Outsourcing warranty repairs: models for the allocation of failed items to multiple vendors

Abstract

We consider a scenario in which several external service vendors are contracted to repair purchased items which fail under warranty. We develop and analyze various allocation models concerning how the repair work should be distributed among the vendors in a cost-effective manner. Furthermore, we depart from previous work by arguing the importance of approaches to the modelling of goodwill costs which penalize long waits experienced by individual customers.We firstly study a simple static allocation model with a fixed warranty population. Both theoretical considerations and numerical results show that a simple greedy approach to the distribution of items under static models works outstandingly well. However, such a static formulation ignores the stochastic nature of the warranty population. Hence, we develop a second allocation model in which new equipment purchases are made according to a compound Poisson process. As in the static allocation model, the current information regarding the repair queue at each vendor is not available to the decision maker. The resulting stochastic dynamic optimization problem is non-standard. We develop an effective allocation procedure to this non-standard problem using a dynamic programming policy improvement approach. We report representative results from a simulation investigation to evaluate the status of the allocation heuristic developed in comparison to two simpler heuristics suggested by static models. Thirdly, we propose a dynamic allocation model which utilizes data on the queue length at each vendor for decisions on the routing of real-time failures to the vendors. Due to the problem size and state space in practice, traditional stochastic dynamic programming is not a realistic and computationally viable option. Hence, Whittle's restless bandits approach is deployed to develop the index-based heuristic for this dynamic allocation problem. A crucial theoretical result in this part of the study is that the system considered is indeed indexable. All the numerical results reported show that the performance of the derived index policy from the restless bandit is superior to that of a range of alternatives.