Page 439 -

ECONOMIC PRODUCTION LOT SIZE MODEL 419

The average inventory, which is one-half the maximum inventory, is given by:

1 d
Average inventory ¼ 1 Q (10:11)
2 p

With an annual per unit holding cost of C h , the general equation for annual holding
cost is as follows:

0 1
Annual
Annual Average B C
¼ @ cost A
holding cost inventory
per unit (10:12)

1 d
¼ 1 QC h
2 p

If D is the annual demand for the product and C o is the setup cost for a
production run, then the annual setup cost, which takes the place of the annual
ordering cost in the EOQ model, is as follows:

Number of production Setup cost
Annual setup cost ¼
runs per year per run
(10:13)
D
¼ C o
Q
So, the total annual cost (TC) model is:

1 d D
TC ¼ 1 QC h þ C o (10:14)
2 p Q

Suppose that a production facility operates 250 days per year. Then we can write
daily demand d in terms of annual demand D as follows:
D
d ¼
250
Now let P denote the annual production for the product if the product were
produced every day. Then:
P
P ¼ 250p and p ¼
250
Thus 4
d D=250 D
¼ ¼
p P=250 P

4
The ratio d/p ¼ D/P holds regardless of the number of days of operation; 250 days is used here merely as an
illustration.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.