INTRODUCTION

Determining the physical organization of a production system is defined to be the facility

layout problem. This well-studied combinatorial optimization problem arises in a variety of

production facilities, including service and communications settings. It is concerned with

finding the most efficient arrangement of m indivisible departments with unequal area

requirements within a facility. The objective is to ensure a smooth workflow or a particular

traffic pattern so as to minimize material handling costs and time. Two sets of constraints

present are: (1) department and floor area requirements and (2) department location

restrictions.

The output of the facility layout problem is a block layout, which specifies the relative

location of each department.

TYPES OF LAYOUT FORMATS

1) Process Layout

Similar equipments or functions are grouped together. A part being worked on then

travels according to the established sequence of operations. This is often reported to

be suited when there is a wide variety of product. Typically found application in job-

shops and hospitals.

2) Product Layout

Equipment work processes are arranged according to the progressive steps by which

the product is made. The path for each part is a straight line. It is used for systems

with high production volumes and a low variety of products. Production line is a

typical example.

3) Fixed-position Layout

The product remains at one location. Manufacturing equipments are moved to the

product. This type of layout is commonly found in industries that manufacture large

size products. Shipyards, construction sites, movie lots etc are examples.

4) Cellular Layout

Dissimilar machines are grouped into work centres to work on products having

similar shapes or processing requirements. 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. Here, one is concerned with finding the best arrangement of

machines in each cell.

5) Office Layout

Process of positioning workers, their equipments and spaces to provide flow of

information. Workers who require frequent contacts are positioned together.

6) Retail Layout

In a retail outlet the shelve space is allocated according to the customer behaviour.

One of the primary strategies is exposing customer to high margin items.

7) Warehouse Layout

Objective is to balance low cost storage with low cost material handling. Hence

tradeoffs between space and material handling are carried out.

TOOLS AND TECHNIQUES

1) Quadratic Assignment Problem Approach

Koopmans and Beckman introduced the quadratic assignment problem (QAP) to

model the problem of locating interacting plants of equal areas. The QAP has been

applied to a wide range of applications, including urban planning, control panel

layout, and wiring design. QAP is a special case of the facility layout problem

assuming that all departments have equal areas. The QAP formulation assigns every

department to one location and at most one department to each location. The cost of

placing a department at a particular location is dependent on the location of the

interacting departments. Such dependency leads to the quadratic objective that

inspires the problem's name. The QAP is NP -complete, which implies that, in

general, it is a hard problem to solve. Optimal solutions to general cases of the

problem can only be found for problems with less no. of departments.

Applications

Cellular and automated machine systems. [1]

2) Mixed-Integer Programming Formulation

A mixed-integer programming formulation for the facility layout problem was

presented by Montreuil in 1990 at a material handling research conference. The model

uses a distance-based objective. The objective is based on flow time rectilinear

distance between centroid of two departments .It utilizes a continuous representation

of a layout. Mixed-integer programming approach is powerful and holds much

promise. However, the model could only be optimally solved for small problems.

3) Graph- Theoretic Approaches

In graph-theoretic approaches, it is assumed that the desirability of locating each pair

of facilities adjacent to each other is known. The area and shape of the departments

are ignored (at the beginning), and each department is then represented by a node in a

graph. Satisfied department adjacency relationships are represented by an arc

connecting the two adjacent departments (nodes) in the graph. The objective function

translates to constructing a graph that maximizes the weight on the adjacencies (arcs)

between department pairs (nodes). These rely on a predefined desirable adjacency of

each pair of facilities

Developing a layout in the graph-theoretic approach requires the following three

steps:

(1) Developing an adjacency graph from department relationships (which departments

are adjacent)

(2) Constructing the dual graph of the adjacency graph (represent departments as

adjacent regions having specific boundaries)

(3) Converting the dual graph into a block layout (specifying departments with

regular shapes and specific areas).

