On the tightness of an LP relaxation for rational optimization and its applications

Vashist Avadhanula, Jalaj Bhandari, Vineet Goyal*, Assaf Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of optimizing a linear rational function subject to totally unimodular (TU) constraints over {0,1} variables. Such formulations arise in many applications including assortment optimization. We show that a natural extended LP relaxation of the problem is “tight”. In other words, any extreme point corresponds to an integral solution. We also consider more general constraints that are not TU but obtained by adding an arbitrary constraint to the set of TU constraints. Using structural insights about extreme points, we present a polynomial time approximation scheme (PTAS) for the general problem.

Original languageEnglish
Pages (from-to)612-617
Number of pages6
JournalOperations Research Letters
Volume44
Issue number5
DOIs
StatePublished - 1 Sep 2016
Externally publishedYes

Funding

FundersFunder number
National Science FoundationCMMI-1351838, CMMI-1201116
International Business Machines Corporation

    Keywords

    • Assortment optimization
    • Linear programming
    • PTAS

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