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Joint product assortment, inventory and price optimization to attract loyal and non-loyal customers Argyro Katsifou a,n, Ralf W. Seiferta,b,1, Jean-Sbastien Tancrezc,2 aEcole Polytechnique Fdrale de Lausanne (EPFL), College of Management of Technology, Chair of Technology fax: 41 21 693 00 20. E-mail addresses: argyro.katsifou , irokatsifou (A. Katsifou), ralf.seifertepfl .ch (R.W. Seifert), js.tancrezuclouvain-mons.be (J.-S. Tancrez). 1 Tel.: 41 21 693 00 22; fax: 41 21 693 00 20. 2 Tel.: 32 65 323 538; fax: 41 21 693 00 20. Omega 46 (2014) 3650 loss making if considered in isolation), they are critically important because they help increase overall store traffi c by attracting non- loyal customers to a store. Non-loyal customers do not regularly visit the same store but are rather opportunistic and are occa- sionally attracted by special offers. This increased store traffi c can also boost sales of standard products, resulting in increased overall sales and profi ts. The demand fl ow generated by non-loyal (respectively loyal) customers for standard (respectively special) products is called the cross-selling effect. The pricing of special products is thus an essential element and should above all aim to attract non-loyal customers and eventually increase the cross- selling effect. Moreover, studies show that customers drawn to promotions not only enjoy shopping but also gain a sense of achievement by buying items on special offer 28. For retailers, providing customers with this sense of achievement by rotating special assortment items might be preferable to promoting stan- dard assortment items, since it allows retailers to maintain a steady sell-through of standard items and avoids the erosion of established price points. The practice of carrying a combined assortment is especially widespread in the grocery industry. Walmart, for example, offers a wide range of standard product categories from food and clothing to home electronics as well as a limited number (around 1% of the total assortment) of weekly “special buys” in order to create excitement 28. Lidl and Aldi, two of the most successful discount retailers, compete effectively with a very narrow product assortment, consisting of standard products such as tooth-paste and orange juice, to which special assortment items are constantly added (called “surprise buys” or “special items”). Aldis special assortment, for example, consists of non-food, very diverse pro- ducts introduced twice per week for 1-week intervals. These products may be electrical items, clothing, sports equipment or pet toys and are rotated throughout the year according to the season (e.g. “back to school” special items or ski wear) with the aim of keeping the shopping experience in the store interesting 41,21. The number of these “special items,” however, varies substantially in percentage terms between the two retailers (approximately 9% for Lidl versus 4% for Aldi). In this paper, we devise a stylized mathematical model to address the integrated product assortment, pricing and inventory optimization problem taking into consideration the role of both standard and special assortments in generating store traffi c when the available shelf space is limited. The proposed integrated approach explicitly models the interdependence between the total assortment decision, the pricing, and the number of customers attracted to the store and the demand per product. In general, a broader product assortment would attract more customers, thus increasing demand for products, but would it also increase opera- tional and inventory cost in a limited shelf space confi guration. Product price is another signifi cant factor that has a direct impact on customers product choice and consequently on demand for a product. It cannot be considered in isolation from comprehensive combined assortment planning including standard and special items. According to McKinsey and Company study 31 “for most companies, better management of pricing is the fastest and most cost-effective way to increase profi ts”. For instance, during the economic recession in 2009 when customers became more price sensitive, Lidl was able to drive down the prices of its products compared with other supermarkets in the UK 35. Although the marginal profi t per product decreased, Lidlexperienced an increase in its market share from 2.2% to 2.4% 36 due to the increased demand. The importance of considering assortment, pricing and inventory decisions jointly is illustrated in the case of JCPenney. The department store chain received the 2004 Fusion Award in supply chain management for “its innovation in inte- grating downstream to merchandising and allocation systems and then upstream to suppliers and sourcing.” A JCPenney vice pre- sident attributes the companys success to the fact that, “assort- ments, allocations, markdown pricing are all linked and optimized together” 26. The rest of the paper is organized as follows. In Section 2, we review the related literature. In Section 3, we present the problem and the mathematical model. In Section 4, we propose a heuristic solution procedure for our problem, and assess its accuracy on instances with 515 products. In Section 5, we present and discuss illustrative examples and insights on larger problem instances (60 products). In Section 6, we conclude our study. 