Management of Multi-Item Retail Inventory Systems with Demand Substitution

Abstract

Customers for retail merchandise can often be satisfied with one of several items. Accounting for demand substitution in defining customer service influences the choice of items to stock and the optimal inventory level for each item stocked. Further, when certain items are not stocked, the resulting substitutions increase the demand for other items, which also affects the optimal stock levels. In this paper, we develop a probabilistic demand model for items in an assortment that captures the effects of substitution and a methodology for selecting item inventory levels so as to maximize total expected profit, subject to given resource constraints. Illustrative examples are solved to provide insights concerning the behavior of the optimal inventory policies, using the negative binomial demand distribution, which has performed well in fitting retail sales data.

Dynamic Assortment with Demand Learning for Seasonal Consumer Goods

“…The actual sales resulting from this original demand and the assortments implemented were simulated according to the substitution structure defined in §3.3. More specifically, following Smith and Agrawal (2000) we assumed that L i = L for all i and considered the following three scenarios:…”

“…See Bultez and Naert (1988) for a classical example in which the demand of a product depends on the allocated shelf space, and the overall space available is a limited resource. In the operations management literature, van Ryzin and Mahajan (1999) and Smith and Agrawal (2000) also consider static assortment problems, but with a stochastic demand model and static product substitution. That is, customer demand reflects aggregated substitution effects depending on the initial assortment decision but not on the actual inventory levels observed by individual customers once arrived at the store.…”

“…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.…”

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.…”