Supply chain scheduling: makespan reduction potential

Supply chain scheduling addresses the coordination of machine and delivery scheduling of two or more supply chain stages. The aim is to improve supply chain performance measured in total logistics costs or the supply chain makespan, for example. However, the potential for improvement has never before been quantified, so this relatively new and ambitious field of study has not yet been properly justified. If performance improvements would barely compensate for the cost of coordination, supply chain scheduling would be expendable. This paper deals with a supply chain consisting of four stages. Focusing on the supply chain makespan, eight scheduling scenarios are compared by means of a numerical study. The simplest scenario is characterised by separate scheduling of all stages. The most promising scenario is a joint scheduling approach that treats the supply chain as a flow shop. In the other six scenarios, different subsets of stages coordinate their schedules. Joint supply chain scheduling of all stages significantly outperforms the other seven scenarios. This result holds for the case with a single machine as well as for two identical parallel machines at each stage. Owing to the complexity of some of the scheduling problems to be tackled in the experiments, the numerical study is based on small-size instances with only five jobs so that it can be solved using a commercial optimisation software. Hence, a simpler two-stage supply chain with a single machine at each stage is investigated to obtain results for large-size instances. Since the shortest processing time priority applied at the first stage leads to permutation schedules which on average result in near-optimum makespans, a joint supply chain coordination approach based on Johnson's algorithm turns out to be unreasonable especially when considering the cost of coordination.