1. Operations Management
William J. Stevenson
8th edition

2. 11 Inventory Management CHAPTER
Operations Management, Eighth Edition, by William J. Stevenson
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

3. Economic Order Quantity Models
Economic production model
Quantity discount model

4. Assumptions of EOQ Model
Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

5. Profile of Inventory Level Over Time
The Inventory Cycle
Figure 11.2
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time

6. Total Cost Annual carrying cost ordering Total cost = + Q 2 H D S TC =
TC= Total annual cost
Q= Order quantity in units
H= Holding cost per unit
D= Annual Demand
S= Ordering cost
Annual
carrying
cost
ordering
Total cost = + Q 2 H D S
TC =

7. Cost Minimization Goal
Figure 11.4C
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q) QO
(optimal order quantity)

8. Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal.
QOPT= Optimum order quantity
Q= Order quantity in units
H= Holding cost per unit
D= Annual Demand
S= Ordering cost

9. EOQ MODEL EXAMPLE
A local distributor for a national tire company expects to sell approximately 9600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year.
D= $ 9600 H= $ 16 S= $ 75
a) What is the EOQ?
b) No. Of orders per year=D/Q=9600/300=32

10. EOQ MODEL EXAMPLE D= $ 9600 H= $ 16 S= $ 75
c) Length of order cycle= Q/D= 300/9600
=1/32 of a year*288 =9 work days.
d) Total Cost=Carrying cost+Ordering cost
=(Q/2)H+(D/Q)S
=(300/2)16+(9600/300)75 =
=$ 4800

11. Economic Production Quantity Assumptions
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts

12. Economic Run (Batch) Size
Qp= Optimum production quantity
H= Holding cost per unit
D= Annual Demand
S= Setup cost
P= Production or delivery rate
U= Usage rate

13. Economic Run (Batch) Size Example
A toy manufacturer uses rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $ $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year.
D= S=$45 H=$1 per year p=800 wheels per day u= wheels per 240 days or 200 wheels per day.
Optimal run size
Minimum total annual cost

14. Economic Run (Batch) Size Example
D= S=$45 H=$1 per year p=800 wheels per day u= wheels per 240 days or 200 wheels per day. c)
Thus, a run of wheels will be made every 12 days. d)
Thus, each run will require three days to complete.