The objective function of the graph-theoretic approach is maximized if all department

pairs with positive flow have an arc between them. Difficult in general, and thus,

heuristics must be used to construct a maximally weighted adjacency graph. Unequal-

area problems of even small size cannot be solved to guaranteed optimality with

graph-theoretic approaches.

4) Branch and Bound Methods

It is used to find an optimum solution of quadratic assignment formulated FLP

because QAP involves only binary variables. Only optimal solutions up to a problem

size of 16 are reported in literature. Beyond n=16 it becomes intractable for a

computer to solve it and, consequently, even a powerful computer cannot handle a

large instance of the problem.

5) Heuristics

Heuristic algorithms can be classified as construction type algorithms where a

solution is constructed from scratch and improvement type algorithms where an initial

solution is improved. Construction based methods are considered to be the simplest

and oldest heuristic approaches to solve the QAP from a conceptual and

implementation point of view, but the quality of solutions produced by the

construction method is generally not satisfactory. Improvement based methods start

with a feasible solution and tries to improve it by interchanges of single assignments.

Improvement methods can easily be combined with construction methods.

Different types of heuristics algorithms can be defined as:

1) Adjacency-Based Algorithms

Adjacency-based algorithms are usually incorporated within a graph based

approach.

Deltahedron Approach

One of the most widely cited adjacency-graph construction approaches is the

Deltahedron Approach (DA). The DA proceeds by determining the sequence

that nodes will enter the graph. At any stage, a node is entered into the centre

of the face (a triangle formed by three nodes) in the graph that will maximize

the adjacency benefits with the other departments in the face. Thus, a planar

graph is always maintained in DA, which allows for an easier transformation

to a block layout. Many heuristics have been developed in an attempt to

improve on DA's performance. The DA has also been modified to consider a

continuous relaxation of the adjacency decision variables using a shortest path

approach.

MATCH

MATCH, developed by Montreuil, Ratliff, and Goetschalckx is an interactive

construction type approach that utilizes a discrete representation and integer

programming to solve a b- matching problem. Their algorithm attempts to find

a matching that maximizes the adjacency score while satisfying the lower and

upper bound on the number of matches with each department, and the total

number of times a department must be matched with all other departments.

The algorithm considers the number of adjacent segments when computing

adjacency scores. The departments generated by MATCH are all rectangular

in shape and the approach is iterative, based on user input.

SPIRAL

SPIRAL, created by Goetschalckx, develops an adjacency graph and then a

block layout from the graph. SPIRAL utilizes the concept of "relationship

tuples" to construct an adjacency graph, where tuples quantify the relationship

between one department and other departments. The graph remains planar due

to its hexagonal structure and is used to construct an approximate relative

location diagram by fitting the unequal-area departments into a row-and-

column structure. SPIRAL compares favourably to layouts generated by other

approaches.

2) Distance-Based Algorithms

The following algorithms employ a distance based objective.

CRAFT (Computerized Relative Allocation of Facilities Technique)

CRAFT is is a popular improvement algorithm that uses pair wise interchange

and was developed by Armour and Buffa in 1963. CRAFT begins by

determining the centroid of each department in the initial layout. It then

performs two-way or three-way exchanges of the centroids of nonfixed

departments that are also equal in area or adjacent in the current layout. For

each exchange, CRAFT will calculate an estimated reduction in cost and it

chooses the exchange with the largest estimated reduction (steepest descent).

It then exchanges the departments exactly and continues until there exists no

estimated reduction due to two-way or three-way exchanges. Constraining the

feasible department exchanges to those departments that are adjacent or equal

in area is likely to affect the quality of the solution, but it is necessary due to

its exchange procedure. The exchange procedure has also been criticized

because it may lead to departments with irregular shape.

SHAPE

SHAPE, developed by Hassan, Hogg, and Smith, is a construction algorithm

that utilizes a discrete representation and an objective based on rectilinear

distances between department centroids. The department selection sequence is

dependent on a ranking, which is based on each department's flows and a user-

defined critical flow value. Department placement begins at the centre of the

layout. Subsequent department placement is based on the objective function

value with the department placed on each of the layout's four sides. The

algorithm is easy to implement; however, because the department shape is

controlled by the objective function, the shape of departments may deteriorate

toward the end.

