www.tjprc.org editor@tjprc.org MULTI-ITEM MULTI-OBJECTIVE INVENTORY MODEL WITH POSSIBLE CONSTRAINTS UNDER FUZZY ENVIRONMENT P. D. PATEL 1 , A. S. GOR 2 & PRAVIN BHATHAWALA 3 1 Lecturer, Department of Mathematics, Government Polytechnic Palanpur, Gujarat, India 2 Director, School of IT, AURO University Surat, Gujarat, India 3 Principal, Pramukh Swami Science & H D Patel Arts College Kadi, Gujarat, India ABSTRACT In this paper a multi item multi objective inventory model with three constraints; warehouse space, investment amount and the percentage of utilization of volume of the ware house space are taken to formulate the problem where the unit cost parameter which is depend upon the demand is imposed in fuzzy environment. Warehouse maintenance is one of the crucial parts of service operation. The warehouse space in the selling stores plays an important role in stoking the goods. In the proposed model, the warehouse space in the selling store is considered in volume. The model is illustrated with numerical example. KEYWORDS: Multi-Objective Inventory Model, Triangular Fuzzy Number, Membership Function, Volume of the Warehouse I. INTRODUCTION The exact meaning of inventory is the stock of goods for future use (production/sales). The control of inventories of physical goods is a trouble common to all enterprises in any sector of an economy. In any industry, the inventories are important but they mean lockup of capital. The excess inventories are unwanted, which calls for controlling the inventories in the most beneficial way. The different types of costs (Purchasing cost, Setup cost, Holding cost, etc.) involved in inventory problems are affect the efficiency of an of an inventory control problem. Warehouse space available in the selling store plays an essential role in inventory model. Warehouse space can be measured in terms of area and / or volume, but most of the researchers think about only the area of the warehouse space. Here the warehouse space in the selling store is measured in volume. Silver [4] considered the classical inventory problem which was designed by considering that the demand rate of an item is constant and deterministic and the unit price of an item is measured to be constant and independent in nature. But in realistic situation, unit price and demand rate of an item may be related to each other. When the demand of an item is high, an item is produced in big numbers and fixed costs of production are spread over a big number of items. Hence the unit cost of the item decreases. i.e., 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 variable. Zadeh [6] first gave the concept of fuzzy set theory to solve decision making problem. Tanaka [5] introduced objectives as fuzzy goals over the α-cut of a fuzzy constraints set. Zimmerman [1] gave the concept to solve multi objective linear programming problem. Now the fuzzy set theory has made an entry into the inventory control systems. International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN(P 2249-6955; ISSN(E): 2249-8060 Vol. 5, Issue 1, Feb 2015, 7-12 TJPRC Pvt. Ltd.