North-west corner method

North-west corner method


We aim to write a C program to solve a transportation problem using North-West Corner Method. A typical transportation problem deals with sources where a supply of some commodity is available and destinations where the commodity is demanded. The objective to solve the transportation problem is to minimize the cost of shipping m units to n destinations or maximize the profit of shipping m units to n destinations. The North West Corner rule is a method for computing the basic feasible solution of a transportation problem, where the basic variables are selected from the north-west corner (i.e. the topmost corner). We will achieve this by using C programming.

The north-west corner method generates an initial allocation according to the following procedure:
1. Allocate the maximum amount allowable by the supply and demand constraints to the variable x 11 (i.e. the cell in the top left corner of the transportation tableau).
2. If a column (or row) is satisfied, cross it out. The remaining decision variables in
that column (or row) are non-basic and are set equal to zero. If a row and column
are satisfied simultaneously, cross only one out (it does not matter which).
3. Adjust supply and demand for the non-crossed out rows and columns.
4. Allocate the maximum feasible amount to the first available non-crossed out element in the next column (or row).
5. When exactly one row or column is left, all the remaining variables are basic and are assigned the only feasible allocation.
The values of the basic variables x ij are entered in the top left of each cell. There should always be m + n - 1 of these; in certain (degenerate) cases some of them may be zero. They must always add up to the total supply and demand in each row and column.

Consider the problem represented by the following transportation tableau. The number in the bottom right of cell...

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