On the optimality of multi item integrated production inventory systems with variable parameters

Most of the classical production inventory systems treat the economic order quantities (EOQ) of raw materials, which are used in producing the same final products, separately of the economic production quantities (EPQ) of these products. This may result in sub-optimization of both the (EOQ)'s of raw materials and the (EPQ)'s of final products. But, when raw materials are used in production, the ordering quantities for raw materials are dependent on the economic batch size and the schedule of the final products. By integrating the procurement and production subsystems, the degree of sub-optimality is reduced. In this paper, a unified inventory model of integrated production inventory systems, where each of production, demand and deterioration rates of final products and deterioration rates of raw materials, as well as all cost parameters are general functions of time, is treated. Shortages are allowed only for final products but are partially backordered. All cost components are affected by both inflation and time value of money. The objective is to find an optimal production schedule for each product in any inventory cycle so that the overall total relevant inventory cost for this integrated system is minimized. We develop an exact formula for the total inventory cost per unit of time. Then, we use rigorous mathematical methods to find the optimal stopping and restarting times for each final product of this integrated inventory systems.

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