Solving Product Line Design Optimization Problems Using Stochastic Programming

Abstract

In this paper, we try to apply stochastic programming methods to product line design optimization problems. Because of the estimated part-worths of the product attributes in conjoint analysis, there is a need to deal with the uncertainty caused by the underlying statistical data (Kall and Mayer, 2011, Stochastic linear programming: models, theory, and computation. International series in operations research & management science, vol. 156. New York, London: Springer). Inspired by the work of Georg B. Dantzig (1955, Linear programming under uncertainty. Management Science, 1, 197–206), we developed an approach to use the methods of stochastic programming for product line design issues. Therefore, three different approaches will be compared by using notional data of a yogurt market from Gaul and Baier (2009, Simulations- und optimierungsrechnungen auf basis der conjointanalyse. In D. Baier, & M. Brusch (Eds.), Conjointanalyse: methoden-anwendungen-praxisbeispiele (pp. 163–182). Berlin, Heidelberg: Springer). Stochastic programming methods like chance constrained programming are applied on Kohli and Sukumar (1990, Heuristics for product-line design using conjoint analyses. Management Science, 36, 1464–1478) and will be compared to its original approach and to the one of Gaul, Aust and Baier (1995, Gewinnorientierte Produktliniengestaltung unter Beruecksichtigung des Kundennutzens. Zeitschrift fuer Betriebswirtschaftslehre, 65, 835–855). Besides the theoretical work, these methods will be realized by a self-written code with the help of the statistical software package R.