Optimal design of uptime-guarantee contracts under IGFR valuations and convex costs

An uptime-guarantee contract commits a service provider to maintain the functionality of a customer's equipment at least for certain fraction of working time during a contracted period. This paper addresses the optimal design of uptime-guarantee contracts for the service provider when the customer's valuation of a contract with a given guaranteed uptime level has an Increasing Generalized Failure Rate (IGFR) distribution. We first consider the case where the service provider proposes only one contract and characterize the optimal contract in terms of price as well as guaranteed uptime level assuming that the service provider's cost function is convex. In the second part, the case where the service provider offers a menu of contracts is considered. Given the guaranteed uptime levels of different contracts in the menu, we calculate the corresponding optimal prices. We also give the necessary and sufficient conditions for the existence of optimal contract menus with positive expected profits.