A hybrid heuristic solution proposal for capacitated location routing problem under demand uncertainty

Nowadays, companies aim to service their customers via distribution center or depot at minimum cost. In this study, a new hybrid heuristic algorithm is proposed to solve the Capacitated Location Routing Problem (CLRP), which combines Variable Neighborhood Search (VNS) and Evolutionary Local Search (ELS) and named DKAxEYA. The CLRP problem consists of determining the depots to be opened, the customers and the vehicles to be assigned to each open depot, and the routes to be performed to meet the demand of the customers. The proposed heuristic algorithm includes a deterministic VNS that consists of seven different neighborhoods and ELS. Further, the proposed algorithm's performance is experimentally compared with number of the most effective heuristics proposed for the solution of the CLRP, on the benchmark instances from the literature. The computational results show that DKAxEYA provides both good average solutions and two best solutions considering the seven different effective heuristics within reasonable computing time. Besides, a Fuzzy Capacitated Location Routing Problem (FCLRP) is solved by using a heuristic method that combines DKAXEYA. Demands of the customer and travel times between customers and depots are considered as fuzzy and deterministic variables, respectively in FCLRP. Heterogeneous and homogeneous fleet sizes are performed together to reach the least multi-objective cost in a case study. The multi-objective cost consists of transportation cost, additional cost, vehicle waiting cost and delay cost. A fuzzy chance constrained programming model is added by using credibility theory. The proposed method reaches the solution by performing four stages. In the first stage, initial solutions are obtained by using a greedy heuristic method, and then VNS heuristic, which consists of seven different neighborhood structures, is performed to improve the solution quality in the second stage. In the third stage, a perturbation procedure is applied to the improved solution using ELS algorithm, and then VNS heuristic is applied again in the last stage. DKAxEYA algorithm is applied to a case study, which has 57 customers and 5 distributing points, effectively in a reasonable time.