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The Repairman Problem Revisited

Author

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  • Claude Crampes
  • Jérôme Renault

Abstract

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

Suggested Citation

  • Claude Crampes & Jérôme Renault, 2016. "The Repairman Problem Revisited," Annals of Economics and Statistics, GENES, issue 121-122, pages 7-24.
  • Handle: RePEc:adr:anecst:y:2016:i:121-122:p:7-24
    DOI: 10.15609/annaeconstat2009.121-122.7
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    File URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.121-122.7
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    More about this item

    Keywords

    Failure; Repair; Markov Chain; Hicks-Leontiev Technology.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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