TLP Paper Facility Layout Problem (2007)

Facility layout problems: A survey

Amine Drira a,b,*, Henri Pierreval a, Sonia Hajri-Gabouj b

a LIMOS, UMR CNRS 6158, IFMA, Institut Francais de Mecanique Avancee, Campus des Cezeaux, BP 265, F-63175 Aubiere Cedex, Franceb URAII, INSAT, Institut National des Sciences Appliquees et de Technologie, Centre Urbain Nord, BP 676, 1080 Tunis, Tunisia

Received 14 January 2007; accepted 4 April 2007

Available online 5 November 2007

Abstract

Layout problems are found in several types of manufacturing systems. Typically, layout problems are related to the location of facilities (e.g.,

machines, departments) in a plant. They are known to greatly impact the system performance. Most of these problems are NP hard. Numerous

research works related to facility layout have been published. A few literature reviews exist, but they are not recent or are restricted to certain

specific aspects of these problems. The literature analysis given here is recent and not restricted to specific considerations about layout design.

We suggest a general framework to analyze the literature and present existing works using such criteria as: the manufacturing system features,

static/dynamic considerations, continual/discrete representation, problem formulation, and resolution approach. Several research directions are

pointed out and discussed in our conclusion.

# 2007 Elsevier Ltd. All rights reserved.

www.elsevier.com/locate/arcontrol

Annual Reviews in Control 31 (2007) 255–267

Keywords: Manufacturing facility; Facility layout; Material handling; Dynamic layout; Optimization methods

1. Introduction

The placement of the facilities in the plant area, often

referred to as ‘‘facility layout problem’’, is known to have a

significant impact upon manufacturing costs, work in process,

lead times and productivity. A good placement of facilities

contributes to the overall efficiency of operations and can

reduce until 50% the total operating expenses (Tompkins et al.,

1996). Simulation studies are often used to measure the benefits

and performance of given layouts (Aleisa & Lin, 2005).

Unfortunately, layout problems are known to be complex and

are generally NP-Hard (Garey & Johnson, 1979). As a

consequence, a tremendous amount of research has been

carried out in this area during the last decades. A few surveys

have been published to review the different trends and research

directions in this area. However, these surveys are either not

recent (Hassan, 1994; Kusiak & Heragu, 1987; Levary &

Kalchik, 1985), or focus on a very specific aspect of layout

* Corresponding author at: URAII, INSAT, Institut National des Sciences

Appliquees et de Technologie, Centre Urbain Nord, BP 676, 1080 Tunis,

Tunisia. Tel.: +216 71703829; fax: +216 71704329.

E-mail addresses: [email protected] (A. Drira),

[email protected] (H. Pierreval), [email protected]

(S. Hajri-Gabouj).

1367-5788/$ – see front matter # 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.arcontrol.2007.04.001

design, such as loop layouts (Asef-Vaziri & Laporte, 2005),

dynamic problems (Balakrishnan & Cheng, 1998) and design

through evolutionary approaches (Pierreval, Caux, Paris, &

Viguier, 2003). Benjaafar, Heragu, and Irani (2002) conducted

a prospective analysis and suggested research directions. Our

conclusion will show that several of their research propositions

remain valid but other issues can also be raised.

In this article, we present a recent survey about layout

problems based on numerous literature references. First, in

Section 2, we consider several possible definitions of layout

problems. Then, we propose a general framework that can be

used to analyze the current literature. Section 3 distinguishes

the major features of the workshops that can be found. In

Section 4, emphasis is put on so called dynamic problems.

Section 5 discusses how facility layout problems can be

formulated. In Section 6, we are interested in the approaches

that are used to solve these problems. Although this review

cannot be exhaustive, it has been conducted from a large

number of literature references.

2. Definition of layout problems

A facility layout is an arrangement of everything needed for

production of goods or delivery of services. A facility is an

entity that facilitates the performance of any job. It may be a

mailto:[email protected]



http://dx.doi.org/10.1016/j.arcontrol.2007.04.001

A. Drira et al. / Annual Reviews in Control 31 (2007) 255–267256

machine tool, a work centre, a manufacturing cell, a machine

shop, a department, a warehouse, etc. (Heragu, 1997).

Due to the variety of considerations found in the articles,

researchers do not agree about a common and exact definition of

layout problems. The most encountered formulations are related

to static layout problems (in opposition to the dynamic layout

problems that will be specifically discussed in Section 3).

Koopmans and Beckmann (1957) were among the first to

consider this class of problems, and they defined the facility

layout problem as a common industrial problem in which the

objective is to configure facilities, so as to minimize the cost of

transporting materials between them. Meller, Narayanan, and

Vance (1999) considered that the facility layout problem consists

in finding a non-overlapping planar orthogonal arrangement of n

rectangular facilities within a given rectangular plan site so as to

minimize the distance based measure. Azadivar and Wang

(2000) defined that the facility layout problem as the

determination of the relative locations for, and allocation of,

the available space among a given number of facilities. Lee and

Lee (2002) reported that the facility layout problem consists in

arranging n unequal-area facilities of different sizes within a

given total space, which can be bounded to the length or width of

site area in a way to minimize the total material handling cost and

slack area cost. Shayan and Chittilappilly (2004) defined the

facility layout problem as an optimization problem that tries to

make layouts more efficient by taking into account various

interactions between facilities and material handling systems

while designing layouts.

