In this paper, a multi-item inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demand-dependent and holding and set-up costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. | Yugoslav Journal of Operations Research 16 (2006), Number 1, 55-66 MULTI-ITEM FUZZY INVENTORY PROBLEM WITH SPACE CONSTRAINT VIA GEOMETRIC PROGRAMMING METHOD Nirmal Kumar MANDAL Department of Mathematics, Silda Chandrasekhar College, Silda, Paschim Medinipu-721515, West Bengal, India Tapan Kumar ROY Department of Mathematics, Bengal Engineering and Science University, Howrah-711103, West Bengal, India Manoranjan MAITI Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India Received: July 2003 / Accepted: May 2005 Abstract: In this paper, a multi-item inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demand-dependent and holding and set-up costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. The problem is then solved using modified geometric programming method. Sensitivity analysis is also presented here. Keywords: Inventory, fuzzy programming, and modified geometric programming. 1. INTRODUCTION In many inventory problems, the unit price and selling price of a product are considered as independent in nature. But when the demand of a product is very high, then to meet the demand, the production is increased. Therefore the total cost of manufacturing is then spread over a large number of items and this will result lower 56 . Mandal, . Roy, M. Maiti / Multi-Item Fuzzy Inventory Problem average unit production cost as well as lower selling price for an item. Hence the unit production cost and selling price are assumed inversely related to the demand of the item. Cheng [3, 4] developed some inventory models .
