Abstract
This paper presents an asymptotic analysis of hierarchical marketing-production systems with stochastic demand and stochastic production capacity modelled as finite state Markov processes. The decision variables used are advertising and production rates which influence capacity, demand, and inventory levels. The objective of this paper is to maximize the expected total discounted profit over an infinite horizon. The authors are interested in situations in which the rate of change in capacity states is an order of magnitude different from the rate of change in demand states. These give rise to upper-level problems in which the stochastic capacity is replaced by the average capacity and/or the random demand is replaced by the average demand. Controls for the corresponding lower-level problems in different cases can be constructed from nearly optimal controls of the upper-level problems in a way that guarantees their asymptotic optimality.
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