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Optimal Product Portfolio Design by Means of Semi-infinite Programming

In: Operations Research Proceedings 2019

Author

Listed:
  • Helene Krieg

    (Fraunhofer ITWM)

  • Jan Schwientek

    (Fraunhofer ITWM)

  • Dimitri Nowak

    (Fraunhofer ITWM)

  • Karl-Heinz Küfer

    (Fraunhofer ITWM)

Abstract

A new type of product portfolio design task where the products are identified with geometrical objects representing the efficiency of a product, is introduced. The sizes and shapes of these objects are determined by multiple constraints whose activity cannot be easily predicted. Hence, a discretization of the parameter spaces could obfuscate some advantageous portfolio configurations. Therefore, the classical optimal product portfolio problem is not suitable for this task. As a new mathematical formulation, the continuous set covering problem is presented which transfers into a semi-infinite optimization problem (SIP). A solution approach combining adaptive discretization of the infinite index set with regularization of the non-smooth constraint function is suggested. Numerical examples based on questions from pump industry show that the approach is capable to work with real-world applications.

Suggested Citation

  • Helene Krieg & Jan Schwientek & Dimitri Nowak & Karl-Heinz Küfer, 2020. "Optimal Product Portfolio Design by Means of Semi-infinite Programming," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 489-495, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_59
    DOI: 10.1007/978-3-030-48439-2_59
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