Solving an integrated scheduling and routing problem with inventory, routing and penalty costs

Abstract 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.