1. IES 371 Engineering Management Chapter 15: Inventory Management Supplement E
Week 14
September 7, 2005
Learning Objectives:
Understand the practical aspects of various inventory systems
Identify the major factors affecting inventory system performance
Understand how to calculate the optimal order quantity in various circumstance

2. Inventory Management
Inventory : Stock of items held to meet future demand
Determine the amount of inventory to keep in stock
Inventory management answers two questions:
How much to order:
Order Quantity or
Economic Order Quantity (EOQ)
When to order: Reorder point (R)

3. Reasons to Hold Inventory Physical Types of Inventory
Meet unexpected demand
Smooth seasonal or cyclical demand
Meet variations in customer demand
Take advantage of price discounts
Quantity discounts
Physical Types of Inventory
Raw materials
Purchased parts and supplies
Labor
In-process (partially completed) products
Component parts
Tools, machinery, and equipment

4. Pressures for Low Inventories
When keeping inventory, there are always some cost incurred Inventory holding cost (or carrying cost)
The variable cost of keeping items on hand
$/ unit-period
Inventory holding cost generally includes:
Interest of opportunity cost
Storage and handling costs
Tax, insurance, and shrinkage

5. Pressures for High Inventories
Customer service
Ordering cost ($ / order)
Setup cost
Transportation cost
Payment to suppliers
Labor and equipment utilization

6. Types of Inventory Cycle Inventory Safety stock inventory
Anticipation inventory
Pipeline inventory

7. Inventory Reduction Approach
Cycle Inventory
Safety stock inventory
Anticipation inventory
Pipeline inventory

8. ABC Analysis
To classify the inventory classes according to how critical (% of dollar value) of each inventory type
Class A
5 – 15 % of units
70 – 80 % of value
Class B
30 % of units
15 % of value
Class C
50 – 60 % of units
5 – 10 % of value

9. ABC Analysis Percentage of dollar value Percentage of items 10 20 3040 50 60 70 80 90
100
Percentage of items
Percentage of dollar value
100 —
90 —
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0 —
Class C
Class A
Class B
Figure 15.2

10. Economic Order Quantity (EOQ)
EOQ: the lot size or order size that minimizes total annual inventory holding and ordering cost
Total inventory cost = Holding cost (HC) + ordering cost (OC)
Assumptions for Basic EOQ Model
Constant demand with no uncertainty
No shortages
Constant order lead time
Receive order quantity all at once
No other constraint

11. Basic EOQ Model Cycle Inventory Levels
Order quantity, Q
Demand rate
Inventory Level
Reorder point, R
Time
Lead time
Lead time
Order placed
Order receipt
Order placed
Order receipt

12. Basic EOQ Model Graphs of Annual Holding, Ordering, and Total Costs
Annual cost (dollars)
Lot Size (Q)
Total cost = HC + OC
Ordering cost (OC)
Holding cost (HC)
Figure 15.4

13. Basic EOQ Model Q = order size (units) D = annual demand (units/year)
Derivation of total annual inventory cost and economic order quantity order quantity functions
Q = order size (units)
D = annual demand (units/year)
S = ordering cost per order ($/order)
H = annual per unit carrying cost ($/unit)

14. Basic EOQ Model Ex 1:Carpet Sell
The I-75 Carpet store stocks carpet in its warehouse and sells it through a showroom. The store keeps several brands and styles of carpet in stock; however, its bigger seller is the BIG C carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150.
The store would like to know the number of orders that will be made annually and the time between orders given that the store is open every except Sunday, Thanksgiving Day and Christmas Day.

15. EOQ Sensitivity Analysis
Use estimates of relevant costs
Ignore uncertainty in demand
What happen if the holding / ordering cost is off by 20%, 30%?
Consider 4 cases of variations of the model parameters.
Both ordering and carrying costs are 10% less than the original estimates
Both are 10% higher
Ordering cost is 10% higher and carrying cost is10% lower
Ordering cost is 10% lower and carrying cost is 10% higher
Determine EOQ in each case. Remark on the sensitivity of Q on the estimated total cost.

