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A time indexed formulation of non-preemptive single machine scheduling problems

A time indexed formulation of non-preemptive single machine scheduling problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

A time indexed formulation of non-preemptive single machine scheduling problems

Mathematical Programming , Volume 54 (3) – Apr 14, 2005

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 1992 by The Mathematical Programming Society, Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
DOI
10.1007/BF01586059
Publisher site
See Article on Publisher Site

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.

Journal

Mathematical ProgrammingSpringer Journals

Published: Apr 14, 2005

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