Optimal newsvendor ordering under stockout-based substitution: a Non-parametric approach

Participant(s)

Activity date	13 Jul 2019 → 15 Jul 2019
Degree of recognition	International

Description

Motivated by the problem faced by a baker who supplies bread to multiple stores, we consider a newsvendor setting with stock-out-based substitution. When a product runs out of stock during shopping hours, a customer may seek a substitute. At the end of a day, all left-over bread is salvaged. The challenge lies in estimating demand and substitution rates from observed (historical) data. Assuming time-increment stationary and independent arrivals during business hours and stochastic substitution upon stock-out, we give a new class of consistent nonparametric estimators of demand and substitute demand, based on the product-limit form of the well-known Kaplan-Meier estimator. We also highlight the existence of an optimal order quantity for each product and propose a data-driven policy for the two-product newsvendor problem with substitution. Extending our analysis to multi-product cases, we show that the number of local optima is limited and can be calculated. We validate the analytical results and show the convergence of the estimates through simulation.

Research Unit / Event Journal/Book Series