Journal of Global Optimization

, Volume 59, Issue 2–3, pp 527–543

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

  • Richard Oberdieck
  • Martina Wittmann-Hohlbein
  • Efstratios N. Pistikopoulos
Article

DOI: 10.1007/s10898-014-0143-9

Cite this article as:
Oberdieck, R., Wittmann-Hohlbein, M. & Pistikopoulos, E.N. J Glob Optim (2014) 59: 527. doi:10.1007/s10898-014-0143-9

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.

Keywords

Multiparametric programming Mixed integer linear programming  Branch and bound 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Richard Oberdieck
    • 1
  • Martina Wittmann-Hohlbein
    • 2
  • Efstratios N. Pistikopoulos
    • 2
  1. 1.Department of Chemistry and Applied Biosciences, Institute for Chemical and BioengineeringETH ZurichZurichSwitzerland
  2. 2.Department of Chemical Engineering, Centre for Process Systems EngineeringImperial CollegeLondonUK

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