MATERIAL MANAGEMENT Job Shop Scheduling.pptx

Job Shop
A work location in which a number of
general purpose work stations exist and are
used to perform a variety of jobs
Example: Car repair – each operator
(mechanic) evaluates plus schedules, gets
material, etc. – Traditional machine shop,
with similar machine types located together,
batch or individual production

Factors to Describe Job Shop
Scheduling Problem
1. Arrival Pattern
2. Number of Machines (work stations)
3. Work Sequence
4. Performance Evaluation Criterion

Two Types of Arrival Patterns
• Static - n jobs arrive at an idle shop
and must be scheduled for work
• Dynamic – intermittent arrival
(often stochastic)

Two Types of Work Sequence
• Fixed, repeated sequence - flow shop
• Random Sequence – All patterns possible

Some Performance Evaluation
Criterion
• Makespan – total time to completely
process all jobs (Most Common)
• Average Time of jobs in shop
• Lateness
• Average Number of jobs in shop
• Utilization of machines
• Utilization of workers

Gantt Chart
• Simple graphical display technique – suitable for
less complex situations
• This does not provide any rules for choosing but
simply presents a graphical technique for
displaying results (and schedule) and for
evaluating results (makespan, idle time, waiting
time, machine utilization, etc.)

Example of Gantt Chart (I)
5 jobs, 2 machines, each job must first go to
machine 1, and then 2 – without changing order.
Processing times are:
Assume order jobs are worked is {3,2,4,5,1}
JOB Machine 1 Machine 2
1 13 3
2 2 5
3 1 3
4 4 6
5 5 7

Example of Gantt Chart (II)
5 10 15 20 25 30 35
3
3
2 4 5 1
2 4 5 1
Machine
1
Machine
2

Example of Gantt Chart (III)
Here we assume setup time is included in process
time.
Makespan = 28
Machine 1 has no idle time except 3 units at end
of day
Machine 2 has 3 units of idle time plus 1 unit at
beginning of day.
Jobs 2, 4 and 5 wait a total of 6 units at
machine 2

Scheduling Solutions
• In Order to begin to attempt to develop
solution, break the problem in categories:
1. N jobs, 1 machine
2. N jobs, 2 machines (flow shop)
3. N jobs, 2 machines (any order)
4. N jobs, 3 machines (flow shop)
5. N jobs, M machines

Scenario 1 – n jobs, 1 machine (I)
• Let P1, P2, … Pn be processing time
for each job – (including setup)
• The schedule possibilities are the
permutations of n, which is equal to
“n!”
• Since the total processing time, or
makespan is independent of sequence,
this is not a criterion for choice –
Consider using minimum mean flow time

Scenario 1 – n jobs, 1 machine (II)
Mean flow time for n jobs:
k
Flow time for job in kth position is:
F[k ]   P[i ]
i1
n n
n n k
F  k 1
 k 1 i1
 F[k ] 
P[i ]
n
(n  i 1)Pi
F  i1

Scenario 1 – n jobs, 1 machine (III)
It can be proven that F is minimized by
taking jobs in order of shortest
processing time [SPT]
That is order by increasing P, so that
P[1]  P[ 2]  P[3]  ...  P[ n]

Scenario 1 – n jobs, 1 machine (IV)
Provide numerical weighting to jobs
by priority
(w) – higher w, more important then
and jobs are sequenced by:
n
F
n
 wi
F[i ]
 i1
w
w[n]
 ... 
P[ n]
P[1]

P[ 2]

P[3]

Scenario 1 - example
SPT sequence = 5,4,3,2,6,1
SPT / Priority sequence = 2,5,3,6,1,4
Job P W P/w
1 10 5 2.0
2 6 10 0.6
3 5 5 1.0
4 4 1 4.0
5 2 3 0.67
6 8 5 1.60
Processing Time:

Scenario 2 – n jobs, 2 machines,
flow shop (I)
These jobs must go to machine 1 first and
2 second – The minimum makespan is
determined using Johnson’s Algorithm
Let Pij = Processing time for job i
on machine j

flow shop (II)
The Algorithm is:
1. Find the job with minimum Pij
2. If j = 1 (machine 1) this job becomes
the first job
3. If j = 2 (machine 2) this job becomes
the last job
4. Remove assigned job from the list
and repeat (break ties at random)

flow shop (III)
• Example: Processing Time as follow
Job Mach 1 Mach 2
1 4 3
2 1 2
3 5 4
4 2 3
5 5 6
P11 = 4, P12 = 3, P41 =2, P42 = 3, … etc.
Using Johnson Rule:
Min Pij = P21 = 1 – now eliminate job
2 Min Pij = P41 = 2 – now job 4
Min Pij = p12 =3 – now job 1 goes to
last Min Pij = p32 …
The Sequence: {2,4,5,3,1}

