Analysis of Unequal Areas Facility Layout Problems

Abstract

The facility layout design has been regarded as the key to improve plantproductivity, which are relevant to both manufacturing problems; variousoptimization approaches for small problems and heuristic approaches for thelarger problems have been proposed to elucidate the problem. Unequal areafacility layout problems comprise a class of extremely difficult and widelyapplicable optimization problems, arising in many diverse areas. There aremany variations on the basic formulation, involving alternative objectivefunctions, side constraints, distance metrics, cost measures, and facilityshapes. Various techniques were applied after finding the solution throughtraditional methods to get much improved optimum solutions. Differentheuristics were used to solve the unequal area facility layout problems. Multiobjectiveapproaches are the norm and developing facility layout software usingmeta-heuristics such as simulated annealing (SA), genetic algorithm (GA), antcolony algorithm (ACO), and concurrent engineering is prevailing nowadays.Sometimes hybrid approaches were used by applying combination of abovetechniques i.e. combining high level genetic algorithm with simulated annealingor genetic algorithm followed by simulation techniques to get the bettersolutions. Application of these facility lay out designs includes constructionsites, manufacturing industry and service industries.and service sectors.Facility Layout Problems (FLPs) are known to be NP-hard

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P. Arikaran, Dr. V. Jayabalan,& R. Senthilkumar

International Journal of Engineering (IJE), Volume (4) : Issue (1)

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Analysis of Unequal Areas Facility Layout Problems

P.Arikaran arivarsini_2006@yahoo.com
Research scholar,
Dept. of Manufacturing, Anna University,
Chennai 600 025 India
Professor & H.O.D.,Dept. of Mechanical Engineering,
M.N.M. Jain Engineering College,
Chennai 600097, phone: 9444154329

Dr. V. Jayabalan jbalan@annauniv.edu
Professor, Dept. of Manufacturing
and Controller of Examinations, Anna University,
Chennai 600 025 India

R. Senthilkumar rskumar1967@yahoo.com
Assistant Professor, Dept.of Mechanical Engineering,
M.N.M. Jain Engineering College,
Chennai 600097, India
______________________________________________________
Abstract

The facility layout design has been regarded as the key to improve plant
productivity, which are relevant to both manufacturing problems; various
optimization approaches for small problems and heuristic approaches for the
larger problems have been proposed to elucidate the problem. Unequal area
facility layout problems comprise a class of extremely difficult and widely
applicable optimization problems, arising in many diverse areas. There are
many variations on the basic formulation, involving alternative objective
functions, side constraints, distance metrics, cost measures, and facility
shapes. Various techniques were applied after finding the solution through
traditional methods to get much improved optimum solutions. Different
heuristics were used to solve the unequal area facility layout problems. Multi-
objective approaches are the norm and developing facility layout software using
meta-heuristics such as simulated annealing (SA), genetic algorithm (GA), ant
colony algorithm (ACO), and concurrent engineering is prevailing nowadays.
Sometimes hybrid approaches were used by applying combination of above
techniques i.e. combining high level genetic algorithm with simulated annealing
or genetic algorithm followed by simulation techniques to get the better
solutions. Application of these facility lay out designs includes construction
sites, manufacturing industry and service industries.and service sectors.
Facility Layout Problems (FLPs) are known to be NP-hard
Keywords—Facility layout, unequal area , Hybrid methods , Genetic Algorithm, Automated layout
Manufacturing Industries, construction sites.

