With the advances of powerful computer capacity and efficient integer programming software, mathematical programming-based scheduling research is beginning to receive more and more attention from researchers. Although it is not an efficient solution method, mathematical programming formulation is a natural way to attack scheduling problems. The purpose of this paper is to present a study of five existing integer programming formulations for job-shop, flow-shop and permutation flow-shop scheduling problems, and a comparison of their model sizes for each particular setting. The results show that Manners model is not only the best formulation for both job-shop and flow-shop problems, but is also the best for the permutation flow-shop problem.
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Chao-Hsien Pan (1997) studied this question.
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