MANAGING INVENTORIES

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OM
CHAPTER 12
MANAGING INVENTORIES
DAVID A. COLLIER AND JAMES R. EVANS
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Chapter 12 Learning Outcomes

l e a r n i n g o u t c o m e s
LO1 Explain the importance of inventory, types
of inventories, and key decisions and costs. LO2
Describe the major characteristics that impact
inventory decisions. LO3 Describe how to
conduct an ABC inventory analysis. LO4 Explain
how a fixed order quantity inventory system
operates. LO5 Explain the logic of the EOQ
model and how to calculate the optimal order
quantity. LO6 Explain how a fixed period
inventory system operates. LO7 Describe how to
apply the single period inventory model.
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Chapter 12 Managing Inventories
anana Republic is a unit of San
Franciscos Gap, Inc. and accounts
for about 13 percent of Gaps 15.9 billion in
sales. As Gap shifted its product
line to basics such as cropped pants, jeans, and
khakis, Banana Republic had to move away from
such staples and toward trends, trying to build a
name for itself in fashion circles. But fashion
items, which have a much shorter product life
cycle and are riskier because their demand is
more variable and uncertain, bring up a host of
operations management issues. In one recent
holiday season, the company had bet that blue
would be the top-selling color in stretch merino
wool sweaters. They were wrong. Marka Hansen,
company president noted, The No. 1 seller was
moss green. We didnt have enough.
What do you think? Can you cite any experiences
in which the lack of appropriate inventory at a
retail store has caused you as the customer to be
dissatisfied?
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Chapter 12 Managing Inventories

• Inventory is any asset held for future use or
  sale.
• The expenses associated with financing and
  maintaining inventories are a substantial part of
  the cost of doing business (i.e., cost of goods
  sold).
• Inventory Management involves planning,
  coordinating, and controlling the acquisition,
  storage, handling, movement, distribution, and
  possible sale of raw materials, component parts
  and subassemblies, supplies and tools,
  replacement parts, and other assets that are
  needed to meet customer wants and needs.

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Chapter 12 Managing Inventories

• Basic Inventory Concepts
• Raw materials, component parts, subassemblies,
  and supplies are inputs to manufacturing and
  service-delivery processes.
• Work-in-process (WIP) inventory consists of
  partially finished products in various stages of
  completion that are awaiting further processing.
• Finished goods inventory is completed products
  ready for distribution or sale to customers.

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Chapter 12 Basic Inventory Concepts

• Basic Inventory Concepts
• Cycle inventory (order or lot size inventory) is
  inventory that results from purchasing or
  producing in larger lots than are needed for
  immediate consumption or sale.
• Safety stock inventory is an additional amount of
  inventory that is kept over and above the average
  amount required to meet demand.

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Exhibit 12.1
Role of Inventory in the Value Chain
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Chapter 12 Managing Inventories

• Inventory managers deal with two fundamental
  decisions
• When to order items from a supplier or when to
  initiate production runs if the firm makes its
  own items
• How much to order or produce each time a supplier
  or production order is placed

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Chapter 12 Managing Inventories

• Inventory Management Decisions and Costs
• Four categories of inventory costs
• Ordering or setup costs
• Inventory-holding costs
• Shortage costs
• Unit cost of the stock-keeping units (SKUs)

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Chapter 12 Managing Inventories

• Inventory Management Decisions Costs
• Ordering costs or setup costs are incurred as a
  result of the work involved in placing purchase
  orders with suppliers or configuring tools,
  equipment, and machines within a factory to
  produce an item.
• Inventory-holding costs or inventory-carrying
  costs are the expenses associated with carrying
  inventory.

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Chapter 12 Managing Inventories

• Inventory Management Decisions Costs
• Shortage costs or stockout costs are the costs
  associated with a SKU being unavailable when
  needed to meet demand.
• Unit cost is the price paid for purchased goods
  or the internal cost of producing them.

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Chapter 12 Managing Inventories

• Characteristics of Inventory Systems
• Number of items each item is identified by its
  stock-keeping unit (SKU).
• A stock-keeping unit (SKU) is a single item or
  asset stored at a particular location.
• Maintaining data integrity on thousands of SKUs
  is difficult but must be done. The quality of
  inventory model decisions is related to the
  quality of information used in the model(s).

