Multilevel Hierarchical Decision Making in Stochastic Marketing-Production Systems

SIAM Journal on Control and Optimization, Vol. 33, No. 2, pp. 528-553, 1995

26 Pages Posted: 26 Feb 2008 Last revised: 25 May 2017

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

University of Georgia - Department of Mathematics

Abstract

This paper presents an asymptotic analysis of hierarchical marketing-production systems with stochastic demand and stochastic production capacity modelled as finite state Markov processes. The decision variables used are advertising and production rates which influence capacity, demand, and inventory levels. The objective of this paper is to maximize the expected total discounted profit over an infinite horizon. The authors are interested in situations in which the rate of change in capacity states is an order of magnitude different from the rate of change in demand states. These give rise to upper-level problems in which the stochastic capacity is replaced by the average capacity and/or the random demand is replaced by the average demand. Controls for the corresponding lower-level problems in different cases can be constructed from nearly optimal controls of the upper-level problems in a way that guarantees their asymptotic optimality.

Keywords: stochastic manufacturing systems, marketing-production planning, hierarchical control, Markov processes, dynamic programming, viscosity solutions

JEL Classification: C61, M11, M, M37

Suggested Citation

Sethi, Suresh and Zhang, Qing, Multilevel Hierarchical Decision Making in Stochastic Marketing-Production Systems. SIAM Journal on Control and Optimization, Vol. 33, No. 2, pp. 528-553, 1995 . Available at SSRN: https://ssrn.com/abstract=1097462

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

University of Georgia - Department of Mathematics ( email )

Athens, GA 30602
United States
(706) 542-2616 (Phone)
(706) 542-2573 (Fax)

HOME PAGE: http://www.math.uga.edu/~qingz/

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