Homework SourseA transportation table is given below Calculate the least co
Solution
In the given matrix, the supply of each source 1, 2 is given 130 units, 115 units respectively. The demand for three retailers A, B, C, D i.e. 80 units, 10 units, 90 units, and 65 units is given respectively. The shipping cost is given for all the routes.
The minimum transportation cost can be obtained by following the steps given below:
1. The minimum cost in the matrix is 5 units. Therefore, 90 units shall be assigned to the cell \"2C\". With this, the demand for retailer C gets fulfilled, and only 25 (115-90) units are left with the source \"2\".
2. Again the minimum cost in the matrix is 8 units. Therefore, 10 units shall be assigned to the cell \"2B\". With this, the demand of retailer B gets fulfilled. Only 15 (115-90-10) units are left with the source \"2\".
3. The next minimum cost is 9 units. Therefore, remaining 15 can be assigned to the cell \"2D\". The demand of \"2\" has been saturated. Demand of \"D\" is 50 now.
4. The next minimum cost is 10 units. But there is a tie among the cells \"1A\",\"1C\", and \"1D\", now the question arises in which cell we shall allocate. Generally, the cost where maximum quantity can be assigned should be chosen to obtain the better initial solution. Therefore, 80 units shall be assigned to the cell \"1A\". With this, the demand for retailer A gets fulfilled.
5.The next minimum cost is 10 units. But the demand has been completed for \"C\".
6. The next minum cost is 10 units again. But there is a tie between the cells \"1C\", and \"1D\". as said above, the maximum demand can be assigned to \'\'1D\" so 50 can be assigned to \'\'1D\".
Now the total cost from the above assigned values is
1A + 1D + 2B + 2C + 2D = 10*80 +10*50+ 8*10 + 5*90 + 9*15
= 1965 units.
So the least cost for transporting materials from origins 1 and 2 to destinations A,B,C,D using minimum cost method is 1965 units.
| From \\ To | A | B | C | D | SUPPLY |
| 1 | 10*80 | 15 | 10 | 10*50 | 130 |
| 2 | 14 | 8*10 | 5*90 | 9*15 | 115 |
| DEMAND | 80 | 10 | 90 | 65 | TOTAL = 245 |
