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The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-1
Shopping center design using a facility layout
assignment approach
Sherif A. Fahmy
Currently- Department of Industrial Engineering
American University of the Middle East, Egaila, Kuwait
On leave- Department of Mechanical Design and Production
Cairo University, Giza, Egypt
sherif.fahmy@aum.edu.kw
Bader A. Alablani1, Tamer F. Abdelmaguid2
Department of Mechanical Design and Production
Cairo University
Giza, Egypt
1alablani@hotmail.com
2 tabdelmaguid@eng.cu.edu.eg
Abstract— In this paper, a study of the problem of
shopping center layout design is presented. Assignment of
shops to locations in a shopping center should be performed in
a way that ensures balance in the distribution of flow across all
shopping center areas. This can lead to the success of the
shopping center, and consequently raise its rent return. This
study proposes a facility layout assignment model for shopping
centers with the objective of maximizing flow capturing in each
location and balancing it across all shopping center areas. Flow
capturing by a given location is controlled by the power of
attraction (weight) of the shop assigned to it, and is affected by
the flow at nearby locations more than flow at more distant
locations. The model also calculates the flow in each area in the
center as a combination of the flows at locations that belong to
that area. The model is tested on a number of randomly
generated problems, and the optimum layout is found for each
generated example.
Keywords— facility layout; flow capturing; shopping center
design
I. INTRODUCTION
Shopping centers are widely spread across the world,
and are hotspots that attract different demographics to spend
quality time, perform all kinds of activities, or to perform all
kinds of purchases. Shopping centers simulates the
complexity and vitality of a city center without the noise,
dirt, and confusion [1]. Victor Gruen, the architect of the
first shopping center, proposed the center as the basic unit of
urban planning, where he designed the suburban center to be
the nucleus of subsequent developments. Shopping centers
were introduced not only as retail environment, but also as
public spaces that permit access to all members of the
community. The idea of the shopping center evolved from
the classical open market spaces as shopping and
communication spaces, through department and chain
stores, reaching the modern environmentally controlled
form of that shopping space called ‘mall’.
This study intends to employ engineering theories and
practices in a new application; namely layout design for
shopping centers. It discusses the facility layout problem for
a shopping center as a service facility, with the objective of
maximizing the average flow across different areas (blocks)
of the center. Shops (entities) are assigned to available
locations in the center in a way that ensures foot-traffic is
evenly distributed across all shopping center areas. Thus,
increasing rent returns, profitability, and success of the
shopping center.
A. Shopping centers
There are three physical configurations of shopping
centers. First is the open air center, where all shop entrances
are on open air space. Second is the mall, which is an
enclosed space, where all shops entrances are facing the
interior. The third type is the hybrid center, which combines
features of the two previous configurations. The first two
configurations are further classified into eight types
according to size and goods sold. For malls, there are the
regional center and the super-regional center. For open air
centers, there are the neighborhood center, the community
center, the power center, the theme/festival center, the outlet
center, and the lifestyle center.
Shopping centers have many design issues, one of which
is the financial aspects of the design [2]; commitment of
shopping center owners/developers to financial return over a
long period of time. Given this long term commitment, there
is greater interest in ensuring profitability on an ongoing
basis, which in turn encourages high quality design. Another
design issue to consider is the financial viability of the
center. Shopping centers are affected by changes in the
market, including level of competition. Although
competition risk is acknowledged in feasibility analysis, but
changes to the retail hierarchy resulting from poor planning
decisions is a risk that cannot be predicted. Given the
significant amounts of capital required to develop and
redevelop a shopping center, the developer needs to be
confident that there is no unforeseen threat to achieving an
appropriate return on their investment.
Considering these two issues gives rise to the need to
develop shopping center layouts that can ensure, among
other requirements, that facility entities will receive
maximum customer flow to increase profitability.
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-2
B. Facility layout problem
Facility layout planning plays a crucial role in the
success and profitability of any organization; an effective
layout can minimize costs substantially, which leads to
improvement in overall performance. A facility is an entity
that facilitates the performance of any task, and the facility
layout is the arrangement of everything needed for
production of goods or delivery of services in that facility
[3]. As per [4], “Layouts are not only concerned with
improved utilization of buildings and land but are very
much concerned with increasing sales. In the retail
environment, layouts must be customer focused and
displays should attract the attention of the purchasing
public.”
The common approach for solving the facility layout
problem is to assign entities to locations with the objective
of minimizing the material handling distances/costs. This
has been done by evaluating the distances/trips to/from
different entities at the assigned locations. Other facility
layout models have also considered the objective of
maximizing the flow through facility entities.
