Trucking companies have to decide each day at which truck stops their trucks should be refueled. The underlying problem is called fixed-route vehicle-refueling problem (FRVRP). Since large trucking companies have more than 10000 trucks, small improvements in the solution quality or the required time lead to substantial cost reductions. This makes the FRVRP an important daily scheduling problem. This paper presents a fast and efficient heuristic solution approach. We introduce an exact algorithm to determine the optimal refueling policy given the selected truck stops. It has a worst case performance of $\mathcal{O}\left(n^2\right)$ but requires linear time on average. Our computational study shows that the heuristic is able to solve instances with up to 2000 truck stops within a fraction of a second to (near) optimality. We propose two variants. The first found for 96.8% of our instances an optimal solution with an average solution gap of 0.001% while requiring 0.001 seconds of computation time on average. The second variant requires 0.1 seconds on average, but reaches an average gap of under 0.001%, and found optimal solutions in 99.0% of all instances.

卡车运输公司必须决定每天应该在哪个卡车停靠站为他们的卡车加油。潜在的问题称为固定路线车辆加油问题 (FRVRP)。由于大型卡车运输公司拥有 10000 多辆卡车，解决方案质量或所需时间的微小改进会导致成本大幅降低。这使得 FRVRP 成为一个重要的日常调度问题。本文提出了一种快速有效的启发式求解方法。我们引入了一种精确的算法来确定给定选定卡车停靠站的最佳加油策略。它具有最坏情况下的性能$\mathcal{欧}\left(n^{\mathrm{2个}}\right)$但平均需要线性时间。我们的计算研究表明，启发式算法能够在几分之一秒内解决多达 2000 个卡车停靠点的实例（接近）最优。我们提出了两种变体。第一个为我们的 96.8% 的实例找到了一个最佳解决方案，平均解决方案差距为 0.001%，同时平均需要 0.001 秒的计算时间。第二个变体平均需要 0.1 秒，但达到低于 0.001% 的平均差距，并在 99.0% 的所有实例中找到最佳解决方案。