A data mining approach to product assortment and shelf space allocation

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A data mining approach to product assortment and shelf

space allocation

Mu-Chen Chen

a,*

, Chia-Ping Lin

b

a_{Institute of Traﬃc and Transportation, National Chiao Tung University, 4F, No. 118, Section 1,}

Chung Hsiao W. Road, Taipei 10012, Taiwan, ROC

b

SAS, Taiwan, Taipei, Taiwan, ROC

Abstract

In retailing, a variety of products compete to be displayed in the limited shelf space since it has a significant effect on demands. To affect customers’ purchasing decisions, retailers properly make decisions about which products to display (product assortment) and how much shelf space to allocate the stocked products (shelf space allocation). In the previous studies, researchers usually employed the space elasticity to optimize product assortment and space allocation models. The space elasticity is usually used to construct the relationship between shelf space and product demand. However, the large number of parameters requiring to estimate and the he non-linear nature of space elasticity can reduce the efficacy of the space elasticity based models. This paper utilizes a popular data mining approach, associ-ation rule mining, instead of space elasticity to resolve the product assortment and allocassoci-ation problems in retailing. In this paper, the multi-level association rule mining is applied to explore the relationships between products as well as between product categories. Because association rules are obtained by directly analyzing the transaction database, they can generate more reliable information to shelf space management.

Keywords: Shelf space management; Data mining; Multi-level association rules; Zero–one integer programming

1. Introduction

Most retailers nowadays face challenges such as how to respond consumer’s ever-changing demands and how to adapt themselves to keen competition in dynamic market. Retail management is to develop a retail mix to satisfy cus-tomers’ demands and to aﬀect cuscus-tomers’ purchasing deci-sions. The factors in retail mix include store location, product assortment, pricing, advertising and promotion, store design and display, services and personal selling

(Levy & Weitz, 1995). Shelf space is an important resource

for retail stores since a great quantity of products compete the limited shelf space for display. Retailers need frequently make decisions about which products to display

(assort-ment) and how much shelf space to allocate these products (allocation) (Borin & Farris, 1995; Borin, Farris, &

Free-land, 1994). Product assortment and shelf space allocation

are two important issues in retailing which can affect the customers’ purchasing decisions. Through the proficient shelf space management, retailers can improve return on inventory and consumer’s satisfaction, and therefore increase sales and margin profit (Yang, 1999).

In the past two decades, numerous models and solution approaches have been developed to deal with product assortment and/or shelf space allocation problems ( Ander-son & Amato, 1974; Borin & Farris, 1995; Borin et al., 1994; Brijs, Goethals, Swinnen, Vanhoof, & Wets, 2000; Brijs, Swinnen, Vanhoof, & Wets, 1999; Bultez & Naert, 1988; Bultez, Naert, Gijbrechts, & Abeele, 1989; Corstjens & Doyle, 1981; Corstjens & Doyle, 1983; Hansen &

Heinsbroek, 1979; Urban, 1998; Yang, 1999). In these

doi:10.1016/j.eswa.2006.02.001

*

Corresponding author. Tel.: +886 2 2771 2171x3417; fax: +886 2 2776 3964.

E-mail address:bmcchen@ntut.edu.tw(M.-C. Chen).

www.elsevier.com/locate/eswa Expert Systems with Applications 32 (2007) 976–986

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cross-elasticity between products are usually applied to estimate the relationship between shelf space and demands. Traditionally, researchers apply the space elasticities to determine which products to stock and how much shelf space to display these products. However, there are two major limitations that reduce the eﬀectiveness of the space elasticity (Borin & Farris, 1995; Borin et al., 1994). First, due to the non-linear nature of space elasticity, the space elasticity based models are very complicated, and the spe-ciﬁc solution approach is developed for each model. Addi-tionally, it is necessary to estimate a large number of parameters by using the space elasticity.

