On the optimality of a general integrated production inventory system with time varying demand, production and deterioration rates
نویسندگان
چکیده
Typical models of the production inventory systems assume that lot sizes of raw materials and final products are treated separately which leads to suboptimization production process. In this paper, a unified inventory model of an integrated production inventory system, where each of production, demand and deterioration rates are general functions of time, is considered. Shortage for the final product is allowed but it is partially backordered. The objective is to find an optimal production schedule that yields a minimum total cost of this integrated system. We develop an exact formula for the total inventory cost per unit of time. Then, we use rigorous mathematical methods to find the optimal solution of the underlying integrated system and to show that this solution is unique and global optimal.
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