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Some Classes of Valid Inequalities and Convex Hull Characterizations for Dynamic Fixed-Charge Problems under Nested Constraints

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  • Fred Glover
  • Hanif Sherali

Abstract

This paper studies the polyhedral structure of dynamic fixed-charge problems that have nested relationships constraining the flow or activity variables. Constraints of this type might typically arise in hierarchical or multi-period models and capacitated lot-sizing problems, but might also be induced among choices of key variables via an LP-based post-optimality analysis. We characterize several classes of valid inequalities and inductively derive convex hull representations in a higher dimensional space using lifting constructs based on the Reformulation-Linearization Technique. Relationships with certain known classes of valid inequalities for single item capacitated lot-sizing problems are also identified. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Fred Glover & Hanif Sherali, 2005. "Some Classes of Valid Inequalities and Convex Hull Characterizations for Dynamic Fixed-Charge Problems under Nested Constraints," Annals of Operations Research, Springer, vol. 140(1), pages 215-233, November.
    • Handle: RePEc:spr:annopr:v:140:y:2005:i:1:p:215-233:10.1007/s10479-005-3972-6
    DOI: 10.1007/s10479-005-3972-6
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    2. Ali, Agha Iqbal & O'Connor, Debra J., 2010. "The impact of distribution system characteristics on computational tractability," European Journal of Operational Research, Elsevier, vol. 200(2), pages 323-333, January.

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