C. Maximum flow capturing problem
The maximum flow capturing problem discusses the
flow in a system, where entities should capture portions of
that flow [5]. The portion of flow that each entity captures
depends on its weight, which is interpreted as the power to
capture flow. Accordingly, the maximum flow capturing
problem can be utilized in shopping center location
assignment problems. The objective in this case would be to
ensure that each assigned shop’s share of customer visits
(flow) is maximized, while maintaining the flow balance
across different areas (blocks) that accommodate these
shops.
II. LITERATURE REVIEW
Fong [6] presented a configuration (morphological)
analysis of shopping malls and a study of the extent to
which location of attractors affects movement through the
mall. The author discussed the idea of a mall that offers
unique shopping experience at several stores under one roof
along with entertainment tools, and that the idea of the
shopping mall was derived from the city center. Shopping
malls usually follow the dumb-bell concept (Fig. 1), in
which large stores (anchors) are placed at the ends of the
mall to work as customer magnets. This creates an artificial
flow between anchors, producing flow at the smaller stores,
and simulating the natural movement in the streets. In
theory, in a shopping mall, all locations are good. The
shopping mall owner's main concern is usually to optimize
rent return by generating equally distributed foot-traffic for
all shops in the mall, not only those who can afford
exceptional locations. Accordingly, the layout design
process should take this into consideration to achieve a
tenant mix that leads to the success of the center by ensuring
maximum benefit for all occupants.
Fig. 1. Shopping mall dumb-bell concept [6]
An analysis was performed in [6] on a selected sample
of shopping malls for a comparative study of the layout
configuration. The results showed that the number of
shoppers differs significantly between main malls and side
malls (Fig. 1). Results also showed that the assignments of
different shops to available locations affect the rate of foot-
traffic across the mall. Furthermore, it was concluded that
there is a strong relationship between the layout
configuration and the distribution of foot-traffic across the
mall.
Brown [7] introduced a study that discusses functionality
problems of real estate and the relationship with
configuration. Space syntax was presented as a way to
describe the configuration of a failed shopping mall due to
poor design, and was represented by a mathematical
network. The study compared the failed mall with another
nearby mall, and it showed that it is not important how big
the mall is, but what matters is how the public area of the
mall makes the goods sold more accessible to shoppers.
With equal effort, shoppers would access more store
entrances in the nearby mall than the failed one. Also, mall
entrances allowed shoppers deep into the nearby mall, and
kept them on the edges at the failed one. The author also
discussed the importance of store entrance being on a core
space (potential high movement rates) or a fringe space (less
movement rate where most vacant stores are found) for the
success of the store. There is a common tendency to locate
large anchor stores in fringe areas to benefit from their high
market capability. It was emphasized that the design of the
failed mall made each store only represent itself as if it is a
stand-alone store not part of a mall, disabling the concept
that the foot-traffic at each store will inevitably generate
foot-traffic at surrounding stores. In other words, separating
mall areas lead to mall failure.
Yin, Xu, and Ng [8] discussed the relation between shop
size, tenant type, and location in the shopping mall. It was
found that the vertical expansion in mall size, by increasing
the number of floors, increases owner concern if shoppers
will reach higher floors or not. The author classified the
shops into non-impulse trades that consumers will usually
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-3
head to with a plan of specific purchases, and impulse trades
that consumers visit only as a last minute decision to
purchase a product. The results showed that more non-
impulse trades are found at higher levels in the shopping
mall. The study concluded that shoppers can be encouraged
to go to the upper floors by placing shops of non-impulse
trade and anchors at the upper floors.
Fong [9] discussed suitable locations of different shop
categories (tenant mix) according to type of shop activities
and goods inside the shopping center. He enumerates rules
to assign certain shops to certain locations on the shopping
center layout, such as fashion shops to be located in main
mall and service stores to be in less attractive locations. The
author claims that managers and decision makers pay
attention to placement of anchors and major shops, leaving
the decision about non-anchors and less important shops to
the leasing agents, which may arise some problems in the
matter of shops placement rules. The objective of the study
is to test the locations of each category of stores in order to
define certain “general rules” that apply to most of the
sample shopping centers. The question asked is should
stores of a certain category be gathered beside each other, or
should they be separated through the whole shopping center
layout. After studying different store types in seven
shopping malls, it is concluded that there are no certain
location rules that stores placement follow. The study
suggests deciding on stores location by simulating the
dynamics of ecology, study of organism interactions, as
studying the effect of a store location on every other store
(store-to-store interactions). The method highlights that
competing stores can be placed apart and stores of different
types of activities can be placed near each other. The author
concludes that choosing stores’ locations is a skill of the
shopping mall manager more than being a scientific
decision.
