A Matheuristic Approach for the Multi-Depot Periodic Petrol Station Replenishment Problem

Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of depots, during a weekly planning horizon. The company must ensure refuelling according to available visiting patterns, which can be different from customer to customer. A visiting pattern predefines how many times (days) the replenishment occurs during a week and in which visiting days how much fuel must be delivered. To fulfil the weekly demand of each petrol station, one of the available replenishment plans must be selected among a given set of visiting patterns. The aim is to minimize the total distance travelled by the fleet of tank trucks during the entire planning horizon. We provide a math-heuristic approach, based on cluster-first route-second paradigm, to solve it. We thoroughly experiment our approach on a set of realistic random instances. Finally, we consider a weekly large real instance with 194 petrol stations and 2 depots.