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Chapter 12 Managing Inventories

• Nature of Demand
• Independent demand is demand for an SKU that is
  unrelated to the demand for other SKUs and needs
  to be forecast.
• Dependant demand is demand directly related to
  the demand for other SKUs and can be calculated
  without needing to be forecast.
• Deterministic demand is when uncertainty is not
  included in its characteristics.
• Stochastic demand incorporates uncertainty by
  using probability distributions.
• Static demand is stable demand.
• Dynamic demand varies over time.

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Chapter 12 Managing Inventories

• Characteristics of Inventory Systems
• Number of time periods in planning horizon short
  or long planning horizon such as days, weeks,
  months, quarters, and years.
• Size of time periods hours, days, weeks, months,
  quarters.
• The lead time is the time between placement of an
  order and its receipt.

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Chapter 12 Managing Inventories

• Characteristics of Inventory Systems
• A stockout is the inability to satisfy demand for
  an item. When a stockout happens, the item is
  either back-ordered or a sale is lost.
• A backorder occurs when a customer is willing to
  wait for an item.
• A lost sale occurs when the customer is unwilling
  to wait and purchases the item elsewhere.

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Chapter 12 ABC Inventory Analysis
Inventory Management Infrastructure ABC inventory
(Pareto) analysis gives managers useful
information to identify the best methods to
control each category of inventory (see Exhibits
12.2 to 12.4). A vital few SKUs represent a high
percentage of the total dollar inventory value.
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Chapter 12 ABC Inventory Analysis

• ABC Inventory (Pareto) Analysis
• A items account for a large dollar value but
  relatively small percentage of total items (e.g.,
  10 to 30 of items, yet 60 to 80 of total
  dollar usage).
• C items account for a small dollar value but a
  large percentage of total items (e.g., 5 to 15
  of items, yet about 50 of total dollar usage).
  These can be managed using automated computer
  systems.
• B items are between A and C.

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Exhibit 12.2
Usage-Cost Data for 20 Inventoried Items
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Exhibit 12.3
ABC Analysis Calculations
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Exhibit 12.4
ABC Histogram for the Results from Exhibit 12.3
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Chapter 12 Managing Inventories

• In a fixed quantity system (FQS), the order
  quantity or lot size is fixed the same amount,
  Q, is ordered every time.
• The process of triggering an order is based on
  the inventory position.
• Inventory position (IP) is the on-hand quantity
  (OH) plus any orders placed but which have not
  arrived (scheduled receipts, or SR), minus any
  backorders (BO).
• IP OH SR BO 12.1

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Chapter 12 Managing Inventories

• Fixed Quantity Systems (FQS) the order quantity
  or lot size is fixed the same amount, Q, is
  ordered every time.
• Notice that the fixed order (lot) size, Q, can be
  a box, pallet, container, or truck load. Q might
  equal 10, 100, or 1,000 units.
• Q does not have to be economically determined,
  such as using EOQ (to be described later).

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Chapter 12 Managing Inventories

• Fixed Quantity System
• When inventory falls at or below a certain value,
  r, called the reorder point, a new order is
  placed.
• Reorder point depends on the lead time and nature
  of demandoftentimes, the reorder point is
  selected using the average demand during the lead
  time (µL).
• r µL (d) (L) 12.2
• Where d is average demand per unit of time and L
  is the lead time expressed in the same units of
  time.