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1.INTRODUCTION
The static facility layout problem (SFLP) is a well-researched problem of finding
positions of departments on the plant floor such that departments do not overlap while some
objective is optimized. The most commonly used objective is minimizing material handling cost
(i.e., minimizing the sum of the product of the flow of materials, distance, and transportation
cost per unit per distance unit for each pair of departments). When material flows between
departments change during the planning horizon, the problem becomes the dynamic facility
layout problem (DFLP).
A solution to the FLP is a block layout that specifies the relative location and the dimensions of
each department. Once a block layout has been achieved, a detailed layout can be designed
which specifies department locations, aisle structures and input/output point locations [3, 6, 7].
Two types of approaches for finding provably optimal solutions for the FLP have been proposed
in the literature. The first type are graph-theoretic approaches that assume that the desirability
of locating each pair of facilities adjacent to each other is known. Initially, the area and shape of
the departments are ignored, and each department is simply represented by a node in a graph.
Adjacency relationships between departments can now be represented by arcs connecting the
corresponding nodes in the graph. The objective is then to construct a graph that maximizes
the weight on the adjacencies between nodes. We refer the reader to [4] for more details. The
second type are mathematical programming formulations with objective functions based on an
appropriately weighted sum of centroid-to-centroid distances between departments. Exact
mixed integer programming formulations were proposed for the above type was shown in
[8,9].
2. UNEQUAL AREA LAYOUTS
The unequal-areas facility layout problem (FLP) is concerned with finding the optimal
arrangement of a given number of non-overlapping indivisible departments with unequal area
requirements within a facility. The block layout design problem with unequal areas, which was
originally formulated by Armour and Buffa in the early 1960s, is a fundamental optimization
problem encountered in many manufacturing and service organizations. Different
were discussed for solving unequal area problems in Literature. These methods are
summarized under the various topics to have a understanding of Unequal area problem.
methods
2.1 Tree structure Model
The facility layout design has been regarded as the key to improve plant productivity, which are
relevant to both manufacturing and service sectors. A tree structure model has been proposed
for representing the unequal-area facility layout by[10]. Each facility has a different rectangular
shape specified by its area and aspect ratio. In this layout problem, based on the assumption
that the shop floor has enough space for laying out the facilities, no constraint is considered for
a shop floor. Objectives are minimizing total part movement between facilities and total
rectangular layout area where all facilities and dead spaces are enclosed. Using the genetic
code corresponding to two kinds of information, facility sequence and branching positions in the
tree structure model, a genetic algorithm has been applied for finding non-dominated solutions
in the two-objective layout problem. [10] used three kinds of crossover (PMX, OX, CX) for the
former part of the chromosome and one-point crossover for the latter part. Two kinds of layout
problems have been tested by the proposed method. The results demonstrated that the
presented algorithm was able to find good solutions in enough short time.
2.2 Genetic Search

