The application of hierarchical control methods to a managerial problem

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Abstract
In this paper the multiproduct inventory holding problem is considered. Joint constraints between product lines and constraints on individual products are allowed. Total costs of holding inventory and backlogging are minimized using recently developed methods of hierarchical control for such dynamic problems. It is shown that such methods lead to economical and efficient algorithms which can be used for a broad class of cost functions and delays in deliveries present little extra difficulty. An algorithm is described for complex costs and stochastic sales. Simulation studies are presented which validate this algorithm. Such hierarchical methods avoid the difficulties of solving two-point boundary problems required by the discrete maximum principle and can be considerably more economical of computer resources than general non-linear programming techniques. The hierarchical algorithms of Lasdon and Tamura are described in full.

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