Kusiak and Heragu [10] presented a survey of the
different formulations and solution algorithms that can be
used to solve the facility layout problem in manufacturing
systems. The study enumerates the types of models that can
be utilized and provided a summary of each. It also
classified the solution algorithms into optimal and sub-
optimal algorithms and showed that facility layout problems
are hard to solve with optimal algorithms because of time
constraints. A comparison between twelve heuristic
algorithms for eight test problems was included, and an
analysis of solution quality and computation time was
provided.
Feizollahi and Feyzollahi [11] discussed the classical
quadratic assignment problem (QAP), in which a set of
facilities are assigned to a set of locations in a way that
achieve the required flow between facility pairs and
minimizes cost of material handling. The study discussed
the QAP problem with uncertain flow of material. The
authors introduced a robust solution for a set of uncertain
flow possibilities.
In [12], Rosenblatand and Golany proposed a new
approach for the facility layout problem other than solving
the classical quadratic assignment problem (QAP). The
approach depends on assigning distances to pairs of
departments and formulating a minimum cost network
problem. The formulation takes advantage of network
theory and algorithms. This distance assignment problem
(DAP) uses the flow in the network to represent the distance
assigned to department pairs. The study provides a solution
algorithm consisting of three phases. In the first phase, the
distance parameters between departments are determined,
where in the second phase these distances are optimized.
The third phase is concerned with interpreting the obtained
optimal distances into facility layout assignments.
Solimanpur and Jafari [13] discussed the concept of two-
dimensional layout, where the problem is concerned with
the arrangement of manufacturing facilities into different
layout patterns taking into consideration some factors, such
as machine dimensions and capacity. The layout is
optimized according to distance or cost minimization
measures. The study uses a nonlinear mixed integer
programming model with a total distance minimization
objective, in a two-dimensional layout arrangement. The
model takes into consideration the required clearance
between machines.
Amaral [14] discussed the single row facility layout
problem (SRFLP), where departments are assigned on a line
or one side of a certain path, with the objective of
minimizing the weighted sum of the distances between
departments. The distances between departments in the
facility are measured between their centers. The author also
discussed the special case of the SRFLP, the linear ordering
problem (LOP), where the distance between all departments
is unit length. The study presents a new mixed-integer linear
programming model for the problem to facilitate a more
efficient solution.
Hassan [15] discussed the problem of layout design and
how it affects the pedestrian flow. He argued that previous
work either studied the layout design or pedestrian flow, but
not both problems simultaneously. The author used
simulation tools to study different layout designs and the
resulting effect on pedestrian flow. The study focused on
flow in normal situations not congestion in panic situations.
The author also discussed the effect of appropriate design in
a shopping mall on the profit. It was concluded that a good
design will produce smooth flow and maximize the flow
across the layout spaces.
Hua, Cheng, and Wang [16] presented the maximum
capture problem (MAXCAP), which is concerned with
locating new stores in a competitive market, with the
objective of maximizing the market share for the new stores,
which is in turn captured from other competitors’ share. The
authors listed previous studies that extend the MAXCAP
problem with the assumption that stores might have equal or
different weights, or with the assumption that competitors
will react to the new entry to the market. The model
objective is to maximize total market share captured from
competitors with respect to total cost, including fixed and
transportation costs. The authors emphasized the practical
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-4
superiority of the concept of maximizing capture per unit
cost over maximizing profit.
Hodgason, Rosing, Leontien, and Storrier [17] explained
the flow capturing location-allocation model by studying
traffic in Edmonton, Canada. The authors provided a new
model to find locations for some facilities with the objective
of maximizing the flow passing by these facilities. The
demand at the facilities is expressed as weights at the nodes,
but not for other type of facilities where the demand is the
traffic flowing between origins and destinations, like
convenience stores, gas stations, and bank ATMs. The
authors used three solution procedures; for small problems,
an exact solution procedure was used. A vertex substitution
procedure was used to solve the medium-sized problems,
and for large problems, they used a greedy heuristic
procedure.
Jun, and Min [5] presented the allocation theory in the
flow capturing location-allocation problem (FCLP), which
discusses assigning facilities to locations depending on the
number of customers(or flow) passing through the system.
