Optimal Contract for Machine Repair and Maintenance

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.