1. ASIA PACIFIC INSTITUTE OF
MANAGEMENT STUDIES
PROJECT ON FACILITY LOCATION
SUBMITTED BY- SUBMITTED TO:-
ANJALI SINGH-H 07 DALJIT RAI
TREHAN
ANUP SAINI-H 09
AMLAN GOGUI-H 05
GURPREET BALI-H 18

2. DIBYAGYAN-H 15
BISWAJIT –H 12
INTRODUCTION
Almost every private and public sector faces with the task of
locating facilities.
For the consideration of this type of work is gaining importance
because of the emerging world is going global. Therefore,
plants are placed in different countries and different regions.
Models developed to analyze facility location decisions for the
optimized one or more objectives, subject to physical,
structural, and policy constraints, governmental
implementations, incentives in variety in a static or
deterministic setting. As because of the large capital outlays
that are involved, facility location decisions are executed in the
long-term. Consequently, there may be considerable
uncertainty of the parameters of the location decision.
Facility location has an important role because the site
selection directly relates with the warehouse systems,
inventory control and handling, customers and suppliers. A
good location gives a strategic advantage against competitors.
To give service to potential customers better by short
distances as locating more outlets a company enhances its
accessibility and hence improves its overall customer service.
The determination of a facility location is a well-known
phenomenon in operational research area. The facility location
means the placement of a planned facility with regard to other
facilities according to some constraints. There are both
quantitative and qualitative methods applied for the facility
location problems.
FACILITY LOCATION FACTORS
In real life there exist many factors directly or indirectly affect
on the facility

3. location selection. As global location factors it can be defined
as; government stability, governed regulations, political and
economic systems, exchange rates, culture, climate, export &
import regulations, tariffs and duties, raw material availability,
availability of suppliers, transportation & distribution systems,
labor force, available technology, technical expertise, cross-
border trade regulations and group trade agreements. On the
other hand, for the selection of the region, city or country the
factors considered are; labor, proximity to customers, number
of customers, construction costs, land cost, availability of
modes and quality of transportation, transportation costs, local
business regulations, business climate, tax regulations financial
services, incentive packages applied to that region and labor
force education are both critical and important in facility
location selection. Therefore it is clear that there is a need in
location problem approaches concentrating on the combination
of qualitative and quantitative factors.
FACILITY LOCATION
At the duration of previous two decades facility location
science has attracted
attention of communities from the academic space as well as
from the business space. A lot of big companies make use of
science even for smaller importance choices, allowing thus at
least a place of full time employment for superior employee
that has the suitable knowledge and possibilities. Facility
location problems have attracted researchers from a lot of
different inquiring sectors as the operational research, the
information technology, the mathematics, the applied
mechanics, the geography, the finances and the marketing as
well as professionals from various sectors of work. At facility
location problems each of the above groups gives emphasis in
different aspects which is up to the needs, the background and
the scientific origin. The humans who research and work in
facility location problems have different background and
different needs. Accordingly, each one creates different way of
resolution for these problems taking into consideration different
factors and criteria. Perhaps the most creative task in making a
decision for location / allocation –relocation facility is to choose
the factors that are important for that decision. Facility location

4. decision concerns those utilities which want to locate, relocate
or they extend their activities. The process of decision covers
the determination, the analysis, the evaluation and the choice
between the alternative solutions. Plants of industrial units,
warehouses, distribution centres, and retail disposal places are
characteristic installations among lot of others that concern
facility location. The choice of regions for facility location begins
usually with the creation of new company while for those which
are in use this happens after the ascertainment of need for
additional productive faculty. After the need of extra industrial
unit installation follows the search of "most optimal" place.
FACILITY LOCATION APPLIED FACTORS
Facility location factors have not changed or they have
changed lightly since the
science of operational research continues using them. Labour
costs, ground costs,
buildings costs, transports costs, operation costs, tax motives
and other financing criteria are the more usually used factors.
The aim of facility location problem solution is the combination
of these factors in order to achieve lower cost per produced
product unit. We can observe that while the facility location
decisions continue be based on the economic elements that
aim in the maximisation of profit or in the minimisation of cost,
environmental, aesthetic, ecological and social influences
increase and have real importance.
The objective of maximisation of profit or minimisation of
expenses in the process of
facility location is obvious, but there is an unanswerable
question if this objective can be achieved when most of the
applied solving processes exclude the not quantitative
factors, as are the immaterial factors that estimate quality of
life and environment.
The optimisation models and other operational research
techniques like the linear
programming can analyze the interdependences between the
economic variables,
without taking into consideration the fact that the persons the
decision concerns are not to be prompted neither to be
effective when they are sent to work and to live in a place does
not satisfy them.

