The petrol station replenishment problem with time windows

In the Petrol Station Replenishment Problem with Time Windows (PSRPTW) the aim is to optimize the delivery of several petroleum products to a set of petrol stations using a limited heterogeneous fleet of tank-trucks. More specifically, one must determine the quantity of each product to deliver, the assignment of products to truck compartments, delivery routes, and schedules. The objective is to maximize the total profit equal to the sales revenue, minus the sum of routing costs and of regular and overtime costs. This article first proposes a mathematical formulation of the PSRPTW. It then describes two heuristics based on arc preselection and on route preselection. Extensive computational tests confirm the efficiency of the proposed heuristics.