retail space design considering revenue and adjacencies using a...
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This article was downloaded by: [Auburn University]On: 02 April 2012, At: 11:47Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
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Retail space design considering revenue andadjacencies using a racetrack aisle networkHaluk Yapicioglu a & Alice E. Smith ba Department of Industrial Engineering, Yunusemre Kampusu, Anadolu University, Eskisehir,Turkey, 26470b Department of Industrial and Systems Engineering, Auburn University, Auburn, AL, 36849,USA
Available online: 04 Nov 2011
To cite this article: Haluk Yapicioglu & Alice E. Smith (2012): Retail space design considering revenue and adjacencies using aracetrack aisle network, IIE Transactions, 44:6, 446-458
To link to this article: http://dx.doi.org/10.1080/0740817X.2011.635177
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IIE Transactions (2012) 44, 446–458Copyright C© “IIE”ISSN: 0740-817X print / 1545-8830 onlineDOI: 10.1080/0740817X.2011.635177
Retail space design considering revenue and adjacenciesusing a racetrack aisle network
HALUK YAPICIOGLU1 and ALICE E. SMITH2,∗
1Department of Industrial Engineering, Yunusemre Kampusu, Anadolu University, Eskisehir, Turkey 26470E-mail: [email protected] of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USAE-mail: [email protected]
Received June 2010 and accepted October 2011
In this article, a model and solution approach for the design of the block layout of a single-story department store is presented. Theapproach consists of placing departments in a racetrack configuration within the store subject to area and shape constraints. Theobjective function considers the area allocated to each department, contiguity of the departments to the aisle network, adjacencyrequirements among departments, and department revenues. The revenue generated by a department is defined as a function of itsarea and its exposure to the aisle network. The aisle network is comprised of two components: the racetrack, which serves as themain travel path for the customers, and the entry/exit aisle. The racetrack aisle itself is treated as a department with area allocationand corresponding revenue generation. A general tabu search optimization framework for the model with variable department areasand an aisle network with non-zero area is devised and tested.
Keywords: Store design, racetrack aisle, tabu search, hybrid optimization
1. Introduction
Broadly, the facility layout problem is defined as locat-ing a number of departments within a given area to op-timize a performance metric. The two most widely usedperformance measures are minimizing the total traffic costamong departments and maximizing adjacency among de-partments. Although there is a rich body of literature ad-dressing facility layout problems, papers addressing ser-vice facilities are very few and quite problem specific, suchas Elshafei’s hospital layout paper (Elshafei, 1977). How-ever, the retail trade sector has the third-largest impact onU.S. Gross Domestic Product (GDP) according to the 2007Economic Census. General merchandise stores provide jobopportunities for 5000 000 people, creating $900 billion insales with 260 000 establishments (Economic Census, 2007).
The most basic distinction between manufacturingfacilities and retail facilities is that in the latter the trafficis mostly human. Hence, the traditional performancemeasure of traffic cost minimization is not appropriate. Inthis article, the design of the block layout of single-storyretail stores is addressed, where the retail establishment is adepartment-type store (the approach would also work forstores with distinct merchandise departments such as book
∗Corresponding author
stores, sporting goods stores, and electronics stores). Theobjective is twofold: (i) revenue maximization and (ii) ad-jacency satisfaction. Constraints are placed on departmentsizes and shapes and the configuration is a single racetrackwith variable aisle area. To solve the model, a special so-lution representation and decoding/encoding mechanismsare developed and utilized in a tabu search framework.
2. Background
There are two previous studies that addressed the retail fa-cility layout problem. Peters et al. (2004) considered threeretail layout settings, aisle-based, hub and spoke, and ser-pentine layouts, and calculated expected tour lengths forgiven shopping lists. Botsali and Peters (2005) built onthis initial study by proposing a network-based model forthe serpentine layout that aimed to maximize revenue byincreasing the customers’ exposure to impulse purchaseitems. This model assumed that the customer shopping listsare known. Three significant differences between this arti-cle and the existing literature are (i) a priori shopping listsare not used; (ii) a racetrack construct with variable area isassumed; and (iii) the revenue relationship is very different.
In today’s retailing world, most companies use oneof three layout types: (i) the grid; (ii) the free form; and(iii) the racetrack (Levy and Weitz, 2001). Among these
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Retail space design 447
Entrance & Exit Entrance & Exit
Toddler
Children
Maternity
Men
Wom
en
Cookware
Bedd
ing
Home
Paint
Electronics Toys
Appliances
Auto
Care
Lawn&
Garden
Jewelry
Books
Checkout Checkout
Checkout
Misses
Health& BeautyInfant
Wom
en
Electronics Toys
Lawn&
Garden
Jewelry
Books
Checkout Checkout
Checkout
Misses
Entrance & Exit Entrance & Exit
Toddler
Children
Maternity
Men
Wom
en
Cookware
Bedd
ing
Home
Paint
Electronics Toys
Appliances
Auto
Care
Lawn&
Garden
Jewelry
Books
Checkout Checkout
Checkout
Misses
Health& BeautyInfant
Wom
en
Electronics Toys
Lawn&
Garden
Jewelry
Books
Checkout Checkout
Checkout
Misses
Fig. 1. An example racetrack layout.
three, the main advantage of the racetrack layout is that itallows shoppers to move past all of a store’s merchandisein an easy and flowing manner. To illustrate, an exampleracetrack layout is provided in Fig. 1. Departments arelined up around the outer rim and are grouped within thecenter space. A racetrack aisle separates the outer rim fromthe inner space and provides one or more entrances. LarryMontgomery, the CEO of Kohl’s, believed that customerscould spend less time in his stores but still buy more itemswhen products were arranged in a simple and logicalmanner in an environment that was attractive to the eye(http://www.answers.com/topic/larry-montgomery). Hisassertion was validated when other retail stores began toadopt Kohl’s store layouts (Tatge, 2003).