5. Factors that really influence the efficiency of utilities which
are involved in the
facility location decision and do not participate in the location
process. The choice of some place for facility location is a
characteristic decision-making multicriteria analysis problem in
which the administrative preference and the quantification of
other potentially invisible factors, between the efficiency ones,
play a fundamental role in the final decision. In order to be
expressly evaluated the leader’s preference with a model of
preference, have been overwhelmed a lot of efforts so as to be
developed the theory and the methodology for the assessment
of this preference.
Recently the quality of life and the environment situation
constitute common concern for a lot of persons who are afraid
that in our society the environmental and human values are
neglected for industrial production, technological and economic
growth. The term quality of life as it is used here is an eclectic
term that is reported in various potentially independent factors
that all together have repercussions in life of somebody.
Research in relative bibliography has shown that the following
team of factors has
the biggest influence in the general quality of life and the
worker’s ego:
• The personality of himself (the faculty, the effectiveness and
the expectations
of somebody).
• His family (spouse, children and relatives).
• His economic resources.
• The residence.
• The amusement in his life (that it is usually connected with
the family).
• His friends
• The use of free time.
It is obvious that the social environment has direct relation with
five from these seven groups of factors. Even if the differences
in the culture, the social class, the familial nurturing, the
education and the personality create diversity in the human
preferences, it is realised that the seven factors are in effect
globally for the population as well as for important subgroups
of population. This research underlines an element that is not
always taken into consideration by the administrative teams of
enterprises. The enterprise should occupy the repercussions
not only from movement of an executive member but also the
movement of his spouse, children, and casually his relatives,
and it should remember that opinions of all of them and same

6. the spouse are critical on quality of life issues and this is in
accordance with the motives and the productivity of this
executive member.
The applied facility location criteria are based on the
quantitative estimate
(measurability), they exist however apart from quantitative and
the qualitative categories.
In one hand the quantitative ones can be measured with
numerical prices, as the cost of ground, operation,
transportation, the tax motives etc In the other the qualitative
incorporates the not-quantitative determinable factors which
are opposite to business transactions facility in a particular
region, as are the environment, the operational climate, the
social environment the quality of life etc Such factors cannot
easily be expressed with numerical prices and be evaluated
from the quantitative models. The problems of location become
more complex when such qualitative factors are taken into
account, because they are under subjective judgement.
It is henceforth acceptable that location choice for the
installation of some industrial
unit has important strategic repercussions in the enterprises in
which they are reported, because such a decision regularly
includes long-term engagement of capitals and of course is not
refundable. Concretely, the location choice for the installation
of industrial unit can practise important strategic effect in the
competitive place of company from the view of the operation
cost, the efficiency of workers, the speed of products delivery
and the flexibility of company rival in the market. For example,
the location choice for the installation of some industrial unit
that will allow the enterprise to achieve the proximity to the
suppliers constitutes a critical strategic advantage in the
market, since the proximity to the suppliers is important for the
time improvement of delivery of products. However the
success of enterprises is in the hands of few persons that
constitute their administrative team. It is the guidance, the
ambition, the initiative and their crisis that determines if the
expected results of enterprises will be achieved. The efficiency
is always result of possibility and motives when the motive in
the work is optimized, the productivity is increased.
Consequently, the executives with given possibilities will not
achieve the expected results in new installations if their
environment creates dissatisfaction that has repercussions in
the motives. There is no reason for someone to achieve more
rapid time of delivery if the productivity of these persons is
decreased.

