The Repairman Problem Revisited

We use a probabilistic model to show that the development of a large number of small production units facing independent risks of failure must be accompanied by an approximately proportional increase in the number of repairmen. We derive the cost function of a machine in working condition, which inc...

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Bibliographic Details
Published in:Annals of economics and statistics 2016-06 (121/122), p.7-24
Main Authors: Crampes, Claude, Renault, Jérôme
Format: Article
Language:English
Subjects:
Constant returns to scale
Cost functions
Economic models
Environmental technology
Failure modes
FEATURE ARTICLES
Heuristics
Industrial production
Machinery
Markov chains
Operating costs
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Summary:We use a probabilistic model to show that the development of a large number of small production units facing independent risks of failure must be accompanied by an approximately proportional increase in the number of repairmen. We derive the cost function of a machine in working condition, which increases with the cost of an installed machine and with the repair cost and failure probability, and decreases with repairman efficiency. We provide a very simple proof and generalize the results of Arrow et al. (1972). We also show that it is redundant to require installers to hire the number of repairmen necessary to reach a fixed availability level for each installed machine. JEL: C61, D24, J3, O33. / KEY WORDS: Failure, Repair, Markov Chain, Hicks-Leontiev Technology.
ISSN:2115-4430
1968-3863
DOI:10.15609/annaeconstat2009.121-122.7