Fuzzy EOQ model using possibilistic approach

Purpose – The purpose of this paper is to derive an economic order quantity (EOQ) for an inventory control problem where the inventory carrying cost and the order cost are uncertain, represented by fuzzy numbers. The fuzzy numbers used herein are most general so far, represented by adaptive trapezoidal fuzzy numbers. This paper attempts to use the most general form of fuzziness to represent the uncertainty of the parameters in the inventory model. Design/methodology/approach – The fuzzy EOQ formula derivation is analytical. Given the inventory cost C c and the order cost C o as fuzzy numbers and the demand, a crisp number and instant replenishment of inventory, a fuzzy EOQ is derived. This is done by using the possibilistic mean and the possibilistic variance of the fuzzy total inventory cost. Then for practical implementation, this quantity is defuzzyfied using the middle of the maxima (MOM) of the fuzzy EOQ, in order to get the crisp value of the EOQ that minimizes the (fuzzy) total inventory cost. Findings – The fuzzy EOQ model derived herein is the most general fuzzy model. It is then converted to a crisp optimal order quantity and a crisp order cycle. The model assumptions cover the uncertainties in estimating the order cost and the inventory carrying cost. However, the results that can be extended in case of the shortage in inventory stock are allowed. Practical implications – Inventories by their nature are the basic part of consideration in any production, supply chain, warehousing and retail policies. The inventories consume a large part of budget, space, overheads and maintenance. Even though the problem considered in this paper is limited to single period and single item inventories, it can be extended to multiple items and multi‐period inventories. The paper gives an illustrative example and its solution at the end. Originality/value – EOQ is the most fundamental concept in making inventory policies. However, in inventory literature, covering the risk of uncertainty in the various cost estimations such as carrying and order or shortage costs, is more recent and is not well developed.