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Indian Institute of Management, Indore

PGP 2011-2013

FOOD CORPORATION OF INDIA

Group 11 - Section D

AJEET KUMAR PGP2011521

JAMMI SUNIL RAO PGP2011661

KANIKA PGP2011677

KASTURI KARUNA PGP2011687

N LAKSHMI SAGAR PGP2011735

NARIMI ANIL SAGAR PGP2011740

SHRIRAMAN S PGP2011879

Summary of the Case:

The regional office of Food Corporation India follows a monthly transportation plan to supply rice to different varieties to a number of towns connected by railways. This decision is taken after considering the supply demand pattern, volume of pattern, storage facilities at the various dispatching and receiving depots. A current plan has been built up for the coming month and we need to find whether this distribution pattern is optimal or not. If not we will suggest an alternative plan.

Objective: To find the desired optimal pattern of rice movement to meet the demands of district with minimum cost.

Thus this is a balanced transportation problem.

Assumption:

1. Despatches are made to Karimnagar by road since railway connection to Karimnagar is not available.Here the distances taken are:

Karimanagar (km) Cost/tonne

East Godavari 469 234.5West Godavari 420 210Krishna 359 179.5Guntur 380 190Nizamabad 148 74

2. It is given that ,where road is to be used,the rate is Rs 0.05 / quintal.Since 1 ton is 10 quintal ,computations are done by taken Rs 0.5 / tone.The costs thus obtained are given above.

Constraints:

1.Sum of all supplies going out from a district =Max supply from that district

2.Sum of all supplies reaching a depot/district = Max demand from that district

3. All values in actual quantity transported >=0

Data given:

The model as currently followed is analysed below :

The cost of transport to the various demands points are as follows:

Transportation(Ralilway Freight per ton) Cost Matrix (Rs)

DepotVishakhapatnam

Timmancheria

Sanathnagar

Mancherial

Bhadrachallam

Karimnagar

Janagaon

Nandyal

Cuddapah

Chittoor

From District/To District

Vishakhapatnam

Anantpur

Hyderabad

Adilabad

Khammam

Karimnagar

Warangal

Kurnool

Cuddapah

Chittoor

East Godavari 50.1 141.9 109.50 105.3 70.8 234.5 61.5

118.5

136.50

132.8

West Godavari 66.6 121.5 93.6 90.6 56.7 210 73.2

115.8

149.40

122.4

Krishna 79.8 112.8 85.5 81 46.2 179.5 65.1102.

6147.9

0112

.8

Guntur 82.5 86.7 82.5 78.3 42.6 190 60.9 82.5126.9

0105

.6

Nizamabad 185.4 120 51 96.9 96.9 74 82.2 96.6145.8

0181

.5

The constraints are as follows:

1)

Sum of all

supplies going

out from a district =

Max supply from that

district 2)

Sum of all supplies

reaching a depot/distric

t =Max demand from

that district

East Godavari 80000 = 80000

Vishakhapatnam 100000 = 100000

West Godavari 140000 =

140000 Timmancheria 100000 = 100000

Krishna 130000 =13000

0 Sanathnagar 70000 = 100000

Guntur 70000 = 70000 Mancherial 10000 = 10000

Nizamabad 10000 = 10000 Bhadrachallam 10000 = 10000

Karimnagar 25000 = 25000

Janagaon 5000 = 5000

Nandyal 70000 = 150000

Cuddapah 10000 = 10000

Chittoor 30000 = 30000

The distribution to the various demand points from supply points are as follows:

Actual Quantity Transported (in ton)

DepotVishakhapatnam

Timmancheria

Sanathnagar

Mancherial

Bhadrachallam

Karimnagar

Janagaon

Nandyal

Cuddapah

Chittoor


Vishakhapatnam

Anantpur

Hyderabad

Adilabad

Khammam

Karimnagar

Warangal

Kurnool

Cuddapah

Chittoor

East Godavari 8000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00West Godavari 2000.00

10000.00

2000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Krishna 0.00 0.008000.0

01000.

00 1000.002500.

00500.

00 0.00 0.00 0.00

Guntur 0.00 0.00 0.00 0.00 0.00 0.00 0.00400

0.001000.

00200

0.00

Nizamabad 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00100

0.00

Current Objective function value (cost): 4078300

Solution : Since it is a balance transportation problem,and the demand and supply for each variety of rice is different we have divided the problem into three parts based on type of rice :

Assumption: In all the cases the transport costs are same for transport of rice.

1)Balanced transportation problem of Superfine rice.

