مدل مقدار تولید اقتصادی فازی مبتنی بر ساختار هزینه واحد

The purpose of this paper is to investigate and propose a fuzzy extended economic production quantity model based on an elaboratively modeled unit cost structure. This unit cost structure consists of the various lot-size correlative components such as on-line setups, off-line setups, initial production defectives, direct material, labor, and depreciation in addition to lot-size non-correlative items. Thus, the unit cost is correlatively modeled to the production quantity. Therefore, the modeling or the annual total cost function developed consists of not only annual inventory and setup costs but also production cost. Moreover, via the concept of fuzzy blurred optimal argument and the vertex method of the αα-cut fuzzy arithmetic (or fuzzy interval analysis), two solution approaches are proposed: (1) a fuzzy EPQ and (2) a compromised crisp EPQ in the fuzzy sense. An optimization procedure, which can simultaneously determine the αα-cut-vertex combination of fuzzy parameters and the optimizing decision variable value, is also proposed. The sensitivity model for the fuzzy total cost and thus EPQ to the various cost factors is provided. Finally, a numerical example with the original data collected from a firm demonstrates the usefulness of the new model.

The economic production/order quantity (EPQ/EOQ) model was first introduced in the earlier decades of the last century. Since then, it is widely accepted by many industries [1] and today many different variations have been solved (e.g., see [2] and [3]). More recently, to cope with the uncertainty or fluctuation problems in the human subjectively originated data, fuzzy EPQ/EOQ models have been proposed using fuzzy set theory. In the treatment of fuzzy EPQ/EOQ models, two directions exist: (1) The total cost function is viewed as a crisp mapping from some fuzzy variable (production quantity) and thus yields fuzzy expressions [4] and [5]. In other words, the fuzziness originates only with the lot size; (2) The mapping itself is fuzzy with fuzzy parameters (e.g. [6], [7] and [8]) and thus blurs the image of some crisp argument (e.g., production quantity). In the second direction, most models have focused only on the directly defuzzified version of the fuzzy total cost function to obtain a compromised crisp EPQ/EOQ. This approach ignores the fact that in a fuzzy environment, the decision of EPQ/EOQ is also blurred. Vujosevic et al. [7] considered four approaches to solving the fuzzy EOQ, two of which involved true minimization of fuzzy total cost. Yet, one of them apparently is a directly fuzzified version of the conventional crisp EOQ formula rather than being derived from the fuzzy total cost function. Therefore, there exists a fuzzy mathematical error (Appendix A). In this paper, by using the concept of fuzzy blurred optimal argument on a nonfuzzy domain and the vertex method of αα-cut fuzzy arithmetic (or fuzzy interval analysis), a newly devised and extended EPQ model is proposed. Furthermore, a new algorithm and a corrective algorithm for the case where local extrema in the fuzzy EPQ exists that enable us to simultaneously obtain the combination of αα-cut vertices of the fuzzy parameters and production quantity are also proposed.

This paper presented a newly extended fuzzy EPQ model by using the concept of fuzzy set theory and an elaborately modeled unit cost structure. The unit cost structure consisted of various cost components. Furthermore, through the concept of fuzzy blurred optimal argument on a nonfuzzy domain and the vertex method of the αα-cut fuzzy arithmetic, two solution approaches were proposed: (1) the fuzzy EPQ and (2) a compromised crisp EPQ in the fuzzy sense, along with two newly proposed algorithms. Moreover, the sensitivity model for the fuzzy total cost and thus EPQ to the various cost items was provided. It has been demonstrated that this new model with the elaborated unit cost structure can be effective and adaptive for solving the economic production quantity problems.