A petrol station replenishment problem: new variant and formulation

One of the most important problems in the petroleum industry is the well-known petrol station replenishment problem with time windows, which calls for the determination of optimal routes by using a fleet of tank trucks to serve a set of petrol stations over a given planning horizon. In this paper, we introduce a model and solve a specific problem that originates from a real-life application arising in the fuel distribution where specific attention is paid to tank trucks with compartments and customers with different types of products and time windows. Literally, we call the resulting problem the multi-compartment vehicle routing problem with time windows (MCVRPTW). To solve the MCVRPTW, we begin by describing the problem, providing its mathematical formulation and discussing the sense of its constraints. As the problem is NP-hard, we propose an efficient tabu search algorithm for its solution. We introduce the Kolmogorov-Smirnov statistic into the framework of the tabu search to manage the neighbourhood size. We evaluate the performance of the algorithm on a set of vehicle routing problems with time windows instances as well as other realistic instances. Our results are compared to CPLEX, to the heuristics reported in the literature and also to those extracted from the company plans.