New product launch decisions with robust optimization

We consider a problem where a company must decide the order in which to launch new products within a given time horizon and budget constraints, and where the parameters of the adoption rate of these new products are subject to uncertainty. This uncertainty can bring significant change to the optimal launch sequence. We present a robust optimization approach that incorporates such uncertainty on the Bass diffusion model for new products as well as on the price response function of partners that collaborate with the company in order to bring its products to market. The decision-maker optimizes his worst-case profit over an uncertainty set where nature chooses the time periods in which (integer) units of the budgets of uncertainty are used for worst impact. This leads to uncertainty sets with binary variables. We show that a conservative approximation of the robust problem can nonetheless be reformulated as a mixed integer linear programming problem, is therefore of the same structure as the deterministic problem and can be solved in a tractable manner. Finally, we illustrate our approach on numerical experiments. Our model also incorporates contracts with potential commercialization partners. The key output of our work is a sequence of product launch times that protects the decision-maker against parameter uncertainty for the adoption rates of the new products and the response of potential partners to partnership offers.

[1]  Trichy V. Krishnan,et al.  Research Note: Multinational Diffusion Models: An Alternative Framework , 2002 .

[2]  Vijay Mahajan,et al.  Adaptive Technological Substitution Models , 1980 .

[3]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[4]  S. Kalish,et al.  A MARKET ENTRY TIMING MODEL FOR NEW TECHNOLOGIES * , 2004 .

[5]  Dipak C. Jain,et al.  Why the Bass Model Fits without Decision Variables , 1994 .

[6]  Huseyin Topaloglu,et al.  Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model , 2012, Oper. Res..

[7]  Michael R. Hyman,et al.  The timeliness problem in the application of bass-type new product-growth models to durable sales forecasting , 1988 .

[8]  Vijay Mahajan,et al.  Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance , 1982 .

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

[10]  Jiawei Zhang,et al.  Appointment Scheduling with Limited Distributional Information , 2013, Manag. Sci..

[11]  Donald R. Lehmann,et al.  A Meta-Analysis of Applications of Diffusion Models , 1990 .

[12]  Elçin Çetinkaya.  Essays in Robust and Data-Driven Risk Management , 2014 .

[13]  Daniel Bienstock,et al.  Computing robust basestock levels , 2008, Discret. Optim..

[14]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[15]  E. Rogers.  Diffusion of Innovations , 1962 .

[16]  J. Keith Ord,et al.  The use of discounted least squares in technological forecasting , 1985 .

[17]  A. Thiele,et al.  Real Options : A Survey , 2015 .

[18]  Charlotte H. Mason,et al.  Technical Note---Nonlinear Least Squares Estimation of New Product Diffusion Models , 1986 .

[19]  J. Arndt.  Role of Product-Related Conversations in the Diffusion of a New Product , 1967 .

[20]  Vijay Mahajan,et al.  New Product Diffusion Models in Marketing: A Review and Directions for Research: , 1990 .

[21]  Dolores Brzycki,et al.  Models of Technology Diffusion at Public Universities , 2001 .

[22]  Gary L. Lilien,et al.  A market entry timing model for new techniques , 1986 .

[23]  Robert J. Thomas,et al.  Innovation diffusion uncertainty, advertising and pricing policies , 2005, Eur. J. Oper. Res..