Optimizing Product Line Designs: Efficient Methods and Comparisons

We take advantage of recent advances in optimization methods and computer hardware to identify globally optimal solutions of product line design problems that are too large for complete enumeration. We then use this guarantee of global optimality to benchmark the performance of more practical heuristic methods. We use two sources of data: (1) a conjoint study previously conducted for a real product line design problem, and (2) simulated problems of various sizes. For both data sources, several of the heuristic methods consistently find optimal or near-optimal solutions, including simulated annealing, divide-and-conquer, product-swapping, and genetic algorithms.

[1]  Thomas S. Gruca,et al.  Optimal new product positioning: A genetic algorithm approach , 2003, Eur. J. Oper. Res..

[2]  Gregory Dobson,et al.  Positioning and Pricing a Product Line , 1988 .

[3]  J. Hauser.  Note---Competitive Price and Positioning Strategies , 1988 .

[4]  J. Frédéric Bonnans,et al.  Numerical Optimization: Theoretical and Practical Aspects (Universitext) , 2006 .

[5]  Paul E. Green,et al.  Models and Heuristics for Product Line Selection , 1985 .

[6]  Varghese S. Jacob,et al.  Genetic Algorithms for Product Design , 1996 .

[7]  R. Kohli,et al.  Heuristics for Product-Line Design Using Conjoint Analysis , 1990 .

[8]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[9]  Fred S. Zufryden,et al.  An Integer Programming Approach to the Optimal Product Line Selection Problem , 1988 .

[10]  Jeffrey D. Camm,et al.  Conjoint Optimization: An Exact Branch-and-Bound Algorithm for the Share-of-Choice Problem , 2006, Manag. Sci..

[11]  Konstantinos Paparrizos,et al.  A genetic algorithm approach to the product line design problem using the seller's return criterion: An extensive comparative computational study , 2001, Eur. J. Oper. Res..

[12]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[13]  Leyuan Shi,et al.  An Optimization Framework for Product Design , 2001, Manag. Sci..

[14]  R. Gupta,et al.  Development of hybrid genetic algorithms for product line designs , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Paul E. Green,et al.  A Componential Segmentation Model with Optimal Product Design Features , 1989 .

[16]  Abilio Lucena,et al.  Lagrangian heuristics for the linear ordering problem , 2004 .

[17]  Jorge Pinho de Sousa,et al.  Metaheuristics: Computer Decision-Making , 2010 .

[18]  Abraham P. Punnen,et al.  The traveling salesman problem and its variations , 2007 .

[19]  John R. Hauser,et al.  Fast Polyhedral Adaptive Conjoint Estimation , 2002 .

[20]  Suresh K. Nair,et al.  Near optimal solutions for product line design and selection: beam search heuristics , 1995 .

[21]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[22]  R. Kipp Martin,et al.  Large scale linear and integer optimization - a unified approach , 1998 .

[23]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[24]  Claudia Sagastizábal,et al.  Dynamic Bundle Methods: Application to Combinatorial Optimization , 2004 .

[25]  Deeparnab Chakrabarty,et al.  Knapsack Problems , 2008 .

[26]  J. M. Katz,et al.  Optimal product design using conjoint analysis : Computational complexity and algorithms * , 2002 .

[27]  Leyuan Shi,et al.  Nested Partitions Method for Global Optimization , 2000, Oper. Res..

[28]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[29]  David W. Beach,et al.  Integrated Product Design for Marketability and Manufacturing , 1997 .

[30]  Oded Netzer,et al.  Alternative Models for Capturing the Compromise Effect , 2004 .

[31]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[32]  G. Dobson,et al.  Heuristics for pricing and positioning a product-line using conjoint and cost data , 1993 .

[33]  Claudia A. Sagastizábal,et al.  Dynamic bundle methods , 2009, Math. Program..

[34]  M. D. Wilkinson,et al.  Management science , 1989, British Dental Journal.

[35]  J. Hauser,et al.  Profit Maximizing Perceptual Positions: An Integrated Theory for the Selection of Product Features and Price , 1981 .

[36]  Joel Huber.  Comparing Perceptual Mapping and Conjoint Analysis : The Political Landscape 1996 Sawtooth Software Conference , 2001 .

[37]  Ramesh Krishnamurti,et al.  A Heuristic Approach to Product Design , 1987 .

[38]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[39]  Vithala R. Rao,et al.  Conjoint Measurement- for Quantifying Judgmental Data , 1971 .

[40]  Harald Hruschka,et al.  Genetic Algorithms for Product Design: How Well do They Really Work? , 2003 .

[41]  Paul E. Green,et al.  Chapter 10 Conjoint analysis with product-positioning applications , 1993, Marketing.