2.1. The shelf space allocation problem
Regardless of the physical layout, a model of revenuemust be devised. While the literature on retail layoutdesign is sparse, there is much on a related topic, shelfspace allocation. The relationship between the shelfspace allotted to merchandise and profit and/or revenuegenerated has drawn the attention of researchers for almost50 years. Brown and Tucker (1961) asserted that the law ofdiminishing marginal returns applies to the space/revenuerelationship in retail settings. They identified three differentproduct groupings based on the effect of increasing shelfspace in sales. Lee (1961) also stated that the effect ofincreasing shelf space must be of diminishing returns.However, neither of these studies specified a functionalform. The assumption of diminishing marginal returnswas validated by the field studies of Frank and Massy(1970), Curhan (1973), and Dreze et al. (1994). Corstjensand Doyle (1981) formulated demand (q) for product i
based on the space elasticity as follows:
qi = ri sβii
K∏j = 1j �= i
sδi j
j , (1)
where βi is the space elasticity for product i , si is theshelf space allocated to product i , δi j is the cross-elasticitybetween product i and product j , and ri is the demandmultiplier for product i .
In this formulation, the demand for product i is definedas a function of the shelf space, and the space elasticityof the product reflects the law of marginal diminishing re-turns. The model also considers the effect of the shelf spaceallocated to complementary and substitute products on thedemand for product i by incorporating the cross-elasticitiesto the formulation.
Using the definition above, Corstjens and Doyle (1981)also performed a field study that suggested that the spaceelasticities for different products fluctuate between 0.06 and0.25 and cross-elasticities between −0.01 and −0.05. TheCorstjens–Doyle formulation has been used by Yang andChen (1999), Irion et al. (2004), and Martınez-de-Albenizand Roels (2011), among others. The approach of Yangand Chen (1999) is especially relevant because their modelstarts by allocating the available space to departments,and for each department a sub-problem is generated forproduct categories. After the shelf space allocated to eachproduct category is determined, individual products areconsidered as yet another sub-problem. Considering thecross-elasticities to be of secondary importance, Irion et al.(2004) simplified the Corstjens–Doyle model by removingthe cross-elasticities from the formulation. They formulatedthe demand function as
qi = ri sβii . (2)
The simplified model proposed by Irion et al. (2004) hasalso been widely accepted by researchers. Using the Brown–Tucker classification, Irion et al. (2004) suggested [0.06,0.1], [0.16, 0.20], and [0.21, 0.25] as the intervals of spaceelasticity for unresponsive, moderately responsive, and re-sponsive products, respectively, to an increase in shelf space.
While Lee (1961) defined space in two dimensions ratherthan a one-dimensional shelf length, his and Dreze et al.’s(1994) studies are the only two that do so. Dreze et al.empirically determined that the area allocated to a productimpacts sales according to the Gompertz model:
qi = ri eβi exp(ωi si ), (3)
where qi is the demand for product i ; ri , βi , and ωi are theparameters of the Gompertz model; and si is the area occu-pied by product i . More specifically, ri is referred to as thehorizontal asymptote where qi ≤ ri , and βi < 0 and ωi < 0together control the increase in demand as a function ofthe increase in area.
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448 Yapicioglu and Smith
2.2. The effect of impulse purchases and customer trafficdensity
The sales made by a store broadly fall into two categories:planned purchases and unplanned purchases. Planned pur-chases constitute the portion of the sales that the customerscome to the store with the intention of buying. Impulsepurchases can be defined as those purchases that are notplanned before the shopping event occurs (Kollat and Wil-let, 1967). Decisions leading to unplanned purchases aremade within the store and are affected by in-store stimuli(Wilkinson et al., 1982). The notion of impulse purchasehas been studied from various perspectives, including de-scriptive studies (Bellenger et al., 1978); effects of spaceallocation, promotion, price; and advertising (Wilkinsonet al., 1982); customer characteristics and customer activi-ties (Kollat and Willet, 1967); and the effects of product dis-play and environmental variables (Fiore et al., 2000). Themarketing literature suggests that different lines of prod-ucts have different impulse purchase rates. For example,Bellenger et al. (1978) found that the percentages of im-pulse purchase are 27% for women’s lingerie and 62% forcostume jewelry.
Customer traffic within a store is another issue inves-tigated by marketing researchers. Traffic density within aretail store can be defined as the number of visits to a cer-tain zone of the store by customers. The customer trafficdensity throughout the store is not uniform, and certainzones of a store have denser traffic than others. Empiricalstudies (Larson et al., 2005), stochastic models (Farley andRing, 1966), and agent-based modeling applications (Batty,2003) support this observation.
3. Model development
The model presented considers two criteria in evaluatinga layout. These are the revenue generated by departmentsand adjacency satisfaction. The revenue generated by a de-partment depends on the area allocated to the department(area effect) and the location of the department within thestore (location effect). Definitions and mathematical for-mulations for the revenue and the layout adjacency arediscussed in the following sections.
