On Demand Estimation and Newsvendor Ordering Decisions under Stockout-Based Substitution

Project: Research

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Motivated by consulting experience in a supermarket, we propose to tackle the repeated newsvendor problem with stockout-based substitution or multiple partially substitutable products. A retailer orders, receives and sells an assortment of product category daily and disposes of any leftover stock at store closing. The firm is challenged by the inaccurate demand information of each product, as stockout of one product would cause substitution with one or more other products. As a result, the demand for a product may not only be censored but also possibly be inflated by other products that have run out of stock during the day. Likewise, the stockout of one product can not only cause censoring of its own demand but also distort demands for its substitutable products. Hence, observed sales are not true demand. Although stockout-caused substitution has been well documented, only a few procedures have been proposed for demand estimation and optimal ordering decisions.This project aims to contribute to both the literature and practice by developing a set of computational methods to achieve demand estimation and optimal ordering decisions. 1) Aggregating the sales transaction data into daily sales data, we will consider a repeated newsvendor problem with a data-driven approach. More specifically, given the historical data containing both sales and ordering decisions, we will adopt a myopic policy based on the Kaplan-Meier Estimator. We then propose to run a stochastic gradient descent with multiple starting points on bootstrapped data to ``learn" the optimal (or near-optimal) solution for ordering decisions. Bounds will be developed and convergency rates will be derived. 2) We will develop algorithms for estimating the primary demands of multiple partially substitutable products from sales transaction (point-of-sale, POS) data. This part of the research serves two purposes: to assess how each of the existing and proposed estimation algorithms perform, and to evaluate existing and to derive new heuristic/optimal algorithms for ordering decisions. Departing from the models in the literature, we allow for an arriving customer to purchase a set of products in one or more units for each, based on which an efficient procedure will be developed for solving the order quantities of multiple partially substitutable products. These models and methods will be calibrated using simulated and sales data, and insights and computational procedures will be developed toward actual implementation. 


Project number9042874
Grant typeGRF
Effective start/end date1/11/19 → …