Presentation of the dynamic capacitated location-routing problem with considering price-sensitive demand

One of the most important problems of logistic networks is designing and analyzing of the distribution network. The design of distribution systems raises hard combinatorial optimization problems. In recent years, two main problems in the design of distribution networks that are location of distribution centres and routing of distributors are considered together and created the location-routing problem. The location-routing problem (LRP), integrates the two kinds of decisions. The classical LRP, consists in opening a subset of depots, assigning customers to them and determining vehicle routes, to minimize total cost of the problem. In this paper, a dynamic capacitated location-routing problem is considered that there are a number of potential depot locations and customers with specific demand and locations, and some vehicles with a certain capacity. Decisions concerning facility locations are permitted to be made only in the first time period of the planning horizon but, the routing decisions may be changed in each time period. In this study, customer demands depend on the products offering prices. The corresponding model and presented results related to the implementation of the model by different solution methods have been analysed by different methods. A hybrid heuristic algorithm based on particle swarm optimization is proposed to solve the problem. To evaluate the performance of the proposed algorithm, the proposed algorithm results are compared with exact algorithm optimal value and lower bounds. The comparison between hybrid proposed algorithm and exact solutions are performed and computational experiments show the effectiveness of the proposed algorithm.