A multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands

We formulate a multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands, which are defined as demands that are generated upon completing site-specific service on their predecessors. When a factory is re-supplied with manufacturing materials, for example, demand for raw materials surfaces only after the existing inventory has been exhausted. A special separable case of the problem was solved, wherein probable demands are estimated by stochastic processes at the demand nodes (the factories) before the vehicle location-routing decisions. Posterior solutions to the complete 90-day instances of the problem help to gauge the performance of the a priori stochastic model. The 90 day-by-day instances also provide researchers with a benchmark data-set for future experimentation. It was shown that the a priori optimization solution provides a robust location-routing strategy for real-time decision-making in a medical-evacuation case study of the U.S. Air Force. Given this modest success, the same methodology can possibly be applied toward "pure" just-in-time deliveries in supply-chain management, where inventory storage is totally eliminated.