Emergency supply contracts for a service provider with limited local resources

We study a problem faced by a service provider, who is responsible for the repair of a group of assets subject to random failures. In case of a failure, both an engineer and a spare part of the right kind need to be available to carry out the repair. A limited number of engineers are employed while also stocks of the various spare parts are limited. In case any resource (engineer or spare part) is not immediately available, the service provider may follow a full backlogging policy. Alternatively, in case of spare parts stock out, he has the option to revert to an emergency supplier with ample capacity of resources. We present an original model to analyze the problem dynamics between this service provider and the emergency supplier. Especially, we determine the optimal emergency shipment cost and the optimal multi-resource level of the service provider. To this end, we propose a computationally efficient algorithm to find the Stackelberg equilibrium. Furthermore, we design a revenue-sharing cooperative contract between these players which always results in coordination. Finally, we examine the risk of uncertainties in such a contract and find the optimal contract parameters by considering the utility functions of the players.