Row-Minima Method

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In the row minima method, the first row that is the lowest cost cell is exhausted. Our aim will be to allocate the maximum either at the first source or demand at the destinations or to satisfy both. This process must be continued for all the other reduced transportation costs until and unless the supply and demand are satisfied.

In this problem, we begin with the lowest cost i.e. Rs. 2000 present at the first cell AX of the first row. So we allocate the lowest out of 1000 and 2200, so it is 1000. This deletes the first row and exhausts the supply capacity of factory A. now comes the next allocation in the next row, row 2, and cell BX. Similar as before we choose the minimum value between 1500 and 1300. So it is 1300. Hence meets the demand requirements of center X and deleting the column 1.

Distribution centers

                                                          X                                      Y                                     Supply

                                  A             Rs.2000                               Rs.5380

                                                    1000                                                                              1000

Factories                 B              Rs. 2500                             Rs.2700

                                                     1300                                    200

                                 C               Rs.2550                               Rs.1700

                                                                                                  1200                                 1200

                            Demand          2300                                     1400                                3700

Similarly we move to row 3 where the minimum cost is Rs. 1700 in the cell CY. Then we allocate the minimum out from 1400 and 1200. As now we see that the demand of the distribution centers is 1400 and we could allocate only 1200 so we add more 200 in the cell BY. This satisfies the column Y and hence crossed. The similar thing we do with row 2. In row 2 the supply was satisfied by 1300+200=1500 and similarly crossed out. Same with row3.

Therefore Z = Rs. (2000 × 1000 + 2500 × 1300 + 2700 200 + 1700 × 1200 = Rs. 78, 30.000.


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