NLT (Nonlinear optimization Layout Technique)

NLT, a construction algorithm developed by van Camp, Carter and Vannelli,

is based on nonlinear programming techniques and utilizes Euclidean

distances between department centroids. In the NLT model, there are three

sets of constraints: departments cannot overlap, cannot be located outside the

facility, and cannot be assigned area less than required. The constrained model

is transformed to an unconstrained form by an exterior point quadratic penalty

function method. With a three-stage approach, successively more difficult

problems are solved using the solution from the previous stage as an initial

solution point. The department shapes are all rectangular.

QLAARP (Qualitative Layout Analysis using Automated Recognition of

Patterns)

QLAARP, a construction approach that was developed by Banerjee et al. uses

qualitative layout anomalies (QLAs) to set binary variables in Montreuil's

MIP. That is, the algorithm heuristically uses context-based information to

reduce the solution tree. A design skeleton is used to structure the QLAs.

LOGIC (named for Layout Optimization using Guillotine-lnduced Cuts)

LOGIC is an improvement- type algorithm developed by Tam, where the

layout is represented as a collection of rectangular partitions organized as a

slicing tree. A slicing tree consists of branches and branching operators that

specify whether the departments on opposite sides of a branch are to the left,

right, above, or below each other. With a given slicing tree and department

area values, the layout can be determined by recursively partitioning a

rectangular area by placing the departments into the area according to the four

specific branching operators. Because this approach is likely to produce long

and narrow department shapes, two shape constraints are added as a penalty

function to the objective. The algorithm uses simulated annealing in an

attempt to find a better layout by two-way exchanges of branching operators.

The final layout of this algorithm has all rectangular shapes, except for

potentially those departments that are placed near fixed departments.

MULTIPLE (MULTI-floor Plant Layout Evaluation)

MULTIPLE, is a single or multi floor improvement- type algorithm developed

by Bozer, Meller, and Erlebacher. MULTIPLE uses a discrete representation

and extends CRAFT by applying space filling curves to single floor or multi

floor facility layout problems. MULTIPLE improves CRAFT by increasing

the number of exchanges considered at each iteration. In addition, MULTIPLE

can restrict the irregularity of department shapes by using an irregularity

measure based on the perimeter and area of each department; however,

because it uses a discrete representation, the department shapes may not be

rectangular. MULTIPLE, like CRAFT, is a steepest descent search and may be

affected by the initial layout. SABLE extends MULTIPLE by employing a

simulated annealing based search and by generalizing the department-

exchange algorithm. SABLE is shown to produce lower cost layout solutions

than MULTIPLE or LOGIC.

FLEX-BAY (named for FLEXible BAY structure)

FLEX-BAY is an improvement-type algorithm based on a continuous

representation developed by Tate and Smith. A dynamic penalty function is

used to evaluate the shape-constrained unequal area facility layout problem. A

layout is represented by a flexible number of vertical bays of varying width,

each divided into one or more rectangular departments. Encoding flexible bay

layouts is a two-part representation: permutation of the departments and

breakpoints for the bays. FLEX-BAY utilizes a genetic algorithm to search the

solution space by varying department-to-bay assignments or by adding or

removing a bay breakpoint. The algorithm generates good layouts and was

shown to outperform CRAFT and NLT.

6) Metaheuristics

Various meta-heuristics such as SA, GA, and ant colony are currently used to

approximate the solution of very large layout design problems.

The SA (Simulated Annealing) technique originates from the theory of

statistical mechanics and is based upon the analogy between the annealing of

solids and solving optimization problems. At each step, the SA heuristic

considers some neighbouring state s' of the current state s, and

probabilistically decides between moving the system to state s' or staying in

state s. These probabilities ultimately lead the system to move to states of

lower energy. Typically this step is repeated until the system reaches a state

that is good enough for the application, or until a given computation budget

has been exhausted. Many researches have been carried out on application of

SA to QAP.

