Allocating outsourced warranty service contracts

Motivated by our interactions with a leading manufacturer of computers, in this paper we consider static allocation as applied to the problem of minimizing the costs of outsourcing warranty services to repair vendors. Under static allocation, a manufacturer assigns each item to one of several contracted repair vendors; every time a particular item fails, it is sent to its preassigned vendor for repair. In our model, the manufacturer incurs a repair cost each time an item needs repair and also incurs a goodwill cost while items are undergoing repair. We model each service vendor as a finite population multi-server queueing system and formulate the resulting outsourcing problem as an integer-variable resource allocation problem. After establishing convexity results regarding the queue lengths at the repair vendors, we show that marginal allocation is optimal. Through a detailed computational study we compare the optimal algorithm with five static allocation heuristics in terms of time and optimality gap. Our study indicates that the optimal algorithm takes less than a minute to solve industry size problems on average. Further, the commonly used heuristics are far away from the optimal on average, thus emphasizing the benefits of the optimal allocation algorithm. We also compare the optimal static allocation to two simple dynamic allocation heuristics. The results of this study further validate the use of static allocation as a justifiable and easy-to-implement policy. Among other computational insights we show that when the number of items to be allocated is large, a single-server approximation leads to optimal allocations in most of the cases.