An example is locating gas stations or bank ATMs with the
objective of capturing the maximum number of customers
that can be served by these facilities. The authors added to
the FCLP some aspects; flow changes with time interval,
facilities are capacitated, and flow can be partitioned. The
authors used the Max-min ant algorithm, and it resulted in
improvement in the results and time required to find a
solution.
A major problem in shopping malls is when the foot-
traffic rate is different from one area to another, which
affects the selling power of shops and the rent return to the
owner, and hence the success of the mall. Previous research
on shopping malls handled this problem from a qualitative
perspective. This study uses the essence of the facility
layout problem, and considers the assignment of shops to
mall locations with the objective of evenly distributing the
customer flow among all areas (blocks) of the mall. The
study uses the facility layout assignment approach and the
flow capturing concept, to solve the facility layout problem
for the mall shops.
III. PROBLEM FORMULATION
Considering an already designed shopping mall, it is
required to assign stores (entities) to available locations. The
objective is to ensure that all areas of the mall will have an
appropriate share of flow (customers’ visits), and that all
locations are desirable, in order to increase rent returns, and
thereby profitability and success of the shopping center.
The layout is divided into occupied locations and
available (free) locations. An example of such arrangement
is shown in Fig. 2. The occupied locations are usually
allocated for entrances and exits, restrooms, and attraction
points (food court, cinema, famous brand stores, etc.).The
available locations are to be assigned to shops, categorized
into high, medium, and low according to their attraction
power. In addition, there are locations that can only be
assigned to special entities, such as locations that can only
work as restaurants or cafes. This reflects the real practice in
which some entities are desired to be assigned to certain
locations while others can be assigned freely to any location
but under the objective of maximizing flow. These entities
are constrained by certain required features such as size,
certain facilities, or location on a view. Attraction points in
the layout have a high weight as their attraction power is
high, and they are different from special locations-entities as
special locations-entities can be of any category of weight.
The objective is to ensure balanced foot-traffic across the
whole facility, by maximizing the flow of customers
captured by each entity in its assigned location. The layout
is separated into areas (blocks), where attraction points work
as magnet to visitors, creating flow through the whole
block, resulting in flow across other smaller stores. At the
same time the average flow of all blocks is maximized.
The model exploits the fact that each entity assignment
to a location affects the flow in the whole facility. Thus,
each entity is assigned a weight we that is related to its
power of attraction (high, medium, or low), and is deduced
from market research on the effect of different entity types.
A location i’s share of customer flow is measured by the
location flow factor fi. fi is measured in reference to the
weight of the entity assigned to it and the weights of entities
assigned to all other locations, and the distance from these
locations to location i. Accordingly, an empty location’s
share of flow is determined only by its distance from other
assigned locations that capture flow by themselves and
share it with other locations, such that an assigned location’s
flow effect (ability to induce flow) is higher on nearby
locations and less on farther locations. A flow factor Fb is
also defined for each block b as the sum of location flow
factors of all locations in block b. The model minimizes the
maximum difference between block flow factors to ensure
balanced flow across the whole facility. The following
assumptions are made:
• Bi-directional flow is allowed.
• All locations have a unit area and the center point of a
location is used as reference point to that location.
• The distance from a location to itself is set to one not
zero to avoid dividing by zero when calculating the
flow factor.
• Adjacent locations are equally spaced.
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-5
Fig. 2. Layout of a functioning shopping mall, illustrating occupied and
available locations (www.eagleridgemall.com)
A. Mathematical model
Indices:
b: block
i, j: locations
e: entity
Sets:
L: set of all locations {1,…..,ℓ}
Lb: set of locations in block b
S: set of all entities {1,…., n}
LA: set of attraction point locations LA⊂ L
LS: set of special locations LS⊂ L
SA: set of attraction point entities SA⊂ S
SS: set of special entities SS⊂ S
Parameters:
m: number of blocks
n: number of entities
ℓ: number of locations
di,j: distance between location i and location j
we: weight (power of attraction) of entity e
r: number of special entities
k: number of attraction points
Variables:
xei: 1 if entity e is assigned to location i; 0 otherwise
fi: flow factor of location i
Fb: flow factor of block b
Model:
max min
.