Numerous articles have been published in this area. In order

to highlight what seems to constitute essential features to

characterize layout problems, we propose in Fig. 1, a first

possible rough tree representation of the different factors taken

into account in the literature. In fact, the problems addressed in

research works differ, depending on such factors as: the

workshop characteristics (e.g. ail, specificities of the manu-

facturing systems, the facility shapes, the material handling

system, and the layout evolution), what is the problem

addressed (e.g., problem formulation, objectives and con-

straints) and the approaches used to solve it (Resolution

approaches). Although this tree representation can probably be

improved in future research works, we have found it helpful in

characterizing existing research works. Consequently, the rest

of this article is organized in accordance with this representa-

tion and with the most important features identified.

3. Workshop characteristics impacting the layout

Several types of workshop are addressed in the literature. In

fact, the layout problems addressed are strongly dependent on

the specific features of manufacturing systems studied. Several

factors and design issues clearly differentiate the nature of the

problems to be addressed, in particular: the production variety

and volume, the material handling system chosen, the different

possible flows allowed for parts, the number of floors on which

the machines can be assigned, the facility shapes and the pick-

up and drop-off locations. Due to their importance, these factors

are detailed below.

3.1. Products variety and volume

The layout design generally depends on the products variety

and the production volumes. Four types of organization are

referred to in existing articles, namely fixed product layout,

process layout, product layout and cellular layout (Dilworth,

1996). These key organizations are sometimes discussed

differently according to the authors.

In Fixed product layout, the products generally circulate

within the production facilities (machines, workers, etc.); in

this particular type of layout, the product does not move, it is the

different resources that are moved to perform the operations on

the product. This type of layout is commonly found in

industries that manufacture large size products, such as ships or

aircrafts. Process layout groups facilities with similar functions

together (resources of the same type). This organization is often

reported to be suited when there is a wide variety of product.

Product layout is used for systems with high production

volumes and a low variety of products. Facilities are organized

according to the sequence of the successive manufacturing

operations. In Cellular layout, machines are grouped into cells,

to process families of similar parts. These cells also need to be

placed on the factory floor. Therefore, one is also generally

concerned with so called intra cells machine layout problems,

as mentioned for example in (Proth, 1992, ch. 3) and (Hamann

& Vernadat, 1992). Here, one is concerned with finding the best

arrangement of machines in each cell.

3.2. Facility shapes and dimensions

Two different facility shapes are often distinguished (Fig. 2):

regular, i.e., generally rectangular (Kim & Kim, 2000) and

irregular, i.e., generally polygons containing at least a 2708angle (Lee & Kim, 2000). As mentioned by Chwif, Pereira

Barretto, and Moscato (1998) a facility can have given

dimensions, defined by a fixed length (Li) and a fixed width

(Wi). In this case, the facilities are called fixed or rigid blocks.

According to the same authors, a facility can also be defined by

its area, its aspect ratio: ai = Li/Wi, an upper bound aiu and a

lower bound ail such that ail � ai � aiu. The aspect ratio was

also used by Meller et al. (1999). If ai = ail = aiu, this

corresponds to the fixed shape blocks case (Chwif et al., 1998).

3.3. Material handling systems

A material handling system ensures the delivery of material

to the appropriate locations. Material handling equipment can

be conveyors (belt, roller, wheel), automated guided vehicles

(AGV), robots, etc. (El-Baz, 2004). Tompkins et al. (1996)

estimated that 20–50% of the manufacturing costs are due to the

handling of parts and then a good arrangement of handling

devices might to reduce them for 10–30%.

When dealing with a material handling system, the problem

consists in arranging facilities along the material handling path.

Two dependent design problems are considered: finding the

facility layout and selecting the handling equipment. The type

of material-handling device determines the pattern to be used

Fig. 1. Tree representation of the layout problems.

A. Drira et al. / Annual Reviews in Control 31 (2007) 255–267 257

Fig. 3. Layout design considering material handling devices. Fig. 4. Multi-floor layout.

Fig. 5. Backtracking and bypassing.

Fig. 2. Regular and irregular facility shapes.


for the layout of machine (Devise & Pierreval, 2000; Heragu &

Kusiak, 1988). Co, Wu, & Reisman (1989) also pointed out that

the facility layout impacts the selection of the handling device.

Given the difficulty of solving both problems jointly, they are

mainly solved sequentially (Hassan, 1994). Among the major

types of layout arrangement based on the type of material

handling, one can distinguish, as depicted in Fig. 3: single row

layout, multi-rows layout, loop layout and open-field layout

(Yang, Peters, & Tu, 2005).

