Transcript Document

OM2
CHAPTER 12
MANAGING INVENTORIES
DAVID A. COLLIER
AND
JAMES R. EVANS
OM2, Ch. 12 Managing Inventories
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posted to a publicly accessible website, in whole or in part.
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Chapter 12 Learning Outcomes
learning outcomes
LO1 Explain the importance of inventory, types of
LO2
LO3
LO4
LO5
LO6
inventories, and key decisions and costs.
Describe the major characteristics that impact
inventory decisions.
Describe how to conduct an ABC inventory analysis.
Explain how a fixed order quantity inventory system
operates, and how to use the EOQ and safety stock
models.
Explain how a fixed period inventory system
operates.
Describe how to apply the single period inventory
model.
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Chapter 12 Managing Inventories
anana Republic is a unit of San Francisco’s Gap, Inc. and
accounts for about 13 percent of Gap’s $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 didn’t 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
Where Is Your Inventory?
Today, tiny radio frequency identification (RFID) chips
embedded in packaging or products allow scanners to track
SKUs as they move throughout the store. RFID chips help
companies locate items in stockrooms and identify where they
should be placed in the store. Inventory on the shelves can
easily be tracked to trigger replenishment orders. Recalled
or expired products can be identified and pulled from the
store before a customer can buy them, and returned items
can be identified by original purchase location and date, and
whether or not they were stolen. One interesting application
has been developed by CVS, a Rhode Island-based pharmacy
chain, which is testing RFID technology to inform when a
customer has not picked up his or her prescription medicine
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Chapter 12 Managing Inventories
Basic Inventory Decisions
Inventory managers deal with two fundamental
decisions:
1. When to order items from a supplier or
when to initiate production runs if the firm
makes its own items
2. 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/value.
• “C” items account for a small dollar value but a
large percentage of total items (e.g., 50% to 60%
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
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ABC Analysis Calculations
20
Exhibit 12.4
ABC Histogram for the Results from Exhibit 12.3
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Chapter 12 Managing Inventories
Fixed Quantity System
• In a fixed quantity system (FQS), the order
quantity or lot size is fixed; the same amount, Q,
is ordered every time.
• 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, as we will do for the EOQ model
(described later).
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Chapter 12 Managing Inventories
Fixed Quantity System
• 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
OM2, Ch. 12 Managing Inventories
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posted to a publicly accessible website, in whole or in part.
[12.1]
23
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 demand—oftentimes, 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.
OM2, Ch. 12 Managing Inventories
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Exhibit 12.5
Summary of Fixed Quantity System (FQS)
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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
Economic Order Quantity Model
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
OM2, Ch. 12 Managing Inventories
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1
= 2 QCh
[12.4]
28
Economic Order Quantity Model
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.
annual
=
ordering cost
(
)(
number of
orders per year
)= ( )
cost
per order
OM2, Ch. 12 Managing Inventories
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D
Q
Co
[12.5]
29
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
Q
2
[12.6]
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.
Q* =
√
2DCo
Ch
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[12.7]
31
Chapter 12 Managing Inventories
Key Assumptions of 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 relevant—
order/setup and inventory holding costs.
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Chapter 12 Managing Inventories
• 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
Safety Stock and Uncertain Demand
One way to reduce the risk of a stockout is to
add safety stock by increasing the reorder point.
• A service level is the desired probability of not
having a stockout during a lead-time period.
For example, a 95 percent service level means
that the probability of a stockout during the lead
time is .05.
Choosing a service level is a management policy
decision.
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Chapter 12 Managing Inventories
When a normal probability distribution provides a good
approximation of lead time demand, the general
expression for reorder point is
r = mL + zsL
[12.8]
where
mL = average demand during the lead time
sL = standard deviation of demand during the lead
time
z = the number of standard deviations necessary to
achieve the acceptable service level
The term “zsL” represents the amount of safety stock.
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Chapter 12 Managing Inventories
We may not know the mean and standard
deviation of demand during the lead time, but
only for some other length of time, t, such as a
month or year. Suppose that mt and st are the
mean and standard deviation of demand for
some time interval t, If the distributions of
demand for all time intervals are identical to and
independent of each other, then
mL = mtL
[12.9]
s L = s t √L
[12.10]
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Chapter 12 Managing Inventories
Solved Problem
Southern Office Supplies, Inc. distributes a wide variety
of office supplies and equipment to customers in the
Southeast. One SKU is laser printer paper, which is
purchased in reams from a firm in Appleton, Wisconsin.
