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

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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.

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Conference

TitleThe Twelfth Annual International Conference of Chinese Scholars Association for Management Science and Engineering (CSAMSE)
Date13/07/1915/07/19
Website
LocationJIN-NIU Hotel Chengdu
CityChengdu
PlaceChina
Degree of recognitionInternational event

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