Recently, the progress of information technology makes retailers easily collect daily transaction data at very low cost. Through the point of sale (POS) system, a retail store can collect a large volume of transaction data. From the huge transaction database, a great quantity of useful infor-mation can be extracted to support the retail management. Data mining is frequently adopted to discover the valuable information from the huge database. In data mining, asso-ciation rule mining is widely applied to market basket ana-lysis or transaction data anaana-lysis (Agrawal, Imielinski, &

Swami, 1993; Srikant & Agrawal, 1997). This study

pro-poses a data mining approach to make decisions about which products to stock, how much shelf space allocated to the stocked products and where to display them. Asso-ciation rules are generated by directly analyzing the trans-action database, and these rules can be used to eﬀectively resolve the product assortment and shelf space allocation problems. This study applies the association instead of the space elasticity to formulate the mathematical model for product assortment. In this paper, multi-level associa-tion rules are generated to express the relaassocia-tionships between products and product categories to allocate the products selected in the assortment stage.

2. Literature review

In retailing, shelf space management refers a routine deci-sion-making on product assortment and space allocation

(Borin & Farris, 1995; Borin et al., 1994). Product

assort-ment planning is the process to determine the number and types of products in a line, which is accomplished by retail-ers (Rajaram, 2001). Product assortment should meet the marketing strategy of retailers, and maintain the sustainable competitive advantages that retailers build up. After the stage of product assortment, the display spaces for the prod-ucts selected from assortment are then determined. Shelf space is one of the most essential resources in logistic deci-sions and shelf space management (Yang & Chen, 1999), and the high-quality space allocation can attract more con-sumers. In practice, product assortment and shelf space allo-cation are usually resolved simultaneously.

Previously, several models and solution approaches have been developed to resolve the product assortment and/or the shelf space size determination problems ( Ander-son & Amato, 1974; Borin & Farris, 1995; Borin et al.,

1994; Brijs et al., 2000; Brijs et al., 1999; Bultez & Naert, 1988; Bultez et al., 1989; Corstjens & Doyle, 1981; Corstj-ens & Doyle, 1983; Hansen & Heinsbroek, 1979; Urban,

1998; Yang, 1999). In the literature, the space elasticity

has been widely used to estimate the relationship between sales and allocated space. Space elasticity is a ratio of rela-tive change of sales to relarela-tive change of display space.

The measurement of space elasticity can be divided into two types: direct elasticity (main eﬀect) and cross-elasticity (cross-eﬀect) (Borin & Farris, 1995; Borin et al., 1994; Bultez & Naert, 1988; Bultez et al., 1989; Chrhan, 1973; Corstjens & Doyle, 1981; Corstjens & Doyle, 1983; Hansen

& Heinsbroek, 1979; Urban, 1998). Direct elasticity is

designed to measure the eﬀect on demand by changing the display space for an individual product. The increase of display space for a product may stimulate the demand of products, but in turn, it may decrease the demand of substitute and/or complementary products. Cross-elasticity is used to measure the eﬀect on demand of substitute and/ or complementary products by changing the display space of an individual product. The mathematical form of space elasticity is then transformed into the optimization model to select products to display and determine shelf space size to these products. Experimental designs have been applied to measure the space elasticity. Due to the estima-tion of a large number of parameters, only one or a small number of products cab be considered in most experiments in a store (Borin & Farris, 1995; Borin et al., 1994;

Corstj-ens & Doyle, 1981; CorstjCorstj-ens & Doyle, 1983; Urban, 1998).

Anderson and Amato (1974), took only the direct

elas-ticity into their model to simultaneously optimize the prod-uct assortment and shelf space allocation. Anderson and Amato formulated the shelf space management model as

a knapsack problem. Hansen and Heinsbroek (1979) also

estimated the demand of products by direct space elasticity, and constructed optimization models to select and allocate products. In their models, proﬁt, inventory cost, and cost for allocating a product on a shelf were taken into consid-eration. The total proﬁt of a retail store was taken as the objective function.

