Flowshops with processing flexibility across production stages

This paper addresses a scheduling problem for a two stage hybrid flowshop (HFS) environment with significant processing flexibility across stages. A job can be either completely processed at one of the stages or its processing is split in a prespecified fashion between stages. For the latter case, the routing is only in one direction, from the ‘upstream’ stage to the ‘downstream’ stage. A stage may consist of one or more parallel identical machines. We first study the special case of a single machine per stage and present a pseudopolynomial dynamic programming algorithm to minimize makespan. Then, we provide a heuristic for the HFS m(1), m(2) problem with m(k) machines at stage k = 1, 2, and prove its worst case and average performance. Also, we extend our algorithms to the case of stage dependent processing times. Finally, we report computational results on the average performance of HFS m(1), m(2) with comparable flowshop and parallel machine environments, and provide managerial guidelines for process choice decisions.