Chapter 3
Organizing National Elections in India to Elect the 543 Members of the Lok Sabha
Conducting the General Elections for the 543 members of the Parliament of India across the
835 thousand polling stations spread over the 35 States is a mammoth exercise. Deployment
of the Central Police Forces is essential to complement the role of the State police during the
elections. However paucity of Central Police Forces necessitates the conduct of elections
over phases, in each phase elections to be held on a single day in a subset of the states. In
this problem we need to (a) schedule the elections with a minimum number of phases (b)
sequencing the phases, such that the movement of Central Police Forces (measured in menmiles) is minimized and (c) sourcing the appropriate number of personnel from the most
convenient Central Police Forces bases.
1.Brief History of Governance and National Polls in India.
Human civilization has been evolving and flourishing in India since ancient times going back
well over 10,000 years. In those days it was not a single unified country, but it was several
little countries, each a dynastic kingdom with each king being succeeded by his eldest son. In
those days the main roles
of a king used to be: regularly holding his court where
performance by famous artists (music and dance performances, poetry recitations, gymnastic
performances etc.) are held, patronizing the arts and skilled trades, complaints and pleas from
his subjects are heard, disputes among his subjects are settled; and finally expanding his
kingdom by waging wars on neighboring kingdoms.
There were two religions in India at that time, each with its own god, and followers of each
religion were divided into various castes based of professions. Each had its own temples for
worship.
There used to be frequent disputes among the various castes each claiming to be superior to
the other, and fights among the religions each claiming that their god is the true god.
In this climate, in the 6th century BCE(Before Current Era), the Crown Prince of one of the
kingdoms whose name was Gautam became totally disillusioned with the conflicts among
various factions. He took the bold step of renouncing his title to the kingdom, and started
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preaching the social equality of all human beings ignoring all castes and gods altogether; and
a way of life based on morality only; which attracted a huge following all over Asia and led
to the creation of Buddhism.
Also at that time the remaining people in the two religions in India realized that their gods are
two different forms of the same Supreme being, and merged themselves into one combined
religion called Hinduism. Ever since, Hinduism has maintained this spirit of accepting any
other religion into its fold, considering their god as another form or ``avatar’’ of that one
Supreme being.
Dynasties of kings continued to rule their individual kingdoms in India the same way. Then
in the 3rd century CE (Current Era) one king Asoka waged a big war on a neighboring
kingdom in which his forces were barely victorious. When he visited the battlefield at the end
of the war and saw all the corpses, torn limbs and blood, he became disgusted with war and
realized that the duty of a king should be to devise means by which the lives of his subjects
become happier, and not that of waging wars for the same of expanding the kingdom; and
started building various amenities to improve the quality of life of his countrymen. For this he
is now recognized as the world’s first Social entrepreneur.
In those days India used to be the center of attraction for people from all over the world, for
traders, travelers, people seeking education and enlightenment, and immigrants.
Then came the muslim invaders who settled down and established their own dynastic
kingdoms, and built their monuments like the well known Tajmahal.
Then in the 17th century CE the British arrived as traders at first, but when they saw an
opportunity they seized it and set themselves up as alien rulers over a large portion of the
territory in India ruled by Governor Generals appointed by an alien kingdom.
Indians had to undergo a long drawn of struggle to gain independence from Britain. Finally
they were able to achieve it with no war but a peaceful struggle under the leadership of
Mohandas Karamchand Ghandhi. The freedom struggle united the whole country under one
nation that became an independent nation in 1947 CE.
Three years after gaining independence from Britain, Bharat (India) became the Bharat
Ganrajya (The Republic of India, or Indian Republic) by adopting the Constitution of India in
1950. Now the Indian republic comprises 28 States and 7 Union Territories, which we will
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refer to as the 35 States of India in the sequel. The Indian parliamentary form of government
is federal in structure with legislative powers distributed between the Parliament of India and