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[23] used Genetic search for solving construction site-level unequal-area facility layout
problems. A construction site represents a conflux of concerns, constantly calling for a broad
and multi-criteria approach to solving problems related to site planning and design. As an
important part of site planning and design, the objective of site-level facility layout is to allocate
appropriate locations and areas for accommodating temporary site-level facilities such as
warehouses, job offices, workshops and batch plants. Depending on the size, location and
nature of the project, the required temporary facilities may vary. The layout of facilities can
influence on the production time and cost in projects. [23]described a construction site-level
facility layout problem as allocating a set of predetermined facilities into a set of predetermined
places, while satisfying layout constraints and requirements. A genetic algorithm system, which
is a computational model of Darwinian evolution theory, was employed to solve the facilities
layout problem. A case study was presented to demonstrate the efficiency of the genetic
algorithm system in solving the construction site-level facility layout problems
2.3 Hybrid Method
[12] presented the solution of the unequal area problem by hybridizing the meta-heuristic
methods i.e. Genetic Algorithm (GA) and Simulated Annealing (SA). (SA) is a related global
optimization technique that traverses the search space by testing random mutations on an
individual solution. A mutation that increases fitness is always accepted. A mutation that lowers
fitness is accepted probabilistically based on the difference in fitness and a decreasing
temperature parameter. In SA parlance, one speaks of seeking the lowest energy instead of the
maximum fitness. SA can also be used within a standard GA algorithm by starting with a
relatively high rate of mutation and decreasing it over time along a given schedule.
[12] could be used in future as a reference for those researchers interested in tackling this
challenging unequal facility layout problem. A mathematical model was developed for the
unequal size facility layout problem with fixed flow between departments. The orientations of
the departments with various sizes were considered to minimize the distance traveled by
people, material, and other supporting services in the safest and most effective manner. Some
of the constraints considered in the modeling were the restricted areas, reserved department
locations, and also the irregularity of the shapes of manufacturing layout. This paper has also
presented the use of hybrid algorithm (GA - SA) as a general methodology to solve the facility
layout problem under consideration.
A hybrid optimization approach was presented in [21] for the layout design of unequal-area
facilities. Simulated annealing was used to optimize a randomly generated initial placement on
an “extended plane” considering the unequal-area facilities enclosed in magnified envelop
blocks. An analytical method was then applied to obtain the optimum placement of each
envelop block in the direction of steepest descent. Stepwise reduction of the sizes of the
envelop blocks allowed controlled convergence in a multi-phase optimization process. The
presented test problems include two large size benchmark problems of 50 and 100 facilities of
unequal areas. The results indicated a significant improvement over previously published
techniques for unequal-area facilities and could yield solutions of the same quality as obtained
by PLANOPT, a general-purpose layout optimization program based on pseudo-exhaustive
search.
2.4 Convex Optimization Framework
[13] presented a convex-optimization-based framework for efficiently finding competitive
solutions for this problem. The framework is based on the combination of two mathematical
programming models. The first model is a convex relaxation of the layout problem that
establishes the relative position of the departments within the facility, and the second model
uses semi-definite optimization to determine the final layout. Aspect ratio constraints, frequently
used in facility layout methods to restrict the occurrence of overly long and narrow departments

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in the computed layouts, are taken into account by both models. It suggested that using
ellipsoids instead of circles to approximate the initial positions of departments could provide
better results and Ellipsoids would likely provide more realistic estimations of department
positions, since departments in real-world applications are not square-shaped. Further work
also included adjusting the ϕ (the parameter that can control what the desired smallest length
or width should be in each department’s layout) and potentially using a different value ϕi for
each department. Finally, different combinations of first stage and second stage models from
past papers tested to get the over all results.
2.5 Tabu search Method
Tabu search (TS) is similar to simulated annealing in that both traverse the solution space by
testing mutations of an individual solution. While simulated annealing generates only one
mutated solution, tabu search generates many mutated solutions and moves to the solution
with the lowest energy of those generated. In order to prevent cycling and encourage greater
movement through the solution space, a tabu list is maintained of partial or complete solutions.
It is forbidden to move to a solution that contains elements of the tabu list, which is updated as
the solution traverses the solution space.
[14] discussed a slicing tree based tabu search heuristic for the rectangular, continual plane
facility layout problem by incorporation of facilities with unequal areas and integrated the
possibility to specify various requirements regarding (rectangular) shape and dimensions of
each individual facility by using bounding curves which made possible to solve problems
containing facilities of fixed and facilities of flexible shapes at the same time. This paper
presented a procedure that calculated the layout corresponding to a given slicing tree on the
basis of bounding curves and integrated the tabu search to find the better results. [19]
proposed a heuristics for the dynamic facility layout problem with unequal-area departments.
The solution is improved using a tabu search heuristic. The heuristics were tested on some
instances from the DFLP and static facility layout problem (SFLP) literature. The results
obtained demonstrated the effectiveness of the heuristics.
2.6 Genetic Algorithm
[15] presented a genetic algorithm-based model for facility layout problems with unequal
departmental areas and different geometric shape constraints. Gene structures of the genetic
algorithm are used to represent layout of departments. The algorithm involved deriving an
initial assignment of departments to the given floor plan and then, possibly, improving the
solution quality through genetic algorithm mechanisms (i.e., exchange parts of layout). Since
genetic algorithm is parameter sensitive, the experiments indicated that crossover type,
mutation type, mutation probability, and population size which are the main parameters that
designers need to consider while designing facility layout with genetic algorithm. Guidelines for
such parameters were also given.
[11] presented a heuristic search methodology, based on genetic algorithms (GA), for unequal
area layout. this methodology was applied to several standard test problems from the literature,
and was showed that the GA method gave solutions which were much better than the best
previously reported solutions.[11] used penalty-directed search to find very good solutions to
problems with difficult-to-satisfy side constraints, and to perform multi-criterion optimization with
respect to cost measures that have been considered incommensurable in the past. The
methodology presented in [11] is not intrinsically restricted to layout problems, but could be
extended to other hard combinatorial problems. The GA/penalty method's ability to find
improved solutions to known problems, together with the ability to address problems with ill-
behaved cost functions, multiple objectives, and/or side constraints, constitutes a significant
contribution to the state of the art in facility layout. Furthermore, GA could be implemented to

