Transcript 10/6 Production Scheduling

10/6 Production Sequencing
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Roll call/collect homework
issues w/ Excel for CPM
lecture: production sequencing
small groups
assign homework
CPM & Excel
• Deceptive: “on critical path”.
• Sensitivity report: shadow price of 1 or
“LaGrange multiplier” of 1.
Go to spreadsheet example.
Production Sequencing
• Multiple jobs, one work center (machine,
person, etc.)
• Schedule to minimize mean flow time.
Production Sequencing: terms
• Work center: machine, person, etc., where
some particular task is done.
• Scheduling: assigning jobs to work centers.
• Sequencing: the order in which to process
the jobs at a given work center.
• Flow time: amount of time that passes from
when an order was received and when it
was finished.
Job Sequencing
• Priority Rules for Dispatching Jobs
–
–
–
–
–
FCFS
LCFS
SOT
LOT
Ddate
- first come, first served
- last come, first served
- shortest operation time
- longest operation time
- due date
Job Sequencing: Example
• Copy shop w/ one color copier.
• Orders arrive in the morning in this order:
–
–
–
–
–
A.
B.
C.
D.
E.
Brochures, 4 hrs.
Presentation, 1 hr.
Flyers, 6 hrs.
Invitations, 8 hrs.
Booklets, 5 hrs.
needed in 8 hrs.
needed in 3 hrs.
needed in 7 hrs.
needed in 12 hrs.
needed in 14 hrs.
Job Sequencing: Example
• How to schedule to minimize the flow time?
• Orders arrive in the morning in this order:
–
–
–
–
–
A.
B.
C.
D.
E.
Brochures, 4 hrs.
Presentation, 1 hr.
Flyers, 6 hrs.
Invitations, 8 hrs.
Booklets, 5 hrs.
needed in 8 hrs.
needed in 3 hrs.
needed in 7 hrs.
needed in 12 hrs.
needed in 14 hrs.
Copy Shop: FCFS
Arr.
Time Due
Arr.
Time Due
Flow Time
A
4
8
A
4
8
0+4=4
B
1
3
B
1
3
4+1=5
C
6
7
C
6
7
5 + 6 = 11
D
8
12
D
8
12
11 + 8 = 19
E
5
14
E
5
14
19 + 5 = 24
tot. flow time = 4 + 5 + 11 + 19 + 24 = 63
mean flow time = 63 / 5 = 12.6 hrs.
Copy Shop: LCFS
Arr.
Time Due
Arr.
Time Due
Flow Time
A
4
8
E
5
14
0+5=5
B
1
3
D
8
12
5 + 8 = 13
C
6
7
C
6
7
13 + 6 = 19
D
8
12
B
1
3
19 + 1 = 20
E
5
14
A
4
8
20 + 4 = 24
tot. flow time = 5 + 13 + 19 + 20 + 24 = 81
mean flow time = 81 / 5 = 16.2 hrs.
Copy Shop: SOT
Arr.
Time Due
Arr.
Time Due
Flow Time
A
4
8
B
1
3
0+1=1
B
1
3
A
4
8
1+4=5
C
6
7
E
5
14
5 + 5 = 10
D
8
12
C
6
7
10 + 6 = 16
E
5
14
D
8
12
16 + 8 = 24
tot. flow time = 1 + 5 + 10 + 16 + 24 = 56
mean flow time = 56 / 5 = 10.2 hrs.
Copy Shop: LOT
Arr.
Time Due
Arr.
Time Due
Flow Time
A
4
8
D
8
12
0+8=8
B
1
3
C
6
7
8 + 6 = 14
C
6
7
E
5
14
14 + 5 = 19
D
8
12
A
4
8
19 + 4 = 23
E
5
14
B
1
3
23 + 1 = 24
tot. flow time = 8 + 14 + 19 + 23 + 24 = 88
mean flow time = 88 / 5 = 17.6 hrs.
Copy Shop: DDate
Arr.
Time Due
Arr.
Time Due
Flow Time
A
4
8
B
1
3
0+1=1
B
1
3
C
6
7
1+6=7
C
6
7
A
4
8
7 + 4 = 11
D
8
12
D
8
12
11 + 8 = 19
E
5
14
E
5
14
19 + 5 = 24
tot. flow time = 1+ 7 + 11 + 19 + 24 = 62
mean flow time = 62 / 5 = 12.4 hrs.