3.1. The effect of area on revenue
The main motivation behind the use of the Gompertzmodel in Dreze et al. (1994) was the assumption of“bounded unit sales” for a given product. This assump-tion implies that there is a limit to the sales of a product,and once that limit (ri ) is reached, increasing the allottedarea, si , does not increase the sales, qi . This assumption,however, is not valid for the model herein. A departmentdefines a set of different merchandise lines and productsthat are grouped together, rather than being composed of
a single item. For example, the shoe department of a retailstore might include men’s shoes and women’s shoes. Whenthe space allotted to the shoe department is increased, theadditional space can be used for sports shoes, children’sshoes, or another brand of women’s shoes. Each of thesealternatives can increase sales so that the asymptotic behav-ior of the Gompertz function is unsuitable. A power model(qi = ri s
βii ) is more suitable to define the relationship be-
tween the area and the revenue for a department store. Thearea effect on the revenue of a department is formulated as
Ri = ri Aβii , (4)
where ri , Ai , and β i are the revenue multiplier, the area,and the space elasticity for department i , respectively. Thetotal expected revenue for the store is
R =n∑
i=1
Ri + Ra (5)
where Ra = ra Aβaa . The total expected revenue is the sum
of the revenues of individual departments and the revenuegenerated by the aisle space, Ra. Ra stems from the use ofaisle space as a promotional display area. As mentioned inSection 2.1, the power model was used by Yang and Chen(1999) to allocate available shelf space to departments, notto products individually, and this approach is used here torepresent the revenue generated by the departments. Thepower model parameters can be estimated using sales datafor different product categories through experimental de-sign (as used by Corstjens and Doyle (1981)) or with re-gression analysis (suggested by Yang and Chen (1999)).
3.2. The effect of location on revenue
Considering impulse purchasing along with uneven cus-tomer traffic within a store, a mechanism that locates de-partments with high impulse purchase likelihoods to morefrequently visited parts of the store is needed. Two sets ofratings are defined: one for the different zones of the storedenoted by z with respect to traffic density; the other isfor the departments denoted by d with respect to the likeli-hood of impulse purchases. Using these classifications, thestore area is divided into three ordinal zones, namely, high-traffic zones (zk = 1), medium-traffic zones (zk = 2), andlow-traffic zones (zk = 3). The partitioning used is depictedin Fig. 2. In the same manner, departments are grouped intothree classes, high impulse purchase departments (di = 1),medium impulse purchase departments (di = 2), and lowimpulse purchase departments (di = 3). These two sets ofrankings can then be used to measure the deviation of thedepartments’ actual locations from their ideal locations. Ifdepartment i would benefit from a high-traffic zone (di = 1)and is placed in a low-traffic zone (zk = 3), the deviationwould be positive, which indicates a missed revenue op-portunity. On the other hand, if department i would notbenefit from a high-traffic zone (di = 3) and is placed in a
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Retail space design 449
Zone 2
Zone 3
Zone1
Zone 2
Entrance& Exit
Fig. 2. Partition of the store area into zones with respect to trafficdensity.
high-traffic zone (zk = 1), there is no missed revenue op-portunity. Thus, for department i , the deviation from itsdesired location can be represented as max (0, zk − di ). If adepartment spans more than one zone, it is considered asbeing in the most advantageous zone (that is, the zone withthe lowest classification).
The revenue of a department is formulated by taking thelocation into account as follows:
Ri = ri Aβii
1 + ∑Kk=1 yik [max (0, zk − di )]
, (6)
where
yik ={
1 if department i is in zone k,
0 otherwise,
and the total revenue generated by the store is defined as
R =n∑
i=1
Ri + Ra. (7)
3.3. Layout efficiency
The layout efficiency, denoted by ε, defines the extent towhich desired adjacencies are satisfied by a given layoutand is formulated as
ε =∑n−1
i=1
∑nj=i+1 (c+
i j xi j ) − ∑n−1i=1
∑nj=i+1 (c−
i j (1 − xi j ))∑n−1i=1
∑nj=i+1 c+
i j − ∑n−1i=1
∑nj=i+1 c−
i j
,
(8)where
xi j ={
1 if department i is adjacent to department j
0 otherwise∀i, j ; i > j.
In measuring the layout efficiency, the well-known close-ness ratings concept from the manufacturing facilities lay-out literature is used. Traditionally, closeness ratings reflect
Table 1. Adjacency ratings
Rating Definition ci j
A Absolutely necessary 125E Especially important 25I Important 5O, U Ordinary closeness 1X Undesirable −25XX Prohibited −125
the level of interaction among departments and six close-ness ratings are defined as depicted in Table 1. The denomi-nator represents the largest possible value of the adjacencyscore for a given matrix of adjacency ratings (i.e., a layoutsuch that all department pairs with c+
i j are adjacent and alldepartment pairs with c−
i j are not). Two departments areconsidered adjacent if they share a common edge. Depart-ments separated only by an aisle are also considered to beadjacent. For instance, in Fig. 3, department L is adjacentto departments A, B, and C, in addition to departments Kand M.
3.4. Overall model
Given the definition of performance metrics, the completemodel is
max z = Rε, (9)
subject to
Pi
4√
Ai≤ αi , ∀i, (10)
ALi ≤ Ai , ∀i, (11)
ALa ≤ Aa, (12)
n∑i=1
Ai + Aa = A, (13)
G H A B
F E D C
I J K
N M L
G H A B
F E D C
I J K
N M L
8 11A B C D E F G H I J K L M N 8 11A B C D E F G H I J K L M N
G H A B
F E D C
I J K
N M L
G H A B
F E D C
I J K
N M L
8 11A B C D E F G H I J K L M N 8 11A B C D E F G H I J K L M N
Fig. 3. Solution representation and the corresponding layout.
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450 Yapicioglu and Smith
n∑i=1
Ai yi = AO, (14)
n∑i=1
Ai (1 − yi ) = AI , (15)
wL ≤ wa ≤ wU, (16)
xi j =
⎧⎪⎨⎪⎩
1 if department i is adjacent todepartment j
0 otherwise∀i, j ; i > j,
yi ={
1 if department i is in the outer rim
0 otherwise∀i.