The models presented by Corstjens and Doyle (1981,

1983) took advantage of both direct space elasticity and

cross-space elasticity to estimate demands. Corstjens and

Doyle (1981) applied a polynomial functional form of

demand, and they found a set of solutions by using

signo-mial geometric programming. Zufryden (1986) extended

the concept of Corstjens and Doyle (1981) and applied

the dynamic programming to solve the shelf management problem. In Zufryden’s model, the integer solutions can be provided because it allows the consideration of general objective function requirements.

Borin et al. (1994) and Borin and Farris (1995)

simulta-neously optimized the product assortment and space allo-cation problems in which the cross-elasticity eﬀects are considered. In their constrained optimization models, objective function is the return on investment of inven-tory. Due to the complexity of model and non-linearity

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of objective function, a meta-heuristic, simulated anneal-ing, was adopted to generate solutions. A critical drawback for applying this model is that it needs to estimate a large number of parameters. The number of estimated parame-ters inBorin et al. (1994)is 2n + n2, in which n is the num-ber of possible products.Rajaram (2001) applied demand forecasts derived from historical sales patterns, and also constructed a non-linear integer-programming model to make the product assortment planning. Due to the high complexity in the model, heuristics were by Rajaram devel-oped to resolve this problem.

Although some existing product assortment and space allocation models (e.g., Borin & Farris, 1995; Borin

et al., 1994) use return on inventory as the objective and

take stockouts into consideration, they do not explic-itly include the conventional inventory control decisions as variables (Urban, 1998). Urban (1998) integrated the inventory control model with the product assortment and space allocation models. In addition, a greedy search and a genetic algorithm were developed to resolve the inte-grated model.Hwang, Choi, and Lee (2005)also proposed an integrated mathematical model, which combines the shelf space allocation model and inventory-control model with the objective of maximizing the retailer’s proﬁt. Due to the complexity of the integrated model, Hwang et al. proposed a gradient search heuristic and a genetic algo-rithm to resolve the model. Using a series of ﬁeld experi-ments to study the impact of shelf positioning and facing allocations on sales of individual items,Dre`ze, Hoch, and

Purk (1994) concluded that location had a large impact

on sales, whereas changes in the number of facings allo-cated to a brand had much less impact as long as a mini-mum stock is maintained.

Except for shelf space allocated to products, other fac-tors such as product price and shelf location have eﬀects on sales.McIntyre and Miller (1999)simultaneously deter-mined what items to stock and how to price the stocked items in retailing. McIntyre and Miller developed a non-parametric approach to deal with the product assortment

and pricing problems. Hwang et al. (2005) assumed that

the level of shelf on which the product is displayed signifi-cantly influences the sales of products. Yang (1999) con-structed a knapsack model for the shelf space allocation problem in which factors of display space and shelf location are taken into consideration. Yang additionally proposed a heuristic for the solution to the knapsack prob-lem, which allocates shelf space with respect to a descend-ing order of sales profit for each item per display length.

Nogales and Suarez (2005)speciﬁcally studied the inﬂuence

of store brand in shelf space management through a case study using direct shelf observation. Additionally, other aspects of assortment, prices and promotions have also been analyzed to construct their relationship with shelf space management.

To overcome the high cost of conducting experiments to measure parameters in space elasticities,Brijs et al. (1999) proposed an association rule based approach, namely

PROFSET (PROFitability per Set), to resolve the product assortment problem in convenience stores. Brijs et al. took the advantage of association rules to develop the product assortment model. Additionally, they considered the proﬁt of cross-selling and store image in terms of basic products in the model. The products that conform to the store’s image and characteristics are called basic products, while the other products are called added products.Brijs et al.

(2000)further generalized the PROFSET model to deal with

large baskets and category management in practice. How-ever,Brijs et al. (1999) and Brijs et al. (2000)only explored the product assortment problem. Therefore, they did not take the shelf space requirement of selected products.

By using space elasticity for solutions to product assort-ment and shelf space allocation, it needs to estimate a great quantity of parameters to obtain space elasticity. Such an estimation procedure results in high cost and errors in the mathematical model. The previous space elasticity based models do not take the shelf location into consider-ation. Although the shelf location is considered inYang’s

approach (1999), it allows one product to appear on two

or more locations on diﬀerent shelves. It is diﬀerent from the practice of retailing which usually displays product according to product category.

