This study focuses on one of the intermodal operational issues: how to select best routes for shipments through the international intermodal network. International intermodal routing is complicated by three important characteristics: (1) multiple objectives; (2) scheduled transportation modes and demanded delivery times; and (3) transportation economies of scale. In this paper, the international intermodal routing problem is formulated as a multiobjective multimodal multicommodity flow problem (MMMFP) with time windows and concave costs. The objectives of this paper are to develop a mathematical model encompassing all three essential characteristics, and to propose an algorithm that can effectively provide answers to the model. The problem is NP-hard. It follows that the proposed algorithm is a heuristic. Based on relaxation and decomposition techniques, the original problem is broken into a set of smaller and easier subproblems. The case studies show that it is important to incorporate the three characteristics into the international intermodal routing problem, and our proposed algorithm can effectively and efficiently solve the MMMFP with time windows and concave costs.
- Economies of scale