Optimal Maintenance Policy and Sale Date of a Machine

A machine is to be bought, used for productive purposes for a length of time, and then sold. It is possible to do preventive maintenance while the machine is being used, if desired, in order to slow down the degradation of the machine's capability. The value of owning the machine is the sum of...

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Bibliographic Details
Published inManagement science Vol. 14; no. 9; pp. 543 - 550
Main Author Thompson, Gerald L
Format Journal Article
LanguageEnglish
Published Hanover, MD., etc INFORMS 01.05.1968
Institute of Management Sciences
Institute for Operations Research and the Management Sciences
SeriesManagement Science
Subjects
Adjoints
Maintenance
Maximum principle
Net profits
Present value
Preventive maintenance
Sales management
Salvage value
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Summary:A machine is to be bought, used for productive purposes for a length of time, and then sold. It is possible to do preventive maintenance while the machine is being used, if desired, in order to slow down the degradation of the machine's capability. The value of owning the machine is the sum of the discounted value of its production while it is owned plus its discounted value when sold. In this paper a modification of a model due to B. Naslund for the problem is discussed. Using Pontryagin's maximum principle, the problem is treated as one of optimal control with the control variables being the use or nonuse of preventive maintenance and the selection of the sale date. It is shown that the optimal maintenance policy is bang-bang, and methods for finding the optimal sale date are determined. Simply examples show the various kinds of solutions that can be obtained with varying assumptions concerning the actual functions used in the model.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.14.9.543