7. Consequently, the final location choice for the installation of
some industrial unit
should contribute in the success of corporate strategic plans
that concerns in the
financing, in the successful correspondence in the objectives of
production and demand as well as in the increased productivity
of human potential, however nothing from the above cannot be
ignored because the result of studies is based on their
harmonious coexistence.
Facility location
The general facility location problem is: given a set of facility
locations and a set of customers who are served from the
facilities then:
which facilities should be used
which customers should be served from which facilities so as
to minimise the total cost of serving all the customers.
Typically here facilities are regarded as "open" (used to serve
at least one customer) or "closed" and there is a fixed cost
which is incurred if a facility is open. Which facilities to have
open and which closed is our decision.
Below we show a graphical representation of the problem.

8. =[One possible solution is shown below.
Other factors often encountered here:
customers have an associated demand with capacities (limits)
on the total customer demand that can be served from a
facility customers being served by more than one facility.
Example

9. The problems of facility size and facility location are very
closely linked and should be considered simultaneously. In fact
the package used here disregards (for reasons of simplicity)
the problem of facility size and deals only with facility location.
We shall illustrate the problem of facility location by means of
an example.
At Gotham City airport terminal there are 10 arrival gates (A to
J respectively). A pictorial representation of the terminal is
given below with the location of the gates being:
Gate x coordinate y coordinate
A 0 2
B 2 4
C 5 6
D 5 10
E 7 15
F 10 15
G 12 10
H 12 6
I 15 4
J 20 2
Luggage from arriving flights is unloaded at these gates and
moved to a passenger luggage pick-up point.

10. It is estimated that the number of pieces of luggage arriving
per day at each gate (A to J respectively) is: 3600, 2500, 1800,
2200, 1000, 4500, 5600, 1400, 1800 and 3000 respectively.
Where should the passenger luggage pick-up point be located
in order to minimize movement of luggage?
Solution
In order to logically locate the passenger luggage pick-up point
we need to make use of the amount of luggage flowing from
the gates to the pick-up point. Logically a gate from which
there is a large flow should be nearer to the pick-up point than
a gate with a small flow.
Informally therefore we would like to position the pick-up point
so as to minimise the sum over all gates g (distance between g
and the pick-up point) multiplied by (flow between g and the
pick-up point).
This approach to choosing the location of the pick-up point is
precisely the approach used by the facility location module in
the package. Typically in such location problems we are
concerned with a load-distance score (the product of load and
distance for all points). The initial input to the package for this
problem is shown below.
Note here the package terminology is somewhat peculiar:
existing facilities - are points where we know in advance
exactly where they are and they are fixed in position new
facilities - are points where we do not know where they are
and their location is what we have to determine (using the
package)

11. In order to enter the data relating to the gates we can ignore
the columns in the package input that are concerned with flows
between existing facilities - here all flows are from the existing
facilities to the new facility.
Note here that in solving the problem we need to specify the
appropriate distance model. This is because as we do not yet
know where the new facility (luggage pick-up point) is to be we
cannot specify the distance between it and the gates without a
general expression for calculating the distance between two
locations. If (xi,yi) and (xj,yj) represent the coordinates of two
locations i and j then the distance model measures can be:
rectilinear - distance between i and j is: |xi-xj| + |yi-yj|
Euclidean - distance between i and j is: [(xi-xj)2 + (yi-yj)2]0.5
squared Euclidean - distance between i and j is: (xi-xj)2 + (yi-
yj)2
The rectilinear distance measure is often used for factories,
American cities, etc which are laid out in the form of a
rectangular grid. For this reason it is sometimes called the
Manhattan distance measure. The Euclidean distance measure
is used where genuine straight line travel is possible. The
squared Euclidean distance measure is used where straight
line travel is possible but where we wish to discourage
excessive distances (squaring a large distance number results
in an even larger distance number and recall that we use the
distance number in the objective which we are trying to
minimise).
The output from the package for each of the distance
measures is shown below.
Rectilinear

12. Euclidean
Squared Euclidean

13. From the package output we can see that the location for the
luggage pick-up point should be:
Distance measure x coordinate y coordinate
Rectilinear 10 6
Euclidean 10.12 8.98
Squared Euclidean 9.05 7.67
The picture below shows these three possible locations with
respect to the terminal (labelled R, E and S for rectilinear,
Euclidean and squared Euclidean respectively).