The single row layout problem occurs when facilities have to

be placed along a line (Djellab & Gourgand, 2001; Ficko,

Brezocnick, & Balic, 2004; Kim, Kim, & Bobbie, 1996;

Kumar, Hadjinicola, & Lin, 1995). Several shapes may be

considered from this basic situation, such as straight line, semi-

circular or U-shape (Hassan, 1994). The loop layout problem

deals with the assignment of m facilities to candidate locations

1, . . ., m, in a closed ring network, around which parts are

transported in one direction (Chaieb, 2002; Cheng & Gen,

1998; Cheng, Gen, & Tosawa, 1996; Nearchou, 2006; Potts &

Whitehead, 2001). The loop layout incorporates a Load/Unload

(L/U) station, i.e., location from which a part enters and leaves

the loop. This station is unique and it is assumed to be located

between position m and 1. The multi-rows layout involves

several rows of facilities (Hassan, 1994). The movements of

parts occur between facilities from the same row and from

different rows (Chen, Wang, & Chen, 2001; Ficko et al., 2004;

Kim et al., 1996). The open field layout corresponds to

situations where facilities can be placed without the restrictions

or constraints that would be induced by such arrangements as

single row or loop layout (Yang et al., 2005).

3.4. Multi-floor layout

Nowadays, when it comes to construct a factory in urban

area, land supply is generally insufficient and expensive. The

limitation of available horizontal space creates a need to use a

vertical dimension of the workshop. Then, it can be relevant to

locate the facilities on several floors, as depicted in Fig. 4. This

figure shows that parts can move horizontally on a given floor

(horizontal flow direction), but also from one floor to another

floors located at a different level (vertical flow direction). The

vertical movement of parts requires a vertical transportation

device: elevator. In such situations, both the position on the

floor and the levels have to be determined for each facility, so

that the related problems are referred to as multi-floor layout

problems (Kochhar & Heragu, 1998).

Johnson (1982) seems to be among the firsts to address a

multiple-floor layout problem. He dealt with the problem of

defining relative locations of facilities in a multiple-floor

building. Later, other researchers focused on taking into

consideration vertical movements of parts from one floor to

another (Bozer, Meller, & Erlebacher, 1994; Meller & Bozer,

1996, 1997). Elevators are often the material handling system

reported (Lee, Roh, & Jeong, 2005). Their number and location

are either known (Lee et al., 2005) or to be determined through

optimization (Matsuzaki, Takashi, & Yoshimoto, 1999). In

(Matsuzaki et al., 1999), the capacity of each elevator was

considered as a constraint. The number of floors can be known

(Lee et al., 2005) or to be determined, depending on each floor

area and on the number and dimensions of the facilities

(Patsiatzis & Papageorgiou, 2002).

3.5. Backtracking and bypassing

Backtracking and bypassing (see Fig. 5) are two particular

movements that can occur in flow-line layouts, which impact

the flow of the products. Backtracking is the movement of a

part, from one facility to another preceding it in the sequence of

facilities in the flow-line arrangement (Braglia, 1996; Kouvelis

Fig. 7. Evolution of the layout over four periods.


& Chiang, 1992; Zhou, 1998). The number of these movements

has to be minimized. Zhou (1998) called this problem

Production Line Formation Problem (PLFP), which consists

in determining the orders (partial or total) of machines so as to

minimize the weighted sum of arrows whose direction is

contrary to the global flow of products, while taking into

account constraints on the rank of machines.

Bypassing occurs when a part skips some facilities during its

moving towards the flow line arrangement (Chen et al., 2001).

Hassan (1994) noticed that several procedures were presented

for dealing with and minimizing backtracking but no procedure

was suggested in the literature for addressing bypassing.

3.6. Pick-up and drop-off locations

It is often necessary to determine the location from which

parts enter and leave facilities, called Pick-up and Drop-off (P/

D) points. Although they can potentially be located at various

places (Kim & Kim, 2000), several researchers restricted their

possible position to reduce the complexity (Das, 1993;

Rajasekharan, Peters, & Yang, 1998; Welgama & Gibson,

1993). An example is given in Fig. 6.

4. Static vs. dynamic layout problems

We have seen that the workshop characteristics introduce

differences in the way to design the layout. In addition, it is well

known that nowadays, manufacturing plants must be able to

respond quickly to changes in demand, production volume and

product mix. Page (1991) reported that, on average, 40% of a

company’s sales come from new products. However, the change

in product mix yields to modify the production flow and thus

affects the layout. Gupta and Seifoddini (1990) stated that 1/3

of USA companies undergo major reorganization of the

production facilities every 2 years. A good number of authors

have tried to take such an important issue into account when

designing the layout. Most articles dealing with layout

problems are implicitly considered as static; in other words

they assume that the key data about the workshop and what it is

intended to produce will remain constant enough over a long

period of time. Recently the idea of dynamic layout problems

has been introduced by several researchers. Dynamic layout

problems take into account possible changes in the material

handling flow over multiple periods (Balakrishnan, Cheng,

Conway, & Lau, 2003; Braglia, Zanoni, & Zavanella, 2003;

Kouvelis, Kurawarwala, & Gutierrez, 1992; Meng, Heragu, &

Zijm, 2004). In this respect, the planning horizon is generally

divided into periods that may be defined in weeks, months, or

years. For each period, the estimated flow data remains

constant. A layout plan for the dynamic layout problem consists

of series of layouts, each layout being associated with a period.

Fig. 6. Example of P/D points of a machine with a regular shape.

Fig. 7 shows a layout with six equal size locations to be

arranged in each of the four periods in the planning horizon.

The objective can be to determine a layout for each period in

the planning horizon, while minimizing the sum of the material

handling costs, for all periods, and the sum of the rearrange-

ment costs between time periods (Balakrishnan, Cheng,

Conway, et al., 2003; Baykasoglu, Dereli, & Sabuncu,

2006). Rearrangement costs have to be considered when

facilities need to be moved from one location to another

(Baykasoglu & Gindy, 2001).