Genetic algorithms are modelling techniques based on biological behaviour.

They rely on the speed of computers either to combine elements from two

solutions (parents) or to mutate a single solution to a complex problem to

produce a third solution (child) and evaluate it. If the third solution is ‘better’

than one of the others, then it ‘survives’ and the worst one ‘dies’—along the

lines of ‘survival of the fittest’ in Darwin’s theory of evolution. The process

continues through a number of iterations or ‘generations’ with each solution

contributing to the next generation in proportion to its ‘goodness.’ Random

factors ensure that the solution space is adequately covered.

Ant Colony Optimization (ACO) is a metaheuristic inspired by the foraging

behaviour of ants, which has been used to solve combinatorial optimization

problems and the Ant System (AS) was the first algorithm within this class. In

order to communicate the individual search experience to the colony, the ants

mark the corresponding paths with some amount of pheromone according to

the type of solutions found. This amount is inversely proportional to the cost

of the path generated. Besides the pheromone, the ants are guided by a

heuristic value in order to help them in the construction process.

Tabu search (TS) is an iterative procedure designed to solve optimization

problems. Helm and Hadley applied TS to solve FLP. The method is still

actively researched, and is continuing to evolve and improve. They are

generally used in combination with other algorithms like AS for enhancing

the obtained results using local search.

Advantages

Better performance

Faster runtime

Suitable for application in large scale DPLP problems

Limits/Disadvantages

Care has to be taken if the surface of the fitness function is relatively flat over

a large area of the site

Determination of layout and the scheduling procedure would need to be

carried out concurrently to demonstrate optimality

Not optimal to solve for problems which have area utilization less than one

May require dummy departments so that the area utilization equals to one.

Consequently, this increases the problem size and results in poorer solution

quality

For discrete representation shapes of the machines are not concerned, so it’s

difficult to define the real locations of machines.

The continuous representation increases the complexity of problem.

Applications

To solve for:

Unequal Area Facility Layout Problems

Layouts which are Highly dynamic, very difficult to specify and interrelated with

other management tasks. e.g.,

Construction site layouts.

Semiconductor industry under fast changing business environment,

life cycles of products become very short and types and

amounts of products vary very fast, new machines and old

machines may need to be added into/removed from the plant in

multi-stages

stochastic layouts

7) Artificial Intelligence Approach

AI approaches which are currently applied to FLP are neural network, fuzzy logic and

expert system. Tsuchiya et al. had proposed near-optimum parallel algorithm for

solving the QAP using two-dimensional maximum neural network for an N-FLP.

Knowledge based expert system has also been applied by Malakooti and Tsurushima,

Abdou and Dutta, Heragu and Kusiak and Sirinavakul and Thajchayapong to tackle

various issues related to FLP such as multi objective, the issue of optimizing material

handling equipment, etc. Kumar et al. applied expert system to handle qualitative

constraints via a symbolic manipulation.

Advantages

Can be used for solving problems involving uncertainty.

Comprehensive view and overcomes the decision maker’s subjective

consciousness.

Offer an environment for incorporating the good capabilities of humans and

the power of computers.

Can be used to solve unstructured problems and when no procedure exists.

Ability of handling a symbolic information and applying a systematic

reasoning process with a very large knowledge base.

Can accommodate new expertise whenever new knowledge is identified and

explain their recommendations.

Provide expert level consultative services to users for productivity

Improvement and reduce the company’s reliance on human experts by

capturing expert knowledge and storing it in computers, they are often cost

effective when human expertise is very expensive, not available, or

contradictory.

Limitations

Require extensive expertise knowledge.

The rules articulated must be cogent, correct, consistent.

A lengthy process depending on the problem domain.

Not good at representing temporal knowledge, representing spatial knowledge,

performing commonsense reasoning, handling inconsistent knowledge, and

recognizing the limits of their ability.

Applications

Dynamic layouts.

