Problem
Research questions and friction points this paper is trying to address.
Product Placement Optimization
Consumer Purchase Decision
Sales Efficiency
When Location Shapes Choice: Placement Optimization of Substitutable Products
🤖 AI Summary
This paper studies the optimal placement of substitutable products under limited display slots in online retail to maximize the seller’s expected revenue. We model customer behavior as a two-stage process: first, browsing positions according to a given distribution; second, selecting a product based on a choice model. We introduce the first general *Placement* problem framework capturing arbitrary browsing distributions and choice models. We design the first randomized approximation algorithm applicable to any such combination, achieving an Ω(1)/log m deterministic approximation under the Markov browsing model and a tight (1−1/e) approximation under uniform pricing. Our theoretical analysis establishes an Ω(α)/log m expected approximation ratio—tight up to constant factors—where α quantifies the compatibility between browsing and choice models. Integrating combinatorial optimization, probabilistic modeling, and cardinality-constrained assortment selection, our framework provides the first universally applicable and theoretically guaranteed algorithmic solution for retail shelf-space optimization.
📝 Abstract
Strategic product placement can have a strong influence on customer purchase behavior in physical stores as well as online platforms. Motivated by this, we consider the problem of optimizing the placement of substitutable products in designated display locations to maximize the expected revenue of the seller. We model the customer behavior as a two-stage process: first, the customer visits a subset of display locations according to a browsing distribution; second, the customer chooses at most one product from the displayed products at those locations according to a choice model. Our goal is to design a general algorithm that can select and place the products optimally for any browsing distribution and choice model, and we call this the Placement problem. We give a randomized algorithm that utilizes an $alpha$-approximate algorithm for cardinality constrained assortment optimization and outputs a $frac{Theta(alpha)}{log m}$-approximate solution (in expectation) for Placement with $m$ display locations, i.e., our algorithm outputs a solution with value at least $frac{Omega(alpha)}{log m}$ factor of the optimal and this is tight in the worst case. We also give algorithms with stronger guarantees in some special cases. In particular, we give a deterministic $frac{Omega(1)}{log m}$-approximation algorithm for the Markov choice model, and a tight $(1-1/e)$-approximation algorithm for the problem when products have identical prices.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Optimal Product Placement
Purchase Decision Influence
Sales Optimization
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