Heuristics for the multi-depot petrol station replenishment problem with time windows

• Published in: European journal of operational research Vol. 220; no. 2; pp. 361 - 369
• Main Authors: Cornillier, Fabien, Boctor, Fayez, Renaud, Jacques
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.07.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied sciences; Assignment problem; Deliveries; Delivery scheduling; Demand; Exact sciences and technology; Gasoline; Heuristic; Logistics; Marketing; Mathematical models; Operational research and scientific management; Operational research. Management science; Petrol station replenishment; Replenishment; Scheduling, sequencing; Service stations; Stations; Studies; Truck-fleet management; Vehicle routing and scheduling; Windows (intervals); Truck-fleet management; Vehicle routing and scheduling; Petrol station replenishment; Stored materials; Fleet; Refeeding; Vehicle routing problem; Routing; Modeling; Delivery lead time; Time window; Lorry; Replenishment; Heuristic method; Multiple depot; Storage tank; Logistics
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.02.007

► We provide a mathematical formulation of the problem considered. ► We present a brief review of the literature related to petrol station replenishment. ► A heuristic approach is proposed to solve real-life instances of the problem. ► A large numerical experience to assess the performance of the heuristic is reported. ► We show that the proposed heuristic outperforms published single-depot heuristics. In the multi-depot petrol station replenishment problem with time windows (MPSRPTW), the delivery of petroleum products stored in a number of different petroleum depots to a set of petrol distribution stations has to be optimized. Each depot has its own fleet of heterogeneous and compartmented tank trucks. Stations specify their demand by indicating the minimum and maximum quantities to be delivered for each ordered product and require the delivery within a predetermined time window. Several inter-related decisions must be made simultaneously in order to solve the problem. For this problem, the set of feasible routes to deliver all the demands, the departure depot for each route, the quantities of each product to be delivered, the assignment of these routes to trucks, the time schedule for each trip, and the loading of the ordered products to different tanks of the trucks used need to be determined. In this paper, we propose a mathematical model that selects, among a set of feasible trips, the subset that allows the delivery of all the demands while maximizing the overall daily net revenue. If this model is provided with all possible feasible trips, it determines the optimal solution for the corresponding MPSRPTW. However, since the number of such trips is often huge, we developed a procedure to generate a restricted set of promising feasible trips. Using this restricted set, the model produces a good but not necessarily optimal solution. Thus the proposed solution process can be seen as a heuristic. We report the results of the extensive numerical tests carried out to assess the performance of the proposed heuristic. In addition, we show that, for the special case of only one depot, the proposed heuristic outperforms a previously published solution method.