06-11-2012, 05:46 PM
A note on JIT purchasing vs. EOQ with a price discount: An expansion of inventory costs
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Abstract
In a previous International Journal of Production Economics article, a comparative model was presented for
inventory costs of purchasing under economic order quantity (EOQ) with quantity discounts and a just-in-time (JIT)
order purchasing system. This paper expands the comparative model to include a relevant cost component not
considered in the previous article. The results of the revised model show di!erences in the conclusions reached in the
previous article, more speci"cally, the superiority of JIT in virtually any type of inventory ordering purchase decision.
( 2000 Elsevier Science B.V. All rights reserved.
Introduction
In Fazel et al. [1], a comparative cost function
was presented that proposed to show where inventory
ordering under an economic order quantity
(EOQ) system or a just-in-time (JIT) system would
be the most cost e!ective. They proposed a total
cost di!erence function.
The revised model
We agree with Fazel et al. [1] that Eqs. (2)}(5)
represent the classic `quantity discount modela
from the family of EOQ models originally proposed
by Harris [3]. This same basic model is
found in virtually every inventory management
textbook. Yet, it should be noted that the quantity
discount model gives the EOQ system the advantage
of a price break that is not available to the JIT
system. No equally obvious cost advantage was
given to the JIT cost function when, in practice, one
very obvious cost advantage does exist for a JIT
system. This cost advantage is the facility size reduction
that occurs in the inventory storage and
production areas as a result of adopting a JIT
system.
Past and present research on JIT system has
clearly documented the inevitable reduction in
facility square feet. The reduction in facility square
footage is caused by the elimination of the space
required to store incoming inventory, work-in-process
inventory, and "nished-goods inventory.
Discussion and results
To illustrate the di!erence between the original
results of Fazel et al. [1] and when using Eqs. (9)
and (10), we revisited their example problem. In
that problem the annual demand was allowed to
vary, to examine the impact on the total costdi
!erence function. The JIT purchasing cost per
unit was $50.50, the EOQ purchasing cost was $50
per unit, but decreased by $0.0004 per unit up to
a maximum order quantity of 2500 units. Cost per
unit for order quantities beyond 2500 units was
"xed at $49 per unit. The annual holding cost per
unit was $15 and the ordering cost per order was
$60.
Summary and conclusions
In this paper, a previous mathematical model
was expanded to more fairly represent the realistic
JIT cost environment that manufacturers face when
implementing a JIT order purchasing system. This
addition involved the consideration of the cost savings
caused by the reduced square footage in facilities
that adopt a JIT ordering system. This study
"nds that by including the reduced square footage
cost-advantage to the JIT side of the comparison
model, a JIT system is preferable to an EOQsystem
for manufacturers whose annual demand is at fairly
low levels. The results of the example problem have
also shown that the cost indi!erence point between
the two systems occurs at a demand level so substantially
large that it would also always require
a substantial additional cost in plant facilities. Such
an additional cost would again result in a favoring
of the JIT system.