A Sufficient Condition for Near-Optimal Stochastic Controls and its Application to Manufacturing Systems

Applied Mathematics & Optimization Vol. 29, No. 1, pp. 67-92, 1994

26 Pages Posted: 14 Jul 2009 Last revised: 6 May 2017

See all articles by Xun Yu Zhou

Xun Yu Zhou

University of Toronto

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 1994

Abstract

This paper presents an asymptotic analysis of control models governed by stochastic ordinary differential equations. A sufficient condition of near-optimal controls is given based on Ekeland's principle. It is shown that, under some concavity assumptions, the e-maximum condition in terms of the Harniltonian implies the SQRT(epsilon)-optimality. By applying this result to a general manufacturing system, the common practice of "hierarchical controls" employed in order to reduce the overall complexity of the system is justified on a rigorous basis. A near-optimal control for the operational level is constructed from a near-optimal control at the corporate level, and an asymptotic error bound is obtained. A stochastic extension of the classical HMMS model is treated as a specific example. The approach of this paper is different from those in the literature, and it allows us to handle some previously unsolved problems with nonlinear state equations as well as nonseparable cost functions.

Keywords: near-optimal stochastic control, sufficient condition, manufacturing systems, random capacity, hierarchical control, HMMS model

JEL Classification: M11, C61

Suggested Citation

Yu Zhou, Xun and Sethi, Suresh, A Sufficient Condition for Near-Optimal Stochastic Controls and its Application to Manufacturing Systems (1994). Applied Mathematics & Optimization Vol. 29, No. 1, pp. 67-92, 1994, Available at SSRN: https://ssrn.com/abstract=1422055

Xun Yu Zhou

University of Toronto

Toronto, Ontario M5S 3G8
Canada

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

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