5. Formulation of layout problems

The workshop characteristics and the static or dynamic

issues being raised, there are several ways of formulating

mathematically the layout problems so that they can be solved.

This formulation of static and dynamic layout problems can be

based on several types of models, which allow the complex

relationships between the different elements involved in a

layout problem to be expressed. Such models can rely on

different principles, which include graph theory (Kim & Kim,

1995; Leung, 1992; Proth, 1992) or neural network (Tsuchiya,

Bharitkar, & Takefuji, 1996). These models are generally used

to suggest solutions to the layout problems, which most

researchers consider as optimization problems, with either

single or multiple objectives. Depending on the manner in

which the problem is formulated, that is, discrete or continuous,

the formulations found in the literature can lead to Quadratic

Assignment Problems (QAP) or Mixed Integer Programmings

(MIP), which are the most commonly encountered. In each

case, a few authors have argued that the available data could not

be perfectly known and have suggested fuzzy formulation.

These approaches are discussed in the following.

5.1. Discrete formulation

The layout is sometimes considered as discrete (Fig. 8a). In

such a case, the associated optimization problem is sometimes

addressed as QAP. The plant site is divided into rectangular

blocks with the same area and shape, and each block is assigned

Fig. 8. Discrete and continual layout representations.


to a facility (Fruggiero, Lambiase, & Negri, 2006). If facilities

have unequal areas, they can occupy different blocks (Wang,

Hu, & Ku, 2005).

A typical formulation, when determining the relative

locations of facilities so as to minimize the total material

handling cost, is as follows (Balakrishnan, Cheng, & Wong,

2003):

minXN

i¼1

XN

j¼1

XN

k¼1

XN

l¼1

f ikd jlXi jXkl (1)

s.t.

XN

i¼1

Xi j ¼ 1; j ¼ 1; . . . ;N (2)

XN

j¼1

Xi j ¼ 1; i ¼ 1; . . . ;N (3)

where N is the number of facilities in the layout, f ik the flow cost

from facility i to k, djl the distance from location j to l and Xij the

0, 1 variable for locating facility i at location j. The objective

function (1) represents the sum of the flow costs over every pair

of facilities. Eq. (2) ensures that each location contains only one

facility and Eq. (3) guarantees that each facility is placed only

in one location.

Discrete formulations are suggested, for example, by

Kouvelis and Chiang (1992) and Braglia (1996) to minimize

part backtrack in single row layouts. The same type of approach

is also used by Afentakis (1989), to design a loop layout, so as

to minimize the traffic congestion, i.e., the number of times a

part traverses the loop before all its operations are completed.

There are two kinds of congestion measures commonly used in

loop layout design: Min-Sum and Min-Max. A Min-Sum

problem attempts to minimize the total congestion of all parts;

while a Min-Max problem attempts to minimize the maximum

congestion among a family of parts (Cheng & Gen, 1998;

Cheng et al., 1996; Nearchou, 2006).

Discrete representation of the layout is commonly used for

dynamic layout problems. The problems addressed are related

to equal size facilities (Baykasoglu & Gindy, 2001; Lacksonen

& Enscore, 1993) and must respect constraints ensuring that

each location is assigned to only one facility at each period, and

that exactly one facility is assigned to each location at each

period (Baykasoglu & Gindy, 2001; McKendall, Shang, &

Kuppusamy, 2006). Budget constraints can be added to carry

out the reconfiguration of facilities on the floor plant

(Balakrishnan, Robert Jacobs, & Venkataramanan, 1992;

Baykasoglu et al., 2006). In fact, the rearrangement costs

must not exceed a certain level of the budget.

Discrete representations are not suited to represent the exact

position of facilities in the plant site and can not model

appropriately specific constraints as the orientation of facilities,

pick-up and drop-off points or clearance between facilities. In

such cases, a continuous representation is found to be more

relevant by several authors (Das, 1993; Dunker, Radonsb, &

Westkampera, 2005; Lacksonen, 1997).

5.2. Continual formulation

In many articles, the layout representation is continual

(Fig. 8b). It is often addressed as Mixed Integer Programming

Problems (Das, 1993). All the facilities are placed anywhere

within the planar site and must not overlap each other (Das,

1993; Dunker et al., 2005; Meller et al., 1999).

The facilities in the plant site are located either by their

centroid coordinates (xi,yi), half length li and half width wi or by

the coordinates of bottom-left corner, length Li and width Wi of

the facility. The distance between two facilities can be, for

example, expressed through the rectilinear norm (Chwif et al.,

1998):

di jððxi; yiÞ; ðx j; y jÞÞ ¼ jxi � x jj þ jyi � y jj (4)

The pick-up and drop-off points can generate constraints in

the layout problem formulation (Kim & Kim, 2000; Welgama

& Gibson, 1993; Yang et al., 2005). In this case, the distance

traveled by a part from the drop-off of facility i to the pick-up of

facility j, can for example, be given by Eq. (5) (Kim & Kim,

2000).

di j ¼ jxOi � xI

jj þ jyOi � yI

jj (5)

where (xOi ; y

Oi ) designate the coordinates of the drop-off point of

facility i, and (xIj; y

Ij) the coordinates of the pick-up point of

facility j.