3. The development of shelf space management model With the rapid development of information technology, transaction data can be easily collected through POS sys-tem. The relationships between products hidden in transac-tion data can be discovered through associatransac-tion rule mining to assist product assortment and shelf space alloca-tion. By using association rule mining, the shelf space man-agement model can directly apply transaction data in a retail store for analysis. It is not necessary to conduct a ser-ies of experiments to estimate a great quantity of parame-ters in space elasticities. This study develops a data mining approach to make decisions about which products to stock, how much shelf space allocated to the stocked products and where to display them.

The proposed procedure of shelf space management begins with multi-level association rule mining from trans-action data to obtain relationships between product items, between product subcategories and between product cate-gories. Next, the procedure proceeds to product assortment in which the proﬁts of frequent itemsets are considered. The products and categories frequently bought together can be displayed together. Finally, the product display locations are determined by considering the relationships between categories, subcategories and between items. The ﬂowchart of the proposed approach is schematically illus-trated inFig. 1.

3.1. Multi-level association rules

In the stage of product display, the relationships between categories, between subcategories and between product

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items are utilized to plan product display. Therefore, multi-level association rules between product items, subcategories and categories are discovered in this paper. The problem of mining association rules involves generating all association rules that have support and confidence greater than the user-specified minimum support and minimum confidence, respectively (Agrawal et al., 1993). With a huge quantity of data being constantly collected and stored in business, since they are easy to comprehend and implement (Agrawal

et al., 1993; Srikant & Agrawal, 1997). Due to the huge

valuable data stored in enterprise information system, the applications of association rules in marketing (Chen, Chiu, & Chang, 2005; Cho, Cho, & Kim, 2005; Wang, Chuang,

Hsu, & Keh, 2004), logistics (Chen, Huang, Chen, & Wu,

2005; Chen & Wu, 2005), medicine (Tang, Jin, & Zhang,

2005) and manufacturing (Chen, 2003; Del Castillo Sobrino & Barrios, 1999) are increasing.

The frequent itemset, frequent subcategory and frequent category are utilized in the shelf space management model.

For many real world applications, due to the sparsity in retail transaction data, there exist relatively few frequent itemsets for products. The level of product category is higher than subcategory, and the level of subcategory is higher than item. The strategy of reduced minimum sup-port is generally used in mining multi-level association rules (Han & Kamber, 2001). The lower the abstraction level, the smaller the corresponding minimum support. Therefore, the support threshold of category is largest; the support threshold of item is least. The product assort-ment model in the study takes the association between items as the basis for selecting products to ﬁll in shelf space, while it additionally takes the associations between catego-ries and between subcategocatego-ries as the basis for determining product display locations.

The problem of mining association rules was ﬁrst pre-sented in Agrawal et al. (1993). The problem is formally stated as follows (Agrawal et al., 1993; Srikant & Agrawal, 1997). Let I = {i1,i2, . . . , im} denote a set of literals, namely

items. Moreover, let D represent a set of transactions, where each transaction T is a set of items such that T I. A unique identiﬁer, namely TID, is associated with each transaction. A transaction T is said to contains X, a set of some items in I, if X T. An association rule is an

implication of the form X) Y, where X I, Y I and

X\ Y = B. The rule X ) Y holds in the transaction set

D with conﬁdence, c, if c% of transactions in D that contain X also contains Y. The rule has support, s, in the transac-tion set D if s% of transactransac-tions in D contain X[ Y.

The proposed shelf space management approach based on multi-level association rules applies the Apriori algo-rithm to extract frequent itemsets, frequent subcategory sets and frequent category sets. The Apriori algorithm is an eﬃ-cient algorithm for mining association rules. It is imple-mented in a speciﬁc way in the shelf space management in this paper. The details of mining association rules can

be found in Agrawal et al. (1993), Srikant and Agrawal

(1997) and Han and Kamber (2001).

