A two-stage optimization model for road-rail transshipment procurement and truckload synergetic routing

Road-rail multimodal transport has increasing importance in modern cargo transport. This paper presents a novel two-stage model for optimizing auction game strategy and route in container road-rail transshipment. Two critical questions are investigated in the two stages, respectively: (a) In the first stage, what is the best pricing strategy for either large-scale or small-scale carriers in a stochastic bid generation problem? (b) In the second stage, what are the best routes of the container trucks to minimize the total expected profit of the carrier ac-cording to its pricing strategy? To deal with the first stage problem, this paper presents an evolutionary game model to capture the long-term strategic behaviors of the carriers and to optimize the choice between historical pricing strategy and combinatorial strategy for each carrier. The equilibrium points of the evolutionary game model and Evolutionary Stability Strategy are derived and discussed. In the second stage, a fleet management problem is presented to determine the routing of the trucks over the whole temporal horizon regarding the transportation price. An A*-based search heuristic is proposed to find the satisfying solution to this difficult problem. To show the efficiency and effectiveness of the proposed method, numerical studies are conducted. The results show that (a) The optimized pricing strategy is impacted by the expected profit rate, the correlation coefficient between different transport ation enterprise carriers, and the probability of winning bids. The equi-librium point of the ordering bidding system depends on whether these critical input parameters exceed a threshold. (b) In the fleet management and route optimization stage, the small-scale carrier has gained about 11.42% more profits than the large-scale carrier.