Experimental Designs for Multi-Item Multi-Period Inventory Control

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.