# SEQUENCING PROBLEM

```Operations Scheduling and
Sequencing
Single-Resource Sequencing Problem:
Consider a workstation that has one maintenance mechanic to repair
failed machines. We can think of the mechanic as the processor and
the machines awaiting repair as the jobs. Let us assume that six
machines are down, with estimated repair times given here, and that
no new jobs arrive.
Job
(machine #)
1
2
3
4
5
6
Processing
time (hours)
10
3
7
2
9
6
• We assume that jobs are ready for processing time at time zero. Using
the SPT, the job sequence is 4,2,6,3,5,1. The flowtime is computed as
follows:
Job Sequence
Flowtime
4
2 hours
2
2 + 3 = 5 hours
6
5 + 6 = 11 hours
3
11 + 7 = 18 hours
5
18 + 9 = 27 hours
1
27 + 10 = 37 hours
The average flowtime for these 6 jobs is 16.67 hours
(2+5+11+18+27+37 = 100/6)
Average flow time was used as the criterion to minimize the average
time a job spends in the workstation. The average flow time of 16.67
hours means the average time a machine will be out of service.
The SPT sequencing rule maximizes workstation utilization and
minimizes average job flow time and work-in-process inventory.
(Try to switch 2 jobs and note the change in the average flow time.
What will be the result?)
Assume the following data:
JOB
PROCESSING TIME
DUE DATE
1
4
15
2
7
16
3
2
8
4
6
21
5
3
9
Sequence by-the-numbers 1,2,3,4,5
Job
Flow time
Due Date
Lateness
Tardiness
1
4
15
-11
0
2
4 + 7 = 11
16
-5
0
3
11 + 2 = 13
8
5
5
4
13 + 6 = 19
21
-2
0
5
19 + 3 = 22
9
13
13
Average
69/5 = 13.8
0
3.6
Use the SPT rule to sequence the job
Job
Flow Time
Due Date
Lateness
Tardiness
3
2
8
-6
0
5
2+3=5
9
-4
0
1
5+4=9
15
-6
0
4
9 + 6 = 15
21
-6
0
2
15 + 7 = 22
16
6
6
Average
53/5 = 10.6
-3.2
1.2
The earliest-due-date (EDD)
Job
Flow Time
Due Date
Lateness
Tardiness
2
2
8
-6
0
5
2+3=5
9
-4
0
1
5+4=9
15
-6
0
2
9 + 7 = 16
16
0
0
4
16 + 6 = 22
21
1
1
Average
54/5 = 10.8
-3.0
0.2
Performance Criteria
Sequence 1-2-3-4-5
Sequence (SPT)
Sequence (EDD)
13.8
10.6
10.8
Average Lateness
0
3.2
3.0
Maximum Lateness
13
6
1
Average Tardiness
3.6
1.2
0.2
Maximum Tardiness
13
6
1
Average Flow Time
PROJECT MANAGEMENT
What is a project?
- It is a temporary and often customized
initiative that consists of any smaller tasks
and activities that must be coordinated and
completed to finish the entire initiative on
time and within budget.
The stages of the project life cycle
1. Define – clearly define the goal of the project, its responsibilities
and deliverables, and when it must be accomplished (statement of
work)
2. Plan – the steps needed to execute the project is defined. It entails
breaking down a project into smaller activities and developing a
project schedule.
3. Organize – involves these activities: forming a team; allocating
resources; calculating costs; assessing risk, preparing project
documentation, and ensuring good communications
4. Control – this stage assesses how well a project meets its goals and
objectives and makes adjustments as necessary.
5. Close – closing a project involves compiling
statistics, releasing and/or reassigning people,
and preparing a “lessons learned” list.
Three Factors Involve in Project Management
Decisions
1. Resource Planning
2. Project Scheduling
3. Project Control
• Resource planning includes developing time estimates for
performing each activity, other resources that may be
required
• Project scheduling with the Critical Path Method (CPM)
• Project Control
- A schedule specifies when activities are to be
performed. A schedule enables a manager to assign resource
effectively and to monitor progress and take corrective action
when necessary
The Critical Path Method
- The CPM is an approach to scheduling and
controlling project activities.
Critical Path – is the sequence of activities that
take the longest time and defines the total
project completion time
```