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•We investigate multichannel assortment planning decisions across retailers.•Retailer’s inventory policy and distribution strategy through an analytical model.•Test relationship between product attributes & retailers’ channel choice.•Retailers are less likely to drop-ship colored/irregularly-sized products.•Detect nonlinearities and thresholds in the effects or product value. [Display omitted] Retailers that sell seasonal products face significant challenges when planning inventory assortment. The incorporation of drop-shipping into their operations, wherein suppliers own and ship products directly to consumers at retailers’ requests, has only complicated these challenges. This study investigates multichannel assortment planning of retailers that sell seasonal products. We first capture structural properties of multichannel retailing of seasonal products through a simple and parsimonious analytical model. The analytical model uncovers key seasonal product attributes that make it more attractive for retailers to allocate a product for sale in the drop-shipping channel than in the store channel. We then empirically assess the findings of the analytical model. Using a rich and unique dataset from the fashion retail industry, we test relationships between product attributes and retailers’ channel choice. The application of a generalized linear latent and mixed model controls for selection bias by jointly estimating retailers’ likelihood of allocating a product’s inventory to the drop-shipping channel and the allocated volume in each channel according to the product’s characteristics. The empirical findings suggest that retailers are less likely to drop-ship products that are colored, irregularly sized, and offered in more style variants. They also unveil cross-channel effects in terms of inventory amounts allocated for sale in each channel according to those characteristics. Our analytical and empirical assessments jointly demonstrate the complementary roles played by drop-shipping and store channels for seasonal products and offer important academic and practical implications.

We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and returns the product back to the firm to be used by other customers. The goal is to find a policy for deciding on the assortment to offer to each customer so that the total expected revenue over a finite selling horizon is maximized. The dynamic-programming formulation of this problem requires a high-dimensional state variable that keeps track of the on-hand product inventories, as well as the products that are currently in use. We present a tractable approach to compute a policy that is guaranteed to obtain at least 50% of the optimal total expected revenue. This policy is based on constructing linear approximations to the optimal value functions. When the usage duration is infinite or follows a negative binomial distribution, we also show how to efficiently perform rollout on a simple static policy. Performing rollout corresponds to using separable and nonlinear value function approximations. The resulting policy is also guaranteed to obtain at least 50% of the optimal total expected revenue. The special case of our model with infinite usage durations captures the case where the customers purchase the products outright without returning them at all. Under infinite usage durations, we give a variant of our rollout approach whose total expected revenue differs from the optimal by a factor that approaches 1 with rate cubic-root of C min, where C min is the smallest inventory of a product. We provide computational experiments based on simulated data for dynamic assortment management, as well as real parking transaction data for the city of Seattle. Our computational experiments demonstrate that the practical performance of our policies is substantially better than their performance guarantees and that performing rollout yields noticeable improvements. This paper was accepted by Yinyu Ye, optimization.

We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total customer demand is random and comprises fixed proportion of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering among products. A customer purchases the highest-ranked product, according to his type (if any), that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help to characterize multiple local maxima. We use the properties of the optima to solve the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the mean demand is large, the degree of substitutability is high, the population is homogeneous, or prices and/or costs vary across products.

We consider revenue management problems when customers choose among the offered products according to the Markov chain choice model. In this choice model, a customer arrives into the system to purchase a particular product. If this product is available for purchase, then the customer purchases it. Otherwise, the customer transitions to another product or to the no purchase option, until she reaches an available product or the no purchase option. We consider three classes of problems. First, we study assortment problems, where the goal is to find a set of products to offer to maximize the expected revenue obtained from each customer. We give a linear program to obtain the optimal solution. Second, we study single resource revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes the resource. We show how the optimal set of products to offer changes with the remaining resource inventory. Third, we study network revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes a combination of resources. A standard linear programming approximation of this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one with a substantially smaller size. We give an algorithm to recover the optimal solution to the original linear program from the reduced linear program. The reduced linear program can dramatically improve the solution times for the original linear program. The online appendix, data files, and source code are available at https://doi.org/10.1287/opre.2017.1628 .

•Large differences in products bought online versus offline in fashion goods market.•These differences impact the measurement and interpretation of long tail effects.•People buying different products (not more variety) online drive long tail effects.•Retailers need to offer or emphasize a different product mix online (not a larger assortment).•We provide guidance to retailers in curating their online and offline assortments. The fast-paced growth of e-commerce is impacting the type and variety of products consumers purchase across channels. A commonly held theory, known as long tail theory, posits that online sales are less concentrated at the top of the sales distribution than offline sales, and that more variety is bought online, making the tails of the overall sales distribution denser with the growth of e-commerce. Most of the literature testing the long tail theory has focused on examining entertainment goods markets that do not require much physical examination, and has predominantly found results consistent with the theory. However, the magnitude and antecedents of the observed long tail effects might be different for product categories containing products that require more physical examination before purchase, such as fashion goods. In this study, using detailed individual and transaction level panel data from two multichannel fashion goods retail brands, we show that while the shift to the online channel results in a decrease in the concentration of overall sales for both brands, this change mostly results from consumers buying different products online rather than consumers buying a greater variety online compared to offline. We show that the flattening of the overall sales distribution with the growth of e-commerce in our data is driven by consumers sorting their purchases into channels based on product characteristics. In contrast to the recommendations from the previous long tail literature, our results show that fashion apparel retailers do not need to offer broader assortments online compared to offline, but they may find it profitable to carry or emphasize a different product mix online compared to offline. Our results also provide guidance to fashion goods retailers in curating their online and offline assortments and setting inventory management strategies across the channels. [Display omitted]

Motivated by the availability of real-time data on customer characteristics, we consider the problem of personalizing the assortment of products for each arriving customer. Using actual sales data from an online retailer, we demonstrate that personalization based on each customer's location can lead to over 10% improvements in revenue compared to a policy that treats all customers the same. We propose a family of index-based policies that effectively coordinate the real-time assortment decisions with the back-end supply chain constraints. We allow the demand process to be arbitrary and prove that our algorithms achieve an optimal competitive ratio. In addition, we show that our algorithms perform even better if the demand is known to be stationary. Our approach is also flexible and can be combined with existing methods in the literature, resulting in a hybrid algorithm that brings out the advantages of other methods while maintaining the worst-case performance guarantees. This paper was accepted by Dimitris Bertsimas, special issue on business analytics .

Assortment planning of substitutable products is a major operational issue that arises in many industries such as retailing, airlines, and consumer electronics. We consider a single-period joint assortment and inventory planning problem under dynamic substitution with stochastic demands, and provide complexity and algorithmic results as well as insightful structural characterizations of near-optimal solutions for important variants of the problem. First, we show that the assortment planning problem is NP-hard even for a very simple consumer choice model, where each consumer is willing to buy only two products. In fact, we show that the problem is hard to approximate within a factor better than 1 − 1/ e . Second, we show that for several interesting and practical customer choice models, one can devise a polynomial-time approximation scheme (PTAS), i.e., the problem can be solved efficiently to within any level of accuracy. To the best of our knowledge, this is the first efficient algorithm with provably near-optimal performance guarantees for assortment planning problems under dynamic substitution. Quite surprisingly, the algorithm we propose stocks only a constant number of different product types; this constant depends only on the desired accuracy level. This provides an important managerial insight that assortments with a relatively small number of product types can obtain almost all of the potential revenue. Furthermore, we show that our algorithm can be easily adapted for more general choice models, and we present numerical experiments to show that it performs significantly better than other known approaches.

Grocery retailers are in a dilemma. They often prioritize availability over other aspects due to strong competition in this sector and the imperative of realizing sales. The target for many grocery retailers has been high on-shelf availability and large variety to increase customer satisfaction. However, this policy contributes to a significant share of overstock. The economic pressure of unsold products, the environmental impact of wasted resources, and the ethical questions arising from discarding edible food, have increasingly thrown the spotlight on grocery retailers to change their strategies. Grocery retailers are thus facing a trade-off between increasing attractiveness via high availability on the one hand, and the environmental, social, and financial impacts of overstock, on the other. One common practice in dealing with overstock is mainly being reactive to mitigate the impact, using initiatives such as price promotions or donations. This explorative study investigates options for how grocery retailers can proactively reduce food waste via better planning of their store operations. Seven case companies participated in this qualitative study, where we focused on ultra-fresh products as the most important waste category. Face-to-face interviews with managers were the primary source for data collection. The heterogeneity of our sample enabled us to build a common understanding of proactive options to reduce food waste with enhanced operations. The analysis reveals six coherent and distinct topics. A basis for all proactive operational planning processes is (1) the use of a comprehensive database and information systems. This builds the foundation for (2) tailored demand forecasts related to perishable product-specific requirements. Subsequently, consideration is needed of (3) the enhanced planning of assortment sizes, (4) the definitions of differentiated service levels and (5) the tailored ordering and replenishment processes that impact food waste. Finally, (6) salvage options, such as dynamic pricing, secondary usage, and sustainable waste streams constitute valuable mitigation strategies. We formulated 15 propositions that could support the decisions of grocery retailers developing proactive food waste reduction practices. These propositions will guide future research, as they provide a coherent and cohesive picture of related topics in grocery retail operations.

When retailers conduct product assortment planning (PAP), they determine (1) The variety of merchandise, (2) The depth of merchandise, and (3) Service level or the amount of inventory to allocate to each stock-keeping unit (SKU). Despite longstanding recognition of its importance, no dominant PAP solution exists, and theoretical and decision support models address only some of the factors that complicate assortment planning. This article simultaneously addresses the variety, depth, and service level aspects of PAP to provide a more thorough understanding. A review of current academic literature and best trade practices identifies open questions and directions for further research and applications.

We examine the effects of product variety and inventory levels on store sales. Using 4 years of data from stores of a large retailer, we show that increases in product variety and inventory levels are both associated with higher sales. We also show that increasing product variety and inventory levels has an indirect negative effect on store sales through their impact on phantom products—products that are physically present at the store, but only in storage areas where customers cannot find or purchase them. Our study highlights a consequence of increased product variety and inventory levels that has previously been overlooked in studies of retail product variety and inventory management. It also quantifies the impact of phantom products on store sales. In addition, our study provides empirical evidence to support earlier claims that higher product variety and inventory levels lead to an increase in defect rate. We discuss the implications of our findings for retail inventory and assortment planning and for the design of retail stores.