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An adaptive method to solve multilevel multiobjective linear programming problems

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  • Mustapha Kaci
  • Sonia Radjef

Abstract

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). We introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible settlements achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bonded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method. Finally, all the construction stages are carefully checked and illustrated with a numerical example.

Suggested Citation

  • Mustapha Kaci & Sonia Radjef, 2023. "An adaptive method to solve multilevel multiobjective linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 29-44.
    • Handle: RePEc:wut:journl:v:33:y:2023:i:3:p:29-44:id:2
    DOI: 10.37190/ord230302
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    References listed on IDEAS

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    1. Anandalingam, G. & Apprey, Victor, 1991. "Multi-level programming and conflict resolution," European Journal of Operational Research, Elsevier, vol. 51(2), pages 233-247, March.
    2. Jerome Bracken & James T. McGill, 1973. "Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 21(1), pages 37-44, February.
    3. Dorota Kuchta, 2005. "Fuzzy solution of the linear programming problem with interval coefficients in the constraints," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 15(3-4), pages 35-42.
    4. Mahmoud A. Abo-Sinna & Ibrahim A. Baky, 2010. "Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-15, March.
    5. Jerome Bracken & James T. McGill, 1974. "Technical Note—A Method for Solving Mathematical Programs with Nonlinear Programs in the Constraints," Operations Research, INFORMS, vol. 22(5), pages 1097-1101, October.
    6. Kailash Lachhwani, 2021. "Solving the general fully neutrosophic multi-level multiobjective linear programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1192-1216, December.
    7. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    8. Wasim Akram Mandal & Sahidul Islam, 2017. "Multiobjective geometric programming problem under uncertainty," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 85-109.
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