3.2. The product assortment procedure

In this study, association rule mining is conducted with the store transaction data. The association rules obtained from the analysis can specify which products are frequently bought by customers at the same market basket (frequent itemsets). With the estimated gross margin of frequent itemsets, the proﬁt of selected product mix can be obtained. This study maximizes the proﬁt of selected product mix under the constraint of available shelf space. The product assortment model is constructed as a zero–one integer program.

3.2.1. Proﬁt estimation of frequent itemsets

The proﬁt estimation follows the idea of Brijs et al.

(2000). Not only the individual proﬁt generated by that

product is considered in evaluating a product value, but the cross-selling eﬀects with other products in the

Mine association rules between:

Product items;

Product subcategories;

Product categories.

Stage 1

Multi-level association rule mining

Estimate the frequent itemset profits

Resolve the product assortment

mathematical model

Generate basic and added products for store

Stage 2

Product assortment

Allocate shelf space for

Product categories;

Product subcategories;

Product items.

Stage 3

Shelf space allocation

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assortment are also taken into account. Brijs et al. devel-oped a proﬁt allocation method to estimate the margin of transaction from various frequent itemsets of that transac-tion. Their method of estimating proﬁt of frequent itemsets is described as follows:

Tj items included in the jth transaction

FI the collection of all frequent itemsets of Tj

X a frequent itemset in the jth transaction

Xmax the maximal frequent itemset in the jth transaction

Ymax the second maximal frequent itemset in the jth

transaction

HTjðX Þ the probability of selecting X in Tjto allocate gross

margin, HTjðXmaxÞ ¼

SupportðXmaxÞ

P

8Y MAXSupportðYmaxÞ

Support(X) support of X

TjnX items included in the jth transaction after

exclud-ing frequent itemset X

m(X) the proﬁt of products in frequent itemsets X

M(X) the summation of m(X)

The procedure of estimating the proﬁt of frequent item-set is described as follows:

Step 1: Input the transaction database, collection of fre-quent itemsets and gross margin of items.

Step 2: For each transaction Tjin transaction database,

(a) If X = Tj, the proﬁt m(X) is the proﬁt of

prod-uct multiplies numbers bought in transaction record Tj. Set M(X) = M(X) + m(X).

(b) Otherwise, the proﬁt m(X) from frequent item-sets Xmax in Tj based on the probability HTj.

Set M(X) = M(X) + m(X). Repeat this substep, if TjnX still has frequent itemsets.

Step 3: Return M(X) for all frequent itemsets.

3.2.2. The product assortment model

The product assortment problem addressed in this study maximizes the total proﬁt of products, which follows the concept of Brijs et al. (2000). However, Brijs et al. only addressed the product assortment problem. The necessary shelf space size of selected products is not taken into account in their model. Furthermore, the model of Brijs et al. cannot ensure the selection of basic products to conveying the store’s image. In this paper, the amount of selected products is restricted due to the limit of shelf space in a retail store. A certain amount of product items for each category should be selected for displaying on shelf. Additionally, the basic products should be selected in the assortment stage.

Before introducing the product assortment model, the notation is ﬁrstly given below.

Model parameters

C the set of categories

S the set of subcategories

I the set of items

FC the collection of frequent category sets

FS the collection of frequent subcategory sets

SFCi the set of subcategories included in the ith frequent

category set

IFIi the set of items included in the ith frequent itemset

ICk the set of items included in kth category

A the set of added products

B the set of basic products

bjk ¼

1; Item j in Categoryk is a basic product;

0; Otherwise.

Gi(X) the estimated gross margin of the ith frequent

itemset

hjk the inventory and handling costs of Item j in

Cat-egory k

fjk the product facing length of Item j in Category k

qjk the minimum quantity of the selected Item j in

Category k

Sk The total shelf space allocated to Category k

Nk the minimum number of items in Category k

se-lected for displaying Decision variables

pi ¼

1; if any item in frequent itemset IFIiis selected; 0; otherwise:

djk ¼

1; if Item j in Category k is selected; 0; otherwise.

