Answer to Question #229314 in English for Mama

Question

Write down a rules for transportation in form ( x;y)

Answer 1

The transportation problem is a special type of linear programming problem, where the 

objective is to minimize the cost of distributing a product from a number of sources to a 

number of destinations.

The general mathematical model may be given as follows

If xij (≥0) is the number of units shipped from ith source to jth destination, then equivalent 

LPP model will be

Minimize 

j

m

i

ij

n

j

ij Z c x

1

Subject to

i

n

j

xij a

1

For i = 1,2, ....., m (supply)

j

m

i

ij x b

1

For j = 1,2, ....., n (demand) 

xij 0 .

For a feasible solution to exist, it is necessary that total capacity equals total to the 

requirements. If 

m

j

j

n

i

ai b

1 1

i.e. If total supply = total demand then it is a balanced 

transportation problem otherwise it is called unbalanced Transportation problem. There will be 

(m + n - 1) basic independent variables out of (m x n) variables

What are the understanding assumptions?

1. Only a single type of commodity is being shipped from an origin to a 

destination.

2. Total supply is equal to the total demand. 

n

j

j

m

i

ai b

1 1

, ai (supply) and bj (demand) are all positive integers.

3. The unit transportation cost of the item from all sources to destinations 

is certainly and preciously known.

4. The objective is to minimize the total cost.