In intermodal transportation, it is essential to balance the trade-off between the cost and duration of a route. The duration of a path is inherently stochastic because of delays and the possibility of overbooking. We study a problem faced by a company that supports shippers with advice for the route selection. The challenge is to find Pareto-optimal solutions regarding the route’s costs and the probability of arriving before a specific deadline. We show how this probability can be calculated in a network with scheduled departure times and the possibility of overbookings. To solve this problem, we give an optimal algorithm, but as its running time becomes too long for larger networks, we also develop a heuristic. The idea of this heuristic is to replace the stochastic variables by deterministic risk measures and solve the resulting deterministic optimization problem. The heuristic produces, in a fraction of the optimal algorithm’s running time, solutions of which the costs are only a few percent higher than the optimal costs.

在多式联运中，必须平衡路线的成本和持续时间之间的权衡。由于延迟和超额预订的可能性，路径的持续时间本质上是随机的。我们研究了一家为托运人提供路线选择建议的公司所面临的问题。挑战在于找到关于路线成本和在特定截止日期之前到达的概率的帕累托最优解决方案。我们展示了如何在具有预定出发时间和超额预订可能性的网络中计算此概率。为了解决这个问题，我们给出了一个最优算法，但是由于它的运行时间对于更大的网络来说太长了，我们也开发了一种启发式算法。这种启发式的想法是用确定性风险度量代替随机变量，并解决由此产生的确定性优化问题。启发式算法在最优算法运行时间的一小部分内产生了其成本仅比最优成本高几个百分点的解决方案。