Non-parametric estimation and replenishment for products with stochastic bidirectional substitution

Participant(s)

Activity date	4 Jan 2020 → 5 Jan 2020
Degree of recognition	International

Description

Consumers deal with retail stock-outs by considering substitutes. Shrewd retailers sometimes use this to induce demand for higher-margin products or to recover sales lost to stock-outs. From a management perspective, this influences both estimation of demand, substitution between products, and the jointly optimal replenishment quantities. We investigate a two-product substitution problem from all three perspectives. Forgoing the dominating approach of multinomial logistic regression, our estimation takes a data-driven approach based on a modified Kaplan-Meier (K-M) estimator. Combining K-M--estimates sampled at different times, we identify empirical distributions of demand and of substitution that converge to the true distributions, with its convergence rates. For optimal ordering, we show that under general conditions, the stochastic substitution problem has a joint product function that is submodular in the replenishment quantities.

Research Unit / Event Journal/Book Series