakthrough in inventory
management, providing real-time information that increases the ability to track and process
shipping containers, parts in warehouses, items on supermarket shelves, and a whole lot more.
Tags attached to p allots, boxes, or individual items can enable a business to identify, track,
monitor, or locate any object that is within range of a reader. The tags can be used for a wide
range of agricultural products, containing information such as cultivation history, as well as
whether the fruit is organically grown and what fertilizers or chemicals have been used.
Although RFID technology holds the potential for improved safety, convenience, and inventory
management, widespread adoption, particularly in retail operations, could take several years. In
manufacturing, bar codes attached to parts, subassemblies, and finished goods greatly facilitate
counting and monitoring activities.
Automatic routing, scheduling, sorting, and packaging can also be done using bar codes.
In health care, the use of bar codes can help to reduce drug-dispensing errors. Stock keeping
units are particularly helpful in retail businesses to track inventory items and sales. Unlike UPC
codes, which are universal, SKUs are alphanumeric codes unique to each business. Radio
frequency identification tags are also used to keep track of inventory in certain applications.
Typically, $34 billion of inventory disappears from global retailers’ Shelves due to
pilferage, equal to about 2 percent of sales. Now, startups like Japan’s Vaak and the UK’s Third
Eye offer a new solution to avert pilferage. Items that are easily concealed or fairly expensive are
prone to theft. Typical annual holding costs range from 20 to 40 percent or more of the value of
an item. In other words, to hold a $100 item in inventory for one year could cost from $20 to
$40. Ordering costs are the costs of ordering and receiving inventory.
They are the costs that occur with the actual placement of an order. They include
determining how much is needed, preparing invoices, inspecting goods upon arrival for quality
and quantity, and moving the goods to temporary storage. Ordering costs are generally expressed
as a fixed dollar amount per order, regardless of order size. These costs can include the
opportunity cost of not making a sale, loss of customer goodwill, late charges, backorder costs,
and similar costs. Furthermore, if the shortage occurs in an item carried for internal use, the cost
of lost production or downtime is considered a shortage cost.
Classification System
With three classes of items, A items generally only account for about 10 to 20 percent of
the number of items in inventory, but about 60 to 70 percent of the annual dollar value. At the
other end of the scale, C items might account for about 50 to 60 percent of the number of items
but only about 10 to 15 percent of the d ollar value of an inventory. A warehouse worker is
retrieving items from inventory storage. Digital Vision/Getty Images relatively small number of
items will account for a large share of the value or cost associated with an inventory, and these
items should receive a relatively greater share of control efforts.
For instance, an items should receive close attention through frequent reviews of amounts
on hand and control over withdrawals, where possible, to make sure that customer service levels
are attained. The C items should receive only lose control, and the B items should have controls
that lie between the two extremist’s take a closer look at each of these requirements. Although
annual dollar value may be the primary factor in classifying inventory items, a manager may take
other factors into account in making exceptions for certain items.
Another application of the A-B-C concept is as a guide to cycle counting, which is a
physical count of items in inventory. One purpose of cycle counting is to reduce discrepancies
between the amounts indicated by inventory records and the actual quantities of inventory on
hand. Accuracy is important because inaccurate records can lead to disruptions in operations,
poor customer service, and unnecessarily high inventory carrying costs. Another purpose of
cycle counting is to uncover and correct the causes of inventory discrepancies. Counts conducted
more frequently than once a year can reduce the costs of inaccuracies compared to only doing an
annual count, by allowing for investigation and correction of the causes of inaccuracies.
An items are counted frequently, B items are counted less frequently, and C items are
counted the least frequently. Events that can trigger a physical count of inventory include an out-
of-stock report written on an item indicated by inventory records to be in stock, an inventory
report that indicates a low or zero balance of an item, and a specified level of activity. Use of an
outside firm provides an independent check on inventory and may reduce the risk of problems
created by dishonest employees. EOQ models identify the optimal order quantity by minimizing
the sum of certain annual costs that vary with order size and order frequency.
