scheduling for engineering and management

Scheduling
Scheduling: Establishing the timing of the use of
equipment, facilities and human activities in an
organization
Answering “when” question for activities
2
Build A
A Done
Build B
B Done
Build C
C Done
Build D
Ship
JAN FEB MAR APR MAY JUN
On time!

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
3
Work Center #1 Work Center #2 Output

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 high-volume systems and made-to-order job
shops
 Economic run size:
5
D
p
p
H
DS
Q


2
0

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

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.
Job time:Time needed for
setup and processing of a job.
It includes set up time unless setup times are
sequence dependent
9
Everything is
#1 Priority

Priority Rules
FCFS - first come, first served
SPT - shortest processing time
EDD - earliest due date
 CR - critical ratio
=time remaining / processing time
 S/O - slack per operation
=slack remaining / # of operations remaining
Rush - emergency
1
0

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
1
1

Example:
Average
number of jobs
 Jobs: A and B with processing times 10 each
1
2
A finishes at 10
Number of jobs
1
2
B finishes at 20 Time
Makespan=20, Total Flow time=10+20
Average number of jobs=30/20
Average number of jobs

Example:
Sequencing
rules
1
3
Jobs Processing time DD=Due date
A 11 61
B 29 45
C 31 31
D 1 33
E 2 32

Ex: FCFS
1
4
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

Ex: SPT to minimize the total flow time
1
5
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

Ex: EDD to minimize the maximum lateness
1
6
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

Example summary
17
235/74=3.17
6.6
47
EDD
135/74=1.82
8.6
27
SPT
268/74=3.62
24.2
53.6
FCFS
Average
Number of
Jobs at the
Work Center
Average
Tardiness
(days)
Average
Flow Time
(days)
Rule

Two Work Center Sequencing
 Johnson’s Rule: technique for minimizing completion time
for a group of jobs to be processed on two
machines or at two work centers.
 Minimizes total idle time and the makespan
 Several conditions must be satisfied
1
8

Johnson’s Rule Conditions
 Job time must be known and constant
 Job times must be independent of sequence
 Jobs must follow same two-step sequence
 Job priorities cannot be used
 All units must be completed at the first
work center before moving to the second
1
9

Johnson’s rule
1. Select a job with the shortest processing time
If the processing time is on the first workcenter
Schedule the job right after the already scheduled at the beginning of the list
If the processing time is on the second workcenter
Schedule the job right before the already scheduled at the end of the list
2. Cross out the scheduled job and go to 1
2
0

Example:
Johnson’s rule
2
1
Job Processing time on 1 Processing time on 2
A 15 25
B 8 6
C 12 4
D 20 18

The sequence that minimizes the makespan
A- D- B- C
2
2
15
25
20
18
8
6
12
4
15
15 35
40
43
58
55
64 68
15
13
Idle time = 28
Makespan = 68
MC1
MC2

Sequence
dependent set
up times
 Set up is basically changing the work center configuration from the existing to the new
 Set up depends on the existing configuration
 Set up time of an operation depends on previous operation done on the same work center
 Which sequence minimizes total set up time?
 There are too many sequences!
2
3

Scheduling Service Operations
Bottleneck operations
Appointment systems
Controls customer arrivals for service
 Consider patient scheduling
Reservation systems
Estimates demand for service
Scheduling the workforce
Manages capacity for service
Scheduling multiple resources
Coordinates use of more than one resource
2
4

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