Coordinating failed goods collecting and repair capacity policies in the maintenance of commoditized capital goods

We study a maintenance organization serving industrial customers operating a commoditized capital good. The maintenance organization provides for availability of the capital good. Upon failure, a substitute good rented from a third party is installed. A logistics service provider picks up the failed good and delivers it to the repair shop. On arrival at the repair shop the failed good is repaired, returned, and installed for use. Rent for the substitute ends at installation of the repaired good. Idle repair shop capacity can be used for other revenue generating tasks, depending on the time the capacity is available. We consider three failed good collection modes. First, a failed good is immediately collected, transported, and immediately admitted to the repair shop. Second, the logistics service provider is allowed a certain slack time for the delivery of the failed good to the repair shop. Third, a failed good is only admitted periodically to the shop and collection and transportation ensures that the failed good is available in the repair shop at the start of the first period possible. We ask under what conditions a transportation slack time, either as a constant slack or as a periodic admission to the repair shop, can be beneficial. We present analytical solutions for immediate transportation and transportation with a constant time slack considering costs. We find that (some) transportation time slack can be beneficial for high failure rates and high transportation costs.