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An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems

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  • Vivek Dua
  • Efstratios Pistikopoulos

Abstract

In this paper, we present an algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems involving (i) 0-1 integer variables, and, (ii) more than one parameter, bounded between lower and upper bounds, present on the right hand side (RHS) of constraints. The solution is approached by decomposing the mp-MILP into two subproblems and then iterating between them. The first subproblem is obtained by fixing integer variables, resulting in a multiparametric linear programming (mp-LP) problem, whereas the second subproblem is formulated as a mixed integer linear programming (MILP) problem by relaxing the parameters as variables. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Vivek Dua & Efstratios Pistikopoulos, 2000. "An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems," Annals of Operations Research, Springer, vol. 99(1), pages 123-139, December.
    • Handle: RePEc:spr:annopr:v:99:y:2000:i:1:p:123-139:10.1023/a:1019241000636
    DOI: 10.1023/A:1019241000636
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    Citations

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    Cited by:

    1. Zukui Li & Marianthi Ierapetritou, 2010. "A method for solving the general parametric linear complementarity problem," Annals of Operations Research, Springer, vol. 181(1), pages 485-501, December.
    2. Efstratios Pistikopoulos & Luis Dominguez & Christos Panos & Konstantinos Kouramas & Altannar Chinchuluun, 2012. "Theoretical and algorithmic advances in multi-parametric programming and control," Computational Management Science, Springer, vol. 9(2), pages 183-203, May.
    3. Faraz Salehi & S. Mohammad J. Mirzapour Al-E-Hashem & S. Mohammad Moattar Husseini & S. Hassan Ghodsypour, 2023. "A bi-level multi-follower optimization model for R&D project portfolio: an application to a pharmaceutical holding company," Annals of Operations Research, Springer, vol. 323(1), pages 331-360, April.
    4. Tan, Zhen & Gao, H. Oliver, 2018. "Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 113-131.
    5. Addis Belete Zewde & Semu Mitiku Kassa, 2023. "A novel approach for solving multi-parametric problems with nonlinear constraints," Journal of Global Optimization, Springer, vol. 85(2), pages 283-313, February.
    6. Mitsos, Alexander & Barton, Paul I., 2009. "Parametric mixed-integer 0-1 linear programming: The general case for a single parameter," European Journal of Operational Research, Elsevier, vol. 194(3), pages 663-686, May.
    7. Richard Oberdieck & Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2014. "A branch and bound method for the solution of multiparametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 59(2), pages 527-543, July.
    8. Li, Lei & Zabinsky, Zelda B., 2011. "Incorporating uncertainty into a supplier selection problem," International Journal of Production Economics, Elsevier, vol. 134(2), pages 344-356, December.
    9. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    10. Huo, Yuchong & Bouffard, François & Joós, Géza, 2022. "Integrating learning and explicit model predictive control for unit commitment in microgrids," Applied Energy, Elsevier, vol. 306(PA).
    11. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    12. F. Borrelli & A. Bemporad & M. Morari, 2003. "Geometric Algorithm for Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 515-540, September.

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