N job m machine.pdf OR job Sequencing problems

OR job Sequencing

1. @stat ac ficing
Sequen cing oblemns
ype TProblems
with
n Jobs hsough 2 machune
Type
I Pso blems
with Jobs
thro ugh 3 mac hine
gpe :
soblems oith
Jobs thwough R
machume
Jobs
thsough K machine
Tpe
Y Pro blems
with
2
Jobs 2
Machine A A A A3 An
Machine B , B Bs B,
Fin cipal Assumbtrions
(d No machune
Com psocess
mose
tham one 0pexaton
at a tme.
must
be omed tl Comble ton
tye
Jobs
sBavled
ges
only ome
T
(i Each operation
bnce
) Jhese
mac hin e each
between machenes is megi
ble.
( The tume eq,
wed to ron her
he

2. Pooble mswith n Jobs Thaough k Machine
@stant sacticing
Con veet the bxo
blem into tuoo mac hime bso ble
solve us vmg Johmsom's algoHthm
Steb
4: fund Min. Mi
amd Min Mk
ond
Max.
o
each
Ma.M3 Mk-(Mks last machine)
amd then
Step
2
: Check
whethex
Min M
2
Max. M
03 (j: 2,3. K-1)
Min Mx
2
Max M
tep 3: It
the n eg,uali ties
in steb
2 ne mot saihied
, the me thod ails
okherwise
30
t0
me xt step.
Gteb
4:1n addi hom
to step
2 ib
M,+Ms+.. MR-
C hee C is bositve
constant
or
all i:1,2..
n.
Then
detesmine the optvmal
sequumce ot
m Jobs,
wheu two
machines
Miand Mk by sUn g
the
optimal sequnce olgoru thm
ate
Step
5 I
the condikom M, + My
+ Mk-1 #
C ne
dekime
too mac huine G
and H
Such that i = M + M2 + Mk-
H M2 + Mgtt M
Detetmine the
obtvm al sequmce
us
Ung
two maC hune ulgoruthm
or
Jo hmsom's agotuthm.

3. @stort fsacticing
30 blems wth m Jobs thzough K machene
Q: Four Jobs oeto be brocessed on each o
the 5 machines Fundl the total mini mum
elabsed tme it no bass ing oh Jobs is pexmited
Als0 und
the dle time ok
each mac hune
Sinte,
Bi+C+DL =
10 (Vf
B,
C+ D2
= 15
Machines
3 B+C+Di #C
we dekhe tuwo
machines q
and H
Such thad
G=At B+C +D
H B CtD +E
D
5
Solutio :
Sinee he pro
blem is to be sequnced
onive machines , '
we Convertthe o blem
tuoo-
machine o
blem
Min (A) -5 Min E) = 6
Max (8,c, D)
= (6, 5, ¢)
Jebs 1
nto
2 20 16
2S 4
Optimal Sequene
Min
(E) Max (G, S.6)
66 (T)
324

4. kind
he mim
todal elapsed
tme and Idle time o machuine A,B 2C
Machine A Machine B MachiineC Machuine D Machune 6
Job
IN OUT IN OUT IN OUT IN OUT IN OUT
12 12 14 17 26
27 27
33 35
35| 45
12 12 6 16 1 21 35
18 24 24 29 28
2 12
18
18 45
26 26 29 29 32 33 5
Total ela bseol tme 5I unis
Tdle time
A s1-26) ums = 25 nis
o
mac hine
me
or
machine B
(51 29)+tt 2t2
22tIl
33k
1dle
Tdle tme mac hune
C (51
-
32)+ 12
2t3+1 = 14 18 =3 7w
machie
D -(S1 -35)+14+
t 1
3 uit
machneE (sl-s1)+ 7t 1 18 unis
Ldle
Jle tme

5. Exam ple-2
BCD Jobs A Machinee
Ma
Job
My
24 22 2
M
24
21
I 92 My2 1S 15 6
22
14
21
32
Min (M)
= 16 Min
(M) =
4
Max (Ma, M,) = ( ?)
M (M4) 2 Max (AMs)
(1,) CT
14
(M Me
3t6 =1y
(M,H)6+?ciy
M+Ms) 1+5 =1y