Inventory
Management
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
 Economic order quantity models identify the optimal
order quantity by minimizing the sum of annual costs
that vary with order size and frequency
1.
2.
3.
The basic economic order quantity model (no quantity
discounts).
The economic order quantity model with quantity
discounts
The economic production quantity model
Instructor Slides
13-2
 The batch mode is widely used in production. In certain
instances, the capacity to produce a part exceeds its usage
(demand rate)
 Assumptions
1.
Only one item is involved
2.
Annual demand requirements are known
3.
Usage rate is constant
4.
Usage occurs continually, but production occurs periodically
5.
The production rate is constant
6.
Lead time does not vary
7.
There are no quantity discounts
Instructor Slides
13-3
Q
Production
and usage
Usage
only
Production
and usage
Usage
only
Production
and usage
Qp
Cumulative
production
Imax
Amount
on hand
Time
Run time
Instructor Slides
13-4
TC min  Carrying Cost  Setup Cost
D
I 
  max  H  S
Q
 2 
where
I max  Maximum inventory

Qp
 p  u
p
p  Production or delivery rate
u  Usage rate
Instructor Slides
13-5
2 DS
Qp 
H
Instructor Slides
p
p u
13-6
Lunch rush time is the busiest time for the restaurant. Rush
hour last for 2 hours. You need to keep the pizza buffet line
supplied with pizzas to keep your customer satisfaction rating
high. Assume your ovens have a capacity of 50 pizzas/hour and
can hold up to 100 pizzas . At peak time your customers will
consume on the average about 40 pizzas/hour. Setup costs
consist of the cost of pre-heating the oven. Setup cost is
estimated at $10 per day. Inventory carrying costs for cooked
pizzas are estimated at $0.50 per pizza/day. Calculate the
following: a) Economic production quantity, b) Maximum
inventory, c) Cycle Time (i.e. the length of time between runs),
d) Length of the pizza run, e) Total cost of baking pizza during
rush hour.
Instructor Slides
7
Q
Production
and usage
Usage
only
Production
and usage
Usage
only
Production
and usage
Qp
Cumulative
production
Imax
Amount
on hand
Time
MAKE + EAT EAT
PIZZAS
Instructor Slides
PIZZAS
ONLY
13-8
D = 2 hr. X 40 pizza/hr. = 80 pizzas
S = $10.00 per setup H = $0.50 p= 50 pizzas/hr,
u = 40 pizzas/hr.
6a. Calculate the EPQ
2 DS
Qp 
H
p
p u
2(80)(10)
50
Qp 
0.50
50  40
EPQ = 127 pizzas
Instructor Slides
9
6b. Calculate the maximum inventory level.
I max  Maximum inventory

Qp
p
 p  u
= (127/50 X (50-40)
= 25.2 or 26 pizzas
Instructor Slides
10
6c. Cycle Time (i.e. the length of time between runs)
Cycle Time = EPQ/u
= 127/40 = 3.2 hours
Instructor Slides
11
6d. Calculate the run time
Run time = EPQ/p
= 127/50
= 2.5 hrs.
Instructor Slides
12
6e. Calculate the Total Cost of Producing and Carrying
Inventory
TC min  Carrying Cost  Setup Cost
D
 I max 

H  S
Q
 2 
80
 26 
   0 .5 
10
127
 2 
Instructor Slides
= $12.79
13