Decomposition algorithms for synchronous flow shop problems with additional resources and setup times

In this paper, we present decomposition algorithms for synchronous flow shop problems with additional resources and setup times. In such an environment, jobs are moved from one machine to the next by an unpaced synchronous transportation system, which implies that the processing is organized in synchronized cycles. In each cycle the current jobs start at the same time on the corresponding machines and after processing have to wait until the last job is finished. Afterwards, all jobs are moved to the next machine simultaneously. During processing, each job needs one additional resource and setup times have to be taken into account when changing from one resource to another. The goal is to find a production sequence of the jobs as well as a feasible assignment of resources to the jobs such that the total production time (makespan) is minimized. We propose two decomposition strategies dealing with the two subproblems of job sequencing and resource assignment hierarchically. Both approaches are computationally evaluated and compared. As a by-product, we also present efficient heuristics for the makespan minimization problem in synchronous flow shops without setup times.