TAILIEUCHUNG - Fuzzy economic order quantity model with ranking fuzzy number cost parameters

In this paper, a multi-objective economic order quantity model with shortages and demand dependent unit cost under storage space constraint is formulated. In real life situation, the objective and constraint goals and cost parameters are not precisely defined. These are defined in fuzzy environment. The cost parameters are represented here as triangular shaped fuzzy numbers with different types of left and right branch membership functions. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 247-264 DOI: FUZZY ECONOMIC ORDER QUANTITY MODEL WITH RANKING FUZZY NUMBER COST PARAMETERS Nirmal Kumar MANDAL Department of Mathematics, Silda Chandrasekhar College, Silda, Paschim Medinipur, West Bengal, India, Pin-721515 E-mail: mandal_n_k@ Received: July 2011 / Accepted: May 2012 Abstract: In this paper, a multi-objective economic order quantity model with shortages and demand dependent unit cost under storage space constraint is formulated. In real life situation, the objective and constraint goals and cost parameters are not precisely defined. These are defined in fuzzy environment. The cost parameters are represented here as triangular shaped fuzzy numbers with different types of left and right branch membership functions. The fuzzy numbers are then expressed as ranking fuzzy numbers with best approximation interval. Geometric programming approach is applied to derive the optimal decisions in closed form. The inventory problem without shortages is discussed as a special case of the original problem. A numerical illustration is given to support the problem. Keywords: Inventory, ranking fuzzy number, geometric programming. MSC: 90B05. 1. INTRODUCTION Classical inventory problems are generally formulated by considering that the demand rate of an item is constant and deterministic. The unit price of an item is usually considered to be constant and independent in nature (Hadley and Whitin (1958), Silver and Peterson (1985)). But in practical situation, unit price and demand rate of an item may be related to each other. When the demand of an item is high, items are produced in large numbers and fixed costs of production are spread over a large number of items. Hence the unit cost of the item decreases, . the unit price of an item inversely relates to the demand of that item. So, demand rate of an item may be considered as a decision 248 N. K., Mandal / Fuzzy .

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