Location-routing problem in multimodal transportation network with time windows and fuzzy demands: Presenting a two-part genetic algorithm

Distribution of products throughout a supply chain could be managed via multimodal transportation networks. This will be more likely in long-haul transportation where a decision-maker has to determine the transportation modes and mode changing nodes to optimize the underlying distribution problem. On the other hand, a corresponding location-routing problem arises in any distribution system involving the plan for depots establishment in customer regions. Combination of the mentioned problems is missing in the literature and this study aims to combine the multimodal routing and location-routing problems. In addition, time window constraints were imposed upon the problem to maximize customer satisfaction. These constraints are in accordance with products that should be delivered within predetermined time intervals. Moreover, demands were represented by fuzzy numbers enabling the problem formulation to be well approximated to the real-world situation. Presenting the mentioned problem with time windows and fuzzy demands is the main contribution of this study. A mixed-integer mathematical fuzzy model was presented for the proposed problem. This model simultaneously determined the locations for establishing depots, multimodal terminals (for provision of mode-changing facilities), multimodal routes to deliver products to depots and tours for products delivery to customers which can be helpful to achieve better solutions for distribution systems. Other contribution of this study included presentation of a two-part genetic algorithm for solving the proposed mathematical model. Finally, numerical examples with different problem sizes and scenarios were used and solved by GAMS software and proposed algorithm to demonstrate the performance of the proposed model and algorithm in different situations. The results showed that time windows and fuzzy demands imposed more difficulty to the problem and increased overall cost and time. Also comparing GAMS and algorithm values and solution time indicated proper performance of the proposed algorithm.