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A polyhedral study of the semi-continuous knapsack problem

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Abstract

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Such structure arises in a wide variety of important problems, e.g. blending and portfolio selection. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch-and-cut scheme for problems with semi-continuous variables. To demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts, we present computational results on real instances of the unit commitment problem, as well as on a number of randomly generated instances of linear programming with semi-continuous variables.

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Authors and Affiliations

  1. Department of Industrial Engineering, Texas Tech University, Lubbock, TX, USA

    Ismael Regis de Farias Jr.

  2. SAS, Cary, NC, USA

    Ming Zhao

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  1. Ismael Regis de Farias Jr.
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  2. Ming Zhao
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Correspondence to Ismael Regis de Farias Jr..

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de Farias, I.R., Zhao, M. A polyhedral study of the semi-continuous knapsack problem. Math. Program. 142, 169–203 (2013). https://doi.org/10.1007/s10107-012-0566-3

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