CONSTRAINED MULTI-ITEM­ INVENTORY MODELS I GEOMETRIC PROGRAMMING I APPROACH

Abstract

Most real world Inventory systems stock many items, and not merely a single item. As. a matter of fact it could be pennissible to study ; each item individually as long as there is no interaction among these . different items. But really there could be many sorts of interactions between the items such as in the case of partial substitutions of one kind of items to other kinds as in case of manufacturing cars.

Many researchers have studied constrained multi-item inventory models under one constraint while others study them tmder two constraints using lagrangian approach, algorithtnic or heuristic approaches, but in fact they got only munerical results. The main objective of this thesis is to achieve an explicit theoretical results by extending of the geometric programming approach due to the pioneering work of Cheng [4] who studied an EOQ inventory model with demand-dependent unit cost without constraints and he got a closed form solution. In tllis extension we add

Duffin and Peterson theorem of geometric programming that enables us to evaluate the optimal T;r and Q; explicitly. The geometric programming

technique changes the primal programming problem that minimizes the total annual cost into a dual programming problem that maximizes an objective function called the posynonlial function fanned of the product of the terms of both the total annual cost and the constraints bounded by unity. This fi.mction depends on the relation between botl1 the arithmetic and the geometric means. In fact this is an easier and much better approach compared with all other familiar approaches.