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Optimal Contract for Machine Repair and Maintenance

Author

Listed:
  • Feng Tian

    (Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

  • Peng Sun

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Izak Duenyas

    (Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

A principal hires an agent to repair a machine when it is down and maintain it when it is up and earns a revenue flow when the machine is up. Both the up- and downtimes follow exponential distributions. If the agent exerts effort, the downtime is shortened, and uptime is prolonged. Effort, however, is costly to the agent and unobservable to the principal. We study optimal dynamic contracts that always induce the agent to exert effort while maximizing the principal’s profits. We formulate the contract design problem as a stochastic optimal control model with incentive constraints in continuous time over an infinite horizon. Although we consider the contract space that allows payments and potential contract termination time to take general forms, the optimal contracts demonstrate simple and intuitive structures, making them easy to describe and implement in practice.

Suggested Citation

  • Feng Tian & Peng Sun & Izak Duenyas, 2021. "Optimal Contract for Machine Repair and Maintenance," Operations Research, INFORMS, vol. 69(3), pages 916-949, May.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:3:p:916-949
    DOI: 10.1287/opre.2020.2018
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    References listed on IDEAS

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