A Two-Stage Stochastic Model for Intermodal Transportation Operational Planning Problem Under Capacity Shortage

The huge freight demand and the shortage of shipping capacity highlight the current dilemma of international intermodal transportation. Due to various uncertain factors in practical operations, it may not be the best decision to choose the shipping orders which have the highest bidder when the available capacity is limited. Therefore, which orders should be accepted and how to serve them effectively become critical issues to be addressed. In this paper, considering the uncertainties of the capacity and the travel time of the transportation services, a two-stage stochastic programming model is developed to maximize the expected profit of the intermodal transportation operator by choosing the optimal order portfolio and planning intermodal routes. By utilizing the sample average approximation method, the two-stage stochastic model is transformed into a mixed-integer linear programming model, integrated with large sampled scenarios. Computational experiments and numerical analyses are conducted to explore the influence of the uncertainty on the operator's operational plans. Several managerial implications for the practical intermodal transportation operations are derived: uncertainties lead to different optimal order portfolios compared with the deterministic situation; orders offering high quotations tend to be preferred by the intermodal transportation operator under capacity shortage in the deterministic condition; but in uncertain environments, the degree of urgency and the freight volume of the orders play important roles.