Hierarchical Production Controls for a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality

STOCHASTIC ANALYSIS, CONTROL, OPTIMIZATION AND APPLICATIONS: A VOLUME IN HONOR OF W.H. FLEMING, W. M. McEneaney, G. Yin, Q. Zhang, eds., Birkhäuser, 1999

17 Pages Posted: 27 Apr 2008

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Hanqin Zhang

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Abstract

This paper presents an extension of earlier research on hierarchical control of stochastic manufacturing systems with long-run average cost in which a positive inventory deterioration/cancellation rate for each product is assumed. Here we drop the assumption of the positive inventory deterioration/cancellation rate for each product, and give an asymptotic analysis of the manufacturing systems as the rates of change of the machine states approach infinity. We obtain a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. We use a near optimal control of the limiting problem to construct nearly asymptotically optimal open-loop piecewise deterministic controls for the original problem.

Keywords: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Dynamic Programming, Asymptotic Optimality, Open-Loop Controls, Open-Loop Controls, Viscosity Solution

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Hanqin, Hierarchical Production Controls for a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality. STOCHASTIC ANALYSIS, CONTROL, OPTIMIZATION AND APPLICATIONS: A VOLUME IN HONOR OF W.H. FLEMING, W. M. McEneaney, G. Yin, Q. Zhang, eds., Birkhäuser, 1999. Available at SSRN: https://ssrn.com/abstract=1124710

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

Hanqin Zhang

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing, Beijing 100080
China

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