Shapley Value Line Optimization: Extension to Continuous Case

• Activity Number: 312
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Marketing
• Author(s): Faina Shmulyian*+ and Michael Conklin
• Companies: Markettools and GfK
• Keywords: Shapley value Line Optimization ; Discrete Choice Models ; Portfolio Management

Abstract

The standard Shapley Value Line Optimization is used when there is a single basic difference between the product variants, i.e. different flavors among similarly priced items. In many categories, there are multiple decisions that need to be made to perform effective portfolio management. For example, the optimal price-size combination should be determined.

Typically, these types of multi-attribute optimization problems have been addressed with Discrete Choice studies, but Discrete Choice Models have some limitations in large categories with a high number of product variants. To address these limitations and still provide a robust modeling solution for complete portfolio management, we have developed a hybrid approach that blends the strengths of DCM with the variant handling capabilities of the Shapley Value Line Optimization. To do that, we extend the Shapley Value definition to continuous case to perform optimization directly with DCM utilities. In this approach, we utilize a DCM to understand the overall global variables in a category. For each prediction the DCM makes, purchases are allocated among the relevant product variants using the Shapley Value model.