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. 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 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.