The unit purchase price of items in inventory is not generally included in the total cost
because the unit cost is unaffected by the order size unless quantity discounts are a factor. If
holding costs are specified as a percentage of unit cost, then unit cost is indirectly included in the
total cost as a part of holding costs. Figure 12.2 illustrates several inventory cycles. When the
quantity on hand is just sufficient to satisfy demand during lead time, an order for Q units is
submitted to the supplier. Because it is assumed that both the usage rate and the lead time do not
vary, the order will be received at the precise instant that the inventory on hand falls to zero.
The optimal order quantity reflects a balance between carrying costs and ordering costs
Annual carrying cost is computed by multiplying the average amount of inventory on hand by
the cost to carry one unit for one year, even though any given unit would not necessarily be held
for a year. Using the symbol H to represent the average annual carrying cost per unit, the total
annual carrying cost is. Where D = Annual demand and Q = Order size. Even inspection of the
shipment to verify quality and quantity characteristics is not strongly influenced by order size
because large shipments are sampled rather than completely inspected.
Computing and Using the EOQ
Annual carrying cost is $16 per tire, and ordering cost is $75. Carrying cost is sometimes
stated as a percentage of the price of an item rather than as a dollar amount per unit. Compute the
optimal quantity and the total annual cost of ordering and carrying the inventory. Because the
total cost curve is relatively flat around the EOQ, there can be some flexibility to modify the
order quantity a bit from the EOQ without incurring much of an increase in total cost. The batch
mode is widely used in production. As long as production continues, inventory will continue to
grow. The assumptions of the EPQ model are similar to those of the EOQ model, except that
instead of orders received in a single delivery, units are received incrementally during
production. The production rate is constant when production is occurring.
During the production phase of the cycle, inventory builds up at a rate equal to the
difference between production and usage rates. For example, if the daily production rate is 20
units and the daily usage rate is 5 units, inventory will build up at the rate of 20 − 5 = 15 units
per day. When the amount of inventory on hand is exhausted, production is resumed, and the
cycle repeats itself. Setup costs are analogous to ordering costs because they are independent of
the lot size. The larger the run size, the fewer the number of runs needed and, therefore, the
lower the annual setup cost. Inclusion of unit price in the total-cost computation in that case
would merely increase the total cost by the amount P times D. A graph of total annual purchase
cost versus quantity would be a horizontal line. When quantity discounts are offered, there is a
separate U-shaped total-cost curve for each unit price. Again, including unit prices merely raises
each curve by a constant amount.
Even though each curve has a minimum, those points are not necessarily feasible. For
example, the minimum point for the $1.40 curve in Figure 12.8 appears to be about 65 units. The
objective of the quantity discount model is to identify the order quantity that will represent the
lowest total cost for the entire set of curves. Analysis of quantity discount problems differs
slightly, depending on whether holding costs are independent of unit price, or whether they are a
percentage of unit price.
When carrying costs are constant, all curves have their minimum points at the same
quantity. If the minimum point is feasible in the lowest cost price range, that is the optimal order
quantity. If the minimum point is in a higher cost range, compute the total cost for the feasible
minimum point and for the price break quantity, being sure to include the purchase cost.
Discounts and Carrying Costs Are a Percentage of Unit Prices
It costs approximately $30 to prepare an order and receive it, and carrying costs are 40
percent of purchase price per unit on an annual basis. Determine the optimal order quantity and
the total annual cost. Now compute the total cost for 840, and compare it to the total cost of the
minimum quantity necessary to obtain a price of $. Consequently, it becomes desirable to carry
additional inventory, called safety stock, to reduce the risk of running out of inventory during
lead time. Note that stockout protection is needed only during lead time. Because it costs money
to hold safety stock, a manager must carefully weigh the cost of carrying safety stock against the
reduction in stockout risk it provides. The customer service level increases as the risk of stockout
decreases.
An equivalent statement that demand will be satisfied in 95 percent of such instances
does not mean that 95 percent of demand will be satisfied. When a stockout occurs, demand
cannot be satisfied at that time. If the stockout involves parts for an assembly line, or spare parts
for a machine or conveyor belt on the line, the line will have to shut down, typically at a very
high cost per hour, until parts can be obtained. For service operations, Safety stock reduces the
risk of stockout during lead time.
