Proposed Algorithm

Step 1:

Subtract the smallest cost ( $c_{ik}$ where $k=1,2,\cdots ,n$ ) from each of the cost along the first row ( $c_{i1},c_{i2},\cdots ,c_{in}$ , where $i=1,2,\cdots ,m$ ) of the transportation table and write those on the right top corner of the corresponding cost. Similar operation is applicable for rest of the rows.

Step 2:

Applying the same process on each of the column and write the result on the left lower corner of the corresponding cost.

Step 3:

By adding the digit of right top corner and left lower corner construct the TOCM.

Step 4:

Determine the penalty cost for each row of the TOCM by taking difference between the highest and the lowest cell cost in the same row and put it on the right of the corresponding rows of the cost matrix. These numbers are called Row Penalties (RP). In a similar fashion, calculate the Column Penalties (CP) for each of the columns and write them in the bottom of the cost matrix below corresponding columns.

Step 5:

Choose the highest penalty costs and observe the row or column along which it appears. If a tie occurs, choose the row/column along which lowest-cost appears. If it is also same then choose any of them.

Step 6:

Allocate maximum to the cell having lowest unit transportation cost in the row or column along which the highest penalty cost appears. If more than one cell contain lowest-cost, we allocate to the cell where allocation is maximum.

Step 7:

Determination of rest of the allocation: