Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application

Abstract

Assortment planning at a retailer entails both selecting the set of products to be carried and setting inventory levels for each product. We study an assortment planning model in which consumers might accept substitutes when their favorite product is unavailable. We develop an algorithmic process to help retailers compute the best assortment for each store. First, we present a procedure for estimating the parameters of substitution behavior and demand for products in each store, including the products that have not been previously carried in that store. Second, we propose an iterative optimization heuristic for solving the assortment planning problem. In a computational study, we find that its solutions, on average, are within 0.5% of the optimal solution. Third, we establish new structural properties (based on the heuristic solution) that relate the products included in the assortment and their inventory levels to product characteristics such as gross margin, case-pack sizes, and demand variability. We applied our method at Albert Heijn, a supermarket chain in The Netherlands. Comparing the recommendations of our system with the existing assortments suggests a more than 50% increase in profits.

Dynamic Assortment with Demand Learning for Seasonal Consumer Goods

“…In contrast, Mahajan and van Ryzin (2001) describe a more detailed assortment model capturing dynamic substitutions, that is substitutions due to stockouts experienced by individual customers, and analyze it using sample path methods. For additional references on assortment problems, we refer the reader to Kök and Fisher (2004). None of the papers just cited considers demand learning, and accordingly the assortment problems they investigate are static, not dynamic.…”

“…1 However, we have not found studies considering a multiarmed bandit problem with switching costs over a finite horizon. Finally, a limited amount of research has been done for bandit problems with dependent arms (see, for instance, Presman and Sonin 1990), but we do not know of any heuristic described elsewhere for the case in which, as in this paper, rewards follow a correlation structure given by a demand substitution model similar to that of Smith and Agrawal (2000) and Kök and Fisher (2004).…”

“…In the marketing literature, substitution effects are often captured through parametric models like the multinomial logit (see Ben-Akiva and Lerman 1985). However, we adopt a substitution model similar to Smith and Agrawal (2000) and Kök and Fisher (2004). That is, we use the concept of the original demand for each product, defined as the demand that would be observed for that product if all the other products were also included in the assortment.…”

Private labels and retail assortment planning: a differential evolution approach

“…Kök and Fisher (2007) define retail product assortment planning (PAP) as the process used to find the optimal combination of products to be carried and set the inventory levels of each product. Hübner and Kuhn (2012) define variety as the number and combination of product categories in a retailer's product portfolio, depth as the number of stock-keeping units within a category and service level as the amount of merchandise inventory within a category.…”

The Role of Component Commonality in Product Assortment Decisions

“…Van Ryzin and Mahajan (1999) consider such a model and demonstrate that the optimal assortment consists of a certain number of the most popular products. Other papers in this area include Smith and Agrawal (2000), Cachon et al (2005), Gaur and Honhon (2006), and Kök and Fisher (2007); see Kök et al (2008) for a detailed review of this stream of work. The literature on component commonality (e.g., van Mieghem 1998van Mieghem , 2004Bernstein et al 2007) and other forms of operational flexibility (e.g., Fine andFreund 1990, Lee andTang 1997) studies inventory and common-component allocation decisions and explores the resulting value of flexibility for a given fixed assortment of products.…”