Abstract
This chapter discusses the realistic albeit complicated situations for flow-shop scheduling problems. It highlights the two-machine scheduling problems and then presents the extension of the treatment to the multidimensional cases involving three or more machines. It focuses on the two-machine flow-shop scheduling problem and the two distinct scheduling problems that result from the classic two-machine scheduling problem when one machine is assumed to have setup times that are dependent on job sequence. For both problems, the objective is to determine a job sequence for each machine (schedule) that minimizes the total elapsed time to complete all jobs (makespan). Two essentially equivalent dynamic programming (DP) formulations for the TSP, or equivalently the single-machine scheduling problem involving sequence dependent setup times can be developed.
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