The determination of the best locations of the P/D stations is

a specific problem, addressed for example by Chittratanawat

and Noble (1999), Kim and Kim (1999), and Aiello, Enea, and

Galante (2002).

Obviously, area constraints on the plant site exist, which

require the total area available to be superior or equal to the sum

of all the facility areas. The area allocated to each machine on

the floor plan must also take into account the space of other

resources or buffers, which are needed to operate the machine

(Lacksonen, 1997). The clearance between facilities can be

included or not in the facility surface (Braglia, 1996; Heragu &

Kusiak, 1988, 1991).

Another very important constraint is that facilities must not

overlap. Welgama and Gibson (1993) set two conditions for the

non-overlapping of facilities: condition of X-projection non-

overlapping and condition of Y-projection non-overlapping:

ðx jt � xibÞðx jb � xitÞ� 0 (6)

ðy jt � yibÞðy jb � yitÞ� 0 (7)

where (xit, yit) and (xib, yib) are the top-left and the bottom right

corners of the facility i and (xjt, yjt) and (xjb, yjb) are the top-left

and the bottom right corners of the facility j. Mir and Imam

(2001) defined an overlap area Aij between two facilities to

formulate this constraint. The layout optimization problem is

expressed as follows:

Minimize objective function

Subject to Ai j � 0(8)


where

Ai j ¼ li jðDXi jÞðDYi jÞ;

DXi j ¼ li jLi þ L j

2

� �� jxi � x jj;

DYi j ¼ li jWi þW j

2

� �� jyi � y jj;

li j ¼�1 for DXi j � 0 and DYi j � 0

þ1 otherwise

�

ðLi;WiÞ are the length and width of facility i, and (xi,yi) are

coordinates of facility i.

Other constraints can also be considered in the layout

formulation, such as a pre-defined orientation of certain

facilities (Dunker et al., 2005). Given such constraints, a typical

formulation of the optimization problem can be as follows:

Minimize C ¼XN

i¼1

XN

j¼1

f i jðjxIj � xO

i j þ jyIj � yO

i jÞ (9)

where N is the number of facilities, fij the amount/cost

of material flow from drop-off point of facility i to pick-up

point of facility j, (xOi ; y

Oi ) the coordinates of drop-off point of

facility i, and (xIj; y

Ij) are the coordinates of pick-up point of

facility j.

Very few works seem to deal with dynamic layout problems

with a continuous representation. Dunker et al. (2005)

addressed unequal size layout problems in a dynamic

environment and assumed that the facility sizes vary from

one period to another.

5.3. Fuzzy formulation

In many concrete cases, data affecting layout problems are

not exactly known. Stochastic approaches, such as the use of

queuing networks (Meng et al., 2004) are seldom seen. Fuzzy

logic has been proposed to handle the imprecision or uncertainty

that is often encountered (Evans, Wilhlem, & Karwowsky, 1987;

Grobelny, 1987a; Raoot & Rakshit, 1991). A few approaches

based on fuzzy concepts exist to design layouts.

Evans et al. (1987) addressed the placement of unequal size

facilities on the plant area. They expressed relations between

every pair of facilities by fuzzy relations describing closeness

and importance. These relations allow the analyst to specify the

importance associated with each pair of facilities to be located

at any distance from each other. The authors proposed a fuzzy

formulation of the problem through linguistic variables and

propose a heuristic. Grobelny (1987a, 1987b) tacked the

problem of locating n facilities to n fixed locations so as to

minimize the total material handling cost. The data impacting

the layout, such as closeness links and traffic intensity, are

fuzzy and modeled with linguistic variables and fuzzy

implications. A heuristic procedure, based on binary fuzzy

relations, is developed for the selection and the placement of

facilities in the available locations. Several principles of this

approach are also used by Raoot and Rakshit (1991), who

considered the problem of finding the best arrangement on

the plant site of facilities based on specifications about their

inter-relationship, which are characterized through linguistic

variables. Gen, Ida, and Cheng (1995) addressed a multi-

objective multi-rows layout problem with unequal area. They

are interested in situations where the clearance cannot be

precisely defined, and is therefore considered as fuzzy. In

Dweiri and Meier (1996), who dealt with a discrete facility

layout problem, the amount of parts circulating between

facilities, the amount of communications between facilities

(information flow) and the number of material handling

equipments used to transfer parts between facilities are

considered as fuzzy factors. The authors developed an Activity

Relationship Chart (ARC) based on the judgment of experts

that is used to specify relationships between each pair of

facilities. ARC is then integrated in the well known heuristic

‘CORELAP’ to find the best placement of facilities. Aiello and

Enea (2001) argued that the product market demands are

uncertain data that can be defined as fuzzy numbers. They

minimize the total material handling cost, along a single row

configuration, under the constraints that the capacity of

production for each department is limited. To solve a single

row layout problem, they split the fuzzy demands in a-cuts and

determine the a-level fuzzy cost for each possible layout. Deb

and Bhattacharyya (2005), addressed the placement of

facilities with pick-up and drop-off points in a continual

plane, so as to minimize the total material handling cost.

