Abstract
In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered, which simultaneously solves two problems: locating the facilities and designing the vehicle routes among the established facilities and customers. In the CLRP-FD, the capacities of the employed vehicles and established facilities cannot exceed, and the demands of the customers are assumed to be triangular fuzzy variables. To model the CLRP-FD, a fuzzy chance constrained programming approach is designed using fuzzy credibility theory. To solve this problem, a hybrid particle swarm optimization (HPSO) algorithm, which includes a stochastic simulation and a local search strategy based on the variable neighborhood search algorithm, is proposed. Finally, the influence of the value of the dispatcher preference index ( DPI ) on the total distribution cost is analyzed by conducting numerical experiments. To evaluate the efficiency of the proposed HPSO and the performance of the CLRP-FD model, the results obtained using the HPSO were compared with their corresponding lower bound provided using the CPLEX solver. Moreover, we also evaluated the performance of HPSO through computational experiments on some well-known benchmark CLRP instances. The numerical results show that the proposed HPSO is competitive, and can give a satisfactory solution in a reasonable amount of time.
Highlights
In modern logistics decisions, facility locations and vehicle routing designs are vitally important to supply chain management because the dependable, efficient, and flexible decisions on the depots and the delivery routes can save distribution cost and time and enhance the company’s ability to compete
In the hybrid particle swarm optimization (HPSO), the path relinking algorithm is used to update the position of each particle, and local search is implemented using variable neighborhood search (VNS) to improve the quality of the solution
In the solution process of the HPSO, stochastic simulation was employed to estimate the additional distances that resulted from fuzzy demands and route failures for every planned route
Summary
Facility locations and vehicle routing designs are vitally important to supply chain management because the dependable, efficient, and flexible decisions on the depots and the delivery routes can save distribution cost and time and enhance the company’s ability to compete. In [24], Mehrjerdi and Nadizadeh presented a fuzzy chance constrained programming approach with a credibility measurement to model the CLRP-FD, which was solved by a greedy clustering method with a stochastic simulation. Without considering the capacities of the depots, Ghaffari-Nasab et al considered an LRP with fuzzy demands and proposed a fuzzy chance-constrained programming model based on fuzzy credibility theory [17] They used a hybrid simulated annealing-based heuristic to solve this problem, in which stochastic simulation was employed to assess the believability of a solution. The CLRP-FD is considered, which is formulated using the approach of fuzzy chance constrained programming with credibility measurement In this problem, the actual demand of a customer can be known only when the vehicle arrives at the customer [24], [28]. Conclusions and some future researches are presented in the section VI
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