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Exhibit 12.5
Summary of Fixed Quantity System (FQS)
Fixed Quantity System
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Exhibit 12.6
Fixed Quantity System (FQS) under Stable Demand
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Exhibit 12.7
Fixed Quantity System (FQS) with Highly Variable
Demand
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Chapter 12 Managing Inventories
The Economic Order Quantity (EOQ) model is a
classic economic model developed in the early
1900s that minimizes total cost, which is the sum
of the inventory-holding cost and the ordering
cost.
(
)
(
)
annual inventory holding cost
average inventory
annual holding cost per unit
1
12.4


QCh
2
Cost of storing one unit in inventory for the
year (denoted by Ch), is given by Ch (I) (C ),
where I is annual inventory-holding charge, C is
unit cost of the inventory item, and Q is the
number of units in inventory.
)
(
)
(
)
(
cost per order
number of orders per year
annual ordering cost
D

12.5

Co
Q
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Exhibit 12.8
Cycle Inventory Pattern for the EOQ Model
Average cycle inventory (maximum inventory
minimum inventory)/2 Q/2
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Chapter 12 Managing Inventories
Total Annual Cost inventory holding cost plus
the order (setup cost)
1
D
TC
QCh
Co


12.6
Q
2
Optimal Order Quantity order quantity that
minimized the total cost expressed in the
equation above. Q is the quantity that minimizes
the total cost and is known as the economic order
quantity, or EOQ.
v
2DCo
12.7
Q
Ch
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Chapter 12 Key Assumptions of the EOQ Model

• Only a single item (SKU) is considered.
• The entire order quantity (Q) arrives in the
  inventory at one time. No physical limits are
  placed on the size of the order quantity, such as
  shipment capacity or storage availability.
• Only two types of costs are relevantorder/setup
  and inventory holding costs.

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Chapter 12 Key Assumptions of the EOQ Model
(continued)

• No stockouts are allowed.
• The demand for the item is deterministic and
  continuous over time. This means that units are
  withdrawn from inventory at a constant rate
  proportional to time. For example, an annual
  demand of 365 units implies a weekly demand of
  365/12 and a daily demand of one unit.
• Lead time is constant.

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Exhibit 12.9
Chart of Holding, Ordering, and Total Costs
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Chapter 12 Managing Inventories

• Fixed Period Systems
• An alternative to a fixed order quantity system
  is a fixed period system (FPS)sometimes called a
  periodic review systemin which the inventory
  position is checked only at fixed intervals of
  time, T, rather than on a continuous basis.
• Two principal decisions in a FPS
• The time interval between reviews (T), and
• The replenishment level (M)

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Chapter 12 Managing Inventories
Fixed Period Systems (no uncertainty) Economic
time interval T Q/D 12.8
Optimal replenishment level M d
(T L) 12.9 Where d average demand
per time period L lead time in the same time
units M demand during the lead time plus
review period
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Exhibit 12.10
Summary of Fixed Period Inventory Systems
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Exhibit 12.11
Operation of a Fixed Period Systems (FPS)
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Chapter 12 Special Models for Inventory
Management

• Fixed Period Systems and the Logic of T L
• In Exhibit 12.11, at the time of the first
  review, a rather large amount of inventory (IP1)
  is in stock, so the order quantity (Q1) is
  relatively small (Q1 M IP1).
• At the third review cycle, the stock level (IP3)
  is closer to zero since the demand rate has
  increased (steeper slope of demand), so the order
  quantity (Q3 M IP3) is much larger and during
  the lead time, demand was high and some stockouts
  occurred.

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Exhibit 12.11
Operation of a Fixed Period Systems (FPS)
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Chapter 12 Special Models for Inventory
Management

• Fixed Period Systems and the Logic of TL
• Note that when an order is placed at time T, it
  does not arrive until time T L. Thus, in using
  a FPS, managers must cover the risk of a stockout
  over the time period T L, and therefore, must
  carry more inventory than in a FQS.

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Chapter 12 Special Models for Inventory
Management

• Single-Period Inventory Model
• Applies to inventory situations in which one
  order is placed for a good in anticipation of a
  future selling season where demand is uncertain.
• At the end of the period, the product has either
  sold out or there is a surplus of unsold items to
  sell for a salvage value.

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Chapter 12 Special Models for Inventory
Management

• Single-Period Inventory Model
• Sometimes called a newsvendor problem, because
  newspaper sales are a typical example of the
  single-period inventory problem.
• Problem is solved using technique called marginal
  economic analysis, which compares loss of
  ordering one additional item (cs) to the cost of
  not ordering an additional item (cu) using
  Equation 12.10.

cu cu cs
12.10
P (demand Q)
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Exhibit 12.12
Probability Distribution for Single Period Model