Project Management Notes by Dr. Abe Feinberg

Network Development

The first phase of project management is network planning, including:

information gathering, task descriptions, constraints, timing, sequencing and resources required.

The result of network planning is the project network.

The network alone is a useful device for project management because:Communication is structured and sequencing is portrayed graphically.

Preparation for network planning includes:determination of project objectives, responsibilities, organization and information.

Basic Terms

Activity = an elemental part of a project that consumes time or resources and has a definable beginning and ending.

Event = beginning or ending point of an activity

Project= a collection of interrelated activities leading to the accomplishment of a major objective.

Representation: Activity = arrow or an arc Event = node Project = network

Note: with this representation, it may be necessary to have dummy activities to reflect exact sequencing. An example is given next.

Example Illustrating the need of a dummy activity when the activities are represented by arrows

Activity Description Predecessors

A Install Machine ---

B Hire operator ---

C Train Operator A,B

D Inspect Machine A

Network Rules

1. Before an activity can begin, all actyivities preceding it must be completed. Note that activities at the beginning of a project can begin at project initiation.

2. Arrows imply logical precedence only. Neither arrow length nor direction on the drawing have any implication.

3. Event numbers cannot be duplicated in a network.4. Any two events may be connected by no more than one activity.5. Networks must have only one initial and one terminal event.6. Activities must connect from a lower numbered node at the tail of the arrow

to a higher numbered node at the head of the arrow. This is necessary to avoid loops or cycles in the network.

Common Errors in Network Diagramming

1. Incorrect representation of sequencing requirements (too much or too little)2. Loops3. Excessive (redundant) dummy activities4. Duplicate activities

Example for Network Diagramming: Office Move

Activity Description Immediate ExpectedPredecessors Activity Time (in weeks)

A Select Office Site --- 3

B Create Org. & --- 5Financial Plan

C Determine Pers. B 3Requirements

D Design Facility A,C 3

E Construct Interior D 8

F Select Personnel C 2To Move

G Hire New Empls. F 4

H Move Records, F 2People, etc.

I Make Arrs. With B 5Inst. In New Loc.

J Train New Persons H,E,G 3

PERT-CPM Terminology and Calculations

Without the loss of generality, assume that the project has its start time or origin at time zero. This simplifies calculations.

EARLY TIME CALCULATIONS

Earliest Start Time = ES is the earliest possible time that an activity can begin assuming that all preceding activities also started at their ES times.

Earliest Finish Time = EF is the earliest possible time that an activity can end assuming that all preceding activities also ended at their EF times.

To Calculate ES and EF times:

1. Label ES = zero at the start of the project.2. Label EF = 0 + activity time for activities without any preceding activities.

For activities with preceding activities, EF = + activity time.3. Label ES for each activity, all of whose predecessors have been labeled =

Maximum of {EF times of all immediately preceding activities including dummy activities}

4. Systematically work from the beginning to the end of the network.

LATE TIME CALCULATIONS

Latest Start Time = LS is the earliest possible time that an activity can begin without delaying the LS time of any succeeding activity.

Latest Finish Time = LF is the latest possible time that an activity can end without delaying the LF time of any succeeding activity..

To Calculate ES and EF times:

1. Assume that the target date for completing the project = EF =LF for the project. Reasoning based on worker motivation will be provided in class.

2. LS for each activity ending the project = LF – activity time. For other activities, once LF is determined: LS = LF - activity time

3. Label LF for each activity, all of whose successors have been labeled = Minimum of {LS times of all immediately succeeding activities including dummy activities}

4. Systematically work backward to the beginning of the network.

Total Slack for an activity = TS = LF – EF or = LS – ES, and is the maximum time that an activity can be delayed without delaying project completion.

PERT Example

ACTIVITY PREDECESSORS TASK TIME ES EF LS LF TS CP

A - 3B A 6C - 3D C 2E A 1F D 5G D,E 7H B,F,G 4DUMMY D 0

Use the network diagram below to calculate ES, EF

Then use the diagram on the next page to calculate LS and LF. Combine the two to determine slack TS and whether or not the activity is on the Critical Path (CP).

aE

B

H

FD

G

C

A

START

END

aE

B

H

FD

G

C

A

START

END