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Mutiobjective Programming

In: Multiple Criteria Decision Analysis: State of the Art Surveys

Author

Listed:
  • Matthias Ehrgott

    (The University of Auckland)

  • Margaret M. Wiecek

    (Clemson University)

Abstract

We present our view of the state of the art in multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts. We then summarize the properties of efficient and nondominated sets. In Section 4 optimality conditions are reviewed. The main part of the chapter consists of Sections 5 and 6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Section 7 we discuss specially-structured problems including linear and discrete MOPs as well as selected nonlinear MOPs. In Section 8 we present our perspective on future research directions.

Suggested Citation

  • Matthias Ehrgott & Margaret M. Wiecek, 2005. "Mutiobjective Programming," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 667-708, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-23081-8_17
    DOI: 10.1007/0-387-23081-5_17
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    Cited by:

    1. Samira Fallah & Ted K. Ralphs & Natashia L. Boland, 2024. "On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 175-220, August.
    2. Chong Hyun Park & Gemma Berenguer, 2020. "Supply Constrained Location‐Distribution in Not‐for‐Profit Settings," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2461-2483, November.
    3. Carlos A. Moreno-Camacho & Jairo R. Montoya-Torres & Anicia Jaegler, 2023. "Sustainable supply chain network design: a study of the Colombian dairy sector," Annals of Operations Research, Springer, vol. 324(1), pages 573-599, May.

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