Optimization Approach for Multi-Period Fuel Replenishment

Abstract

This paper proposes mathematical models and solution approaches for solving the multi-period fuel replenishment planning problem. The model aims to search for a set of routes, determining the quantity of several petroleum products to be loaded on individual vehicle compartments, and specifying the quantity to be discharged to customer tanks over a given planning horizon in which multiple constraints are satisfied. The objective function is to minimize the transportation unit cost, equal to the total transportation cost divided by the sum of replenished quantity. As the model size grows exponentially when the number of customers, vehicles, and time period increases, an exact algorithm is not feasible. Hence, in this study, we propose two heuristic approaches: two-phase method (2PM) and three-phase method (3PM). The 2PM is primarily designed for solving small problems whereas the 3PM adopts a similar approach but has the ability to solve larger problems. The proposed solutions were tested using a real-life scenario and randomly generated test instance. The results showed that our solution outperforms the solution constructed by experienced planners and also proved that considering multiple periods when devising the fuel replenishment plan, gives superior results in comparison to single periods.