International Journal of Mechanical Engineering and Technology (IJMET)

Volume 8, Issue 4, April 2017, pp. 112–119 Article ID: IJMET_08_04_013

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=4
ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

OPTIMIZATION OF FACILITY DESIGN BY

USING MATLAB PROGRAMME
Abhishek Kumar Jain
PhD Scholar, Department of Mechanical Engineering,
Maulana Azad National Institute of Technology (Deemed University), Bhopal (M.P)

Dr. P. M. Mishra
Assistant Professor, Department of Mechanical Engineering,
Maulana Azad National Institute of Technology (Deemed University), Bhopal (M.P)

ABSTRACT
Objective: Production industry continuously needs betterment of the layout/facility
design. So as to get better results with minimum uses of resources. Thus giving rise to
the need of facility planning. To assign a given facility one need a defined piece of land
with proper material handling effort. Keeping in mind these given feature, facility
distribution works by preparing its structural plan, layout plan & the subject
arrangement plan. Thereby producing a organized facility plan many researchers had
underwent in the past so as to get a optimized facility representation. Every research
published in the earlier could not meet the required scheme as something is always
lacking. So the main purpose is to get optimization of facility plan including every part
of it.
Method: This paper is primarily focusing on detailed analysis of methodology of
optimization of facility planning by applying different formulas on the representation
and its aspects. The results are shown using mathematical equation in a computerised
technique.
Findings: The outcomes thus got after applying the above method is extremely
beneficial for the planners and developers as it accompanies the consideration of
related feature. So as to minimize the management expenses to minimal.
Application: This optimized facility planning is quite helpful in shrinking the
handling charges to the minimum possible extent and thereby securing maximum
outflow scheme.
Key words: Facility Planning; Plant Layout; Optimization Methods
Cite this Article: Abhishek Kumar Jain and Dr. P. M. Mishra, Optimization of Facility
Design By Using Matlab Programme. International Journal of Mechanical Engineering
and Technology, 8(4), 2017, pp. 112–119.
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 Abhishek Kumar Jain and Dr. P. M. Mishra

1. INTRODUCTION
The concept of facilities planning is vast and at the same time this concept is complicated as
well. It is a broad subject and it covers several fields of engineering that is, it covers several
disciplines1. It includes various engineering fields such as- civil engineering, electrical
engineering, mechanical engineering, industrial engineering, architectural engineering and
therefore, architects, consulting managers and urban area planners2. So looking at the
involvement of varied aspects of engineering, it is obvious, that the concept of facility planning
is not only vast, broad or extremely large but also of complex nature3. The concept of facility
planning is about the location of the facilities and the design of the facilities. The concept of
facilities planning is related to achieving the activity’s best possible result through activity’s
tangible fixed assets. That is – what is the objective of the facility and how the objective is
achieved? There are two components of facilities planning4. The first component of the facilities
planning is the location of the facilities and the second component of the facilities planning is
the design of the facilities5. To define the first component of the facilities planning, that is, the
facilities location, it can be said that the facilities location means the placement or the placing
of the facility on a particular plot of land, or it can be said that the placement of the facility on
a specific piece, or plot of land, with respect to other facilities and also with respect to the
customers and suppliers6. So in facilities planning, the location of facilities relates to the
placement of the facilities according to the suppliers and other facilities. The second component
of facilities planning is facilities design7. Now this second component of facilities planning that
is the facilities design is divided in to three parts. The first part of the facilities design is the
design of the system of the facility8. The second part of the facilities design is the design of the
layout. The last part of the facilities design is the design of the handling system. So in all, the
second component of the facilities planning that is the facilities design consists of the facility
system design, the layout design and the systems handling design9.

2. FACILITY-DESIGN
The term Facilities Layout is also known as Plant Layout in manufacturing units or industries.
Plant Layout is the most crucial part of the entire facilities planning, because more than half of
the entire output depends upon the successful layout of the plant. Plant Layout is most important
in a manufacturing unit because it directly affects the financial aspect of the manufacturing
unit10.
The financial aspect is the base of any production or manufacturing unit. Maximum profit
by minimum cost spent or minimum expenditure is the basic mantra and this is what today’s
industrial system has truly adopted. The material handling costs and the cost of transportation
are the two costs which directly affects the financial layout of manufacturing units. Fluctuation
in any of these results in less profit and the hurdles the achievement of the facility’s objectives.
So the Plant Layout, as mentioned earlier does affect the overall production system and its
effectiveness in achieving the facility’s actual objectives. The problems or difficulties that arise
in facilities layout or the plant layout decrease the overall effectiveness of the production
system. Many countries such as United States spends more than 8% of their Gross National
Product annually upon employing new facilities so that the cost reduction can e done most
effectively specially the cost of transportations11.
If new facilities are employed in a proper duration of time, then the effectiveness of the
facilities planning will be the maximum because new facilities will reduce the cost of material
handling and the cost of transportation by 10% to 30%.Since facilities planning has major role
in the productivity and the effectiveness of the entire production system, so the investment it
requires is huge. Now, facilities planning require huge amount of investment, it is this fact, that
the facilities planning is the topic for search. That is, most of the industries have the same search

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 Optimization of Facility Design By Using Matlab Programme

topic, how facilities planning can be made more effective’? Because huge investment is
involved the importance of facilities planning is obviously raised. Facilities Planner considers
the facility as a dynamic entity. Therefore continuous improvement is an integral element of FP
cycle12.

