Multilevel hierarchical controls in dynamic stochastic marketing-production systems

The authors present an asymptotic analysis of hierarchical marketing-production systems with stochastic demand and stochastic production capacity (machines are subject to breakdown and repair). The 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. Situations in which the rate change in machine states is large and/or when the rate of perturbation in demand is small are of interest. 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