• Example con’t.
flow shop (IV)
5 10 15 20 25
2
2
4 5 3 1
4 5 3 1
Machine
1
Machine
2
Makespan = 21
Mach 1 = 0 idle plus 4 end of day
Machine 2 = 2 idle + 1 beginning of
day 2 wait units (job 3,1)

Scenario 3, n jobs, 2 machines,
any order including only 1
machine (I)
• Establish 4 sets:
– {A} – set of jobs only on machine 1
– {B} – set of jobs only on machine 2
– {AB} – set of jobs processing on 1, then 2
– {BA} – set of jobs processing on 2, then 1
• Sequence jobs in {A,B} by Johnson’s Rule
• Sequence jobs in {B,A} by Johnson’s Rule
• Sequence jobs in {A} and {B} at random
• Combined as follows without changing order in any set:
– Machine 1 : Jobs in {A,B} before jobs in {A} before jobs in
{B,A}
– Machine 2 : Jobs in {B,A} before jobs in {B} before jobs in
{A,B}

Scenario 3 – example processing
time for each machine
JOB PA PB Order
1 4 3 AB
2 1 0 A
3 9 8 AB
4 0 8 B
5 5 1 AB
6 3 7 AB
7 4 6 BA
8 2 1 BA
9 0 6 B
10 4 0 A
11 3 4 BA
12 9 4 BA

Scenario 3 – Example Con’t.
• Set {A, B} – {1,3,5,6)
Sequence : 6,3,1,5
• Set {B,A} – {7,8,11,12}
Sequence: 8,12,7,11
• Set {A} – {2,10}
Sequence: 2,10
• Set {B} – {4,9}
Sequence: 9,4
Machine A:
6,3,1,5,2,10,8,12,7,1
1
Machine B:
8,12,7,11,9,4,6,3,1,5

Scenario 3 - Example
6 3 1 5 11
5
48
7
12
8 2 7 11 9 4 6 3 1
5 10 15 20 25 30 35 40 45
8
2 10
Machine
A
MachineB

2 Jobs, m Machines
Example:
Job 1 Sequence – Machine D, B, A, C
Job 2 Sequence – Machine A, B, C, D
Processing time for each job on each
machine
Job Machine A Machine B Machine C Machine D
1 2 5 3 2
2 3 5 2 6

Job 1
Machine A Machine C Machine D
5
Machine B
10
Machine
D
Machine
A
Machine
C
5
10
15
Job
2
Machine
B
Time Unit
Time
Unit
Schedule by graph

N Jobs, M Machines
Number of possible schedules is
extremely large, (n!)m
Almost all solved by heuristics which
are based on sequencing or
dispatching rules.

N Jobs, M Machines
List of Heuristics are as follows:
1. R (Random) – Pick any Job in Queue with equal probability. This rule is often used as
benchmark for other rules
2. FCFS (First Come First Serve) – Jobs are processed in the order in which they arrived at
the work center (also called earliest release date)
3. SPT (Shortest Processing Time) –This rule tends to reduce both work-in-
process inventory, the average job completion (flow) time, and average job
lateness.
4. EDD (Earliest Due Date) – Choose Job that has earliest due date
5. CR (Critical Ratio) = Processing Time / Time until due (Due Date – Current
Time). Take the highest value.
6. LWR (Least Work Remaining) – This rule is an extension of SPT variant that
considers the number of successive operations
7. ST (Slack Time) = Time until job is due - (Sum of processing time remaining). Take
the job with the smallest amount of slack time.
8. ST/O (Slack Time per Remaining Operation) = slack time divided by number of
operations remaining. Take the job with the smallest amount of slack time per remaining
operation
When in Doubt, use SPT. Also, use SPT to break ties.

MATERIAL MANAGEMENT Job Shop Scheduling.pptx

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MATERIAL MANAGEMENT Job Shop Scheduling.pptx