Figure 1 Continuous improvement facilities planning cycle

3. ALGORITHM FOR FLEXIBILITY IN LAYOUT DESIGN

Algorithm for flexibility in layout design is detailed in this section. This algorithm considers
the material flow as input data then channelizes the layout and reschedule the flows14. This is
done so that the transportation cost is reduced. So the main function of algorithm is to reduce
the transportation costs there by reducing the total material flow. If there is any unexpected
material flow, it can be kept in check by this algorithm. This algorithm thus provides various
profits- channelizing the layout will provide for re-structure or re-schedule and re-schedule will
further provide for reduction in total handling cost of the material13, 15.

Problem Statement and Modelling

Now the difficulty arising in the process plant for optimizing the total material handling cost
gives many possible future material flows. The material flows can have the different cost per
unit distance16, 17.

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 Abhishek Kumar Jain and Dr. P. M. Mishra

The final equation is as follows:

n n
Minimum T = ∑ ∑ fijdijcij
i=1 j=1

Where:
fij=frequency/quantity of flow
cij=cost to flow one unit load per unit distance between two machines
dij=distance amid machine i and j
Considering the cost cij remain steady, the aim would be reduced to minimizing the total
distance travelled for the parts.

Example of three machine layout:

There are six possibilities for three machine layout that is given below in Table-1:

Table 1 Three machine layout

1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1

Table-2 Material handling cost calculation for three machine layout

1 2 3 f12*d12+f13*d13+f21*d12+f23*d23+f31*d13+f32*d23

1 3 2 f13*d12+f12*d13+f31*d12+f32*d23+f21*d13+f23*d23

2 1 3 f21*d12+f23*d13+f12*d12+f13*d23+f32*d13+f31*d23

2 3 1 f23*d12+f21*d13+f32*d12+f31*d23+f12*d13+f13*d23

3 1 2 f31*d12+f32*d13+f13*d12+f12*d23+f23*d13+f21*d23

3 2 1 f32*d12+f31*d13+f23*d12+f21*d23+f13*d13+f12*d23

Below is flow matrix and distance matrix considering “c” as a unit cost in table 2:

Table 3 Flow and Distance Matrix of three machine layout

fij 1 2 3 dij 1 2 3
1 - 2 4 1 - 1 3
2 6 - 3 2 1 - 2
3 5 1 - 3 3 2 -
n n
Minimum T = ∑ ∑ fijdijcij
i=1 j=1

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 Optimization of Facility Design By Using Matlab Programme

Table 4 Transportation cost for three machine layout

`Layout T
1 2 3 38
1 3 2 37
2 1 3 43
2 3 1 43
3 1 2 47
3 2 1 46
Here we can see that the layout 1-3-2 is most optimum layout.

Example of four machine layout

There are 24 possibilities for four machine layout that is given below in Table-5:

Table 5 Material handling cost calculation for four machine layout

1-2-3-4 f12*d12+f13*d13+f14*d14+f21*d12+f23*d23+f24*d24+f31*d13+f32*d23+f34*d34+f41*d14+f42*d24+f43*d34

1-2-4-3 f12*d12+f14*d13+f13*d14+f21*d12+f24*d23+f23*d24+f41*d13+f42*d23+f43*d34+f31*d14+f32*d24+f34*d34

1-3-2-4 f13*d12+f12*d13+f14*d14+f31*d12+f32*d23+f34*d24+f21*d13+f23*d23+f24*d34+f41*d14+f43*d24+f42*d34

1-3-4-2 f13*d12+f14*d13+f12*d14+f31*d12+f34*d23+f32*d24+f41*d13+f43*d23+f42*d34+f21*d14+f23*d24+f24*d34

1-4-2-3 f14*d12+f12*d13+f13*d14+f41*d12+f42*d23+f43*d24+f21*d13+f24*d23+f23*d34+f31*d14+f34*d24+f32*d34

1-4-3-2 f14*d12+f13*d13+f12*d14+f41*d12+f43*d23+f42*d24+f31*d13+f34*d23+f32*d34+f21*d14+f24*d24+f23*d34

2-1-3-4 f21*d12+f23*d13+f24*d14+f12*d12+f13*d23+f14*d24+f32*d13+f31*d23+f34*d34+f42*d14+f41*d24+f43*d34

2-1-4-3 f21*d12+f24*d13+f23*d14+f12*d12+f14*d23+f13*d24+f42*d13+f41*d23+f43*d34+f32*d14+f31*d24+f34*d34

2-3-1-4 f23*d12+f21*d13+f24*d14+f32*d12+f31*d23+f34*d24+f12*d13+f13*d23+f14*d34+f42*d14+f43*d24+f41*d34