Adjacency maximization is treated as a damper to therevenue to avoid scaling problems of the two (often con-flicting) objectives. An ideal layout, insofar as adjacency isconcerned, has no effect on revenue, whereas as depart-ments adhere less to desired adjacencies, revenue is de-creased accordingly. Constraints (10) impose aspect ratiorequirements for each department where Pi denotes theperimeter of department i . These ensure that departmentsare of reasonable squareness. Constraints (11) and (12) en-sure that the areas allocated to the departments and to theaisle are larger than their lower bounds. Constraint (13)ensures that the total department and aisle areas cannotexceed the area of the store. Constraints (14) and (15) en-sure that the areas allocated to the departments in the outerrim and in the inner region do not exceed the area avail-able in those regions. Constraint (16) guarantees that thewidth of the aisle is within some pre-specified limits. Notethat the racetrack aisle is treated as a department in thisformulation.
There are limitations on the designs possible with thismodel. First, there is a single racetrack aisle with the sameaspect ratio as the bounding facility. There are upper andlower bounds imposed on the width of that aisle. Second,in the inner region of the racetrack, departments can onlybe split into two rows; that is, only split into two bays.Third, in the outer region of the racetrack, departmentsare only one layer deep and those spanning a corner doso by use of a continuous representation. Since the areais not discretized, corners are spanned using the area ofthe department and the width of the outer region. Fourth,an aspect ratio constraint using a perimeter measure is setfor each department to ensure reasonable shapes. Finally,there is a single entrance aisle located midway across thebottom of the facility, and the area of this entry aisle istreated identically to that of the racetrack aisle. While theseare restrictions, they are reasonable considering the lay-out of most racetrack retail enterprises, and they make theoptimization more tractable.
3.5. Solution approach
Due to the non-linear nature of the revenue function, a two-stage optimization procedure is devised. In the first stage,the area allotments including the aisle area are determinedby solving the following model:
max R =n∑
i=1
Ri + Ra, (17)
subject ton∑
i=1
Ai + Aa ≤ A, (18)
ALi ≤ Ai , ∀i. (19)
The objective function is denoted by R since these equa-tions disregard the zone requirements of departments. Anon-linear optimization package can be used to solve thisproblem. Then, using the area allotments, tabu search isperformed to optimize the block layout of the store by as-signing departments to the outer rim or to the inner areaand specifying their sequence. This assignment determinesthe satisfaction of adjacency and aspect ratio constraintsalong with revenue generated by the region placement. Thedetails of the tabu search are presented in Section 3.6.
3.6. Tabu search for retail spatial design with flexibledepartment areas
Tabu search (TS) was introduced in the combinatorial op-timization literature by Glover (Glover, 1986, 1989, 1990;Reeves, 1995; Glover and Laguna, 1997). The procedure isa neighborhood search algorithm with a mechanism thatprohibits certain moves within the neighborhood to avoidcycling. TS has been successfully implemented in manycombinatorial, NP-hard optimization problems, includingquadratic assignment (Taillard, 1991), unequal area facilitylayout (Kulturel-Konak et al., 2004), vehicle routing (Tail-lard et al., 1997), redundancy allocation (Kulturel-Konaket al., 2003), job shop scheduling (Barnes and Cham-bers, 1995), and weighted maximal planar graphs (Osman,2006).
In following sections, the overall TS scheme is discussed,starting with the solution representation.
3.6.1. Solution representation and decodingThe solution representation is depicted in Fig. 3. It is anextension of the flexible bay structure (FLEXBAY) repre-sentation that was introduced by Tong (1991) and popular-ized by Tate and Smith (1995).The encoding is composed ofthe sequence of departments, p, followed by two baybreaks.The departments from the beginning of the permutation upto the first baybreak, b1, are assigned to the outer bay. Thedepartments starting from the first baybreak up to the sec-ond baybreak are assigned to the upper inner bay, while theremaining departments are assigned to the lower inner bay.
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Retail space design 451
A B C D E 2 4
B A C D E 1 2C B A D E 1 3D B C A E 1 4E B C D A 2 3A C B D E 2 4A D C B E 3 4A E C D BA B D C EA B E D CA B C E D
(a) (b)
(d)
(c)
Fig. 4. The initial solution: (a) permutation; (b) partitioning; (c)permutation neighborhood; and (d) partitioning neighborhood.
Assignment of departments to the outer bay starts fromthe lower midpoint of the rectangular store area (the entryaisle) and continues counterclockwise. The placements in-side the racetrack are done using Boustrophedon orderingstarting from the upper left corner. The initial permutationand its corresponding baybreaks are generated randomly.
3.6.2. Move operatorTwo move operators are used: one for the sequence and onefor the baybreaks.
Swap: The swap operator exchanges the places of the twodepartments located in the i th and j th positions in thepermutation p where i = 1, . . . , n – 1 and j = i + 1, . . . ,n.
Re-partite: The re-partite operator is used to change thenumber of departments allocated to each bay.
3.6.3. Tabu list entriesIn the dynamically sized tabu list, the most recent depart-ment pairs that are swapped are kept.
3.6.4. Neighborhood definitionFirst, partitioning is kept constant and all other permuta-tions that can be reached by a single swap operation are con-sidered. Then, with the fixed new permutation, the search isperformed in the partition neighborhood. An example so-lution representation and the corresponding neighborhoodare provided in Fig. 4.
