Employing efficient algorithms to reduce the distance traveled in location-routing problem considering travel and service

The study aims to present a mathematical model for the reduction of the system costs through the proper location of the required warehouses and the routing of vehicles that carry the products from the warehouses within a time window.

With regard to the specific nature of a location-routing problem, the consumption of fuel and the depreciation of vehicles are directly affected by the distance covered. The model proposed in this research seeks to minimize the undue length of the distance that vehicles have to travel. Moreover, for the approximation of the model to real-world conditions as much as possible, the concept of ‘time window’ is employed to determine the maximum allowable time for the distribution of goods.

Three metaheuristic algorithms including NSGA-II, PAES and MOICA are used to solve the proposed model. To evaluate the efficiency of the solutions, several problems of different sizes are introduced and solved, and then the results are compared in terms of the SM, MID and QM criteria. The comparative results suggest the superiority of the MOICA algorithm for big-size problems.

Setting a time window for the reduction of the distance traveled by the vehicles gets the model close to real-world conditions. It also makes it possible to estimate the costs more accurately.