Multilevel Hierarchical Controls in Dynamic Stochastic Marketing-Production Systems

Proceedings of the 3lst IEEE-CDC, Tucson, Arizona, Dec. 16-18, 1992, 2090-2095

Posted: 6 May 2020

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

Department of Mathematics, University of Georgia

Date Written: 1992

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

Suggested Citation

Sethi, Suresh and Zhang, Qing, Multilevel Hierarchical Controls in Dynamic Stochastic Marketing-Production Systems (1992). Proceedings of the 3lst IEEE-CDC, Tucson, Arizona, Dec. 16-18, 1992, 2090-2095, Available at SSRN: https://ssrn.com/abstract=3590789

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Qing Zhang

Department of Mathematics, University of Georgia ( email )

Athens, GA 30602-6254
United States

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