The mathematical model of product assortment is as follows: Maximize X i GiðX Þpi X k X j hjkdjk ð1Þ Subject to: X j2ICk djkqjkfjk6Sk; 8k; ð2Þ djkP pi; 8i; 8k; 8j 2 IFIi; ð3Þ X j djkP Nk; 8k; ð4Þ djkP bjk; 8k; 8j 2 ICk; ð5Þ p_i2 f0; 1g; djk2 f0; 1g. ð6Þ

The model is described as follows. The objective func-tion expressed in Eq.(1)is to maximize the total proﬁt of products. Constraint(2)speciﬁes the maximum shelf space allowed to be displayed for each product category. Con-straint(3) ensures that once a frequent itemset is selected, the products in this frequent itemset have to be selected.

Constraint(4) speciﬁes the maximum number of items in

each category can be selected for displaying on shelf. Con-straint (5) ensures that the basic product items (B) of the store have to be selected in the optimization procedure. The basic products are identiﬁed by retailers to express their store image. The added product items (A) can be selected by taking the frequent itemsets and proﬁt into account. Constraint(6) limits the decision variables to be binary. The above model for product assortment is a zero–one integer program.

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3.3. The shelf space allocation procedure

After the products are selected from the assortment pro-cedure, the allocation procedure is adopted to assign the assorted products to the shelf space. In this paper, the pro-posed space allocation procedure takes shelf levels and associations between categories, between subcategories and between product items into consideration. Retailers usually adopt the grid display to allocate the shelf space

(Levy & Weitz, 1995). The grid display has the longer

dem-onstration shelf and walkway. Therefore, the grid display shown inFig. 2is used in this paper. Each shelf is divided into three levels: high profit, middle profit and low profit. One product may have different sales if it is displayed on different levels. In this paper, the profit weights of high, middle and low shelf levels are assumed to be 2/6, 3/6 and 1/6, respectively. The shelf space allocation procedure only takes the facing width into account. The length and depth of shelf and product are disregarded.

The proposed approach allocates products on shelf according to average profit, association among categories and shelf profit weight. The product with the higher profit is allocated to the shelf with the higher weight in order to increase the sales and profit. Additionally, prod-ucts are allocated closer if they have higher supports. Before introducing the shelf space allocation proce-dure, several primary principles are firstly presented as follows:

1. To allocate frequent categories as close as possible, or on the same shelf, if possible;

2. To allocate frequent subcategories as close as possible, or on the same shelf, if possible;

3. To allocate the product items in the same frequent item-set and in the same category as close as possible, or on the same shelf, if possible;

4. To allocate product items of the same category on the same area, if possible;

5. To allocate product items of the same subcategory on the same shelf, if possible;

6. The product with the higher proﬁt is allocated to the shelf with the higher weight, if possible.

The proposed allocation procedure based on multi-level association rules mainly includes three steps. The ﬁrst step is to allocate the shelf space for product category; the sec-ond step is to allocate shelf space for subcategory and the third step is to allocate shelf space for product item. Before presenting the proposed allocation procedure, some addi-tional notation is ﬁrstly listed as follows.

SCk the set of subcategories included in the kth category

ISl the set of items included in the lth subcategory

IFIi the set of items included in the ith frequent itemset

fj the product facing length of Item j

qj the minimum quantity of the jth selected item

pj the proﬁt of the jth selected item

PCk the average proﬁt per shelf space for the kth

cate-gory

PSl the average proﬁt per shelf space for the lth

sub-category

PIj the average proﬁt per shelf space for the jth

se-lected item

The proposed allocation procedure is described as follows: 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 33 34 35 36 37 38 39 40 9

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Step 1: Sequentially allocate the categories.

(a) Join the categories included in each frequent category set to be a virtual category by consid-ering the support of frequent category set.

(b) Keep those categories that are not included in

any frequent category set (non-frequent

category).

