Joint optimization of spare parts inventory and service engineers staffing with full backlogging

We consider the integrated planning of spare parts and service engineers that are needed for serving a group of systems. These systems are subject to different failure types, and for each failure, a service engineer with the necessary spare part has to be assigned to repair the system. The service provider follows a backlogging policy with part reservations. That is, a repair request is backlogged if one of the required resources is not immediately available upon demand. Moreover, a spare part is reserved if the requested spare part is in stock but no service engineer is immediately available. The spare parts are typically slow-movers and are managed according to a base-stock policy. The objective is to jointly determine the stock levels and the number of service engineers to minimize the total service costs subject to a constraint on the expected total waiting times of the repair calls. For the evaluation of a given setting, we present an exact method (computationally feasible for small problems) and an accurate approximation. For the joint optimization, we present a greedy heuristic that efficiently produces close-to-optimal results. We test how the heuristic performs compared to the optimal solution and the separate optimization of spare parts and service engineers in an extensive numerical study. In a case study with 93 types of spare parts, we show that the solution of the greedy algorithm is always within 2% of the optimal solution and is up to 20% better than a separated optimization approach encountered in practice.