Answer to Question #258660 in Operations Research for Ahmad

Question

Solve the following job sequencing problem by giving an optimal sequence of jobs, and find the total elapsed time also. Note that M1, M2, M3, M4, M5, and M6 are machines, and A, B, C, D are jobs.

Jobs → A B C D

M1 20 19 13 22

M2 10 8 7 6

M3 9 11 10 5

M4 4 8 7 6

M5 12 10 9 10

M6 27 21 17 14

Answer 1

An optimal solution to this problem can be obtained, if either or both of the following conditions hold(s):

$min\ t_{1j}\ge max\ t_{ij}$

$min\ t_{mj}\ge max\ t_{ij}$

for i=2,3, ..., m-1

We have:

$min\ t_{1j}= t_{13}=13$

$max\ t_{ij}=\ t_{61}=27$

$min\ t_{1j}<max\ t_{ij}$

$min\ t_{mj}= t_{64}=14$

$min\ t_{mj}< max\ t_{ij}$

So, optimal solution to this problem cannot be obtained.