Chapter 15

Scheduling

1

Scheduling
• Scheduling: Establishing the timing of the use of equipment, facilities and human activities in an organization • Answering “when” question for activities
JAN

FEB

MAR

APR

MAY

JUN

Build A
A Done
Build B
B Done
Build C
C Done
Build D
Ship

On time!
2

High-Volume Systems
• Flow system: High-volume system with Standardized equipment and activities.
– Assembly line balancing
– Auto, computer industry

• Flow-shop scheduling
– Due to Repetition, scheduling is not a big issue

• Project scheduling

Work Center #1

Work Center #2

Output
3

High-Volume Success Factors
• Process and product design
• Preventive maintenance
• Rapid repair when breakdown occurs
• Optimal product mixes
– Most profit subject to capacities = LP

• Minimization of quality problems
• Reliability and timing of supplies
4

Intermediate-Volume Systems
• Outputs are between standardized highvolume systems and made-to-order job shops • Economic run size:
2 DS
Q0 
H

p p D

5

Scheduling Low-Volume Systems
• Low volume systems
– Minimal repetition
– Schedule from scratch every time

• Loading - assignment of jobs to process centers • Sequencing - determining the order in which jobs will be processed
– Sequencing vs. Scheduling
6

Gantt Load Chart
• Gantt chart - used as a visual aid for loading and scheduling – Resources into rows
– Time periods into columns

Work Mon. Tues. Wed. Thurs. Fri.
Center
1
Job 3
Job 4
2
Job 3 Job 7
3
Job 1
Job 6
Job 7
4
Job 10
7

Loading
• Infinite loading: unlimited capacity, like MRP
• Finite loading: consider capacity
• Schedule construction
– Vertical loading
• Load on 1 work center with different jobs at once

– Horizontal loading
• Load operations of 1 job to all work center at once

• Forward scheduling
– Too much wip

• Backward scheduling
– Risky
8

Sequencing
• Priority rules: Simple heuristics used to select the order in which jobs will be processed.

Everything is

#1 Priority

• Job time: Time needed for setup and processing of a job.
• It includes set up time unless setup times are sequence dependent
9

Priority Rules
• FCFS
• SPT
• EDD
•

CR

•

S/O

- first come, first served
- shortest processing time
- earliest due date

- critical ratio
=time remaining / processing time
- slack per operation
=slack remaining / # of operations remaining

• Rush

- emergency

10

Performance measures
• Flow time of a job: Duration of time from a job enters into the system until it leaves
• Lateness of a job: Amount by which completion date exceeds due date. Could be negative.
• Tardiness=max(lateness,0)
• Makespan: total time needed to finish a group of jobs • Average number of jobs until the last is finished:
=Total flow time / Makespan
11

Example: Average number of jobs
• Jobs: A and B with processing times 10 each
Number of jobs
2

Average number of jobs

1

A finishes at 10

B finishes at 20 Time

Makespan=20, Total Flow time=10+20
Average number of jobs=30/20

12

Example: Sequencing rules
Jobs

Processing time

DD=Due date

A

11

61

B

29

45

C

31

31

D

1

33

E

2

32

13

Ex: FCFS
Jobs

Proc.time Flow time

DD

Late Tardy

A

11

11

61

-50

0

B

29

40

45

-5

0

C

31

71

31

40

40

D

1

72

33

39

39

E

2

74

32

42

42

Total

268

202

66

121

Aver.

53.6

40.4

13.2

24.2
14

Ex: SPT to minimize the total flow time
Jobs

Proc.time Flow time

DD

Late Tardy

D

1

1

33

-32

0

E

2

3

32

-29

0

A

11

14

61

-47

0

B

29

43

45

-2

0

C

31

74

31

43

43

Total

135

202

-67

43

Aver.

27.0

40.4 -13.4

8.6
15

Ex: EDD to minimize the maximum lateness
Jobs

Proc.time Flow time

DD

Late Tardy

C

31

31

31

0

0

E

2

33

32

1

1

D

1

34

33

1

1

B

29

63

45

18

18

A

11

74

61

13

13

Total

235

202

33

33

Aver.

47.0

40.4

6.6

6.6
16