14. Note here that (in reality) the initial choice of distance measure
is often between rectilinear and Euclidean (based upon the
technology of how the luggage flows within the terminal). If the
luggage flows in an Euclidean (straight-line) manner then
choosing to use squared Euclidean, rather than Euclidean,
penalises excessively long distances.
One point to note about the above picture is that we are not
really interested in determining positions down to the nearest
millimetre (the data is probably not accurate enough anyway!).
Instead we are using the package to get an indication of the
approximate region where it would be sensible to site a
luggage pick-up point.
Note too that the package uses a "centre of gravity" approach
to decide where to locate a single pick-up point.
Extension
Suppose now we are interested in having two luggage pick-up
points. We have two types of decisions:
location decisions - where to locate luggage pick-up points;
and
allocation decisions - which gates to allocate to which luggage
pick-up points.

15. Ideally we would like a way of automatically solving both these
decision problems simultaneously (since obviously location
affects allocation and vice-versa).
The package we are using cannot do this. Instead we must
ourselves decide the allocation and allow the package to solve
to produce appropriate locations.
However more sophisticated packages can solve both
decisions simultaneously.
Suppose therefore that we make an (arbitrary) allocation
decision, based upon the map of the terminal, namely that we
will have one luggage pick-up point dealing with gates C to H
(inclusive) and the other dealing with gates A, B, I and J.
With this allocation decision made we can solve the problem
using the package, the input being shown below. Note here
that in this input we have made new facility number 1 the
luggage pick-up point for gates C to H (inclusive) and new
facility number 2 the luggage pick-up point for gates A, B, I and
J.
Note the cells associated with flows between New Facilities.
This is for flows between new facilities, whose locations we do
not yet know. For example, we could be moving luggage using
a concentrator system. Luggage flows to a central point (new
facility, a concentrator point) before being passed onward to a
collection point (new facility). In such a case the flow from the
concentrator point to the collection point would need to be
given in this matrix.
The output from the package for each of the three distance
measures is shown below.
Rectilinear

16. Euclidean
Squared Euclidean

17. From this output we can see that the locations for the luggage
pick-up points should be:
Distance measure Facility x coordinate y coordinate
Rectilinear 1 10.03 10.02
2 2.04 2.06
Euclidean 1 11.00 10.50
2 2.54 3.38
Squared Euclidean 1 9.45 10.89
2 8.44 2.79
The picture below shows all these locations with respect to the
terminal (labelled R, E and S for rectilinear, Euclidean and
squared Euclidean respectively).

18. Concentrator
Suppose now that in the example we just considered the
luggage pick-up point for gates C to H (inclusive) is merely
acting as a concentrator, concentrating luggage before
passing it to the other pick-up point, which collects luggage
from gates A,B, I and J directly. In this system all passengers
see is a single pick-up point at which they collect their luggage.
To locate this concentrator (and the final pick-up point) we
make use of flows between new facilities. Here the total
amount of luggage collected from C to H will flow to the final
pick-up point from this intermediate concentrator. This will total
1800+2200+1000+4500+5600+140 =16500 pieces of luggage.
Hence the input to the package is:

19. The solutions are:
Rectilinear
So in this case the final and concentrator locations coincide.

20. Euclidean
So in this case the final and concentrator locations are near to
each other.
Squared Euclidean

21. So in this case the final and concentrator locations are not
particularly close to each other.
Other approaches
Technically the approach used above for location, where any
point is a potential location for a new facility, is called the
infinite set approach.
More commonly nowadays location studies are done using a
feasible set approach. With this approach there are a finite set
of alternatives for the new facilities and the problem is to
choose from these alternatives the best subset to service a
known set of customers (existing facilities in the terminology of
the package used above). The advantage of this approach is
that it can take explicit account of items such as fixed costs
and capacities associated with facilities (i.e. items connected
with facility size), as well as the issue of deciding the allocation
of customers to facilities.
Location models based upon the feasible set approach
typically use integer programming. More about such models
can be found here.
Example