3.6.5. Fitness functionThese fitness functions (Equations (20) to (22)) are the ad-jacency score only (Fa), revenue only (Fr ), and the com-bination of adjacency score and revenue (F f ). The fitnessfunctions Fa and Fr are used to gauge the extent the revenueand the adjacency components can be maximized individ-ually. All fitness functions include a penalty function thatpenalizes layouts with departments violating the aspect ra-
tio, constraint. The penalty term is (n − s/n)κ , where n isthe number of departments, s is the number of departmentsviolating the aspect ratio, and κ is the exponent controllingthe severity of the penalty function:
Fa = ε
(n − s
n
)κ
, (20)
Fr = R(
n − sn
)κ
, (21)
F f = R ε
(n − s
n
)κ
. (22)
3.6.6. Aspiration criterionIf a solution within the neighborhood has a better fitnessfunction than the best solution encountered so far, a moveto that solution is allowed even if the move is tabu.
3.6.7. Candidate list strategiesFor this problem, n (n − 1)2(n − 2)/4 neighboring solu-tions can be reached from any given solution. Of thesesolutions, n (n − 1)/2 are due to permutations, and for eachpermutation there are (n − 1) (n − 2)/2 baybreak combina-tions. Recall that the location of the first baybreak, b1, de-termines the number of departments inside and outside theracetrack and thus determines the width of the racetrack.As the value of b1 increases, the number of departmentsoutside the racetrack increases, and the racetrack is locatedcloser to the store center, making the aisle shorter. The re-verse is also true: as the value of b1 decreases, the numberof departments outside the racetrack decreases, making theaisle longer. Therefore, there are natural limits on b1 thatare imposed by the lower and upper bounds on the aislewidth. Given the total area of the departments inside theracetrack and the aisle area, the width of the aisle can becalculated from geometry:
wa = 12
(√(AI + Aa)/α f −
√AI/α f
), (23)
where AI is the total area of the departments inside theracetrack, Aa is the aisle area, and α f is the facility’s aspectratio.
Then, the set of feasible first baybreaks for the sequenceof departments, p, is defined as
b1 = {k|wa ≥ wL
a ∧ wa ≤ wUa
}. (24)
Finally, for each k ∈ b1, the set of second baybreaks isdefined as
b2 = {m|m > k ∧ m < n, k ∈ b1, b1 < b2} , (25)
where n is the number of departments in the permutation.With Equations (24) and (25), the number of baybreakcombinations is reduced substantially.
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N
Y
N
Readproblem data
START
Op�mize areaallotments
•Facility data•Department data•Adjacencymatrix
Generate a randomsolu�on
•Facility data•Area allotments•Adjacencymatrix
•Solu�on representa�on•Fitness func�on•Tabu tenure•Candidate list strategies•Aspira�on criterion
Diversifica�onTermina�on criteria
Generate neighborhood
Update current solu�onUpdate the best solu�on
Report the best solu�on
END
Y
Y
Fig. 5. Overall optimization framework.
3.6.8. Diversification strategyThe search restarts from a randomly generated solutionand the tabu list is reset after 50 consecutive non-improvingmoves.
3.6.9. Termination criterionIf the best available solution has not been improved for acertain number of consecutive moves, the search terminates.
3.7. Overall optimization algorithm
Given the area allotment model, neighborhood generation,and the TS algorithm, the overall optimization procedurecan be depicted as in Fig. 5.
4. Computational experience
Because of the novelty of this research, no test problemsfrom the literature were identified. Two problem cases withn = 12 and n = 20 were devised. For both of these problems,adjacency matrices were generated randomly and other pa-rameters such as β, r, d, and AL were chosen randomly
using a pre-specified range for each parameter. The prob-lem data are available from the authors.
For each case, three available store areas (24 × 16, 25.5× 17, 27 × 18), three fitness functions (Fr , Fa, F f ), and twomodes for penalization of aspect ratio violations (κ > 0,κ = 0) were used. For κ > 0 in the 12-department problem,κ = 3 and for the 20-department problem κ = 1.
First, area allotments were determined using in a non-linear program (NLP) written in Lingo. Figures 6(a) and6(b) show the percentage increases in department areas withrespect to the departments’ minimal area requirements.
The additional area allotments are generally made in de-creasing order of space elasticities of departments, βi , butthey are also affected by the revenue multiplier, ri . For in-stance, for the smallest available store area (24 × 16 = 384sq. units), the excess space is shared among departments E,G, and K for n = 12. Departments E and K have the high-est space elasticities for this set of departments, and depart-ment G’s unit revenue is the highest among all ri values. Bythe same token, departments C, K, and P share the excessspace for the available store area of 384 sq. units when n =20. Even though departments E and Q have higher spaceelasticities than C, they do not receive additional area untilthe available store space increases to 433.5 sq. units. The in-creased space returns less for departments E and Q than for
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Retail space design 453
0%
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Fig. 6. Increase in area allotments as a percentage of minimum required area: (a) n = 12 and (b) n = 20.
department C due to the larger minimal area requirementsof E and Q. Under all scenarios, departments with a spaceelasticity less than 0.1 do not receive additional space. Asgiven in the model by Equations (16) to (18), the aisle alsocompetes for additional space. The racetrack aisle does notreceive additional area allotment when the store area is 24× 16. Thereafter the aisle area increases as more store spacebecomes available. The excess area allotted to the aisle issubject to the same limitations and considerations as forthe departments (e.g., space elasticity and unit revenue).
Once the area allocations were made to departments,the sequence and baybreaks were found by TS. For n =12, the termination criteria was set to 1000 non-improvingmoves. For n = 20, the termination criteria for Fr , Fa, andF f were 1000, 5000, and 10 000 non-improving moves,respectively. Maximizing Fr is the equivalent of assigningthree groups of departments as defined by their zone re-quirements to their respective regions within the facility,
a straightforward optimization (while adhering to aspectratio constraints). However, Fa is more complex with inter-actions among departments as governed by the adjacencymatrix. F f considers both Fr and Fa simultaneously andrequires more search time to converge.