Stochastic layouts.

Service layouts like hospitals.

8) Facility Layout Software Packages

Layout software packages incorporate an algorithm for layout generation (in addition to

layout evaluation). Each package is listed with its associated algorithm.

FactoryOPT by CIMTECHNOLOGIE incorporates a licensed version of the

SPIRAL algorithm as well as some CRAFT-like improvement routines to

provide the user with a choice of algorithms. Previous layout packages by

CIMTECHNOLOGIES (for example, FactoryPlan and FactoryFlow) were

based on a computerized graphical representation of the manual systematic

layout procedure (SLP) developed by Muther.

SPIRAL is distributed by Marc Goetschalckx and, as the name implies, is his

implementation of the SPIRAL algorithm with other options for improvement

routines.

Fig.

LayOPT by the Production Modeling Corp. is an implementation of

MULTIPLE and SABLE.

Factory Modeler by Systems Espace Temps Inc., implements the MIP-based

approach. Various procedures are used to set the binary variables in the MIP.

The Factory Layout Planner is a client/server application that enables the

collaborative development of a factory layout. It allows the multi-user,

network-based visual creation and management of a factory layout: the design

team can co-operate on the same layout both acting on a common multi-touch

device and collaborating from different part of the world. Moreover, a key

element in this revolution is the capability to provide an adherent to reality

representation of manufacturing process There are three key features of the

FLP: the 3D visual editing of the layout, the possibility to act on the same

layout in a distributed environment, the ability to perform Discrete Events

Simulation (DES) on the layout that the user is composing. Most important

references are Dassault Systemes – Delmia V6,Siemens - Tecnomatix 9,

Rockwell Automation – Arena 13.0,Autodesk Factory Design Suite etc.

Most of the application window is occupied by the 3D view of the layout. The

user can interact with it using the mouse and the desired interaction mode:

• Camera: In this mode, the mouse is used to explore the layout: pan,

zoom and rotate function are available for natural navigation in the 3D

scene.

• Edit: This is the main mode used to modify the layout. The objects can

be selected, grouped, moved, rotated and their properties viewed and

edited. A snap grid can optionally be enabled to assist the positioning

of the objects.

• Connection: When this mode is enabled, the user can connect objects

to create logical relationship useful for the DES simulation. The

available ports are shown and the user can connect then tracing lines

from one port to the other.

F

F

5D simulation: Simulating layout construction planning showing

how the layout and its cost evolve through time (5D simulation)

can clarify and give a good image about the construction activities

sequence and spatial arrangement before starting the construction

phase. Moreover during the layout construction, team members

need to understand the progress of a project compare to their plan.

This is traditionally done by using project management documents

such as Gantt chart. However it is a difficult task to understand all

the details due to the complexity of the factory layouts. This

implies the joining the 3D visualization of the project with the

planning document can prevent misunderstanding among different

members, increasing comprehension and intuitive of designers

about physical progress of layout and identify errors in process

sequence and spatial arrangement of the layout planning process.

Figure 4 represents such a model. Users can travel in time to see

the planning and real time progress of the layout construction.

Fig

Fig

Advantages

Algorithmic approaches can generate layout alternatives efficiently, particularly,

when commercial software is available, e.g., Spiral.

Algorithmic approaches usually simplify both design constraints and objectives in

order to reach a surrogate objective function, the solution of which can then be

obtained.

The capability to support a collaborative editing of the layout (possibly distributed) in

a 3D environment, and the integrated DES possibilities, makes FLP to be an high

value adding tool for cost-effective and rapid creation, management and use of the

Next generation factory.

Fit-checking if components collide- through viewing or through automatic checking

of the geometry model.

Checking requirements on safety and ergonomics through if-then rule bases.

Productivity through material flow analysis.

Ergonomics through immersion in the layout model or manikins with load analysis.

Limitations

The resulting quantitative results of algorithmic approach often do not capture all of

the design objectives.

An algorithmic approach is usually less effective in solving a practical design

problem.