ABSTRACT

This paper models a single liner service design and operations problem. The model selects the ports to be included, their sequence, the sailing speed of vessels, the number of vessels and the amounts of cargo to transport by the service. The objective is to maximise profit. First, a relaxation with a mixed-integer nonlinear programming (MINLP) formulation is proposed. We show how to obtain the optimal speed value. Once this value is obtained, the mathematical programming formulation becomes a mixed-integer linear program (MILP). Then, a two-step exact algorithm is presented to solve the problem. Using real data, the optimal solution was found in less than 1 min for small-size problems and in few hours for relatively large-size problems. More tests were carried out on randomly generated data sets with up to 25 ports. The results of these tests are rather promising, and they enabled us to identify the performance limits of the algorithm.

摘要

本文模拟了一个单一的班轮服务设计和运营问题。该模型选择要包括的港口、它们的顺序、船只的航行速度、船只的数量和服务运输的货物数量。目标是利润最大化。首先，提出了具有混合整数非线性规划 (MINLP) 公式的松弛方法。我们展示了如何获得最佳速度值。一旦获得该值，数学规划公式就变成了混合整数线性规划 (MILP)。然后，提出了一个两步精确算法来解决这个问题。使用真实数据，对于小规模问题在不到 1 分钟的时间内找到了最佳解决方案，对于规模相对较大的问题则在几小时内找到了最佳解决方案。对多达 25 个端口的随机生成的数据集进行了更多测试。