Canned Anchovies, Canned Clams, Canned Oysters, Canned Sardines, and Canned Shrimp

Canned Soup and Canned Tuna Cleaning Supplies and Decongestants

Candles, Hardware and Miscellaneous Electrical

Paper Products Paper Products

Snack Foods Vegetables

Vegetables Jams and Jellies

Jams and Jellies Meat

Dairy Candy

Candy Fruit

Starchy Foods Eggs

Frozen Desserts and Frozen Entrees Frozen Desserts and Frozen Entrees

Cold Remedies and Pain Relievers Hot Beverages and Pure Juice Beverages

Magazines Plastic Products

Bread Bread

Seafood and Side Dishes Pizza

Specialty Baking Goods

Baking Goods Drinks

Kitchen Products Beer and Wine

Beer and Wine Breakfast Foods

Breakfast Foods Bathroom Products

Carbonated Beverages Hygiene

Information Center

Receiving and Stprage Snack Foods Snack Foods Snack Foods Snack Foods Vegetables Vegetables Vegetables Vegetables Meat Meat Dairy Dairy Fruit Fruit

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(c) For the kth category, the average proﬁt per

shelf space is computed as PCk¼_jIC1_k_j

P j2ICk pj fj .

(d) Sequentially allocate the categories (virtual cat-egories and non-frequent catcat-egories) on shelf space with respect to shelf profit weight and average profit per shelf space. The more profit-able category is allocated on the shelf with a higher weight.

Step 2: Sequentially allocate the subcategories.

(a) Within each category, join the subcategories included in each frequent subcategory set to be a virtual subcategory by considering the sup-port of frequent subcategory set.

(b) Keep those subcategories that are not included in any frequent subcategory set (non-frequent subcategory).

(c) For the lth subcategory, the average proﬁt per shelf space is calculated as PCl¼_jIS1_l_j

P

j2ISl

pj

fj

. Sequentially allocate the subcatego-ries (virtual subcategosubcatego-ries and non-frequent subcategories) on shelf space with respect to shelf profit weight and average profit per shelf space. Within each category, the more profit-able subcategory is allocated on the shelf with a higher weight.

Step 3: Sequentially allocate the items.

(a) Within each subcategory, join the product items included in each frequent itemset to be a virtual item by considering the support of frequent itemset. Keep those product items that are not included in any frequent itemset (non-frequent item).

(b) For the jth item, the average proﬁt per shelf space is calculated as PIj¼_jIFI1_i_j Pj2IFIi

pj

fj

. (c) The required shelf space of each virtual item

and non-frequent item is set to fj· qj.

Snack Foods Vegetables Chips Chips Chips Chips Popcorn Popcorn Dried Fruit Dried Fruit Dried Fruit Dried Fruit Dried Fruit Dips Dried Fruit Dried Fruit Dried Fruit Dips Dips Chips Popcorn Popcorn Pretzels Pretzels Crackers Crackers Cookies Cookies Cookies _Donuts

Donuts Dried Fruit Snack Foods Snack Foods Snack Foods Snack Foods Vegetables Vegetables

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(d) Sequentially allocate the items (virtual subcate-gories and non-frequent subcatesubcate-gories) on shelf space with respect to shelf significance weight and average profit per shelf space. Within each subcategory, the more profitable subcategory is allocated on the shelf with a higher weight. Step 4: Return the product allocation.

4. The implementation 4.1. Data and assumptions

The proposed data mining based procedure for product assortment and allocation is implemented with an example of a retail store. The database for implementation is derived from Foodmart in Microsoft SQL Sever 2000. The database includes product data, customer data and transaction records. There are 1560 product items, which are divided into 45 categories and 102 subcategories. To conduct the implementation, some additional assumptions are made as follows:

1. In the supermarket, the grid display is adopted. The size of shelf is 300· 210 cm (width · height) with six layers.

Fig. 2 illustrates the top-view of shelf display in this

implementation.

2. This study neglects the height and depth of products and considers only facing width of products.

3. The product items are divided into two types of basic product and added product. Basic products aims to build up the characteristics of store and have to be selected for displaying. Added products are included to increase the product varieties in addition to basic products. There are 804 basic products as well as 756 added products in the store.

