An objective review and perspectives on the permutation flowshop scheduling with no-wait constraint and setup times

One of the most important decisions in any manufacturing company is how to schedule the operations on the available machines. In several industries, the nature of the job imposes certain constraints to operations scheduling. In a no-wait flowshop, once a job starts on the first machine, it has to continue being processed on the next ones, without any interruptions. As an extension of the flowshop scheduling problem, the no-wait version is also very difficult to be solved to optimality within a reasonable time, and many heuristics have been proposed for it. This paper aims to classify existing solution algorithms proposed to solve the no-wait flowshop scheduling problem with setup times and some of its variants. Our classification is based on the type of setup considered; we also review all available performance measures in the literature. We show how combining a heuristic to generate a good initial solution, local search procedures, insertion and swapping of job positions and techniques developed originally to solve transportation problems are among the popular and efficient techniques for this problem. We identify the main available benchmark instance sets and propose several promising avenues to guide future research.