Assumptions of Linear Programming
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Decision modeling Assgnimenttraining manual, training manual
Table1. Initial Solution
Table 2.
Since the unoccupied cell (S3, D1) has the largest negative opportunity cost of -11, therefore, ell (S3, D1) is entered into the new solution mix. The closed path for (S3, D1) is shown in Table 2. The maximum allocation to (S3, D1) is 30. However, when this amount is allocated to (S3, D1) both cells (S2, D1) and (S3, D2) become unoccupied because these tow have same allocations. Thus, the number of positive allocation became less than the required number, m + n - 1 = 3 + 3 - 1 = 5. Hence, this is a degenerate solution as shown in Table 3, Table .3
To remove degeneracy a quantity is assigned to one of the cells that have become unoccupied so that there are m + n - 1 occupied cells. Assign to either (S3, D2) and proceed with the usual solution procedure. The optimal solution is given in Table 4. Table 4.
12 Formulate a linear Programming problem Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time. Use the Hungarian Method Answer Row reduction: A B C D E 1 7 0 5 6 10 2 3 0 7 0 5 3 0 5 3 4 1 4 4 0 0 8 7 5 4 3 0 6 2 Coloumn reduction: A B C D E 7 0 5 6 9 3 0 7 0 4 0 5 3 4 0 4 0 0 8 6 4 3 0 6 1 A B C D E 7 0 5 6 9 3 0 7 0 4 0 5 3 4 0 4 0 0 8 6 4 3 0 6 1 √ √
Final step is as follows: A B C D E 6 0 5 5 8 3 1 8 0 4 0 6 4 4 0 4 0 0 7 5 3 3 0 5 0 B → 1
C → 4 A → 3
D → 2 E → 5
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