A decomposition-based algorithm for flexible flow shop scheduling with stochastic processing times

Abstract

Since real manufacturing is dynamic and tends to suffer a wide range of uncertainties, research on production scheduling with uncertainty has received much more attention recently. Although various approaches have been investigated on the scheduling problem with uncertainty, this problem is still difficult to be solved optimally by any single approach, because of its inherent difficulties. This paper considers makespan optimization of a flexible flow shop (FFS) scheduling problem with stochastic processing times. It proposes a novel decomposition-based algorithm (DBA) to decompose an FFS into several 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 clusters, based on weighted cluster validity indices. 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 cluster. If two neighbouring 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 with stochastic processing times.