Robustness and duality in linear programming

被引:26
|
作者
Gabrel, V. [1 ]
Murat, C. [1 ]
机构
[1] Univ Paris 09, LAMSADE, CNRS, F-75016 Paris, France
关键词
linear programming; decision analysis; robustness; INTERVAL OBJECTIVE FUNCTION; REGRET; COEFFICIENTS;
D O I
10.1057/jors.2009.81
中图分类号
C93 [管理学];
学科分类号
12 ; 1201 ; 1202 ; 120202 ;
摘要
In this paper, we consider a linear program in which the right hand sides of the constraints are uncertain and inaccurate. This uncertainty is represented by intervals, that is to say that each right hand side can take any value in its interval regardless of other constraints. The problem is then to determine a robust solution, which is satisfactory for all possible coefficient values. Classical criteria, such as the worst case and the maximum regret, are applied to define different robust versions of the initial linear program. More recently, Bertsimas and Sim have proposed a new model that generalizes the worst case criterion. The subject of this paper is to establish the relationships between linear programs with uncertain right hand sides and linear programs with uncertain objective function coefficients using the classical duality theory. We show that the transfer of the uncertainty from the right hand sides to the objective function coefficients is possible by establishing new duality relations. When the right hand sides are approximated by intervals, we also propose an extension of the Bertsimas and Sim's model and we show that the maximum regret criterion is equivalent to the worst case criterion. Journal of the Operational Research Society (2010) 61, 1288-1296. doi: 10.1057/jors.2009.81 Published online 26 August 2009
引用
收藏
页码:1288 / 1296
页数:9
相关论文
共 50 条
  • [41] A SHORT PROOF OF DUALITY THEOREM OF LINEAR PROGRAMMING
    SREEDHAR.VP
    JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1965, 13 (02): : 423 - &
  • [42] Interior penalty functions and duality in linear programming
    Eremin, I. I.
    Popov, L. D.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (03): : 83 - 89
  • [43] EXTENSION OF LINEAR-PROGRAMMING DUALITY TO PIECEWISE LINEAR MAPS
    BLEIER, R
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (07): : A641 - A641
  • [44] Robustness, Evolvability, and Accessibility in Linear Genetic Programming
    Hu, Ting
    Payne, Joshua L.
    Banzhaf, Wolfgang
    Moore, Jason H.
    GENETIC PROGRAMMING, 2011, 6621 : 13 - +
  • [45] Linear and Integer Programming vs Linear Integration and Counting: A Duality Viewpoint
    Almehdawe, E.
    JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 2010, 61 (12) : 1795 - 1796
  • [46] Duality for Robust Linear Infinite Programming Problems Revisited
    Dinh, N.
    Long, D. H.
    Yao, J-C
    VIETNAM JOURNAL OF MATHEMATICS, 2020, 48 (03) : 589 - 613
  • [47] A GEOMETRIC INTERPRETATION OF DUALITY THEOREM IN LINEAR-PROGRAMMING
    YANAI, H
    ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, 1987, 4 (01) : 69 - 82
  • [48] Lexicographic Regularization and Duality for Improper Linear Programming Problems
    Popov, L. D.
    Skarin, V. D.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2016, 295 (01) : S131 - S144
  • [50] Lagrangian duality and saddle points for sparse linear programming
    Chen Zhao
    Ziyan Luo
    Weiyue Li
    Houduo Qi
    Naihua Xiu
    ScienceChina(Mathematics), 2019, 62 (10) : 2015 - 2032