State Legislatures. The Parliament of India comprises two legislative bodies – the Rajya
Sabha (Upper house, corresponds to the ``Senate’’ in the US, or the ``House of Lords’’ in the
UK), and the Lok Sabha (Lower House, corresponds to the ``Congress’’ in the US, or the
``House of Commons’’ in the UK). The 250 members of the Rajya Sabha are indirectly
elected by legislators of States and Union Territories comprising the Union of India. The 543
members of the Lok Sabha are directly elected by universal adult franchise by the electorate
of all the 35 States through the ``National Elections’’,
called ``General Elections’’ in
India. The term of office each Lok Sabha is five years from the date of its first meeting,
unless dissolved earlier due to the ruling party losing a vote on a no-confidence motion in
the Lok Sabha. These General Elections have been regularly held since 1952, after adoption
of the Constitution of India, as depicted in Table 1. This problem deals with only the
organization of Indian general elections for electing the members of the Lok Sabha.
Lok Sabha
General Elections
1
25 October 1951 to 21 February
1952
24 February to 14 March 1957
19 to 25 February 1962
17 to 21 February 1967
1 to 10 March 1971
16 to 20 March 1977
3 to 6 January 1980
24 to 28 December 1984
22 to 26 November 1989
20 May to 15 June 1991
27 April to 30 May 1996
16 to 23 February 1998
5 September to 6 October 1999
20 April to 10 May 2004
16 April to 13 May 2009
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Date of first meeting
after constitution
13 May 1952
Date of dissolution
10 May 1957
16 April 1962
16 March 1967
19 March 1971
25 March 1977
21 January 1980
15 January 1985
18 December 1989
9 July 1991
22 May 1996
23 March 1998
20 October 1999
2 June 2004
1 June 2009
31 March 1962
3 March 1967
27 December 1970
18 January 1977
22 August 1979
31 December 1984
27 November 1989
13 March 1991
10 May 1996
4 December 1997
26 April 1999
6 February 2004
18 May 2009
-
4 April 1957
Table 1: General Elections held in India
The total membership of the Lok Sabha is distributed amongst the 35 States in such a manner
that the ratio of the population to number of seats allotted to any State is nearly the same. The
geographical area of the State is then demarcated into a number of territorial constituencies
(with geographical boundaries), equal to the number of seats allotted, such that the population
of all constituencies in that State is nearly the same. Since there are large variations in
population densities across States, constituencies vary largely in terms of geographical areathus Ladakh (the constituency with largest area) covers 173266 sq.km in contrast to DelhiChandni Chowk (the constituency with smallest area) which covers only 11 sq.km. Each
constituency has a large number of polling stations distributed across the constituency such
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that voters can reach the polling stations to cast their vote with minimum travel. The
distribution of membership of the Lok Sabha and the total number of polling stations for each
state is given in Table 2.
Sl.No
State
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Andhra Pradesh
Assam
Goa
Haryana
Jammu & Kashmir
Kerala
Maharashtra
Meghalaya
Nagaland
Punjab
Sikkim
Tripura
West Bengal
Jharkhand
Andaman &
Nicobar Islands
Dadra & Nagar
Haveli
NCT of Delhi
Puducherry
31
33
35
Number of
Members of
the Lok
Sabha
42
14
2
10
6
20
48
2
1
13
1
2
42
14
1
Total Number of
polling stations
Sl.No
State
Number of
Members of
the Lok Sabha
66760
18828
1339
12894
9129
20510
82598
2117
1692
18846
493
3008
66109
23696
347
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Arunachal Pradesh
Bihar
Gujarat
Himachal Pradesh
Karnataka
Madhya Pradesh
Manipur
Mizoram
Orissa
Rajasthan
Tamil Nadu
Uttar Pradesh
Chattisgarh
Uttarakhand
Chandigarh
2
40
26
4
28
29
2
1
21
25
39
80
11
5
1
Total
Number of
polling
stations
2057
57020
42568
7253
46576
47812
2193
1028
31617
42699
52158
129446
20984
9003
422
1
161
32
Daman & Diu
1
94
7
1
11348
856
34
Lakshadweep
1
40
Table 2: Number of constituencies and polling stations in each State
The General Elections of India are the world’s biggest election exercise. During the 2009
General Elections, a 717 million strong electorate exercised their franchise through 1.3
million Electronic Voting Machines deployed in 835 thousand polling stations spread across
the length and breadth of India to elect 543 Members of the Lok Sabha from amongst 8
thousand candidates contesting the elections. The only other comparable elections are the
European Parliament elections with an electorate of 500 million and the US Congress
elections with electorate of 312 million.
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Fig 1: Political Map of India showing the States
2. The problem statement and description of all the data
Elections in the past have been marked by instances of voter intimidation through violence or