4.2. Product assortment

After the data being transformed into the format, which can be read by Apriori algorithm, the multi-level associa-tion rules of product category, subcategory and item are discovered for product assortment and allocation. The transaction data in this study is sparse since there are 6568 transaction records with 1560 product items. There may exist relatively few frequent itemsets for product items. The reduced minimum support is used in mining multi-level association rules. The lower the abstraction level, the smaller the corresponding minimum support and minimum conﬁdence. The minimum supports and minimum conﬁdences for subcategory and item are set to a very low threshold in order to discover enough associa-tion rules for further analysis. The minimum supports for

Snack Foods

Vegetables Vegetables

300cm

Horatio Low Fat Chips Best Choice Potato Chips Nationeel Potato Chips

Best Choice Corn Chips Fort West Potato Chips Fort West Low Fat BBQ Chips

Best Choice Low Fat Chips

Horatio BBQ Potato Chips Fort West Corn Chips Fast BBQ Potato Chips

Horatio Corn Chips Nationeel Corn Chips Horatio Low Fat BBQ Chips

Nationeel BBQ Potato Chips Fast Potato Chips Fast Low Fat BBQ Chips Fast Corn

Chips Horatio Buttered Popcorn

Fort West No Salt Popcorn Fast Buttered Popcorn

Snack Foods Snack Foods

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product category, subcategory and item are, respectively, set to 30%, 1% and 1%. The minimum conﬁdences for product category, subcategory and item are set to 10%.

For the above threshold setting, there are 54, 54 and 3238 rules, respectively, for product category, subcategory and item. After mining the multi-level association rules, the margin gross proﬁts of frequent itemsets are estimated by

the approach discussed in Section 3. The mathematical

model of assortment (refer to Eqs.(1)–(6)) is resolved by using ILOG CPLEX. Totally, 894 items are selected for allocating on shelf.

4.3. Shelf space allocation

From the results obtained from the product assortment model, the shelf space for each category can then be gener-ated in production allocation stage. The product catego-ries, subcategories and items with high associations are allocated as close as possible to increase the cross-selling eﬀects. The product category allocation is schematically illustrated inFig. 3.

After allocating the shelf space for categories, the prod-uct allocation procedure then proceeds to the allocation of subcategories and items. Taking the snack food category as an example, the allocations subcategories and items are partially illustrated in Figs. 4 and 5. In this paper, the width of each shelf space is increased by 10% to easily tol-erate and adjust the allocation.

5. Conclusions

To face the keen competition in retail market, retailers need to accurately and quickly respond the dynamic customers’ requirements. Shelf space management is an important issue to keep the competitive advantage in retail-ing sector. Retailers can try to satisfy the diverse cus-tomers’ demands and to aﬀect cuscus-tomers’ purchasing decisions by using the systematic approach for product assortment and allocation. With the rapid development of information technology, retailers have put a huge amount of transaction data in storage, and they potentially can be used to support shelf space management. This paper develops a data mining based approach to simultaneously make decisions about which products to stock, how much shelf space allocated to the stocked products and where to display them. There exist some advantages in the proposed product assortment and space allocation approach. Firstly, because association rules are obtained by directly analyzing the transaction database, therefore they are reliable for shelf space management. Secondly, the massive estimation of parameters in space elasticity can be eliminated, and the estimation error and costly experiment can thus be reduced. Thirdly, association rules can quickly respond to market changes since the transaction data are timely col-lected by retailer’s POS system. Forth, the assortment model ensures to include the basic products for expressing the store’s image, and the added products are determined

by using the associations between product items. Fifth, by mining the multi-level association rules, retailers can allocate the product categories, subcategories and items with respect to their associations and proﬁts.

Acknowledgment

The authors would like to thank the National Science Council of the Republic of China, Taiwan for ﬁnancially supporting this research under Contract No. NSC 94-2416-H-027-004.

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