Summary
In this paper we consider two variants of the Two Machine Flow Shop Problem. In these variants a makespan is given and the problem is to find a schedule that meets this makespan, thereby minimizing the infeasibilities of the jobs in some sense: in the max-variant the maximum infeasibility of the jobs is to be minimized, whereas in the sum-variant the objective is to minimize the sum of the infeasibilities of the jobs.
For both variants observations about the structure of the optimal schedules are presented. In particular, it is proved that every instance of these problems has an optimal permutation schedule. It is also shown that the max-variant can be solved by Johnson’s Rule. For the sum-variant this is not the case: for solving this problem something quite different is necessary.
Both variants can be applied in Systems Theory to find minimal factorizations of specific rational matrix functions that are optimal in some sense.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kroon, L.G., Bart, H. (1995). Variants of the Two Machine Flow Shop Problem. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_29
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DOI: https://doi.org/10.1007/978-3-642-79459-9_29
Publisher Name: Springer, Berlin, Heidelberg
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