2. Related literature Product assortment, pricing and inventory optimization are critically important retailing decisions that have a substantial impact on retailers profi tability. Yet these decisions have been examined somewhat independently due to the increased com- plexitythattheirjointoptimizationentails.Furthermore, researchers from different fi elds, operations management and marketing in particular, have been interested in assortment plan- ning and these three decisions. Maddah et al. 26 offer a very good review of representative works in assortment planning. They discuss the various decisions at hand, and refer to contributions in the fi elds of operations management as well as of marketing. In this section, we review the scientifi c literature in assortment planning, focusing on the operations management literature and on the three decisions that we aim to jointly analyze in our work: products assortment, pricing and inventory. Kk et al. 20 provide a detailed review of the product assortment and inventory planning literature. One of the fi rst papers in the operations research literature that integrates inven- tory management into the product assortment planning problem is by van Ryzin and Mahajan 37. They study the trade-off between product variety benefi ts and inventory costs using a Multinomial Logit (MNL) model. The MNL model is a widely used utility-based model where each consumer chooses the product with the highest utility out of the set of available choices (5). In the model presented by van Ryzin and Mahajan 37, customers have homogeneous expected utilities and can substitute if their favorite variant is not carried (assortment-based substitution). The sale is lost if their favorite variant is carried but temporarily unavailable(nostock-out-basedsubstitution).Inthesame research stream, Li 22 studies a joint product assortment and inventory optimization problem for a single period and differs from van Ryzin and Mahajan 37 in that he allows different cost parameter values across products. Both studies share the same limitation: they assume that consumers are homogeneous with respect to their preferences. Our research is focused on “customer type” heterogeneity (loyal and non-loyal customers), which results in the so-called latent-class logit assortment problem. Mndez- Daz et al. 29 also study this problem, but compared to our work they do not consider the retail space constraint and product pricing optimization together. The product selection problem becomes even more challenging when limited shelf space is included. The shelf space constraint plays a key role in our work, since it has an impact on both the product assortment problem and the accompanying inventory decisions. The impact of the space constraint on product selection is studied by Kk and Fisher 19. They note that the constrained shelf space implies that average inventory per stock keeping unit (SKU) is inversely related to the breadth of the assortment. They consider stock-out and assortment-based substitution using an exogenous demand model that specifi es a priori the demand for each product and the probability that customers will substitute. A. Katsifou et al. / Omega 46 (2014) 365037 They provide a process for estimating demand and substitution rates as well as an iterative optimization heuristic to solve the assortment planning problem. Furthermore, Ycel et al. 40 investigate the integrated problem of product assortment, supplier selection and inventory management, taking into account limited shelf space. Both Kk and Fisher 19 and Ycel et al. 40 adopt an exogenous demand model without capturing the preference heterogeneity among customers, which is critical in our approach. The above research works focus on assortment optimization, assuming that store traffi c is given. In other words, the number of customers attracted to the store is fi xed, but the demand of these customers may depend on the product assortment. In our paper, special assortment items serve to attract more non-loyal customers to the store while the standard assortment mainly attracts loyal customers. Thus, the relationship between product assortment and store choice cannot be ignored. Smith 34 provides an operational assortment optimization model that includes heterogeneous con- sumers store and product choices in the MNL framework. In particular, he uses the notion of “consideration set” to narrow customer choices between similar products. In our paper, we build on Smith 34 consumer and store choice model to formulate the demand model, but we adapt it by clustering consumers into two categories (loyal and non-loyal). Moreover, we consider a shelf space constraint in the product selection, and we include pricing decisions. All of the aforementioned papers study the static product assortment planning problem with one type of product, ignoring the impact of frequently rotated special products. In a more recent paper, Caro et al. 8 focus exclusively on special product assort- ment planning. Their objective is to fi nd when to introduce each special product to maximize the total profi t over the selling season based on the products preference weight and profi t margins. In our research, we assume that the special products are intro- duced all together and then new ones are supplied at fi xed time intervals. Our decision is which special and standard products to include in the assortment to maximize the total profi t taking into account the cross-selling effect between them. Katsifou et al. 17 consider the joint problem of product assortment planning and inventory optimization with limited shelf space while separating the customer base into loyal and non-loyal customers, but they do not consider the pricing decision. None of the papers referenced so far incorporate product pricing as a decision. Dye 10 developed an inventory model to determine both the inventory and the price of a single product assuming a deterministic demand model. Meanwhile, Lim 24 considered a robust optimization model to jointly optimize a products inventory and price when its demand is stochastic. Chen and SimchiLevi 9 provide an extensive review of the pricing and inventory problem for a fi xed product assortment. In this literature stream, Aydin and Porteus 2 model customers product choice using an MNL model, and they apply a newsvendor framework to examine the interdependence between products inventory costs and their price. Aydin and Ryan 3 