harassment in various forms, as well as clashes between political opponents. These
incidences have been largely arrested through deployment of additional police forces during
the polling process in order to bring peace, restore confidence in candidates and voters and
thereby ensure fair and free elections.
The Constitution of India mandates that maintenance of law and order is the responsibility of
the States. But as the State police are the arm of the State governments, allegations of
partisan conduct of police in enforcing law and order during the campaign closing phases and
during the day of elections are likely. It has therefore become universal practice to deploy
Central Police Forces (CPF), in addition to State police at all polling stations during the
General Elections.
The movement of CPF personnel from their bases to the polling stations in the different
phases and their subsequent return to the bases is a gigantic exercise, requiring coordination
between different agencies such as CPF operations, Election Commission and State Chief
Electoral Officers, District Election Officers, Railways, airlines and the Indian Air Force. In
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the 2009 General Election, 119 special trains, 65 sorties by Indian Air Force transport
aircraft, 600 sorties by Indian Air Force helicopters and Air India chartered flights were used
for the cross-country movement of CPF personnel.
However the process of scheduling the elections and movement of police personnel is done
manually by the Election Commission. This case study deals with the problem of organizing
the General Elections for all the 543 parliamentary constituencies in the minimum possible
time, with the available CPF personnel, while minimizing the total cost for the police
movement involved. The number of CPF personnel available is not sufficient to conduct
elections for all the 543 constituencies on one day, so elections have to be conducted in
phases, with each phase conducting elections on a single day in a subset of states.
While conducting the elections in phases, the Election Commission requires that the
following constraints should be satisfied as far as possible:
(a) In every State , the elections in all constituencies in it should be
held on a single day
(b) As far as possible, States in which elections are held on a day must be contiguous
(c) Set of States in which elections are held on consecutive polling days
should be
contiguous
(d) General elections over the whole country should be completed using the smallest number
of polling days
(e) At every polling station, 4 CPF personnel should be deployed on the election day
(f) The total number of CPF personnel available for deployment at polling stations on any
polling day is at most 1,500,000 or 1.5 million.
Assume
that the CPF personnel movement will be entirely by air, except the ‘last mile’
movement between the airports and the constituencies, we have to determine the number of
phases for conducting the elections, and the states in which elections are held in each phase,
such that the total cost of travel of all the CPF personnel for conducting these elections in
minimized..
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All the data for the problem can be accessed in the folder “Election Data” at the website in
the file corresponding to Chapter 3.. Here is the description of the data made available.

Table D1 gives the number of polling stations in each constituency in each state, the
name of the nearest airport to that constituency (CPF personnel deployed to polling
stations in this constituency will use this airport to arrive in this constituency and
depart from it to their next assignment), and the road distance of this constituency to
that airport.

Table D2 provides the air travel cost in Indian Rupees
between various pairs of
airports.
Actual air travel cost of CPF polling personnel is hard to get exactly since some of it
is on Indian Air Force Transport Aircraft, helicopters, and some on Air India
chartered flights. So this data is based on estimated average cost in Rupees10/mile
(based on 2012 prices) on these different types of flights used, and the air distance
data between pairs of airports.

Table D3 provides the estimated cost in ` (Rupees) of the road or train travel of CPF
polling personnel from airport used to the polling stations in the constituency and
back for each constituency. This data is based on estimated average cost in Rs.3/mile
by these modes of travel(road or rail).

Table D4 provides for each state all its adjacent states. Two states are defined to be
adjacent if they share a common boundary line.

Table D5 gives the cost in ` of travel/person from the various bases from where CPF
polling personnel come from, to each constituency;

Table D6, the number of personnel that come from each base.

Table D7 gives the cost of travel/person from each constituency to each constituency
across the country.
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