الفهرس 
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Abstract
Most real world inventory systems stock many items, and not merely a single item. as a matter of fact it could be permissible 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 substituation 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 other study them under two constraints using lagrangian approach, algorithmic or heuristic approaches, but in fact they got only numerical 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 who studied an EOQ inventory model with demand-dependent unit cost without constraints and he got a closed form solution. In this extension we add duffin and peterson theorem of geometric programming that enables us to evaluate the optimal t and q explicity. the geometric programming techniqes change the primal programming problem that minimizes the total annual cost into a dual programmimg problem that maximizes an objective function called the posynomial function formed of the product of the terms of both the total annual cost and the constraints bounded by unity. this function depends on the relation between both the arithmetic and the geometric means. in fact this is an easier and much better approach compared with all other familiar approaches.