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Experimental Designs for Multi-Item Multi-Period Inventory Control

Xinqi Chen, Xingyu Bai, Zeyu Zheng, Nian Si

Abstract

Randomized experiments, or A/B testing, are the gold standard for evaluating interventions, yet they remain underutilized in inventory management. This study addresses this gap by analyzing A/B testing strategies in multi-item, multi-period inventory systems with lost sales and capacity constraints. We examine two canonical experimental designs, namely, switchback experiments and item-level randomization, and show that both suffer from systematic bias due to interference: temporal carryover in switchbacks and cannibalization across items under capacity constraints. Under mild conditions, we characterize the direction of this bias, proving that switchback designs systematically underestimate, while item-level randomization systematically overestimate, the global treatment effect. Motivated by two-sided randomization, we propose a pairwise design over items and time and analyze its bias properties. Numerical experiments using real-world data validate our theory and provide concrete guidance for selecting experimental designs in practice.

Experimental Designs for Multi-Item Multi-Period Inventory Control

Abstract

Randomized experiments, or A/B testing, are the gold standard for evaluating interventions, yet they remain underutilized in inventory management. This study addresses this gap by analyzing A/B testing strategies in multi-item, multi-period inventory systems with lost sales and capacity constraints. We examine two canonical experimental designs, namely, switchback experiments and item-level randomization, and show that both suffer from systematic bias due to interference: temporal carryover in switchbacks and cannibalization across items under capacity constraints. Under mild conditions, we characterize the direction of this bias, proving that switchback designs systematically underestimate, while item-level randomization systematically overestimate, the global treatment effect. Motivated by two-sided randomization, we propose a pairwise design over items and time and analyze its bias properties. Numerical experiments using real-world data validate our theory and provide concrete guidance for selecting experimental designs in practice.
Paper Structure (34 sections, 11 theorems, 180 equations, 7 figures, 4 tables)

This paper contains 34 sections, 11 theorems, 180 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Model Formulation
  4. System Dynamics
  5. Clairvoyant Optimal Inventory Policy
  6. Demand Estimation
  7. Treatment Effect Estimator and Experimental Designs
  8. Bias Analysis under Different Interventions
  9. Scenario 1: Demand Estimation Bias
  10. Scenario 2: Demand Estimation Variance
  11. Numerical Experiments
  12. Dataset and Experiment Configuration
  13. A/B Tests for Scenario 1: Biased Demand Mean
  14. A/B Tests for Scenario 2: Lower Estimation Variance
  15. Conclusion
  16. ...and 19 more sections

Key Result

Proposition 1

For any period $t$, the myopic clairvoyant policy follows a modified newsvendor solution. Specifically, the optimal order-up-to level $S_{n,t}^*(\lambda_t^*)$ for item $n$ is given by: where the optimal multiplier $\lambda_t^*$ is determined by

Figures (7)

  • Figure 1: An example of a switchback experiment. Each row corresponds to an item, and each column corresponds to a time period.
  • Figure 2: An example of item-level randomized experiment.
  • Figure 3: An example of pairwise randomized experiment.
  • Figure 4: A/B tests (Scenario 1, no stockout-substitution)
  • Figure 5: A/B tests (Scenario 1, with stockout substitution)
  • ...and 2 more figures

Theorems & Definitions (12)

  • Proposition 1
  • Remark 1
  • Lemma 1: Existence of a common structural interval
  • Proposition 2: Sign of the GTE
  • Theorem 1: Bias in SW experiment
  • Theorem 2: Bias in IR experiment
  • Theorem 3: Bias in PR experiment
  • Lemma 2: Mean-field limit of the Lagrange multiplier
  • Proposition 3: Asymptotic non-negative GTE
  • Theorem 4: Asymptotic non-negative bias of SW
  • ...and 2 more