Optimal Design of Uptime-Guarantee Maintenance Contracts

Abstract

This paper analyzes the contracting of maintenance services provided by an original equipment manufacturer (OEM) to an operator for a device. The service provider can exert different levels of maintenance effort during the course of the contract and the device's reliability (uptime) is influenced by these levels. However, the service provider's effort level is non-contractible. We obtain the optimal design of performance-based maintenance contracts in this context by singling out a unique uptime-guarantee contract structure that contains profit-maximizing contracts in all situations. With the optimal contract structure, the service provider guarantees 100% uptime and compensates the operator's downtime at a higher unit rate than it charges him/her for maintenance services (with the factor of inverse expected downtime under no contract). This finding shows that some of the well-known performance-based contract structures used in practice (e.g., pay-for-performance contracts) can be sub-optimal for the OEMs. When the operator's revenue rate from the device is known to the service provider, the optimal contract compensates for any lost revenue due to downtime yet leaves the operator with zero expected profit from the contract. Under asymmetric information, we provide a closed-form formula for calculating the optimal compensation rate. We also demonstrate the advantages and limitations of offering menus of contracts to increase the service provider's expected profits.

Keywords: Reliability, Maintenance-Repairs, Game Theory, Contracting, Optimization