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Robust portfolio optimization model for electronic coupon allocation

Yuki Uehara, Naoki Nishimura, Yilin Li, Jie Yang, Deddy Jobson, Koya Ohashi, Takeshi Matsumoto, Noriyoshi Sukegawa, Yuichi Takano

TL;DR

This work tackles the problem of allocating electronic coupons under a budget constraint to maximize sales uplift. It introduces a robust portfolio optimization approach grounded in customer segmentation, contrasting it with a multi-choice knapsack baseline and a mean–variance optimization baseline. The method is validated on a large real-world dataset with six coupon types, showing that robust optimization yields larger uplifts, especially under budget constraints and estimation uncertainty. The findings highlight the practical potential of robust optimization for coupon allocation and suggest directions toward further robust formulations and dynamic allocation strategies.

Abstract

Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget constraint on an e-commerce website. We apply a robust portfolio optimization model based on customer segmentation to the coupon allocation problem. We also validate the efficacy of our method through numerical experiments using actual data from randomly distributed coupons. Main contributions of our research are twofold. First, we handle six types of coupons, thereby making it extremely difficult to accurately estimate the difference in the effects of various coupons. Second, we demonstrate from detailed numerical results that the robust optimization model achieved larger uplifts of sales than did the commonly-used multiple-choice knapsack model and the conventional mean-variance optimization model. Our results open up great potential for robust portfolio optimization as an effective tool for practical coupon allocation.

Robust portfolio optimization model for electronic coupon allocation

TL;DR

This work tackles the problem of allocating electronic coupons under a budget constraint to maximize sales uplift. It introduces a robust portfolio optimization approach grounded in customer segmentation, contrasting it with a multi-choice knapsack baseline and a mean–variance optimization baseline. The method is validated on a large real-world dataset with six coupon types, showing that robust optimization yields larger uplifts, especially under budget constraints and estimation uncertainty. The findings highlight the practical potential of robust optimization for coupon allocation and suggest directions toward further robust formulations and dynamic allocation strategies.

Abstract

Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget constraint on an e-commerce website. We apply a robust portfolio optimization model based on customer segmentation to the coupon allocation problem. We also validate the efficacy of our method through numerical experiments using actual data from randomly distributed coupons. Main contributions of our research are twofold. First, we handle six types of coupons, thereby making it extremely difficult to accurately estimate the difference in the effects of various coupons. Second, we demonstrate from detailed numerical results that the robust optimization model achieved larger uplifts of sales than did the commonly-used multiple-choice knapsack model and the conventional mean-variance optimization model. Our results open up great potential for robust portfolio optimization as an effective tool for practical coupon allocation.
Paper Structure (19 sections, 13 equations, 5 figures, 3 tables)

This paper contains 19 sections, 13 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Related work
  4. Our contribution
  5. Optimization models
  6. Coupon effect estimation
  7. Multiple-choice knapsack (MCK) model
  8. Mean--variance optimization (MVO) model
  9. Robust optimization (RO) model
  10. Numerical experiments
  11. Dataset
  12. Coupon allocation strategies
  13. Evaluation methodology
  14. Results of coupon effect estimation
  15. Results of customer segmentation
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Uplift curves of GMV for six types of coupons
  • Figure 2: Uplift-GMV with respect to the consumed cost
  • Figure 3: Allocated coupons without the lower/upper bounds with respect to the budget
  • Figure 4: Allocated coupons with the lower/upper bounds $(L,U) = (0.05, 0.50)$ with respect to the budget
  • Figure 5: Uplift-GMV of the RO model without the lower/upper bounds with respect to the three hyperparameters