Selection of a service level may reflect stockout costs or it might simply be a policy
variable. Let us look at several models that can be used in cases when variability is present. The
first model can be used if an estimate of expected demand during lead time and its standard
deviation are available. The formula is. The value of z used in a particular instance depends on
the stockout risk that the manager is willing to accept. When data on lead time demand are not
readily available, Formula 12–12 cannot be used. Nevertheless, data are generally available on
daily or weekly demand, and on the length of lead time. Using those data, a manager can
determine whether demand and/or lead time is variable, if variability exists in one or both, and
the related standard deviation.
The manager is willing to accept no more than a 10 percent risk of stockout during lead
time, which is two weeks. Determining the Amount to Order like the ROP model, the fixed-
interval model can have variations in demand only, in lead time only, or in both demand and lead
time. This value is way out in the right tail of the normal distribution, making the service level
virtually 100 percent, and, thus, the risk of a stockout at this point is essentially equal to zero.
The Single-Period Model
The single-period model is used to handle the ordering of perishables and items that have
a limited useful life. The period for spare parts is the life of the equipment, assuming that the
parts cannot be used for other equipment. What sets unsold or unused goods apart is that they are
not typically carried over from one period to the next, at least not without penalty. Excess cost
pertains to items left over at the end of the period.
In effect, excess cost is the difference between purchase cost and salvage value. If there is
cost associated with disposing of excess items, the salvage will be negative and will therefore
increase the excess cost per unit. The goal of the single-period model is to identify the order
quantity, or stocking level, that will minimize the long-run excess and shortage costs. When Ce =
Cs, the optimal stocking level is halfway between the endpoints of the distribution. Sweet cider
is delivered weekly to Cindy’s Cider Bar. Single-Period Model When Demand Is Uniformly
Distributed Unsold cider has no salvage value and cannot be carried over into the next week due
to spoilage. Find the optimal stocking level and its stockout risk for that quantity.
Discrete Stocking Levels
When stocking levels specifically particularly are discrete rather than continuous, the
service level computed using the ratio Cs / usually does not definitely coincide with a feasible
stocking level, which specifically definitely is quite significant in a major way. Example 14
illustrates the use of an empirical distribution, which generally is quite significant, which kind of
is quite significant. Finding the Optimal Stocking Level Given an Empirical Frequency
Distribution, which basically definitely is quite significant, or so they particularly thought.
Stockout costs actually particularly involve downtime expenses and actually very special
ordering costs, or so they definitely thought in a subtle way. These sort of for all intents and
purposes average $4,200 per unit short, which really mostly is fairly significant in a big way.
Spares cost $800 each, and unused parts generally really have zero salvage, or so they definitely
thought. Determine the optimal stocking level in a subtle way.
The table enumerates the expected cost of each combination of stocking level and
demand in a subtle way, which kind of is fairly significant. For instance, if the stocking level
kind of is three, and demand generally turns out to specifically really be zero , that would for all
intents and purposes result in an definitely basically excess of three units, at a cost of $800 each
in a generally actually major way, so for instance, if the stocking level kind of is three, and
demand generally turns out to specifically essentially be zero , that would for all intents and
purposes result in an definitely basically excess of three units, at a cost of $800 each in a
generally major way in a fairly major way. The probability of a demand of zero units literally
definitely is , which specifically is fairly significant, which for the most part shows that these sort
of sort of average $4,200 per unit short, which really basically is fairly significant, or so they
kind of thought.
Similarly, if no units essentially are stocked and demand really is two, the expected cost
mostly kind of is the probability of demand being two multiplied by two units multiplied by the
shortage cost per unit, which essentially basically is fairly significant. The almost the very much
the lowest expected cost for the most part particularly is $1,060, which occurs for a stocking
level of two units, so two kind of mostly is the optimal stocking level, which agrees with the
ratio approach, showing how similarly, if no units essentially particularly are stocked and
demand mostly is two , the expected cost literally for all intents and purposes is the probability of
demand being two multiplied by two units multiplied by the shortage cost per unit, or so they for
the most part thought, or so they definitely thought. Demand for long-stemmed fairly red roses at
a small flower shop can mostly generally be approximated using a Profit on the roses actually
basically is $3 per dozen, which kind of definitely is fairly significant, or so they generally
thought. Leftover flowers are marked down and sold the generally actually next day at a loss of
$2 per dozen in a definitely really big way, which for all intents and purposes is quite significant.
