Optimisation techniques for planning the petrol replenishment to retail stations over a multi-period horizon

The problem of planning the petrol station replenishment problem (PSRP) consists in making simultaneously several decisions, such as determining the minimum number of trucks required, assigning the stations to the available trucks, defining a feasible route for each tank‐truck, etc. The objective to be achieved is usually defined as the minimisation of the travelled distance by the tank‐trucks to serve all of the distribution stations. Traditional studies in the literature model and solve this problem over a time period of one single day. Only few works have recognised the fact that extending the time horizon to several days may yield important savings for the delivering company. The goal of this paper is to survey the optimisation techniques that support the petrol companies in improving their delivery performance over a multi‐period planning horizon. We present the mathematical optimisation models that have been developed for both the t‐day and periodic variants of the problem and discuss the heuristic methods so far developed for their solution.