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take advantage of parallel hardware to an extent not possible for other heuristic optimization
methods.
[18] outlined a GA based algorithm for solving the single-floor facility layout problem with
departments of both equal and unequal sizes. The GA performance was evaluated using
several test problems available in the literature. The results indicated that GA may provide a
better alternative in a realistic environment where the objective is to find a number of
“reasonably good” layouts. The implementation also provided the flexibility of having fixed
departments and to interactively modify the layouts produced.
[24] gave a solution to the unequal area facilities layout problem by genetic algorithm. The
majority of the issued facilities layout problems (FLPs) minimize the material handling cost and
ignore other factors, such as area utilization, department shape and site shape size. These
factors, however, might influence greatly the objective function and should give consideration.
The research range of [24] was focused on the unequal areas department facilities layout
problem, and implement analysis of variance (ANOVA) of statistics to find out the best site size
of layout by genetic algorithm. The proposed module took the minimum total layout cost (TLC)
into account. TLC was an objective function combining material flow factor cost (MFFC), shape
ratio factor (SRF) and area utilization factor (AUF). In addition, a rule-based of expert system
was implemented to create space-filling curve for connecting each unequal area department to
be continuously placed without disjoint (partition). In this manner, there was no gap between
each unequal area department. The experimental results showed that the proposed approach
is more feasible in dealing with the facilities layout problems in the real world.
2.7 Swarm Optimisation
Layout of temporary facilities on a construction site is essential to enhancing productivity and
safety, and is a complex issue due to the unique nature of construction. [16] proposed a particle
swarm optimization (PSO)-based methodology to solve the construction site unequal-area
facility layout problem. A priority-based particle representation of the candidate solutions to the
layout problem was proposed. The particle-represented solution in terms of priorities should be
transformed to the specific layout plan with consideration of non-overlap and geometric
constraints. In addition, a modified solution space boundary handling approach was proposed
for controlling particle updating with regard to the priority value range. Computational
experiments were carried out to justify the efficiency of the proposed method and to investigate
its underlying performances. This paper claimed to provide an alternative and effective means
for solving the construction site unequal-area layout problem by utilizing the PSO algorithm.
2.8 Space Partitioning
[17] proposed a space partitioning method for facility layout problems with shape constraints A
heuristic algorithm was developed for the problems with the objective of minimizing the sum of
rectilinear distances weighted by flow amounts between the facilities. The suggested algorithm
was a simulated annealing algorithm in which a solution is encoded as a matrix that has
information about relative locations of the facilities on the floor. A block layout was constructed
by partitioning the floor into a set of rectangular blocks according to the information while
satisfying the areas of the facilities. [17] suggested three methods for the partitioning.
2.9 Ant System
Ant Colony Optimization (ACO) is a young metaheuristic algorithm which has shown promising
results in solving many optimization problems. To date, a formal ACO-based metaheuristic has
not been applied for solving Unequal Area Facility Layout Problems (UA-FLPs). [20] proposed
an Ant System (AS) (one of the ACO variants) to solve them. As a discrete optimization
algorithm, the proposed algorithm used slicing tree representation to easily represent the