The position of facilities depends on such factors as: the

personal flow, the supervision relationships, the environmental

relationships and the information relationships, which are

rated using linguistic variables (e.g., high, medium, low). The

authors developed a fuzzy decision support system based on

a set of fuzzy IF–THEN rules. A construction heuristic is

then used do determine the placement of facilities in the plant

site.

5.4. Multi-objective layout problems

In most articles about layout problems, the main objective is

to minimize a function related to the travel of parts (the total

material handling cost, the travel time, the travel distance, etc.).

To be more realistic, some researchers have considered more

than a single objective. For example, Dweiri and Meier (1996)

aimed at minimizing simultaneously the material handling flow

and the equipment flow and the information flow. Most authors

combine the different objectives into a single one either by

means of Analytic Hierarchy Process (AHP) methodology

(Harmonosky & Tothero, 1992; Yang & Kuo, 2003) or using a

linear combination of the different objectives (Chen & Sha,

2005).

Few researchers used a Pareto approach to generate a set of

non-dominated solutions. Aiello, Enea, and Galante (2006)

dealt with a layout problem related to the minimization of the

material handling cost and the maximization of an adjacency

function (assessment of the proximity requests between two

departments). The set of non-dominated solutions is then found

and a ‘‘best’’ solution is then selected from this set using the

well known ‘Electre method’.


5.5. Simultaneous solving of different problems

It is common that other problems have to be solved together

with the layout design. For example, this occurs when

designing cellular manufacturing systems, where one has both

to assign machines to cells (cell formation problems) and to

determine the position of each machine in the cell (intra cell

layout). The position of each cell in the floor plant has also to be

determined. Instead of formulating and solving these problems

sequentially, it is sometimes possible to address these two

issues as a same problem (Gupta, Gupta, Kumar, & Sundaram,

1996).

6. Resolution approaches

Several approaches exist to address the different types of

problems that are formulated in the literature. They aim either

at finding good solutions, which satisfies certain constraints

given by the decision maker or at searching for an global or

local optimum solutions given one or several performance

objectives. This has yield heuristic based methods or

optimization algorithms, as explained in the following of this

section.

Some attempts of using artificial intelligent approaches

have been made to address layout problems. Expert systems

were, for example, proposed in (Heragu & Kusiak, 1990).

Hamann and Vernadat (1992) also used this approach for

intra-cell problems. More recently, an expert system based

on artificial neural networks was implemented for facility

layout construction in a manufacturing system (Chung,

1999).

Several types of optimization approaches have been

proposed in the literature. In the following, we distinguish:

exact methods, such as branch and bound, and approximated

approaches, such as heuristics and metaheuristics.

6.1. Exact approaches

Among articles that dealt with exact methods, Kouvelis

and Kim (1992) developed a branch and bound algorithm

for the unidirectional loop layout problem. Meller et al.

(1999) also used this approach to solve the problem of

placing n rectangular facilities within a given rectangular

available area. They proposed general classes of valid

inequalities, based on an acyclic sub-graph structure, to

increase the range of solvable problems and use them in a

branch-and-bound algorithm. Kim and Kim (1999) addressed

the problem of finding P/D locations on fixed size facilities

for a given layout. The objective of the problem is to

minimize the total distance of material flows between the

P/D points. Authors suggested a branch and bound

algorithm to find an optimal location of the P/D points of

each facility. Rosenblatt (1986) used a dynamic program-

ming method to solve a dynamic layout problem with

equal size facilities. However, only small problem instances

have been solved optimally (six facilities and five time

periods).

6.2. Approximated approaches

Since exact approaches are often found not to be suited for

large size problems, numerous researchers have developed

heuristics and metaheuristics.

Construction approaches build progressively the sequence of

the facilities until the complete layout is obtained whereas

improvement methods start from one initial solution and they try

to improve the solution with producing new solution. Construc-

tion heuristics include: CORELAP (Lee & Moore, 1967),

ALDEP (Seehof & Evans, 1967) and COFAD (Tompkins &

Reed, 1976), SHAPE (Hassan, Hogg, & Smith, 1986). Example

of improvement heuristics are: CRAFT (Armour & Buffa, 1963),

FRAT (Khalil, 1973) and DISCON (Drezner, 1987).

Among the approaches based on metaheuristics, one can

distinguish global search methods (Tabu search and simulated

annealing) and evolutionary approaches (genetic and ant

colony algorithms).

Chiang and Kouvelis (1996) developed a tabu search

algorithm to solve a facility layout problem. They used a

neighborhood based on the exchange of two locations of facilities

and included a long term memory structure, a dynamic tabu list

size, an intensification criteria and diversification strategies.

Chwif et al. (1998) used a simulated annealing algorithm to

solve the layout problem with aspect ratio facilities sizes. Two

neighborhood procedures are proposed: a pairwise exchange

between facilities and random moves on the planar site in the

four main directions (upwards, downwards, leftwards and

rightward). McKendall et al. (2006) suggested two simulated

annealing approaches for a dynamic layout problem with equal

size facilities. The first simulated annealing approach used a

neighborhood based on a descent pairwise exchange method,

which consists in randomly changing the location of two

facilities while the solution is improved. The second approach

combines the first simulated annealing algorithm and improve-

ment strategy called ‘‘look-ahead and look-back strategy’’.

