Decomposition-Based Scheduling for Makespan Minimisation of Flexible Flow Shop with Stochastic Processing Times

Since real manufacturing is dynamic and tends to suffer a wide range of uncertainties, research on production scheduling under uncertainty has received much more attention recently. Although various approaches have been developed for scheduling under uncertainty, this problem is still difficult to tackle by any single approach, because of its inherent difficulties. This paper considers makespan minimisation of a flexible flow shop (FFS) scheduling problem with stochastic processing times. It proposes a novel decomposition-based approach (DBA) to decompose an FFS into several machine clusters which can be solved more easily by different approaches. A neighbouring K-means clustering algorithm is developed to firstly group the machines of an FFS into an appropriate number of machine clusters, based on a weighted cluster validity index. A back propagation network (BPN) is then adopted to assign either the shortest processing time (SPT) or the genetic algorithm (GA) to generate a sub-schedule for each machine cluster. If two neighbouring machine clusters are allocated with the same approach, they are subsequently merged. After machine grouping and approach assignment, an overall schedule is generated by integrating the sub-schedules of the clusters. Computation results reveal that the proposed approach is superior to SPT and GA alone for FFS scheduling under stochastic processing times.