M
in Z F F=−
1, ,
b
bj
jL
F
fb m
∈
=∀=…
∑ (1)
()
max max b
F
F= (2)
()
min b
min FF= (3)
11
1, .,
nl
e
jei
ei ij
w
f
xj l
d
==
=∀=…
∑∑ (4)
1
11,,
n
ei
e
xi l
=
=∀ = …
∑ (5)
1
11,,
l
ei
i
xe n
=
=∀ = …
∑ (6)
ei
iLSeSS
xr
∈∈
=
∑∑ (7)
ei
iLAeSA
xk
∈∈
=
∑∑ (8)
{
}
0,1 , , 0
ei b j
xFf=≥
The objective function minimizes the difference between
the maximum block flow factor Fmax and the minimum one
Fmin, thus distributing flow across all blocks. Constraint set
(1) defines Fb the flow factor of block b, as the summation
of all flow factors of all locations in that block. Constraint
sets (2) and (3) identify the maximum and minimum block
flow factors, respectively, for objective function
calculations. Constraint set (4) calculates the flow factor fj
of each location j as the summation of weights of other
entities divided by their distances from location j; djj is
assumed to be equal to one (minimum distance). Constraint
set (5) ensures that each location is assigned to only one
entity, and constraint set (6) ensures that each entity is
assigned to only one location. Constraint (7) ensures the
assignment of entities in the special entities set to locations
in the special locations set only. Finally, constraint (8)
ensures that only attraction point entities are assigned to
attraction point locations.
IV. ILLUSTRATION AND ANALYSIS
In this section, the proposed model is tested on 3
generated instances of the problem. Three size categories
are assumed for the problem; small (1-10 locations/entities),
medium (11-30 locations/entities), and large (more than 30
locations /entities). The generated instances have the
following sizes; small (6 locations/entities in 2 blocks),
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-6
medium (20 locations/entities in 5 blocks), and large (49
locations/entities in 7 blocks). Entities weights are
categorized into 4 classes; low ranges from 0 to 30, medium
ranges from 30 to 60, high ranges from 60 to 80, and
attraction point ranges from 80 to 100. The examples are
solved using LINGO 11 on a 2.20 GHz processor and 4GB
RAM computer, and the results are as shown in Table 1.
TABLE I. SOLUTIONS FOR THE GENERATED EXAMPLES
Generated
example
Number of
locations
Objective
function value
Run time
hh:mm:ss
1 6 19.39 00:00:01
2 20 58.22 00:03:11
3 49 51.87 00:13:12
For example 1, six-entities {A,B,C,D,E,F} are assigned
to six locations {1,2,3,4,5,6}. It is assumed that the mall is
divided into two blocks, where each has three locations.
There is one special location {2} and one special entity {C},
and one attraction point location {4} and one attraction
point entity {E}. The solution is shown in Fig 3.
Fig. 3. Optimal layout for Example 1
The optimal solution for example 2 is shown in Fig. 4
and that for example 3 is shown in Fig 5.
Fig. 4. Optimal layout for Example 2
Fig. 5. Optimal layout for Example 3
The model formulation proves to be efficient in
distributing flow through the mall areas, under the assumed
special and attraction point restrictions, as can be seen from
the block flow factor values in Figs. 3, 4, and 5. In example
3, Fig. 5 shows that the second block captures the maximum
flow with 553 and the 6th block captures the minimum flow
with 502. The minimum difference between maximum flow
and minimum flow ensures that the flow is balanced and
distributed across the whole shopping center space. The
generated examples are solved using LINGO software,
which provided solutions in reasonable time up to 52
locations. However, for larger number of locations the
software was unable to provide a solution within a 24 hours
period.
V. CONCLUSIONS
In this paper, the problem of designing a successful
shopping center and its relation to the efficient assignment
of shops in its available locations is discussed. To the best
of the authors’ knowledge, this is the first proposed
mathematical model to address this problem. The presented
mathematical model is proven to be successful in fulfilling
the problem objective of balancing customer circulation
around all shopping center areas, and distributing foot-
traffic across all shopping center locations. The model
utilizes the high power of attraction of some shops to attract
reasonable flow at other shops with lower power of
attraction, located at the same area, or in neighboring areas.
The presented model is tested for a number of examples,
and solved using an exact method. While solved problems
prove that model formulation results in a good distribution
of flow across the whole shopping center for small to
medium sized problems, for larger problems the exact
methods fails to provide a solution in a reasonable time.
Accordingly, heuristic methods should be developed to
tackle this problem and solve large sized problems in future
studies.
The 9th International Conference on Informatics and Systems (INFOS2014) – 15-17 December
Operations Research and Decision Support Track
Copyright© 2014 by Faculty of Computers and Information–Cairo University ORDS-7
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