Homework #6 solutions / IEOR4405
1
1 Consider the following jobs (
a,b,c,d
) with the processing times (7
,
8
,
9
,
11). The algorithm to
solve is LRPTFM. Denote the machines with speeds 1,2,4 as M1, M2 and M3 respectively.
Machine/Job present at each time instant
M/T 0 1 2 3 4
M1 : B C B A B
M2 : C B C B A
M3 : D A D C D B
The job with the shortest processing time is A, it is clear from the table that the job is processed
in all the 3 machines.
2 Look at the algorithm in the lecture slides.
5.8 Applying LRPT we get
t
J
1
J
2
J
3
J
4
Assignment
t
= 0
36
24
16
12
J
1

M
1
,J
2

M
2
t
= 4
28
20
16
12
J
1

M
1
,J
2

M
2
t
= 8
20
16
16
12
J
1

M
1
,J
2

M
2
t
= 12
12
12
16
12
J
3

M
1
,J
2

M
2
t
= 16
12
8
8
12
J
1

M
1
,J
4

M
2
t
= 20
4
8
8
8
J
2

M
1
,J
4

M
2
t
= 24
4
0
8
4
J
3

M
1
,J
4

M
2
t
= 28
4
0
0
0
J
1

M
1
t
= 32
0
0
0
0
Therefore, the schedule for M1 is 1,1,1,3,1,2,3,1
and for M2 is 2,2,2,2,4,4,4 with
C
max
= 30
The table is,
t
J
1
J
2
J
3
J
4
Assignment
t
= 0
36
24
16
12
J
1

M
1
,J
2

M
2
t
= 2
32
22
16
12
J
1

M
1
,J
2

M
2
t
= 4
28
20
16
12
J
1

M
1
,J
2

M
2
t
= 6
24
18
16
12
J
1

M
1
,J
2

M
2