22. One example of a facility location problem that I have worked
on was to do with church location for Church of England
churches. The idea here was to investigate which churches
could best be closed.
For the purposes of this study a 100 kilometre square to the
north-east of London was chosen. An obvious first question is
How many churches are there in this area and where are they?
Alas the organisation did not seem too sure of the answers to
this question. Eventually we consulted maps of the area and
came to the conclusion that we thought there were 504
(Church of England) churches in this area. A plot of the location
of these churches is shown below (church positions to one-
tenth of a kilometre). You can see that they are clustered
together in a number of distinct areas.
Now if a church (facility) is to be closed then logically we
should consider information like cost of operating the church
revenue from land sale/disposal if church closed
size of the church etc. Unfortunately this was an extremely
data-poor environment. The only data (aside from the above
location data) we had was the average congregation
(attendance) size for each of the 504 churches. This data is

23. plotted below as a histogram. You can see that the average
congregation size for a significant number of churches is very
small.
We concluded that we had to work with the limited data we
had, rather than attempt to discover data for 504 different
churches, effectively an impossible task.
The approach we decided upon was to say that if a church was
closed its congregation was displaced to their nearest open
church. This leads naturally to the idea of displacement
distance - defined to be congregation size multiplied by
distance they are displaced. Our problem therefore is to
choose the churches to close so as to minimise total
displacement distance.
To solve this problem we took a simple interchange heuristic
from the literature and coded it. The effect of closing churches
in terms displacement distance (measured in people
kilometres) is shown below. You can see that as more
churches are closed the total displacement distance increases.

24. One complication to this study was that closer examination of
the data revealed a number of churches very close to each
other (say within 0.5 of a kilometre of each other) but with
relatively large congregations. The algorithm attempted to
close one of these churches (displacing the congregation to
the other). Now all churches, even within the Church of
England, are not the same in terms of the type of church
service which they offer. Some are more evangelical, some
more traditional, etc. It seemed likely that two churches very
close to each other, but both with large congregations, were
offering a different type of church service, so closing one and
displacing the congregation to the other would not be
satisfactory in practice.
We therefore modified our algorithm to ensure that no
churches with a congregation of 50 or more could be closed
(i.e. only "small" churches with a congregation less than 50
could be closed). The effect of this upon total displacement
distance can be seen in the diagram below. In that diagram the
lower line is as above (all churches available for closure) and
the upper line is when only small churches can be closed.

25. CONCLUSIONS

26. Many applications of the facility location problem such as
caching in the Internet inherently apply to distributed settings.
In this paper, we have given a classification of the trade-off
between the amount of communication and the quality of the
obtained global solution. Our solution technique is based on the
distributed approximation of a linear program which is not a
covering or packing problem. By thus pushing the boundaries
of distributed LP approximation, we hope that our paper is a
step towards understanding the nature of more general linear
programs in a distributed context. Our results give raise to
several questions. First, the fact that in the centralized case,
the metric facility location problem allows constant
approximations raises hope for faster approximations
algorithms in distributed settings, too. Moreover, our problem
setting is a complete bipartite graph. Interestingly, there are
virtually no lower bounds for the bounded message. For
instance, all lower bounds for the MST problem apply to graphs
with diameter at least 3. Finding lower bounds for this model
appears to be an outstanding open problem. We have given
strategies for one-dimensional competitive facility location,
allowing the second player, Red, to win. We have also shown
that the _rst
player, Blue, can keep the winning margin as small as he
wishes. For all practical
purposes.
Similarly, if players are allowed to place points in_nitesimally
close to their
opponent (that is, on the same location, but indicating a side"),
then Blue's
defense strategy will guarantee a tie. Do our endings have any
bearing on the two-dimensional Voronoi Game? The concept of
keypoints turned out to be essential to our strategies. We have
seen that a player governing all keypoints cannot possibly lose
the game. Surprisingly, the situation in two dimensions is quite
different: It can be shown that for any given set of n blue points
in, say, a unit square, we can understand a set of n red points
so that the area dominated by Red is at least for an absolute
constant _ > 0 not depending on n.