Ordering costs are $45.00 per order, one ream of paper
costs $3.80, and Southern uses a 20 percent annual
inventory-holding cost rate for its inventory. Thus, the
inventory-holding cost is Ch = IC = 0.20($3.80) = $0.76
per ream per year. The average annual demand is
15,000 reams, or about 15,000/52 = 288.5 per week,
and historical data shows that the standard deviation of
weekly demand is about 71. The lead time from the
manufacturer is two weeks.
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Chapter 12 Managing Inventories
Using Equations 12.9 and 12.10, the average
demand during the lead time is (288.5)(2) =
577 reams, and the standard deviation of
demand during the lead time is
approximately 71√2 = 100 reams. The EOQ
model results in an order quantity of 1333,
reorder point of 577, and total annual cost of
$1,012.92.
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Chapter 12 Managing Inventories
Suppose Southern’s managers desire a service level of
95%, which results in a stockout of roughly once every 2
years. Using the normal distribution tables in Appendix
A, we find that a 5 percent upper tail area corresponds
to a standard normal z-value of 1.645. That is, the
reorder point using Equation (12.8), r, is 1.645 standard
deviations above the mean, or
r = mL + zsL = 577 = 1.645(100) = 742 reams
This policy increases the reorder point by 742 – 577 =
165 reams, which represents the safety stock. The cost
of the additional safety stock is simply Ch times the
amount of safety stock, or ($0.76/ream)(165 reams) =
$125.40.
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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 system—in 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:
1. The time interval between reviews (T), and
2. The replenishment level (M)
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Chapter 12 Managing Inventories
Fixed Period Systems (no uncertainty)
T = Q*/D
Economic time interval:
[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.
OM2, Ch. 12 Managing Inventories
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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
• 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
P (demand ≤ Q*) = c + c
u
s
OM2, Ch. 12 Managing Inventories
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[12.13]
49
Chapter 12 Managing Inventories
Solved Problem
Let us consider a buyer for a department store
who is ordering fashion swimwear about six
months before the summer season. The store
plans to hold an August clearance sale to sell
any surplus goods by July 31. Each piece costs
$40 per pair and sells for $60 per pair. At the
sale price of $30 per pair, it is expected that any
remaining stock can be sold during the August
sale.
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Exhibit 12.12
Probability Distribution for Single Period Model
We will assume that a uniform probability distribution ranging
from 350 to 650 items describes the demand. The expected
demand is 500.
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Chapter 12 Managing Inventories
The cost per item of overestimating demand is equal to
the purchase cost per item minus the August sale price
per item; that is, cs = $40 – $30 = $10. The per-item
cost of underestimating demand is the difference
between the regular selling price per item and the
purchase cost per item; that is, cu = $60 – $40 = $20.
The optimal order size Q must satisfy this condition:
P(demand ≤ Q*) = cu /(cu + cs) = 20(20+10) = 2/3
From the uniform distribution assumption, this results in
Q* = 550.
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Chapter 12 Managing Inventories
ASR Electronics Case Study
1. Using Anita’s current ordering policy of 70 units, calculate her expected
annual order and inventory carrying costs. Show how a fixed order
quantity system operates by calculating the ending inventory each day
over the 10-week period using the data provided and Equation (12.1),
realizing that there are no backorders (we suggest doing this on a
spreadsheet). Assume that 70 units have arrived and are in inventory at
the start of week 1. What is the average ending inventory? How often
does a shortage occur and when it does, what is the average amount?
2. Compute the optimal EOQ (round any fractional values up). How does
the expected annual cost compare with the 70-unit order policy?
Illustrate the results of using the EOQ by calculating the ending inventory
each day over the 10-week period in the same fashion as in question 1.
Assume that all orders arrive at the beginning of the day. What is the
average ending inventory? How often does a shortage occur and when it
does, what is the average amount?
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Chapter 12 Managing Inventories
3. By experimenting, with different order quantities (in 10unit increments), identify an order quantity that reduces
the chance of a stockout to less than 5% (that is, less
than 4 times over the 10 week period).
4. Compare the total costs of the current ordering policy
(Q = 70), the optimal EOQ policy, and your best answer
to question 3 over the 10-week period based on the
average inventory and the number of orders placed.
What would you recommend to Anita?
OM2, Ch. 12 Managing Inventories
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