international journal of production economics ELSEVIER Int. J. Production Economics 45 (1996) 499-504 EOQ formula when inventory cost is fuzzy Mirko VujoBevi?*, Dobrila Petrovika, Radivoj Petrovikb zyxwvutsrqponmlkjihgfe aMihajlo Pupin Institute, Volgina 15, 11000 Belgrade, Yugoslavia bFaculty of TrafJic and Transport Engineering, Vojvode Stepe 305, 11000 Belgrade, Yugoslavia Abstract Various types of uncertainties and imprecision are inherent in real inventory problems. They are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment and how to interpret optimal solutions arise. This paper considers the modification of EOQ formula in the presence of imprecisely estimated parameters. For example, holding and ordering costs are often not precisely known and are usually expressed by linguistic terms such as: “Holding cost is approximately of value c:, or: “Ordering cost is about value c, or more”. These imprecise parameters are presented by fuzzy numbers, defined on a bounded interval on the axis of real numbers. Alternative approaches to determining the optimal order quantity in a fuzzy environment are developed, illustrated by a selection of examples, and discussed. Keywords: EOQ; Uncertainty; Imprecision; Fuzzy number; Fuzzy arithmetic 1. Introduction Classical inventory model assumes the ideal situ- ation which is characterized by a deterministic con- tinuous demand and zero lead time. This is illus- where N is the annual demand in units, cP the purchase cost of an item, c, the ordering cost per order, ch the holding cost as a percentage of the average inventory value, and Q the order quantity in units. trated by Fig. 1. The size of an order Q which minimizes the total inventory cost is known as the The EOQ which minimizes C in (1) is economic order quantity EOQ. If stockouts are not 200~~ N permitted, the total inventory cost is as follows: Q*= p. J-- (2) zyxwvut ChCp ‘VpQ C=Nc,+y+-, 2.100 *Corresponding author. (1) An interesting real problem when human orig- inated data like holding cost and ordering cost are not precisely known but subjectively estimated or linguistically expressed is examined in this paper. In Section 2 the formulation of the problem when the imprecision of costs is described by fuzzy numbers 0925-5273/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved SSDI 0925-5273(95)00149-2