Hierarchical control approach to a composite inventory-marketing problem

A composite inventory-marketing problem is considered and treated for the case where there exist distributed time delays in the supply and/or the advertisement process, as well as product losses at constant rates. Since in a real large-scale situation a centralized solution may be impractical, two hierarchical coordinated control algorithms are presented which are based on a proper decomposition of the overall problem. Backlogging is not permitted and the delays are assumed fixed and known. The first algorithm makes use of the dual optimization technique, whereas the second algorithm is based on a decentralized procedure which allows each of the company's departments to solve its problem individually, and then with the coordination of an upper level to obtain the overall solution. Numerical examples are included which illustrate the effectiveness of the two algorithms.

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