Operations Management: William J. Stevenson

11-1 Inventory Management
Operations Management
William J. Stevenson
8th edition
CHAPTER
11
Inventory
Management
Operations Management, Eighth Edition, by William J. Stevenson

McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
Economic Order Quantity Models
 Economic order quantity model

 Economic production model
 Quantity discount model
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
The Inventory Cycle

Figure 11.2
Profile of Inventory Level Over Time

Q Usage
Quantity rate
on hand
Reorder
point
Time
Receive Place Receive Place Receive
order order order order order
Lead time
Total Cost
TC= Total annual cost

Q= Order quantity in units
H= Holding cost per unit
D= Annual Demand
S= Ordering cost
Annual Annual
Total cost = carrying + ordering
cost cost
Q + DS
TC = H
2 Q
Cost Minimization Goal

Figure 11.4C
The Total-Cost Curve is U-Shaped

Q D
TC  H  S
Annual Cost
2 Q
Ordering Costs
Order Quantity
QO (optimal order quantity)
(Q)
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.
2DS 2(Annual Demand)(Order or Setup Cost)
Q OPT = =
H Annual Holding Cost
D
Annual ordering cos t  S
Q
Length of order cycle  Q / D
No. of orders per year  D / Q
QOPT= Optimum order quantity

Q= Order quantity in units
D= Annual Demand
S= Ordering cost
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? Q OPT = 2DS  2(9600)75  300 tires
H 16
 b) No. Of orders per year=D/Q=9600/300=32
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
=2400+2400
=$ 4800
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
Economic Run (Batch) Size

2 DS p
Qp 
H p u
I 
TC min  Carrying Cost  Setup Cost   max H   D / Q S
 2 
Qp
I max  Maximum inventory  ( p  u)
p
Qp
Cycle time 
u
Qp
Run time 
p
Qp= Optimum production quantity

D= Annual Demand
S= Setup cost
P= Production or delivery rate
U= Usage rate
Economic Run (Batch) Size Example
A toy manufacturer uses 48000 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= 48000 S=$45 H=$1 per year p=800 wheels per day u= 48000 wheels
per 240 days or 200 wheels per day.
a)Optimal run size
2 DS p 2(48000)45 800
Qp    2400wheels
H p u 1 800  200
b) Minimum total annual cost
Qp 2400
I max  ( p  u)  (800  200)  1800 wheels
p 800
I  D  1800   4800 
TC min   max  H  
 
 S   1    45  $1800
 2  Q  2   2400 
Economic Run (Batch) Size Example
D= 48000 S=$45 H=$1 per year p=800 wheels per day u= 48000 wheels
per 240 days or 200 wheels per day.
c) Qp
Cycle time   2400 wheels / 200wheels per day
u
Thus, a run of wheels will be made every 12 days.
d)
Qp
Run time   2400 wheels / 800wheels per day  3days
p
Thus, each run will require three days to complete.

Operations Management: William J. Stevenson

Uploaded by

Copyright:

Available Formats

Operations Management: William J. Stevenson

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Operations Management: William J. Stevenson

Uploaded by

Copyright:

Available Formats

11-1 Inventory Management

Operations Management, Eighth Edition, by William J. Stevenson

Economic Order Quantity Models

 Economic order quantity model

Assumptions of EOQ Model

 Only one product is involved

The Inventory Cycle

Profile of Inventory Level Over Time

TC= Total annual cost

Cost Minimization Goal

The Total-Cost Curve is U-Shaped

Deriving the EOQ

Using calculus, we take the derivative of the total cost function

QOPT= Optimum order quantity

EOQ MODEL EXAMPLE

EOQ MODEL EXAMPLE

=1/32 of a year*288 =9 work days.

Economic Production Quantity Assumptions

 Only one item is involved

 Usage rate is constant

 Usage occurs continually

 Production rate is constant

 Lead time does not vary

Economic Run (Batch) Size

Qp= Optimum production quantity

Economic Run (Batch) Size Example

Economic Run (Batch) Size Example

You might also like