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10/6 Production Sequencing
• 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 - first come, first served– LCFS - last come, first served– SOT - shortest operation time– LOT - longest operation time– Ddate - due date
Job Sequencing: Example
• Copy shop w/ one color copier.
• Orders arrive in the morning in this order:– A. Brochures, 4 hrs. needed in 8 hrs.– B. Presentation, 1 hr. needed in 3 hrs.– C. Flyers, 6 hrs. needed in 7 hrs.– D. Invitations, 8 hrs. needed in 12 hrs.– E. Booklets, 5 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. Brochures, 4 hrs. needed in 8 hrs.– B. Presentation, 1 hr. needed in 3 hrs.– C. Flyers, 6 hrs. needed in 7 hrs.– D. Invitations, 8 hrs. needed in 12 hrs.– E. Booklets, 5 hrs. needed in 14 hrs.
Copy Shop: FCFS
Arr. Time Due
A 4 8
B 1 3
C 6 7
D 8 12
E 5 14
Arr. Time Due Flow Time
A 4 8 0 + 4 = 4
B 1 3 4 + 1 = 5
C 6 7 5 + 6 = 11
D 8 12 11 + 8 = 19
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
A 4 8
B 1 3
C 6 7
D 8 12
E 5 14
Arr. Time Due Flow Time
E 5 14 0 + 5 = 5
D 8 12 5 + 8 = 13
C 6 7 13 + 6 = 19
B 1 3 19 + 1 = 20
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
A 4 8
B 1 3
C 6 7
D 8 12
E 5 14
Arr. Time Due Flow Time
B 1 3 0 + 1 = 1
A 4 8 1 + 4 = 5
E 5 14 5 + 5 = 10
C 6 7 10 + 6 = 16
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
A 4 8
B 1 3
C 6 7
D 8 12
E 5 14
Arr. Time Due Flow Time
D 8 12 0 + 8 = 8
C 6 7 8 + 6 = 14
E 5 14 14 + 5 = 19
A 4 8 19 + 4 = 23
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
A 4 8
B 1 3
C 6 7
D 8 12
E 5 14
Arr. Time Due Flow Time
B 1 3 0 + 1 = 1
C 6 7 1 + 6 = 7
A 4 8 7 + 4 = 11
D 8 12 11 + 8 = 19
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 copy: 3 fold: 2– brochures copy: 6 fold: 8– catalogs copy: 5 fold: 6– packets copy: 7 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 copy: 6 fold: 8– catalogs copy: 5 fold: 6– packets copy: 7 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 copy: 6 fold: 8– catalogs copy: 5 fold: 6– packets copy: 7 fold: 4 – booklets copy: 3 fold: 2
2 work centers - Example
• Repeat: find lowest (remaining) time.
• 4 jobs to do, w/ times for each machine– brochures copy: 6 fold: 8– catalogs copy: 5 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 copy: 6 fold: 8– catalogs copy: 5 fold: 6– packets copy: 7 fold: 4 – booklets copy: 3 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 copy: 7 fold: 4 – booklets copy: 3 fold: 2
2 work centers - Example
• Repeat: 1st machine, move to front of line.
• 4 jobs to do, w/ times for each machine– catalogs copy: 5 fold: 6– brochures copy: 6 fold: 8– packets copy: 7 fold: 4 – booklets copy: 3 fold: 2
2 work centers - Example
• Done.
• 4 jobs to do, w/ times for each machine– catalogs copy: 5 fold: 6– brochures copy: 6 fold: 8– packets copy: 7 fold: 4 – booklets copy: 3 fold: 2
catalogs
catalogs
brochures
brochures
packets
packets
booklets
booklets
Copy
fold IDLE
IDLE
Small Group ExerciseYou 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?
Small Group Exercisetime due
Bracelet 10 25
Locket 6 15
Award 24 40
Pen 12 50
FCFS LCFS SOT LOT Ddate
B 10 P 12 L 6 A 24 L 6
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
# late 2 2 1 2 1
Choose DDate
10/6 Homework
• DUE 10/8: Handout
• DUE 10/13: pg. 176, #20, pg. 177, #23
