One of the challenging issues in developing analytical tools to assist the multi-product (item) procurement decisions is how attributes (features) of products can be accommodated to address the substitution effect. It is challenging because the historical sales data seldomly captures whether a sale of a product was caused by its primary demand or a substitution for another product that was stocked out. This would be further exacerbated when preference and substitution behaviors from different customers varied one by one. However, a firm may keep a good record of the historical point-of-sales in sequence, where each sale may contain information about the features of a sale and other available products at that time point, such as color, item type, fabric, design style, selling season, price, etc., in the case of apparels. Such feature information will play an important role in shoppers’ choice of one product over another. Intuitively, the uncertain demand for a product is constructed by linking the “choice” of an arriving shopper to the “choice” made by comparing historical shoppers in “similar” situations (e.g., with facing the “similar” available product sets).In particular, we propose to study the problem when a retailer determines the initial order quantities of all products based on the transaction data, which along with the feature information of each product, records which product past shoppers bought from an assortment and what products are available at the time of their “shopping”. We will not assume a model on the distribution of shoppers’ valuations but only impose, instead, that choices are made based on their ranking orders of the available products, which in turn are determined by product features. That is, one product is purchased over others because the shopper ranks it the highest. (No purchase is also regarded as an option.) The individual ranking order is partially observable from the data. Then, the individual ranking orders – preferences - are “converted” into the probabilities of purchasing individual products by preference learning via ranking kernels which measure similarities among products. Next, the average profit over the selling season is derived, upon which the optimal order quantities will be determined. Consistency of estimation and asymptotic optimality will be established, and approximation strategies will be developed. Comprehensive numerical experiments will be conducted based on synthetic and real data to test the effectiveness of the framework and solutions
