Multilevel Hierarchical Controls in Dynamic Stochastic Marketing-Production Systems

Abstract

This paper presents an asymptotic analysis of hier­archical marketing-production systems with stochastic demand and stochastic production capacity (machines are subject to bre­akdown and repair). Our control variables are advertising and production rates which influence demand and inventory levels. The objective of the controls is to maximize the expected total profit over a finite horizon. We are interested in situations in which the rate of change in machine states is large and/or when the rate of perturbation in demand is small. These give rise to upper level problems in which the stochastic machine availabi­lity is replaced by the equilibrium mean availability and/or the random demand is replaced by the average demand. Controls for the lower level problems in different cases can be construc­ted from nearly optimal controls of the corresponding upper level problems in a way which guarantees their asymptotic optimality. The error estimates for the constructed asymptotically optimal controls are also obtained.

Keywords: asymptotic analysis, stochastic demand, stochastic production capacity

JEL Classification: C61, M11, M20