Job Sequencing: notes
• Note that the ending flow time was identical
for all methods. (Additivity rule)
• The MEAN flow time varied.
• SOT will ALWAYS produce the lowest
mean flow time.
Job Sequencing: 2 work centers
• Multiple jobs to do
• 2 work centers, jobs must be done
sequentially (EX: first copy, then staple)
Johnson’s Rule: 2 work centers
• List the time for each job on each machine.
• Select the shortest operation time.
• If the shortest time is on 1st machine,
schedule that job first.
• If the shortest time is on 2nd machine,
schedule that job LAST.
• Repeat steps until all jobs are scheduled.
2 work centers - Example
• Copy shop:
• 4 jobs to do, w/ times for each machine
–
–
–
–
booklets
brochures
catalogs
packets
copy: 3
copy: 6
copy: 5
copy: 7
fold: 2
fold: 8
fold: 6
fold: 4
2 work centers - Example
• Step 1: find shortest time.
• 4 jobs to do, w/ times for each machine
– booklets
copy: 3
fold: 2
– brochures
– catalogs
– packets
copy: 6
copy: 5
copy: 7
fold: 8
fold: 6
fold: 4
2 work centers - Example
• Step 2: on 2nd machine, so schedule it last.
• 4 jobs to do, w/ times for each machine
–
–
–
–
brochures
catalogs
packets
booklets
copy: 6
copy: 5
copy: 7
copy: 3
fold: 8
fold: 6
fold: 4
fold: 2
2 work centers - Example
• Repeat: find lowest (remaining) time.
• 4 jobs to do, w/ times for each machine
– brochures
– catalogs
copy: 6
copy: 5
fold: 8
fold: 6
– packets
copy: 7
fold: 4
– booklets
copy: 3
fold: 2
2 work centers - Example
• Repeat: 2nd mach., so move (next to) last.
• 4 jobs to do, w/ times for each machine
–
–
–
–
brochures
catalogs
packets
booklets
copy: 6
copy: 5
copy: 7
copy: 3
fold: 8
fold: 6
fold: 4
fold: 2
2 work centers - Example
• Repeat: find lowest time.
• 4 jobs to do, w/ times for each machine
– brochures
copy: 6
fold: 8
– catalogs
copy: 5
fold: 6
– packets
– booklets
copy: 7
copy: 3
fold: 4
fold: 2
2 work centers - Example
• Repeat: 1st machine, move to front of line.
• 4 jobs to do, w/ times for each machine
–
–
–
–
catalogs
brochures
packets
booklets
copy: 5
copy: 6
copy: 7
copy: 3
fold: 6
fold: 8
fold: 4
fold: 2
2 work centers - Example
• Done.
• 4 jobs to do, w/ times for each machine
–
–
–
–
catalogs
brochures
packets
booklets
Copy
catalogs
fold
IDLE
copy: 5
copy: 6
copy: 7
copy: 3
brochures
catalogs
fold: 6
fold: 8
fold: 4
fold: 2
packets booklets IDLE
brochures
packets booklets
Small Group Exercise
You have an engraving business in a kiosk at
the mall. Today, while you were out buying
nachos, your clueless assistant received 4
orders in this sequence: a bracelet, which
will take 10 min. to engrave, a locket (6 min.),
an award plaque (24 min.), and a pen (12
min.). Your assistant also promised that they
would be ready at 12:25, 12:15, 12:40, and
12:50, respectively. It is now 12:00 exactly.
Minimize the number of dissatisfied
customers by seeing which priority rule you
should use. Should you fire your assistant?
time
Small Group Exercise
# late
FCFS LCFS SOT
LOT
Ddate
B 10
P 12
L6
A 24
L6
L 16
A 36
B 16
P 36
B 16
A 40
L 42
P 28
B 46
A 40
P 52
B 52
A 52
L 52
P 52
2
2
1
2
1
due
Bracelet 10
25
Locket 6
15
Award 24
40
Pen
50
12
Choose DDate
10/6 Homework
• DUE 10/8: Handout
• DUE 10/13: pg. 176, #20, pg. 177, #23