Multi-Objective Optimization of the Multimodal Routing Problem Using the Adaptive ε-Constraint Method and Modified TOPSIS with the D-CRITIC Method

This paper proposes a multi-criteria decision-making approach for the multimodal routing problem (MRP) of bulk transportation in Thailand to minimize the total cost, transportation time, and total carbon dioxide-equivalent (CO 2 e) emissions simultaneously. The proposed approach has three phases: The first phase is generating all nondominated solutions using Kirlik and Sayin’s adaptive ε-constraint method. In the second phase, the Distance Correlation-based Criteria Importance Through Inter-criteria Correlation (D-CRITIC) method is used to determine the weight of each objective function and assign it to the modified technique for order of preference by similarity to ideal solution (modified TOPSIS) model in next phase. The third phase consists of ranking Pareto solutions obtained from the first phase using the modified TOPSIS. This proposed approach is applied to a real-world problem to enable the selection of the best route for transporting goods from the anchorage area in the Gulf of Thailand to the destination factory throughout a multimodal transportation network in Thailand. The computational results indicate that the proposed approach is superior to the current approach utilizing the ε-constraint method (ECM) regarding the number of Pareto solutions obtained and the proportion of computational time to the number of Pareto solutions obtained. Finally, the proposed method can solve the MRP with three or more objective functions and provide a multimodal route selection approach that is suitable for decision makers to offer a multimodal route to customers in the negotiation process for outsourcing transportation.