Turnpike Sets in Stochastic Production Planning Problems

Proceedings of the 29th IEEE CDC, Honolulu, HI, Dec. 5-7, 1990, 590-595

Posted: 6 May 2020

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Halil Mete Soner

Koc University - College of Administrative Sciences and Economics

Qing Zhang

Department of Mathematics, University of Georgia

Jiong Jiang

Independent

Date Written: 1990

Abstract

This paper summarizes the results of its detailed version, which considers optimal infinite horizon stochastic production planning problems with capacity and demand to be finite state Markov chains. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is shown that the turnpike set is an attractor set for the optimal trajectories provided that the capacity is assumed to be fixed at a level exceeding the maximum possible demand. Conditions under which the optimal trajectories enter the convex closure of the set in finite time are given. The structure of turnpike sets is described, it is shown that t,he turnpike sets exhibit a monotone property with respect to capacity and demand. It turns out that the monotonicity property helps in solving the optimal production problem numerically, and in some cases, analytically.

Keywords: Turnpike Sets, Stochastic Production

JEL Classification: C61, M11, M20

Suggested Citation

Sethi, Suresh and Soner, Halil Mete and Zhang, Qing and Jiang, Jiong, Turnpike Sets in Stochastic Production Planning Problems (1990). Proceedings of the 29th IEEE CDC, Honolulu, HI, Dec. 5-7, 1990, 590-595, Available at SSRN: https://ssrn.com/abstract=3593802

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

Halil Mete Soner

Koc University - College of Administrative Sciences and Economics ( email )

Rumelifeneri Yolu
Sariyer 80910, Istanbul
Turkey

Qing Zhang

Department of Mathematics, University of Georgia ( email )

Athens, GA 30602-6254
United States

Jiong Jiang

Independent ( email )

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