Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 22 Issue 4

V. M athematical A nalysis Let us take a problem of 8 jobs and 5 processing components with associated execution costs as given in Table 2. Table 2 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 270 260 220 190 300 320 180 250 C 2 210 190 300 200 290 180 190 310 C 3 190 260 230 220 280 190 300 290 C 4 250 210 180 190 290 240 190 300 C 5 160 180 160 140 210 170 180 200 Table 3: Follows steps 1, 2 and, 3 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 50 80 60 90 40 150 0 50 C 2 50 0 130 70 40 0 0 100 C 3 60 60 50 50 10 0 100 70 C 4 40 20 10 70 80 60 0 90 C 5 0 0 0 0 0 0 0 0 Table 4: Follows step 4 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 40 80 60 50 90 150 0 50 C 2 40 0 130 50 70 0 0 100 C 3 10 60 50 60 50 0 100 70 C 4 80 20 10 40 70 60 0 90 C 5 0 0 0 0 0 0 0 0 By step 5; from the uncovered costs, choose the lowest cost (i.e. 10) i. Deduct 10 from each exposed cost in the matrix above. ii. To get Table 5, sum up 10 at each of the intersection points. Table 5 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 30 80 50 40 80 150 0 40 C 2 30 0 120 40 60 0 0 90 C 3 0 60 40 50 40 0 100 60 C 4 70 0 0 30 60 60 0 80 C 5 0 10 0 0 0 10 0 0 Following steps 6 and 7, we allocate job J 3 to component M 1 and cross off the remaining zeros in the row corresponding to J 3 ; as a result, row four has just one zero. As stated in Table 6, allocate work J 7 to component M 4 . Table 6 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 30 80 50 40 80 150 0 40 C 2 30 0 120 40 60 0 0 90 C 3 0 60 40 50 40 0 100 60 C 4 70 0 0 30 60 60 0 80 C 5 0 10 0 0 0 10 0 0 © 2022 Global Journals 1 Year 2022 32 Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) An Improved Hungarian Algorithm for a Special Case of Unbalanced Assignment Problems N otes