For each case, 10 trials were conducted. The results forall of these cases are summarized in Tables 2 and 3 for n =12 and n = 20, respectively.
Solutions found by the TS were compared to the upperbounds denoted by Fr , Fa, and F f . Fr was calculated usingEquation (5). Fa is at most 3n − 6 departments that can beadjacent to each other (Askin and Standridge, 1993). F f isthe multiplication of Fr and Fa.
Considering revenue only, the search identified a layoutwhere Fr equals the upper bound when κ = 0. When κ >
0 the layout for the 20-department problem was also atthe upper bound, while the layout for the 12-departmentproblem had a slightly lower revenue.
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Table 2. Summary of results for n = 12
24 × 16 25.5 × 17 27 × 18
n = 12 κ > 0 κ = 0 κ > 0 κ = 0 κ > 0 κ = 0
Fr 12 782 12 782 13 117 13 117 13 404 13 404Fa 0.948 0.948 0.948 0.948 0.948 0.948F f 12 117 12 117 12 435 12 435 12 707 12 707Fr 12 056 12 782 11 804 13 117 12 691 13 404Deviation (%) 6 0 10 0 5 0Fa 0.756 0.905 0.697 0.906 0.72 0.906Deviation (%) 20 5 26 4 24 4F f 8364 10 905 7804 11 254 8177 11 885Deviation (%) 31 10 37 9 36 6
Deviation is the deviation from the upper bound for that revenue function.Average is over 10 runs.
Considering Fa only, the upper bound cannot be reachedwhen the aspect ratio constraint is enforced. In fact, max-imization of Fa is the equivalent of the weighted maximalplanar graph problem, which is a very difficult problemeven without the additional constraints imposed by thislayout model.
Considering the dual-objective F f , the amount of devia-tion from the upper bound increases because of the partiallyconflicting objectives. Enforcing the aspect ratio constraintincreases the deviation from the upper bound.
The best layouts obtained for n = 12 and n = 20 usingFf and κ > 0 are provided in Figs. 7 and 8, respectively.Departments in white are those with high-impulse pur-chase likelihoods (di = 1), gray departments are those withdi = 2, and black departments are those with di = 3. InFig. 7, many of the locations of departments are not in
agreement with their ideal locations. This is because in the12-department problem, adhering to the aspect ratio con-straint and attending to the adjacency objective reducesthe flexibility to place departments in their desired zone.This effect lessens in the larger problem as there are morepossible department arrangements.
All experiments were performed using wLa = 0.75 and
wUa = 1.00. The average aisle widths with different store
areas under different fitness configurations are provided inTable 4. For n = 12, the aisle width is significantly largerwhen the aspect ratio penalty is enforced because in or-der to maintain the aspect ratio requirements, the TS clus-ters smaller departments inside the racetrack, leading to awider aisle. For the 20-department problem, aisle width isbetween 0.76 and 0.82, independent of whether or not theaspect ratio is enforced. When the aisle is narrower there
Table 3. Summary of results for n = 20
24 × 16 25.5 × 17 27 × 18
n = 20 κ > 0 κ = 0 κ > 0 κ = 0 κ > 0 κ = 0
Fr 15 989 15 989 16 494 16 494 16 915 16 915Fa 0.935 0.935 0.935 0.935 0.935 0.935F f 14 950 14 950 15 421 15 421 15 815 15 815
Best Fr 15 989 15 989 16 494 16 494 16 915 16 915Deviation (%) 0 0 0 0 0 0
Fa 0.809 0.834 0.819 0.839 0.82 0.843Deviation (%) 13 11 12 10 12 10
F f 12 061 12 770 12 786 13 274 13 263 13 795Deviation (%) 19 15 17 14 16 13
Average Fr 15 989 15 989 16 494 16 494 16 915 16 915Deviation (%) 0 0 0 0 0 0
Fa 0.799 0.826 0.810 0.829 0.81 0.836Deviation (%) 15 12 13 11 13 11
F f 11 872 12 710 12 631 13 185 13 065 13 619Deviation (%) 21 15 18 15 17 14
Deviation is the deviation from the upper bound for that revenue function.Average is over 10 runs.
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Table 4. Average aisle widths (over 10 runs)
n = 12 n = 20
Config. 24 × 16 25.5 × 17 27 × 18 24 × 16 25.5 × 17 27 × 18
Fr , κ > 0 0.85 0.98 0.92 0.76 0.76 0.81Fa, κ > 0 0.90 0.96 0.99 0.76 0.77 0.78F f , κ > 0 0.90 0.96 0.89 0.76 0.77 0.79Fr , κ = 0 0.79 0.76 0.82 0.82 0.79 0.80Fa, κ = 0 0.81 0.80 0.81 0.82 0.79 0.80F f , κ = 0 0.86 0.78 0.77 0.78 0.79 0.79
are more departments inside the racetrack. Allowing moredepartments inside the racetrack increases the chances forthose departments to be adjacent to the other departments,leading to better adjacency scores.
The average execution times of the TS in secondsfor the 12 configurations are listed in Table 5. For the12-department problem, the average execution time wasaround 2 minutes, and the difference between the execu-tion times using different fitness functions was negligible.However, with the 20-department problem, the differencesbetween execution times for the different fitness functionsare more apparent and, overall, more than 16 times longerthan the 12-department problem on average. Even withthese increases in average execution times, the number ofsolutions evaluated is less than one-trillionth of all possiblesolutions.