Constraints for Superfine rice

1)

Sum of all supplies going out

from a district =

Max supply from

that distric

t 2)

Sum of all supplies

reaching a depot/district =

Max demand from

that district

East Godavari 2000.00 = 2000Vishakhapatnam 2000.00 = 2000

West Godavari 2000.00 = 2000 Timmancheria 0.00 = 0Krishna 3000.00 = 3000 Sanathnagar 5000.00 = 5000Guntur 0.00 = 0 Mancherial 0.00 = 0Nizamabad 0.00 = 0 Bhadrachallam 0.00 = 0

Karimnagar 0.00 = 0Janagaon 0.00 = 0Nandyal 0.00 = 0

Cuddapah 0.00 = 0Chittoor 0.00 = 0

Actual Quantity Transported for Superfine rice (in ton)

DepotVishakhapatnam

Timmancheria

Sanathnagar

Mancherial

Bhadrachallam

Karimnagar

Janagaon

Nandyal

Cuddapah

Chittoor


Vishakhapatnam

Anantpur

Hyderabad

Adilabad

Khammam

Karimnagar

Warangal

Kurnool

Cuddapah

Chittoor

East Godavari 2000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00

West Godavari 0.00 0.00

2000.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00

Krishna 0.00 0.003000.0

0 0.00 0.00 0.00 0.00 0.00 0.000.0

0

Guntur 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.0

0

Nizamabad 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.0

0

Objective function : 543900

2)Balanced transportation problem of coarse rice

Constraints for coarse rice

1)

Sum of all

supplies going

out from a district =

Max supply from that

district 2)

Sum of all supplies


Max demand from that district

East Godavari 6000.00 = 0

Vishakhapatnam 8000.00 = 0

West Godavari 7000.00 = 5000 Timmancheria 5000.00 = 5000

Krishna 2000.00 = 8000 Sanathnagar 2000.00 = 3000

Guntur 2500.00 = 4500 Mancherial 0.00 = 1000

Nizamabad 0.00 = 1000Bhadrachallam 0.00 = 1000

Karimnagar 0.00 = 2500

Janagaon 0.00 = 500

Nandyal 1000.00 = 3000

Cuddapah 500.00 = 500

Chittoor 1000.00 = 2000

Actual Quantity Transported for Coarse rice (in ton)

DepotVishakhapatnam

Timmancheria

Sanathnagar

Mancherial

Bhadrachallam

Karimnagar

Janagaon

Nandyal

Cuddapah

Chittoor


Vishakhapatnam Anantpur

Hyderabad

Adilabad

Khammam

Karimnagar

Warangal

Kurnool

Cuddapah

Chittoor

East Godavari 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00

0.00

West Godavari 0.00 500.00 3000.00

500.00 0.00 0.00

500.00

0.00

500.00

0.00

Krishna 0.00 0.00 0.00500.

00 1000.001500

.00 0.00

3000.0

0 0.00

2000.0

0

Guntur 0.00 4500.00 0.00 0.00 0.00 0.00 0.000.0

0 0.000.0

0Nizamabad 0.00 0.00 0.00 0.00 0.00

1000.00 0.00

0.00 0.00

0.00

Objective function (cost) : 1851650

3)Balanced transportation problem of fine rice

Constraints of fine rice

1)

Sum of all supplies going out

from a district =

Max supply from

that distric

t 2)

Sum of all supplies


Max demand from that district

East Godavari 6000.00 = 6000 Vishakhapatnam 8000.00 = 8000West Godavari 7000.00 = 7000 Timmancheria 5000.00 = 5000Krishna 2000.00 = 2000 Sanathnagar 2000.00 = 2000Guntur 2500.00 = 2500 Mancherial 0.00 = 0Nizamabad 0.00 = 0 Bhadrachallam 0.00 = 0

Karimnagar 0.00 = 0Janagaon 0.00 = 0Nandyal 1000.00 = 1000Cuddapah 500.00 = 500Chittoor 1000.00 = 1000

Actual Quantity Transported for Fine rice (in ton)

DepotVishakhapatnam

Timmancheria

Sanathnagar

Mancherial

Bhadrachallam

Karimnagar

Janagaon

Nandyal

Cuddapah

Chittoor


Vishakhapatnam

Anantpur

Hyderabad

Adilabad

Khammam

Karimnagar

Warangal

Kurnool

Cuddapah

Chittoor

East Godavari 6000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00West Godavari 2000.00

2500.00

2000.00 0.00 0.00 0.00 0.00 0.00

500.00 0.00

Krishna 0.00 0.00 0.00 0.00 0.00 0.00 0.00100

0.00 0.00100

0.00

Guntur 0.002500.0

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Nizamabad 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Objective Function : 1431600

Thus Total costs are =543900 + 1851650 + 1431600 = 3791150. Thus decrease in cost is 4078300 - 3791150. =287150.(7%) .Hence the new model is more suitable as it would help food corporation of India in reducing its cost by 7%.

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