# Transportation Problem

(A)Feasible Solution (F.S.)

Aset of non-negative allocations xij ≥ 0 which satisfies the row and column restrictions is known as feasible solution.

(B)Basic Feasible Solution (B.F.S.)

Afeasible solution to a m-origin and n-destination problem is said to be basic feasible solution if the number of positive allocations are (m+n–1).

If the number of allocations in a basic feasible solutions are less than (m+n–1), it is called degenerate basic feasible solution (DBFS) (otherwise non-degenerate).

(C)Optimal Solution

A feasible solution (not necessarily basic) is said to be optimal if it minimizes the total transportation cost.

In order to find the solution of this transportation problem we have to follow the steps given below.

(A)Initial basic feasible solution

(B)Test for optimization

(A) Initial Basic Feasible Solution :

There are three different methods to obtain the initial basic feasible solution viz.

(I) North-West corner rule

(II) Lowest cost entry method

(III) Vogel’s approximation method

(B)Test for optimization

After finding feasible solution the two methods for solving a transportation model are the stepping-stone method and the modified distribution method (also known as MODI).