INVENTORY MANAGEMENT
Importance of Inventory Management -- Good inventory management is essential to the successful operation for
most organizations because of:
1. The amount of money invested in inventory represents, and
2. The impact that inventories have on daily operations of an organization
Definitions:
Inventory – a stock or store of goods
Independent vs. Dependent demand items
Independent demand items are the finished goods or other end items that are sold to someone
Dependent demand items are typically subassemblies or component parts that will be used in the production of a
final or finished product
Our focus: inventory management of finished goods, raw materials, purchased parts, and retail items
Functions of Inventories
1.
2.
3.
4.
5.
6.
7.
To meet anticipated demand
To smooth production requirements
To decouple components of the production
To protect against stockouts
To take advantage of order cycles
To hedge against price increases, or to take advantage of quantity discounts
To permit operations (work in process)
Objectives of Inventory Control
1. Maximize level of customer service
2. Minimize costs (carrying costs and ordering costs)
Requirements for Effective Inventory Management
(1) A system to keep track of the inventory
 periodic,
 perpetual,
 two-bin, and
 universal product code (UPC)
(2) A reliable forecast of demand
(3) Knowledge of lead times and lead time variability
-lead time  time between submitting a purchase order and receiving it
-lead time variability  reliability of the supplier
(4) Estimates of inventory holding costs, ordering costs, and shortage costs
Holding cost
Ordering cost
Stockout cost
(5) A classification system for inventory items
ABC approach – classifies inventory
according to some measure of importance
($ value) where A – very important,
C – least important
Formula for EOQ with Non-instantaneous Replenishment
Qo 
2 DS
H
p
p u
where: D – annual demand
S – setup cost
H – Holding (carrying cost) per unit
p – production or delivery rate
d – usage rate
C.
Quantity Discounts Model
1. Compute the common EOQ
2. Only one of the unit prices will have the EOQ in its feasible range. Identify the range
that:

If the feasible EOQ is on the lowest price range, that is the optimal order quantity

If the feasible EOQ is in any other range, compute the total cost for the EOQ and
for the price breaks of all lower unit costs. Compare the total costs – EOQ is the
one that yields the lowest total cost.
When to Order (reorder points - ROPs) Models
Objective: minimize the risk (probability) of stockouts
4 Determinants of the ROP
1. rate of demand
2. lead time
3. extent of demand and/or lead time variability
4. degree of stockout risk acceptable to management
Basic Formula for Computing ROP
ROP  Expected demand during lead time  Safety stock
A.
Constant demand and constant lead time
ROP  d  LT or simply dLT
B.
Variability is present in demand during lead time
ROP  dLT  z dLT
use this formula if an estimate of expected demand during lead time and its
standard deviation are available
ROP  d LT  z LT  d
use this formula when data on lead time and demand are not readily
available
Shortages and Service Levels
The ROP computation does not reveal the expected amount of shortage for a given lead time
service level
Information on expected number of shortage per cycle, or per year can be determined using
the following:
A.
Expected number of units short per cycle, E(n)
E (n)  E ( z ) dLT
where : E (n) - expected number of units short per cycle
E ( z ) - standardiz ed number of units short using Table 11 - 13 (p. 510)
 dLT - standard deviation of lead time demand
B.
Expected number of units short per year, E(N)
E ( N )  E ( n)
C.
D
Q
Annual Service Level
AnnualServiceLevel  1 
E ( z ) dLT
E ( n)
1
Q
Q
Service Level for Single-period Model
Used to handle ordering of perishables
(fresh fruits, vegetables, seafood, flowers), and
Items that have a limited useful life
(newspaper, magazines)
Analysis focuses on two costs: shortage and excess
SL 
Cs
C s  Ce
where : C s  shortage cost per unit
C e  excesscost per unit
Problems:
2 – ABC Inventory Classification
3 – Basic EOQ
4 – Basic EOQ
11– EOQ with Non-instantaneous Delivery
13 – EOQ with Discount
28 – EOQ, ROP, Shortages
33 – EOQ for multiple products
Problem 2(525)
The following classification table contains figures on the monthly volume
and unit costs for a random sample of 16 units from a list of 2,000
inventory items at a health care facility.
Item
K34
K35
K36
M10
M20
Z45
F14
F95
F99
D45
D48
D52
D57
N08
P05
P09
Unit Cost
10
25
36
16
20
80
20
30
20
10
12
15
40
30
16
10
Usage
200
600
150
25
80
200
300
800
60
550
90
110
120
40
500
30
Problem 3(586)
A large bakery buys flour in 25-lb bags. The bakery uses an average of 4,680 bags
a year. Preparing an order and receiving a shipment of flour involves a cost of $4
per order. Annual carrying costs are $30 per bag.
(a) Determine the economic order quantity
(b) What is the average number of bags on hand?
(c ) How many orders per year will there be?
(d) Compute the total cost of ordering and carrying flour.
Problem 11 (527)
A company is about to begin production of a new product. The manager of the
department that will produce one of the components for the product wants to know
how often the machine used to produce the item will be available for other work.
The machine will produce the item at a rate of 200 units per day. Eighty units will
be used daily in assembling the final product . Assembly will take place 5 days a
week, 50 weeks per year. The manager estimates that it will take almost a full day
to get the machine ready for production run, at a cost of $60.
Inventory holding costs will be $2 per unit per year.
(a) What run quantity should be used to minimize total annual cost?
(b) What is the length of a production run in days?
© During production, at what rate will inventory build up?
(d) If the manager wants to run another job between runs of this item, and
needs a minimum of 10 days per cycle for the other work, will there be enough time?
Problem 13 (527)
A mail-order house uses 18,000 boxes a year. Carrying costs are 20 cents per year per box,
and ordering costs are $32. The following price schedule applies. Determine:
Number of
Boxes
1000 to 1999
2000 to 4999
5000 to 9999
10000 or more
Price per
Box
1.25
1.2
1.18
1.15
(a) The optimal order quantity
Problem 28 (529)
A regional supermarket is open 360 days per year. Daily use of cash register tape
averages 10 rolls. Usage appears normally distributed with a standard deviation of 2
rolls per day. The cost of ordering tape is $1, and carrying costs are $0.40 per roll.
a year. Lead time is three days.
(a) What is the EOQ?
(b) What ROP will provide a lead time service level of 96%?
© What is the expected number of units short per cycle with 96%? Per year?
(d) What is the annual service level?
Problem 33 (530)
Given the following list of items,
Item
H4-010
H5-201
P6-400
P6-401
P7-100
P9-103
TS-300
TS-400
TS-041
V1-001
Estimated
Annual
Ordering
Demand
Cost
D
S
20000
50
60200
60
9800
80
16300
50
6250
50
4500
50
21000
40
45000
40
800
40
26100
25
Holding
Cost (%) Unit Price
P
20%
2.5
20%
4
30%
28.5
30%
12
30%
9
40%
22
25%
45
25%
40
25%
20
35%
40
(a) Classify the items as A, B, and C
(b) Determine the EOQ for each item.