عنوان مقاله [English]
Nowadays, due to concerns about economic efficiency and also the energy and environmental issues, multi-modal rail-road transport has attracted a lot of attention among transportation planners. Although multi-modal transportation has economic justification, yet its planning process is complex and challenging. Accordingly, the need for scientific and practical tools for designing efficient and effective systems for multi-modal rail-road transport is necessary. In this study, in order to investigate the collaboration between the rail and road carriers based on cooperative game theory, the mechanisms of cooperation between road and rail operators and fair division of the benefits are provided by employing innovative mathematical programming tools. In the proposed mathematical model, routing decisions, along with rail and road service network design and the rail blocking are most important decisions which are considered simultaneously in the integrated network. To manage interactions between rail and road carriers, a mechanism is devised by employing cooperative game theory concepts and borrowing some ideas of goal programming, which effectively divides the resulted savings of coalition between coalition's members. Accordingly, the participation of members and adherence of each member to collective decisions is led to the optimality of coalition. By taking advantage of proofing some mathematical theorems and lemmas, an efficient method to allocate the resulted savings of coalition to members even in
large-scale problems is provided. In order to validate and assess the suggested models and methods, a diverse range of test problems have been designed and solved with CPLEX solver. The results show that the collaboration between rail and road carriers will lead to significant savings. In addition, a factorial design of experiments was conducted to study the sensitivity of savings on key parameters of the cooperative game. The result of sensitivity analysis indicates that with the increase in per unit cost of the road mode or reduction in per unit cost of the rail mode, the level of cost savings and consequently the desire to cooperation will increase.