5. Discussion and future research
Retail facility layout is inherently distinct from manufactur-ing facility layout, and to approach this problem new ideasmust be devised and formulated. This article proposes amodel and solution approach for the department store fa-cility layout problem with a racetrack layout with a singleentrance. The quality of a layout is evaluated consideringtwo criteria: (i) the degree of adjacency satisfaction amongthe departments and (ii) the revenue generated. The lat-ter is affected by department area and department locationwithin the store. The aisle (racetrack and entry) is treated asa department for revenue purposes where width engendersdisplay area and shopping pleasure. This is a new approachin the facility layout literature as before aisles were assumed
Table 5. Average execution times in seconds (over 10 runs)
Config. n = 12 n = 20
Fr , κ > 0 112 211Fa, κ > 0 129 2205F f , κ > 0 139 4498Fr , κ = 0 118 217Fa, κ = 0 148 1769F f , κ = 0 127 3906
to not exist, to be of zero area, or to be of fixed area. Be-sides the objectives considered, the formulation enforcesreasonable departmental shapes and assigns excess storearea optimally to departments.
Because a standard mixed integer programming ap-proach could not capture the aspects desired and provedcomputationally impractical, a hybrid optimization ap-proach was applied. The solution approach involves atwo-stage optimization where the areas are assigned to de-partments first by an NLP. Then, with the areas fixed, thepermutation of departments and the location of the bay-breaks defining the racetrack structure are chosen by TS. Apenalty approach is used to enforce aspect ratio constraintson the departments. This solution approach is tractable andeffective as demonstrated by the computational experiencewith several test problems.
Evidence is provided that often the revenue objective isin conflict with the adjacency objective. While these wereweighted to be essentially equal in this article (through themultiplier approach), it may be that certain establishmentsplace stronger desire on one versus the other. Furthermore,clearly the adjacency objective is only there to account forrevenue generated by proper department relative locations.If an appropriate formula that maps adjacencies to rev-enue could be devised, the objective function reduces toa single objective—that of revenue. When allocating storespace, beyond the minimums needed for each department,an interaction between a department’s revenue multiplier(margin per unit area) and its elasticity to increased areatakes place. Some departments would never increase in sizebeyond their minimums. Note that in the optimization thisincrease is determined prior to the department placement.During the layout phase, there is competition among de-partments for the prime locations in the store, and the ul-timate winners of that competition depend on the revenueelasticity for impulse purchases, the size of the department,and the margin per unit area (revenue multiplier). The opti-mization takes all these factors into account when seekingthe best store design.
A future direction will be to enlist the cooperation of oneor more retail enterprises so that actual data can be used inthe model and results compared with current layouts andwith those crafted by a subject-matter expert. This is chal-lenging as retailers regard sales data as highly proprietary.
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Fig. 7. The best layouts obtained for n = 12, F f , κ > 0 for available areas of: (a) 24 × 16; (b) 25.5 × 17; and (c) 27 × 18.
Fig. 8. The best layouts obtained for n = 20, F f , κ > 0 for available areas of: (a) 24 × 16; (b) 25.5 × 17; and (c) 27 × 18.
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Data that would be useful include traffic patterns and den-sity in the store, product elasticities with regard to impulsepurchases, product revenue margins, and relationship of in-creased merchandise within a department to increased sales(the area to revenue aspect). Data that would be interestingbut very difficult for even a retailer to ascertain would bequantifying the effect of desired adjacencies on sales.
Another step forward would be to treat the adjacencyobjective separate from the revenue objective and performbi-objective optimization. This is readily achievable withinthe TS framework. This would create a Pareto set of alter-native designs from which a human could choose. Anotheralgorithmic extension would be to assign area to the otheraisles (the entry/exit aisles) and to consider multiple pointsof entry/exit. Similarly, considering the double racetrackconstruct would be important, as this is closer to the actualstructure used by Kohl’s and some other retailers.
References
Askin, R.G. and Standridge, C.R. (1993) Modeling and Analysis of Man-ufacturing Systems, John Wiley & Sons, New York, NY.
Barnes, J.W. and Chambers, J.B. (1995) Solving the job shop schedulingproblem with tabu search. IIE Transactions, 27, 257–263.
Batty, M. (2003) Agent based pedestrian modeling. Working paper, Cen-tre for Advanced Spatial Analysis, University College London, Lon-don.
Bellenger, D.N., Robertson, D.H. and Hirschman, E.C. (1978) Impulsebuying varies by product. Journal of Advertising Research, 18, 15–18.
Botsali, A. and Peters, B.A. (2005) A network based layout design modelfor retail stores, in Proceedings of the 2005 Industrial EngineeringResearch Conference, pp. 1–6.
Brown, W.M. and. Tucker, W.T. (1961) The marketing center: vanishingshelf space. Atlanta Economic Review, 11, 9–13.
Corstjens, M. and Doyle, P. (1981) A model for optimizing re-tail shelf space allocations. Management Science, 27, 822–833.
Curhan, R.C. (1973) Shelf space allocation and profit maximization inmass retailing. Journal of Marketing, 37, 54–60.
Dreze, X., Hoch, S.J. and Purk, M.E. (1994) Shelf management and spaceelasticity. Journal of Retailing, 70, 301–326.
Economic Census. (2007) Summary of census data, available athttp://factfinder.census.gov/servlet/IBQTable? bm=y&-geo id=&-ds name=EC0700CADV1&- lang=en on 04/07/2009, accessedApril 7, 2009.
Elshafei, A.N. (1977) Hospital layout as a quadratic assignment problem.Journal of the Operational Research Society, 28, 167–179.