Genetic algorithms seem to become quite popular in solving

facility layout problems (Pierreval et al., 2003). In fact, a large

number of studies using such approaches have been published:

see Banerjee and Zhou (1995), Mak, Wong, & Chan (1998),

Tam and Chan (1998), Azadivar and Wang (2000), Wu and

Appleton (2002), Dunker, Radonsb, & Westkampera (2003),

and Wang et al. (2005) for the static layout problems, and

Balakrishnan and Cheng (2000), Balakrishnan, Cheng, Con-

way, et al. (2003), and Dunker et al. (2005) for the dynamic

layout problems.

A very important problem when developing a genetic

algorithm is related to the coding of a candidate floor plan. A

popular representation of the continual layout is the slicing tree

(Shayan & Chittilappilly, 2004). A slicing tree is composed of

internal nodes partitioning the floor plan and of external nodes

representing the facilities. Each internal node can be labeled

either h (horizontal) or v (vertical), indicating whether it is a

horizontal or vertical slice whereas external nodes label the

facility index (1, 2, 3, . . ., n for n facilities). Each rectangular

partition corresponds to a space allocated to a facility. Fig. 9

shows a particular layout and the corresponding slicing tree.

Fig. 9. Slicing tree representation of the floor plan.


Wu and Appleton (2002) suggested a slicing tree to represent

simultaneously the layout and the aisles and adapted genetic

operators.

From a given layout, the slicing tree is generally encoded

into a string form, in order to use particular genetic operators.

Tam (1992) suggested coding a solution by a binary string with

two parts, which represent operators and operands, and latter in

three parts: the tree structure, the operators and the operands

(Tam & Chan, 1998). Al-Hakim (2000) improved Tam Chan’s

approach (1998) and proposed a new operator named

‘transplanting’, to ensure the coherence of an offspring. The

problem of avoiding reparation procedures when dealing with

slicing trees is tackled by Shayan and Chittilappilly (2004).

When authors addressed discrete layout problems, the

coding scheme differs from continual representation. For

discrete representation, a popular solution for coding layouts is

based on Space Filling Curves (SFC) (Wang et al., 2005). The

plant area being divided into grids, a space filling curve defines

a continuous sequence through all neighbored squares in the

underlying layout (Fig. 10). Space-filling curves ensure that a

facility is never split (Bock & Hoberg, 2007). Nevertheless, this

technique requires many rules to verify the connection of all

positions of a layout as for example using expert rules (Wang

et al., 2005).

When a space filling strategy is defined, solutions have to be

coded. Islier (1998) decomposed strings into three segments,

encoding the sequence of facilities, the area required for each

facility and the width of each sweeping band. Recently, Wang

et al. (2005) encoded the chromosome’s genes through five

segments strings. The first segment shows the department

Fig. 10. String scheme of a discrete layout representation based on a space

filling curve (Wang et al., 2005).

placement sequence. The second gives the required areas of each

department. The third segment indicates the site size (length and

width). The fourth segment shows the sweeping direction

(1: horizontal, 2: vertical) and the fifth segment indicates the

sweeping bands. An example is illustrated in Fig. 10.

The objective function used in evolutionary methods is

generally expressed as a mathematical cost function, which is

derived from the problem formulation under consideration. To

take into account in a more realistic way the system

performance, simulation models have been connected to

evolutionary methods to evaluate the candidate solutions

(Azadivar & Wang, 2000). Hamamoto, Yih, and Salvendy

(1999) addressed a real problem of pharmaceutical industry.

The chromosome evaluation is performed through the

simulation of a 4 months production.

Ant colony optimization has been recently applied for

solving layout problems. Solimanpur, Vrat, and Shankar (2005)

developed an ant algorithm for a sequence-dependent single

row machine layout problem. Baykasoglu et al. (2006)

proposed an ant colony algorithm for solving the unconstrained

and budget constrained dynamic layout problems.

The hybridization of different metaheuristics has also been

considered for solving facility layout problems. Mahdi, Amet,

and Portman (1998) proposed a hybrid approach for minimiz-

ing the material handling cost. They used a simulated annealing

algorithm to solve the geometrical aspect of the problem, a

genetic algorithm to make decisions about the material

handling system and an exact method (Hitchcock’s method)

to minimize the total material handling utilization cost. Mir and

Imam (2001) presented a hybrid approach for a layout problem

with unequal area facilities. Starting from an initial solution

given by a simulated annealing algorithm, the optimal positions

of facilities are determined by an analytical search technique in

a multi-stage optimization process. Lee and Lee (2002)

presented a hybrid genetic algorithm for a fixed shape and

unequal area facility layout problem. Tabu search and

simulated annealing are first used to find global solutions

and the genetic algorithm is introduced in the middle of the

local search process to search for a global solution.

Balakrishnan, Cheng, Conway, et al. (2003) developed a

hybrid genetic algorithm to solve the dynamic layout problem

previously tackled by Rosenblatt (1986). The initial population

is generated with two methods: a random method and an

Urban’s procedure (Urban, 1993). The crossover is based on a

dynamic programming approach and the mutation is achieved

by the CRAFT heuristic (Armour & Buffa, 1963). McKendall

and Shang (2006) developed and compare three hybrid ant

colony algorithms for a dynamic facility layout problem. They

combine an ant colony with three local search procedures: (1) a

random descent pairwise exchange procedure, (2) a simulated

annealing algorithm and (3) a look-ahead/look-back procedure.

