Decision ScienceOperations Research- Transportation ProblemTransportation Problem (TP) is one of the subclasses of LPP in which objective is to transport various quantities of a single homogeneous commodity that are initially stored at various origins to different destinations in such a way that the transportation cost is minimum

1) A dairy farm has 3 plants located in a state. The daily milk production at each plant is as follows

Plant 1 : 6 mn litres

Plant 2 : 1 mn litres

Plant 3 : 10 mn litres

Each day, the firm must fulfil the needs of its 4 distribution centres. Minimum requirements at each centre are as follows:

Distribution Centre 1 : 7 mn litres

Distribution centre 2 : 5 mn litres

Distribution centre 3 : 3 mn litres

Distribution centre 4 : 2 mn litres

Cost in hundreds of Rs of shipping 1 mn litre from each plant to each distribution centre is given in the following table

D1D2D3D4

P123117

P21061

P358159

Find IBFS using i) NWCR

ii) LCM

iii) VAM

2) Determine the IBFS for the following TP using i) NWCR ii) LCM and iii) Vogels Approximation methods where Di represents the demand centre and Si represents the supply centre.The numbers in cell SiDi indicates the cost ( 00 Rs ) of transporting 1 unit of a product/commodity from Si to Di.

a)

D1D2D3D4Supply

S1211615311

S21718142313

S33227184119

Demand6101215

b)

D1D2D3D4Supply

S1121430

S2332150

S3425920

Demand20403010

3) Find the Optimal solution to the following TP using MODI method

D1D2D3D4Supply

S1193050107

S2703040609

S3408702018

Demand58714

b)

W1W2W3Supply

F1162012200

F214818160

F326241690

Demand180120150

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Compiled by...Rajesh Devasia | [Type the company address]