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Exceptional Paper--Parametric and Postoptimality Analysis in Integer Linear Programming

Author

Listed:
  • A. M. Geoffrion

    (University of California, Los Angeles)

  • R. Nauss

    (University of Missouri-St. Louis)

Abstract

The purpose of this paper is to take stock of what is known and to suggest some conceptual foundations for future progress in the areas of postoptimality analysis and parametric optimization techniques for integer programming.

Suggested Citation

  • A. M. Geoffrion & R. Nauss, 1977. "Exceptional Paper--Parametric and Postoptimality Analysis in Integer Linear Programming," Management Science, INFORMS, vol. 23(5), pages 453-466, January.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:5:p:453-466
    DOI: 10.1287/mnsc.23.5.453
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    Cited by:

    1. Crema, Alejandro, 1998. "A procedure to verify the completeness of the right-hand-side parametric analysis for a mixed integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 108(3), pages 684-695, August.
    2. Huang, G. H. & Baetz, B. W. & Patry, G. G., 1997. "A response to "A comment on 'Grey integer programming: An application to waste management planning under uncertainty"' by Larry Jenkins," European Journal of Operational Research, Elsevier, vol. 100(3), pages 638-641, August.
    3. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    4. 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.
    5. Benjamin Johnson & Alexandra Newman & Jeffrey King, 2017. "Optimizing high-level nuclear waste disposal within a deep geologic repository," Annals of Operations Research, Springer, vol. 253(2), pages 733-755, June.
    6. Tcha, Dong-wan & Myung, Young-soo & Chung, Ki-ho, 1995. "Parametric uncapacitated facility location," European Journal of Operational Research, Elsevier, vol. 86(3), pages 469-479, November.
    7. Babacar Thiongane & Anass Nagih & Gérard Plateau, 2005. "An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual," Annals of Operations Research, Springer, vol. 139(1), pages 353-373, October.
    8. Yilmaz, Hasan Ümitcan & Kimbrough, Steven O. & van Dinther, Clemens & Keles, Dogan, 2022. "Power-to-gas: Decarbonization of the European electricity system with synthetic methane," Applied Energy, Elsevier, vol. 323(C).
    9. M N Jalil & R A Zuidwijk & M Fleischmann & Jo A E E van Nunen, 2011. "Spare parts logistics and installed base information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(3), pages 442-457, March.
    10. Ramaswamy, R. & Chakravarti, N. & Ghosh, D., 2000. "Complexity of determining exact tolerances for min-max combinatorial optimization problems," Research Report 00A22, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    11. Crema, Alejandro, 1997. "A contraction algorithm for the multiparametric integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 130-139, August.
    12. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    13. 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.
    14. Crema, Alejandro, 2002. "The multiparametric 0-1-integer linear programming problem: A unified approach," European Journal of Operational Research, Elsevier, vol. 139(3), pages 511-520, June.
    15. Mukherjee, Saral & Chatterjee, A.K., 2006. "The average shadow price for MILPs with integral resource availability and its relationship to the marginal unit shadow price," European Journal of Operational Research, Elsevier, vol. 169(1), pages 53-64, February.
    16. Crema, Alejandro, 2000. "An algorithm for the multiparametric 0-1-integer linear programming problem relative to the objective function," European Journal of Operational Research, Elsevier, vol. 125(1), pages 18-24, August.
    17. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    18. Jenkins, Larry, 1996. "A comment on "Grey integer programming: an application to waste management planning under uncertainty" by Guo H. Huang, Brian W. Baetz, Gilles G. Patry : European Journal of Operational Rese," European Journal of Operational Research, Elsevier, vol. 89(3), pages 671-670, March.
    19. repec:dgr:rugsom:00a22 is not listed on IDEAS
    20. Crema, Alejandro, 2002. "An algorithm to perform a complete parametric analysis relative to the constraint matrix for a 0-1-integer linear program," European Journal of Operational Research, Elsevier, vol. 138(3), pages 484-494, May.
    21. George Kozanidis & Eftychia Kostarelou, 2023. "An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 573-607, May.
    22. Wang, Yi & Yang, Zhifang & Yu, Juan & Liu, Sixu, 2023. "Pricing in non-convex electricity markets with flexible trade-off of pricing properties," Energy, Elsevier, vol. 274(C).
    23. Myung, Young-Soo & Kim, Hu-gon & Tcha, Dong-wan, 1997. "A bi-objective uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 100(3), pages 608-616, August.
    24. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.
    25. Wang, Hsiao-Fan & Horng, Jyh-Shing, 1996. "Structural approach to parametric analysis of an IP on the case of the right-hand side," European Journal of Operational Research, Elsevier, vol. 92(1), pages 148-156, July.

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