A heuristic proǵramminǵ procedure for sequencinǵ the static flowshop

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Abstract
This paper describes a heuristic procedure for sequencing the n job m machine static flowshop. Basically, the procedure is performed in two overall steps. In the first step, each of the n jobs is tested as a potential immediate follower to each of the other jobs. In effect, this step of the procedure asks the question, ‘how well does a particular job fit in terms of job blocking or machine idleness if it were to follow some other job?’ An overall figure of merit, or cost cij, is determined for each job j as a follower to another job i. Six different heuristics are presented for determining sets of cij values. Using these values of cij, the second step then heuristically develops a job sequence by solving the travelling salesman problem. The paper also presents computational experience with the algorithm for a variety of randomly generated test problems (up to 50 jobs and 50 machines in size), and compares its performance with other published heuristic techniques.