Solving the dynamic capacitated location-routing problem with fuzzy demands by hybrid heuristic algorithm

In this paper, the dynamic capacitated location-routing problem with fuzzy demands (DCLRP-FD) is considered. In the DCLRP-FD, facility location problem and vehicle routing problem are solved on a time horizon. 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. Furthermore, the vehicles and depots have a predefined capacity to serve the customers with altering demands during the time horizon. It is assumed that the demands of customers are fuzzy variables. To model the DCLRP-FD, a fuzzy chance-constrained programming is designed based upon the fuzzy credibility theory. To solve this problem, a hybrid heuristic algorithm (HHA) with four phases including the stochastic simulation and a local search method are proposed. To achieve the best value of two parameters of the model, the dispatcher preference index (DPI) and the assignment preference index (API), and to analyze their influences on the final solution, numerical experiments are carried out. Moreover, the efficiency of the HHA is demonstrated via comparing with the lower bound of solutions and by using a standard benchmark set of test problems. The numerical examples show that the proposed algorithm is robust and could be used in real world problems.