Outsourcing warranty repair services: Static and dynamic allocation for a fixed population

We consider a manufacturer that has a fixed population of items that are sold with a warranty. Rather than maintaining a repair facility of its own, the manufacturer outsources the repairs of items covered under warranty to several external repair vendors. The manufacturer must decide how to allocate items to repair vendors in order to minimize the total relevant costs. In doing so, the manufacturer has two choices for allocation schemes: static allocation or dynamic allocation. Under static allocation, the manufacturer assigns each item to a vendor at the time of sale, and all failures of that item are handled by the preassigned vendor. Under dynamic allocation, the manufacturer delays all allocation decisions until the times of failure, and uses the current state of each vendor in deciding where to route the failed item.; For the static allocation problem, 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. We show that under certain conditions on the problem parameters, a simple greedy algorithm can be used to find an optimal allocation; we also give a solution technique that can be used when the conditions are not satisfied. Through a computational study, we compare the optimal static allocation to several simple static allocation heuristics.; For the dynamic allocation problem, we develop a model based on a continuous-time Markov decision process. Since this approach is numerically infeasible for large problems, we consider two different approaches to develop effective, simply structured index-type routing policies. The first uses dynamic programming policy improvement, while the second uses a restless bandit model. Using simulation, we compare the dynamic allocation index policies to optimal static allocations and to commonly used dynamic allocation heuristics. For small problems, we compare the index policies to optimal dynamic allocations, and show that the index policies are nearly optimal.; For a large manufacturer with annual warranty costs in the tens of millions of dollars, the cost reductions that can be achieved using the allocation policies we develop can be practically significant in many cases.