Abstract
A two-machine flow shop scheduling scenario with an availability constraint on one of the two machines is considered. Seven mixed integer programming formulations (MIPFs) are proposed for the problem where the availability constraint is imposed on the first machine. Seven analogs are proposed for its counterpart. Size complexity analysis of these MIPFs is provided. Numerical results indicate that, for either one of the two problems, each of the corresponding first three MIPFs can solve instances of size up to 100 jobs in reasonable times.
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