Farley, J.U. and Ring, W.L. (1966) A stochastic model of supermarkettraffic flow. Operations Research, 14, 555–567.
Fiore, A.M., Yah, X. and Yoh, E. (2000) Effects of a product display andenvironmental fragrancing on approach responses and pleasurableexperiences. Psychology and Marketing, 17, 27–54.
Frank, R.E. and Massy, W.F. (1970) Shelf position and space effects onsales. Journal of Marketing Research, 7, 59–66.
Glover, F. (1986) Future paths for integer programming and links toartificial intelligence, Computers and Operations Research, 13, 533–549.
Glover, F. (1989) Tabu search part I. ORSA Journal on Computing, 1,190–206.
Glover, F. (1990) Tabu search part II. ORSA Journal on Computing, 2,4–32.
Glover, F. and Laguna, M. (1997) Tabu Search, Kluwer, Boston, MA.
Irion, J., Al-Khayyal, F. and Lu, J-C. (2004) A piecewise lin-earization framework for retail shelf space management models,available at http://www.optimization-online.org/DB FILE/2004/10/967.pdf, accessed April 7, 2009.
Kollat, D.T. and Willet, R.P. (1967) Customer impulse purchase behavior.Journal of Marketing Research, 4, 21–31.
Kulturel-Konak, S., Norman, B.A., Smith, A.E. and Coit, D.W. (2004)Exploiting tabu search memory in constrained problems. IN-FORMS Journal on Computing, 16, 241–254.
Kulturel-Konak, S., Smith, A.E. and Coit, D.W. (2003) Efficiently solvingthe redundancy allocation problem using tabu search. IIE Transac-tions, 35, 515–526.
Larson, J.S., Bradlow, E.T. and Fader, P.S. (2005) An exploratory look atsupermarket shopping paths. Technical Report, Wharton School ofBusiness, University of Pennsylvania, Philadelphia.
Lee, W. (1961) Space management in retail stores and implica-tions to agriculture, in Marketing Keys to Profits in the 1960’s,Dolva, W.K. (ed), American Marketing Association, Chicago, IL,pp. 523–533.
Levy, M. and Weitz, B.A. (2001) Retailing Management, McGraw-HillIrwin, Boston, MA.
Martınez-de-Albeniz, V. and Roels, G. (2011) Competing for shelf space.Production and Operations Management, 20, 32–46.
Osman, I.H. (2006) A tabu search procedure based on a random roulettediversification for the weighted maximal planar graph problem.Computers & Operations Research, 33, 2526–2546.
Peters, B.A., Klutke, G.A. and Botsali, A.R. (2004) Research issues in re-tail facility layout design, in Progress in Material Handling Research,Meller, R.D., Ogle, M.K., Peters, B.A., Taylor, G.D. and Usher, J.S.(eds). Material Handling Institute of America, Charlotte, NC, pp.399–414.
Reeves, C.R. (ed). (1995) Modern Heuristic Techniques for CombinatorialProblems, McGraw Hill, London.
Taillard, E.D. (1991) Robust tabu search for the quadratic assignmentproblem. Parallel Computing, 17, 443–455.
Taillard, E.D., Badeau, P., Gendreau, M., Guertin, F. and Potvin, J.Y.(1997) A tabu search heuristic for the vehicle routing problem withsoft time windows. Transportation Science 31, 170–186.
Tate, D.M. and Smith, A.E. (1995) Unequal area facility layout usinggenetic search. IIE Transactions, 27, 465–472.
Tatge, M. (2003) Same store sighs, available at http://www.forbes.com/forbes/2003/1208/262.html, accessed April 7, 2009.
Tong, X. (1991) SECOT: A sequential construction technique for facilitydesign. Doctoral Dissertation, University of Pittsburgh, Pittsburgh,PA.
Wilkinson, J.B., Mason, J.B. and Paksoy, C.H. (1982) Assessing the im-pact of short-term supermarket strategy variables. Journal of Mar-keting Research, 19, 72–86.
Yang, M.H. and Chen, W.C. (1999) A study on shelf space allocationand management. International Journal of Production Economics,60–61, 309–317.
Biographies
Haluk Yapicioglu received his Ph.D. in Industrial and Systems Engineer-ing from Auburn University in 2008. After working as a postdoctoralresearch fellow and teaching at the same university, he joined AnadoluUniversity of Turkey in 2010. He works in the Department of IndustrialEngineering and also acts as the Director of the Project Support Officeof Anadolu University.
Alice E. Smith is a Professor at the Industrial and Systems EngineeringDepartment at Auburn University. She holds one U.S. patent and severalinternational patents and has authored more than 200 publications, which
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have garnered over 1400 citations (ISI Web of Science). She currentlyholds editorial positions on INFORMS Journal on Computing, Com-puters & Operations Research, International Journal of General Systems,and IEEE Transactions on Evolutionary Computation. She has served asa principal investigator on over $5 million of sponsored research. Herresearch in analysis, modeling, and optimization of complex systemshas been funded by NASA, the U.S. Department of Defense, NIST, theU.S. Department of Transportation, Lockheed Martin, Adtranz (nowBombardier Transportation), the Ben Franklin Technology Center of
Western Pennsylvania, and the U.S. National Science Foundation, fromwhich she has been awarded 15 grants including a CAREER grant in1995 and an ADVANCE Leadership grant in 2001. She is a Fellow ofthe Institute of Industrial Engineers; a senior member of the Instituteof Electrical and Electronics Engineers and the Society of Women Engi-neers; a member of Tau Beta Pi, the Institute for Operations Researchand Management Science, and the American Society for EngineeringEducation; and a Registered Professional Engineer in Alabama andPennsylvania.
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