In this paper we consider the final distribution of fuel oil from a storage depot to a set of petrol stations faced by an oil company, which has to decide the weekly replenishment plan for each station, and determine petrol station visiting sequences (vehicle routes) for each day of the week, assuming a fleet of homogeneous vehicles (tankers). The aim is to minimize the total distance travelled by tankers during the week, while loading tankers possibly near to their capacity in order to maximize the resource utilization. The problem is modelled as a generalization of the Periodic Vehicle Routing Problem (PVRP). Due to the large size of the real instances which the company has to deal with, we solve the problem heuristically. We propose a hybrid genetic algorithm that successfully address the problem inspired to a known hybrid genetic algorithm from the literature for the PVRP. However, the proposed algorithm adopts some techniques and features tailored for the particular fuel oil distribution problem, and it is specifically designed to deal with real instances derived from the fuel oil distribution in the European context that are profoundly different from the PVRP instances available from literature. The proposed algorithm is evaluated on a set of real case studies and on a set of randomly generated instances that hold the same characteristics of the former.

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