A simultaneous facility location and vehicle routing problem arising in health care logistics in the Netherlands

This paper introduces a simultaneous facility location and vehicle routing problem that arises in health care logistics in the Netherlands. In this problem, the delivery of medication from a local pharmacy can occur via lockers, from where patients that are within the coverage distance of a locker can collect their medication, or by home delivery. The aim of the problem is to determine which lockers from a set of potential locker locations to open and to generate routes that visit the opened lockers and routes that visit the patients that are not covered by the opened lockers, while minimizing the routing costs and the opening costs of the lockers. We formally define this problem and solve it by applying a branch-and-bound algorithm to this mathematical formulation. Moreover, we propose a fast hybrid heuristic to solve the problem. Extensive computational results are given on a randomly generated instance set and an instance set inspired by practice from Alliance Healthcare Netherlands, an industrial partner. Our results indicate that our heuristic is able to consistently outperform a commercial solver applied to the mathematical formulation, and that its solutions are extremely robust. We provide important business insights on several parameters of the problem.