Location-Routing Problem with Demand Range

This research proposes a new variant of the location-routing problem (LRP) called LRP with Demand Range (LRPDR) by allowing flexibility in the delivery quantity. The goal of the LRPDR is to minimize the objective value calculated by the total cost minus the extra revenue. The total cost consists of the travelling cost of vehicles, the opening cost of the depots, and the activation cost of vehicles. This study proposes a new hybrid algorithm, SAPSO, that combines simulated annealing (SA) and particle swarm algorithm (PSO) for solving the LRPDR. Since this problem has not yet been studied in the literature, a mathematical model is proposed and solved by the Gurobi solver. The results obtained by Gurobi are then compared with those obtained by the proposed SAPSO algorithm. In addition, the performance of the proposed SAPSO algorithm is assessed by solving the LRP benchmark instances, and comparing the results with those of existing state-of-the-art algorithms for LRP. Based on the experimental results, the proposed SAPSO algorithm improves the performance of the basic SA algorithm and outperforms Gurobi. Moreover, the benefits of the LRPDR over LRP are presented in terms of total cost reduction.