Equivalent Formulations of Inventory Control Problems

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Abstract
A general multi-item periodic-review inventory control problem is formulated in several ways, each reflecting a different point of view of the decision maker. These formulations are evaluated with respect to implementation criteria of: (i) technical difficulty in obtaining an optimal solution from the model, (ii) estimation effort required to find the values of the parameters in the model, (iii) effort needed to maintain the model continuously updated during the inventory management process. The most promising one is then compared with the conventional formulation, where the objective function is expressed as the sum of expected inventory holding and shortage costs. It is shown that both formulations lead to the same optimal solution under a certain budgetary constraint. This result offers an instrument for implementation improvements in inventory control systems.