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.
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References
Green, P.E., Krieger, A.M.: Models and heuristics for product line selection. Mark. Sci. 4, 1–19 (1985)
Tsafarakis, S., Saridakis, C., Baltas, G., Matsatsinis, N.: Hybrid particle swarm optimization with mutation for optimizing industrial product lines: an application to a mixed solution space considering both discrete and continuous design variables. Ind. Mark. Manage. 42, 496–506 (2013)
Krieg, H.: Modeling and solution of continuous set covering problems by means of semi-infinite optimization. Ph.D. dissertation. University of Kaiserslautern (2019)
Hettich, R., Kortanek, K.O.: Semi-infinite programming: theory, methods, and applications. SIAM Rev. 35, 380–429 (1993)
Reemtsen, R., Rückmann, J.-J.: Semi-infinite Programming, vol. 417. Springer, Boston, MA (1998)
Blankenship, J.W., Falk, J.E.: Infinitely constrained optimization problems. J. Optim. Theory Appl. 19, 261–281 (1976)
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Krieg, H., Schwientek, J., Nowak, D., Küfer, KH. (2020). Optimal Product Portfolio Design by Means of Semi-infinite Programming. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_59
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DOI: https://doi.org/10.1007/978-3-030-48439-2_59
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