Abstract
We consider the formulation of non-preemptive single machine scheduling problems using time-indexed variables. This approach leads to very large models, but gives better lower bounds than other mixed integer programming formulations. We derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities. A cutting plane/branch-and-bound algorithm based on these inequalities has been implemented. Computational experience on small problems with 20/30 jobs and various constraints and objective functions is presented.
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The research of this author was partially supported by JNICT/INVOTAN under grant No. 30/A/85/PO and by the PAC, contract No. 87/92-106, for computation.
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Sousa, J.P., Wolsey, L.A. A time indexed formulation of non-preemptive single machine scheduling problems. Mathematical Programming 54, 353–367 (1992). https://doi.org/10.1007/BF01586059
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DOI: https://doi.org/10.1007/BF01586059