and, more recently, Rodrguez and Aydin 32 study the pricing and the assortment decisions for a product line with horizontally differentiated items (e.g. fl avor or color) under an MNL customer choice process, without consider- ing the inventory management problem. The vast majority of current research does not simultaneously integrate product assortment, pricing and inventory decisions due to the increased complexity of the problem. The research works by Bish and Maddah 7, Maddah and Bish 25 and Hbner 14 are notable exceptions. Bish and Maddah 7 study this joint problem with the restrictive assumption that all products have identical cost structures and utilities and thus the main decision is the size of the assortment rather than the product selection. In Maddah and Bish 25 this assumption is relaxed, and they develop a model to simultaneously address the product, pricing and inventory optimization of a product line. Compared with the paper by Maddah and Bish 25, our research considers the optimization of an assort- ment with different product characteristics (such as inventory costs and utilities), and not the optimization of a single product line, and it separates the customer base into two heterogeneous customer types. Furthermore we take into account the limited available shelf space and price optimization. Hbner 14 addresses the assortment planning and pricing problem but differs from our paper since he focuses on the shelf space allocation decision among products, assuming effi cient in-store replenishment, instead of the product inventory level decision that we consider. A comprehensive review of the shelf space allocation and the assortment planning literature is provided by Hbner and Kuhn 15. In this paper, we explicitly analyze the impact of standard and special assortments on retailers store traffi c, the impact of cross- selling between these products on overall profi tability, and the interdependence between demand for a product, its pricing and the total assortment decision. We propose a heuristic algorithm to defi ne the total product assortment and both the price and inventory level per product, taking into account the limited shelf space and assessing the trade-off between a products attractive- ness and its operational costs. 3. Problem and model formulation The objective of our research is to jointly optimize the product assortment, the price and the inventory level per product carried by a retailer. In this section we derive a mathematical model to analyze the interdependence between these three decisions. As introduced in Section 1, the customer base is separated into two groups, with loyal and non-loyal customers represented by the sets L and L respectively. Even if loyal and non-loyal customers are attracted to the store by standard and special products respec- tively, they are also assumed to buy products from both groups once they enter the store (cross-selling effect). For example, non- loyal customers who come to the store to buy some special products that are temporarily offered may decide to cover their daily needs by buying some standard products. These customer fl ows are illustrated in Fig. 1. Standard and special products have different characteristics and thus, require different inventory control policies. Standard products constitute a multiperiod problem due to their long sales period, and the retailer has to pay a holding cost for the units stored at the end of each period. Special products, by contrast, are rotated periodically, resulting in a sequential one-period problem. Loyal Customers Non loyal Customers Special Assortment :;nsg and NV fns1;nsnvg be the set of candidate standard and special products respectively (“v” stands for “special” as “s” is already used). We assume that each one of these products constitutes a unique category. Thus, product substitution is not considered and stock-outs result in lost sales. This is typically a fair assumption for retailers like Lidl or Aldi that carry only one product per category (e.g. only one brand of milk). After the assortment decision, the standard and special assortments are represented by the binary vectors S S1;Sns and V V1;Vnv respectively, where Sj 1 (Vj 1) if the retailer carries standard (special) product j and 0 otherwise. In this section, we derive the mean demand for each standard and special candidate product jANSor NVbased on the choice process of loyal and non-loyal customers. We use a multinomial logit model (MNL) 1,27 to model the heterogeneous customer store choice and product choice process. Customers choice process is used as a tool to obtain the mean demand per period for a product j, j. Due to the large number of customers (e.g. 5000 potential customers per week in our experiments), we use a Normal distribution for the demand distribution, fx;j, with jmean demand per period and standard deviation ffi ffi ffi ffi j p as an approximation to the Poisson distribution 37. According to the MNL approach, to compute the average demand, it is assumed that each product has a unique utility indicating its attractiveness for each segment of customers. The attractiveness is dependent on the intrinsic utility of a product as well as on the products price and the willingness of customers to pay this amount. In particular, the utility of a standard product j for loyal customers is given by Us jpsj sj? s jp s j 25, where j sis the intrinsic utility that loyal customers assign to standard product j due to its characteristics, independent of its price; j s is the price sensitivity of loyal customers for a standard product j; and pj s is its price. The error term is used to capture both customers imprecise knowledge of the utility of products and the retailers imperfect knowledge of customers utilities. are independent and identically distributed Gumbel random variables with mean 0 and positive scale parameter . Following Smith 34, we rescale the utility f