Multilevel hierarchical open-loop and feedback controls in stochastic marketing-production systems

This paper presents an asymptotic analysis of hierarchical marketing-production systems with stochastic demand and stochastic production capacity due to machine breakdown and repair. The authors´ 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. The authors are interested in situations in which the rate of change in machine states is large and/or when the rate of perturbations 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. Both open-loop and feedback 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