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Assortment Planning with Sponsored Products

Shaojie Tang, Shuzhang Cai, Jing Yuan, Kai Han

TL;DR

This work studies assortment planning in online marketplaces when sponsored products are present, bridging a gap where prior models largely treat all items as organic. By adopting a Multinomial Logit choice model, the authors formulate the revenue-maximization objective $f(\pi)=\sum_{i\in\pi} r_i\,\theta_i(\pi)$ with $\theta_i(\pi)=\frac{w(i,\pi^{-1}(i))}{w_0+\sum_{j\in\pi} w(j,\pi^{-1}(j))}$ and cast the problem as a combinatorial optimization with sponsorship-placement constraints. They show that the core problem P.0 reduces to a total unimodular LP (P.1), enabling exact solutions; they further extend the model to include downward-closed organic constraints $\mathcal{I}$ and provide a principled two-candidate approximation framework (P.3 vs. P.4–P.5) with a provable $(\beta/(\beta+1))$-approximation, where $\beta$ depends on the constraint family (e.g., knapsack or partition matroid). The paper also develops an approximation pipeline for P.5 via P.6, yielding concrete ratios under standard constraint classes, and the Appendix clarifies structural optimality aspects. Overall, it delivers theoretically grounded guidance for integrating sponsored placements into revenue-maximizing assortments with practical applicability to platforms and advertisers.

Abstract

In the rapidly evolving landscape of retail, assortment planning plays a crucial role in determining the success of a business. With the rise of sponsored products and their increasing prominence in online marketplaces, retailers face new challenges in effectively managing their product assortment in the presence of sponsored products. Remarkably, previous research in assortment planning largely overlooks the existence of sponsored products and their potential impact on overall recommendation effectiveness. Instead, they commonly make the simplifying assumption that all products are either organic or non-sponsored. This research gap underscores the necessity for a more thorough investigation of the assortment planning challenge when sponsored products are in play. We formulate the assortment planning problem in the presence of sponsored products as a combinatorial optimization task. The ultimate objective is to compute an assortment plan that optimizes expected revenue while considering the specific requirements of placing sponsored products strategically.

Assortment Planning with Sponsored Products

TL;DR

This work studies assortment planning in online marketplaces when sponsored products are present, bridging a gap where prior models largely treat all items as organic. By adopting a Multinomial Logit choice model, the authors formulate the revenue-maximization objective with and cast the problem as a combinatorial optimization with sponsorship-placement constraints. They show that the core problem P.0 reduces to a total unimodular LP (P.1), enabling exact solutions; they further extend the model to include downward-closed organic constraints and provide a principled two-candidate approximation framework (P.3 vs. P.4–P.5) with a provable -approximation, where depends on the constraint family (e.g., knapsack or partition matroid). The paper also develops an approximation pipeline for P.5 via P.6, yielding concrete ratios under standard constraint classes, and the Appendix clarifies structural optimality aspects. Overall, it delivers theoretically grounded guidance for integrating sponsored placements into revenue-maximizing assortments with practical applicability to platforms and advertisers.

Abstract

In the rapidly evolving landscape of retail, assortment planning plays a crucial role in determining the success of a business. With the rise of sponsored products and their increasing prominence in online marketplaces, retailers face new challenges in effectively managing their product assortment in the presence of sponsored products. Remarkably, previous research in assortment planning largely overlooks the existence of sponsored products and their potential impact on overall recommendation effectiveness. Instead, they commonly make the simplifying assumption that all products are either organic or non-sponsored. This research gap underscores the necessity for a more thorough investigation of the assortment planning challenge when sponsored products are in play. We formulate the assortment planning problem in the presence of sponsored products as a combinatorial optimization task. The ultimate objective is to compute an assortment plan that optimizes expected revenue while considering the specific requirements of placing sponsored products strategically.
Paper Structure (10 sections, 7 theorems, 30 equations, 2 figures)

This paper contains 10 sections, 7 theorems, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Choice model
  4. Feasible sequence
  5. Problem formulation
  6. Optimal Algorithm
  7. Extension: Incorporating additional constraints on organic products
  8. Approximation algorithm for $\textbf{P.5}$
  9. Conclusion
  10. Appendix

Key Result

Lemma 1

Let $\pi^I$ denote the optimal solution of $\textbf{P.3}$, we have $f(\pi^I) \geq \sum_{i\in \pi^*\cap \mathcal{S}} \frac{r_i\cdot w(i, {\pi^*}^{-1}(i))}{w_0+\sum_{j\in \pi^*}w(j, {\pi^*}^{-1}(j)) }$. I.e.,$f(\pi^I) \geq \hbox{part I in (}eq:8\hbox{)}$.

Figures (2)

  • Figure 1: A recommendation system displaying a list of cameras, with sponsored products highlighted in the red box.
  • Figure 2: Structure of an assortment selection system. Our primary focus is on designing an assortment planning module.

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Lemma 3
  • Lemma 4
  • Theorem 2
  • Lemma 5