[Paper Review] Predictive and Prescriptive Analytics for Location Selection of Add-on Retail Products

Teng Huang, David Bergman+1 more|arXiv (Cornell University)|Apr 3, 2018

Consumer Market Behavior and Pricing30 references3 citations

TL;DR

This paper proposes a joint predictive and prescriptive analytics framework for optimizing add-on retail product expansion, using machine learning to forecast derived demand and mixed-integer optimization to select high-impact locations. The approach increases expected sales by up to 14.25% over baseline policies, with spatial autocorrelation significantly improving predictive accuracy when modeled via a distance-decay spatial weight matrix.

ABSTRACT

In this paper, we study an analytical approach to selecting expansion locations for retailers selling add-on products whose demand is derived from the demand of another base product. Demand for the add-on product is realized only as a supplement to the demand of the base product. In our context, either of the two products could be subject to spatial autocorrelation where demand at a given location is impacted by demand at other locations. Using data from an industrial partner selling add-on products, we build predictive models for understanding the derived demand of the add-on product and establish an optimization framework for automating expansion decisions to maximize expected sales. Interestingly, spatial autocorrelation and the complexity of the predictive model impact the complexity and the structure of the prescriptive optimization model. Our results indicate that the models formulated are highly effective in predicting add-on product sales, and that using the optimization framework built on the predictive model can result in substantial increases in expected sales over baseline policies.

Motivation & Objective

• To develop a data-driven framework for selecting optimal locations to expand add-on product sales in retail chains.
• To address the challenge of derived demand, where add-on product sales depend on base product sales at physical locations.
• To integrate predictive modeling with optimization to automate and improve expansion decisions beyond simple base-product sales heuristics.
• To evaluate the impact of spatial autocorrelation on predictive accuracy and optimization performance in retail expansion.

Proposed method

• Train multiple machine learning models—linear regression, linear-kernel SVR, and radial-kernel SVR—on point-of-sale data, demographic data (income, population), and a spatial weight matrix.
• Incorporate a spatial weight matrix that decays with distance to model spatial autocorrelation in base-product demand.
• Use the Moran’s I test to validate spatial autocorrelation and determine when to include spatial features in predictive models.
• Formulate a mixed-integer optimization model (EO-P*) to select the optimal set of expansion sites under capacity constraints, using predictions from the best-performing model.
• Evaluate solution robustness by testing EO-P* solutions across alternative predictive models (LR, LK, RK) to ensure consistency and reliability.
• Implement a prescriptive optimization framework that maximizes expected sales while accounting for the complexity introduced by non-linear predictive models.

Experimental results

Research questions

• RQ1 How does spatial autocorrelation in base-product demand affect the predictive accuracy of add-on product sales models?
• RQ2 What is the impact of incorporating a spatial weight matrix on the performance of predictive models for derived demand?
• RQ3 Can a joint predictive-prescriptive framework outperform baseline expansion policies based solely on base-product sales?
• RQ4 How robust are the optimal expansion decisions across different predictive models and data configurations?
• RQ5 What is the trade-off between model complexity and optimization performance in the context of non-linear predictive models?

Key findings

• The predictive models achieved an out-of-sample mean absolute percent error of approximately 20%, outperforming existing literature for similar contexts.
• Including a spatial weight matrix improved predictive accuracy only when spatial autocorrelation was present, as confirmed by the Moran’s I test.
• The EO-P* optimization framework increased expected sales by up to 14.25% compared to baseline policies, with consistent gains across multiple regions and predictive models.
• Solutions from EO-P* consistently outperformed baseline methods across all tested predictive models, with only one exception (LK model in Region 2), indicating strong robustness.
• The optimization model’s structure and complexity were directly influenced by the non-linear nature of the predictive model, highlighting the interdependence between prediction and prescriptive modeling.
• Robustness checks confirmed that EO-P* solutions maintained superior performance even when evaluated on alternative predictive models, increasing manager confidence in the recommendations.