A branch and bound method for the solution of multiparametric mixed integer linear programming problems

Richard Oberdieck, Martina Wittmann-Hohlbein and Efstratios Pistikopoulos ()

Journal of Global Optimization, 2014, vol. 59, issue 2, 527-543

Abstract: In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bound strategy that involves the solution of a multiparametric linear programming sub-problem at leaf nodes and appropriate comparison procedures to update the tree. McCormick relaxation procedures are employed to overcome the presence of bilinear terms in the model. The algorithm generates an envelope of parametric profiles, containing the optimal solution of the mp-MILP problem. The parameter space is partitioned into polyhedral convex critical regions. Two examples are presented to illustrate the steps of the proposed algorithm. Copyright Springer Science+Business Media New York 2014

Keywords: Multiparametric programming; Mixed integer linear programming; Branch and bound (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-014-0143-9

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