16. Basic Types of Inventory Control System
Continuous review system
Reorder point (ROP) system
Fixed order quantity system
The ordering interval may not be consistent
Manager has direct control
Periodic review System (P)
Fixed interval reorder system or periodic reorder system
The amount to order may not be equal
No direct control
Tend to have higher inventory to prevent stockout

17. Continuous review system
Order
placed IP Q OH
Order
received Q OH
placed IP
Time
On-hand inventory
Order
received R
TBO L
TBO L
Figure 15.7

18. Continuous review system Selecting Reorder Point
When demand is certain
Reorder point (R) = demand during lead time
When demand is uncertain
Reorder point (R) = Avg demand during lead time + Safety stock

19. Variable Demand Safety Stocks
buffer added to on hand inventory during lead time
Stockout
an inventory shortage
Service level
probability that the inventory available during lead time will meet demand
Reorder
point, R Q LT
Time
Inventory level
Variable Demand with Reorder Point

20. Variable Demand Safety Stocks
Prevent stockout under uncertain demand Q
Inventory level
Reorder
point, R
Safety Stock LT LT
Time

21. Reorder Point for a Service Level
Probability of
meeting demand during
lead time = service level
Average demand during lead time
Probability of
a stockout
Safety stock
zt L
Demand R

22. Reorder Point with Variable Demand
Reorder point with safety stock
Service level = probability of NO stockout

23. Variable Demand Ex 2: PM computer
PM Computers assembles microcomputers from generic components. It purchases its color monitors from a manufacturer in Taiwan. There is a long lead time of 25 days. Daily demand is normally distributed with a mean of 2.5 monitors and a standard deviation of 1.2 monitors. Determine the safety stock and reorder point corresponding to a 90% service level

24. Periodic Review System (P system)
Time
On-hand inventory T Q1
Order
placed L
received Q2 Q3 OH
Protection interval
IP1
IP3
IP2 IP
Figure 15.12

25. Special Inventory Model Noninstantaneous Replenishment
Relax assumption of receiving all orders at one time
Order quantity received gradually
Inventory is used up at the same time
Maximum inventory < Q
Average inventory level  Q/2
Production quantity Q
Demand during production interval
Imax
On-hand inventory
Maximum inventory
p – d
Time
Production and demand
Demand only
TBO
Figure E.1

26. Special Inventory Model Noninstantaneous Replenishment
Imax = (p – d) = Q( ) Q p
p – d
C = (H) (S)
Imax 2 D Q
C = ( ) (S) D Q
Q p – d p
ELS = p
p – d
2DS H

27. Noninstantaneous Replenishment Ex 3: Cheese Maker
The Wood Valley Dairy makes cheese to supply to stores in its area. The dairy can make 250 lbs of cheese per day, and the demand at area stores is 180 lbs per day. Each time the dairy makes cheeses, it costs $125 to set up the production process. The annual cost of carrying a pound of cheese is $12.
Determine the followings:
The optimal order size and the minimum total annual inventory cost
Length of time to receive an order, production run
Number of orders per year
Maximum inventory level

28. Special Inventory Model Quantity Discount
Price discount for higher quantity orders
Include the purchase price in EOQ model
P = Unit price of item
TC = ($10 )
TC (d1 = $8 )
TC (d2 = $6 )
Inventory cost ($)
Carrying cost
Ordering cost
Q(d1 ) = 100
Qopt
Q(d2 ) = 200

29. Quantity Discount Ex 4: Sweatshirt in bookstore
The UW bookstore purchases sweatshirts with school logo from a vendor. The vendor sells the sweatshirts to the store for $38 a piece. The cost to bookstore for placing an order is $120, and the annual carrying cost is 25% of the cost of sweatshirt sweatshirts are estimated to be sold during the year. The vendor has offered the bookstore the following volume discount:
What is an optimal order quantity?
Order Size
Discount
1-299
800 and up 0% 2% 4% 5%