This paper considers an integrated routing and scheduling problem where the routing part takes into account routing costs and tardiness penalties and the scheduling part is modelled by a permutation flow shop with inventory costs. We assume that each batch is served by a dedicated vehicle, and that the number of batches and their compositions (the number of jobs and the parameters of those jobs) are known in advance. The problem is to determine the starting times of the jobs on each machine in the flow shop, the departure dates of the batches and their delivery route, such that the total cost (sum of inventory, routing and penalty costs) is minimised. A two-step approach is proposed. In a first step, the optimal delivery routes for each batch and each possible departure date are calculated. This is possible as determining the min cost route for a particular delivery batch and a particular departure date is easy. In a second step, we use the delivery cost function for each batch, depending on the departure date, from the first step, to find a schedule that minimises the total cost. Computational experiments are performed on randomly generated instances.

本文考虑了一个集成的路由和调度问题，其中路由部分考虑了路由成本和拖延惩罚，而调度部分则由带有库存成本的置换流水车间建模。我们假设每个批次都由专用车辆服务，并且批次的数量及其组成（作业的数量和这些作业的参数）是预先已知的。问题是要确定流水车间中每台机器上作业的开始时间，批次的离开日期及其交货路线，以使总成本（库存总值，工艺路线和罚款成本）最小化。提出了一种两步法。第一步，计算每个批次的最佳交货路线和每个可能的出发日期。这是可能的，因为确定特定交货批次的最低成本路线和特定的出发日期很容易。在第二步中，我们根据第一步的出发日期为每批使用交付成本函数，以找到使总成本最小化的时间表。计算实验是在随机生成的实例上执行的。