Integrating Equipment Investment Strategy with Maintenance Operations under Uncertain Failures

47 Pages Posted: 16 Apr 2009 Last revised: 17 Oct 2011

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management; Hong Kong Polytechnic University - Faculty of Business; Ajou University

Qi Feng

Purdue University - Krannert School of Management

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: April 2009

Abstract

This paper studies the issue of coordinating equipment maintenance operations with capital investment strategy in the presence of random equipment failures. This problem represents an important extension of the celebrated Kamien and Schwartz (KS) paper published in Management Science. The traditional KS approach is to formulate the problem as a deterministic optimal control problem with the probability of machine failure as the state variable. Consequently, a deterministic policy is derived. As a major departure from the KS approach, we explicitly model the underlying stochastic process of machine failures. Our analysis of the stochastic dynamic programming model offers new insights into the problem. Under a long planning horizon with a limited replacement opportunity, each individual machine serves as a revenue generator and contributes a significant amount to the profit of the system. On the other hand, when the replacement budget is quite generous in a relatively short planning horizon, adding one extra machine only helps as a backup for unexpected failures of the machines purchased before it. An interesting result derived from this comparison is that a deterministic policy turns out to be optimal for the former, while a state-contingent policy must be applied to the latter. In other words, the deterministic KS approach does not work when a chain of machine replacement is considered. We further discuss the implications of the discount rate, productivity deterioration, learning, decision delay, and technology advancement on the optimal policy.

Keywords: Maintenance and replacement, optimal control, impulse control, equipment investment; stopping time; variational inequality, reliability, hazard rate, the Kamien-Schwartz model, dynamic programming, chain of machines model

JEL Classification: M1, M2, C61, D24

Suggested Citation

Bensoussan, Alain and Feng, Qi and Sethi, Suresh, Integrating Equipment Investment Strategy with Maintenance Operations under Uncertain Failures (April 2009). McCombs Research Paper Series No. IROM-12-09, Available at SSRN: https://ssrn.com/abstract=1384762

Alain Bensoussan

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

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Hong Kong Polytechnic University - Faculty of Business

Dept SEEM
Systems Engr * Engr Mgmt
Hong Kong, Hong Kong
China

Ajou University ( email )

Ajou
France

Qi Feng

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

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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