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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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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.

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Authors and Affiliations

  1. Leeds School of Business, University of Colorado, Boulder, CO, 80309-0419

    Fred Glover

  2. Grado Department of Industrial and Systems Engineering (0118), Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061

    Hanif D. Sherali

Authors
  1. Fred Glover
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  2. Hanif D. Sherali
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Correspondence to Fred Glover.

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Glover, F., Sherali, H.D. Some Classes of Valid Inequalities and Convex Hull Characterizations for Dynamic Fixed-Charge Problems under Nested Constraints. Ann Oper Res 140, 215–233 (2005). https://doi.org/10.1007/s10479-005-3972-6

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  • DOI: https://doi.org/10.1007/s10479-005-3972-6

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