7. Conclusion and research directions

In this article, we have presented a recent comprehensive

survey related to facility layout problems. Although this survey

cannot be exhaustive, the analysis carried out is based on a large


number of literature references. From this analysis, it appears

that articles related to layout design continue to be regularly

published in major research journals and that facility layout

remains an open research issue. Several current trends and

directions seem worth being mentioned.

First of all, recent papers include more and more complex

and/or realistic characteristics of the studied manufacturing

systems. Typical examples are P/D points, aisles, complex

geometrical constraints, several floors, which are taken into

account together when formulating the layout design problem.

This is indeed an important issue because many articles contain

restrictive assumptions that are not adapted to the complexity of

many manufacturing system facilities. This is an old trend

(Benjaafar et al., 2002). However, research is still needed. The

use of a third dimension when designing a plant is a recent

consideration that certainly requires more research, for

example to select and optimize resources related to the vertical

transportation of parts between different floors.

The often unrealistic aspect of static approaches, which

consider that the data available are relevant to characterize the

future operating conditions of the system, seems to be now well

identified by researchers. Dynamic approaches may sometimes

be a potential alternative; meanwhile, they often rely on

knowledge of the future operating conditions. Fuzzy methods

can offer interesting possibilities to include uncertainty.

However, as already noted by Benjaafar et al. (2002), research

is still needed to suggest or improve methods for designing (1)

robust and adaptive layouts, (2) sensitivity measures and

analysis of layouts and (3) stochastic models used to evaluate

solutions.

In terms of methods used to solve layout problems, one can

obviously see that the use of metaheuristics is more and more

reported in articles, in order to cope with problems of a larger

size and to take into account more realistic constraints.

Evolutionary algorithms seem to be among the most popular

approaches. Solving methods are also hybridized, either to

solve complex problems (e.g., metaheuristics embedding

heuristics or connected with exact methods) or to provide

more realistic solutions (e.g., connection of evolutionary

principles with simulation). Approaches based on artificial

intelligence are now seldom published. Given the fact that it is

probably difficult to solve everything without using some kind

of expert knowledge about the system, there is probably still a

need for hybrid methods capable of optimizing the layout while

taking into account expert available knowledge.

We have noticed that most published works focus on

determining the position of facilities. However, in practice this

problem is often consider together with other design problems,

such as the choice of the type of manufacturing or

transportation resources, the design of cells, the determination

of resources capacities, etc. These problems are often not

independent (for example, the choice of a conveyor as a

material handling device does not induce the same constraints

as the choice of automated guided vehicles). Therefore, there is

still research needed for solving the different problems involved

in the design of the workshop simultaneously instead of

sequentially. Such combinations, that start to be addressed, turn

out to be promising and would worth being developed and

improved. This would lead to favor more global research about

workshop design, instead of concentrating on facility layout

problems.

The articles studied in this article focus on manufacturing

system applications. However, layout design problems also

concern other types of systems, such as ports, supermarkets,

airports, etc. These constitute interesting areas that could

benefit from the advances made in the specific area of

manufacturing.

As a final remark, let us note that commercial software tools

available on the market to globally assist in the design of

manufacturing are currently limited. Therefore, there is

probably a need for trying to make the resolution approaches

more generic, so that they can be embed as layout procedures in

software tools supporting the design of manufacturing systems.

The combination with graphical tools would also render such

tools more efficient and attractive and a few authors have

started to consider possible interfaces with virtual reality

systems.

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Strasbourg 1.

Amine Drira is a doctoral student in industrial computing at the Institute of

Applied Sciences and Technology of Tunis, Tunisia (University of 7 November

at Carthage). He is currently working as an assistant professor at the High

Institute of Medical Technologies (University Tunis El Manar). His research

interests include facility layout, fuzzy computation, metaheuristics and multi-

objective optimization.

Henri Pierreval is a professor at the French Institute of Mechanical Engineer-

ing (IFMA) of Clermont-Ferrand in France. His research activities are carried

out within the LIMOS laboratory of Clermont-Ferrand (Laboratory of Comput-

ing, System Modeling and Optimization): UMR CNRS 6158. He received his

doctoral degree and ‘‘qualification to direct research’’ degree from the Uni-

versity of Lyon in France. The design, modeling, operation of manufacturing

systems and of networks of firms are the main focuses of Dr. Pierreval’s

research. He is the author or co-author of numerous articles in these areas,

published in well-known international refereed journals. He participates in

national and international research collaborations and is on the editorial board

of scientific journals.

Sonia Hajri-Gabouj is an associate professor at the Institute of Applied

Sciences and Technology of Tunis, Tunisia. She received her BS degree in

electrical engineering from the National Engineering School of Monastir,

Tunisia, in 1994. She got her MS and PhD degrees in industrial computing

and automatic from the University of Sciences and Technologies of Lille,

France, in 1994 and 1997, respectively. She received a ‘‘qualification to direct

research’’ degree from the National Engineering School of Tunis in 2003. She is

co-responsible for the URAII research unit in automatic and industrial comput-

ing of the Institute of Applied Sciences and Technology of Tunis. Her research

interests include fuzzy modeling, design and control of manufacturing systems,

scheduling and optimization and metaheuristics.

Documents

TLP Paper Facility Layout Problem (2007)