A polyhedral study of the semi-continuous knapsack problem |
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Authors: | Ismael Regis de Farias Jr Ming Zhao |
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Institution: | 1. Department of Industrial Engineering, Texas Tech University, Lubbock, TX, USA 2. SAS, Cary, NC, USA
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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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