2-3-4-1 f23*d12+f24*d13+f21*d14+f32*d12+f34*d23+f31*d24+f42*d13+f43*d23+f41*d34+f12*d14+f13*d24+f14*d34

2-4-1-3 f24*d12+f21*d13+f23*d14+f42*d12+f41*d23+f43*d24+f12*d13+f14*d23+f13*d34+f32*d14+f34*d24+f31*d34

2-4-3-1 f24*d12+f23*d13+f21*d14+f42*d12+f43*d23+f41*d24+f32*d13+f34*d23+f31*d34+f12*d14+f14*d24+f13*d34

3-1-2-4 f31*d12+f32*d13+f34*d14+f13*d12+f12*d23+f14*d24+f23*d13+f21*d23+f24*d34+f43*d14+f41*d24+f42*d34

3-1-4-2 f31*d12+f34*d13+f32*d14+f13*d12+f14*d23+f12*d24+f43*d13+f41*d23+f42*d34+f23*d14+f21*d24+f24*d34

3-2-1-4 f32*d12+f31*d13+f34*d14+f23*d12+f21*d23+f24*d24+f13*d13+f12*d23+f14*d34+f43*d14+f42*d24+f41*d34

3-2-4-1 f32*d12+f34*d13+f31*d14+f23*d12+f24*d23+f21*d24+f43*d13+f42*d23+f41*d34+f13*d14+f12*d24+f14*d34

3-4-1-2 f34*d12+f31*d13+f32*d14+f43*d12+f41*d23+f42*d24+f13*d13+f14*d23+f12*d34+f23*d14+f24*d24+f21*d34

3-4-2-1 f34*d12+f32*d13+f31*d14+f43*d12+f42*d23+f41*d24+f23*d13+f24*d23+f21*d34+f13*d14+f14*d24+f12*d34

4-1-2-3 f41*d12+f42*d13+f43*d14+f14*d12+f12*d23+f13*d24+f24*d13+f21*d23+f23*d34+f34*d14+f31*d24+f32*d34

4-1-3-2 f41*d12+f43*d13+f42*d14+f14*d12+f13*d23+f12*d24+f34*d13+f31*d23+f32*d34+f24*d14+f21*d24+f23*d34

4-2-1-3 f42*d12+f41*d13+f43*d14+f24*d12+f21*d23+f23*d24+f14*d13+f12*d23+f13*d34+f34*d14+f32*d24+f31*d34

4-2-3-1 f42*d12+f43*d13+f41*d14+f24*d12+f23*d23+f21*d24+f34*d13+f32*d23+f31*d34+f14*d14+f12*d24+f13*d34

4-3-1-2 f43*d12+f41*d13+f42*d14+f34*d12+f31*d23+f32*d24+f14*d13+f13*d23+f12*d34+f24*d14+f23*d24+f21*d34

4-3-2-1 f43*d12+f42*d13+f41*d14+f34*d12+f32*d23+f31*d24+f24*d13+f23*d23+f21*d34+f14*d14+f13*d24+f12*d34

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 Abhishek Kumar Jain and Dr. P. M. Mishra

Table 6 Flow and Distance Matrix of four machine layout

fij 1 2 3 4 dij 1 2 3 4
1 - 5 6 2 1 - 3 5 7
2 3 - 6 5 2 3 - 2 4
3 4 6 - 2 3 5 2 - 3
4 2 5 8 - 4 7 4 3 -
n n
Minimum T = ∑ ∑ fijdijcij
i=1 j=1

Table 7 Transportation cost for four machine layout

`Layout T
1 2 3 4 196
1 2 4 3 212
1 3 2 4 192
1 3 4 2 204
1 4 2 3 218
1 4 3 2 214
2 1 3 4 220
2 1 4 3 236
2 3 1 4 218
2 3 4 1 214
2 4 1 3 232
2 4 3 1 212
3 1 2 4 222
3 1 4 2 234
3 2 1 4 224
3 2 4 1 220
3 4 1 2 236
3 4 2 1 220
4 1 2 3 224
4 1 3 2 220
4 2 1 3 214
4 2 3 1 194
4 3 1 2 212
4 3 2 1 196
Here we can see that the layout 1-3-2-4 is most optimum layout.

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 Optimization of Facility Design By Using Matlab Programme

4. RESULT & CONCLUSIONS

A. Initialization
Input data: Flow matrix and Distance matrix.

B. Calculation of Transporting Cost

It is found that arrangement 1-3-2(For three machine layout), 1-3-2-4 (For four machine
layout) is optimum flow path.

C. Result

Found the optimum and fresh layout

The explicated attributes of algorithms and computer based system explained in this study,
exemplify the importance of the flexibility for the layout design. The study performed in this
research with all type of illustrations along with the highly-developed computer based program
is not only highly useful for the researchers and designers but also exceptionally sort after for
flexible layout design.
This approach is method based. In a functioning plant many factors are required to be
considered. Like aisle- arrangement, office requirements, personnel requirements- such as-
lockers, restrooms, food services, health services etc. This includes the material handling costs
as well.

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 Abhishek Kumar Jain and Dr. P. M. Mishra

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