Network Analysis: CPM | Construction Materials & Management - Civil Engineering (CE) PDF Download

Project Management

Project management coordinates and controls all project activities so that objectives are achieved in an efficient and cost-effective manner.

The salient features of a project are:

• A project has identifiable beginning and end points.
• Each project can be broken down into many identifiable activities that consume time and resources during execution.
• A project is scheduled to be completed by a specified target date.
• A project is usually large and complex and consists of many interrelated activities.
• Execution of project activities is always subject to uncertainties and risks.

Network Techniques

Network techniques are graphical methods to represent and analyse the logical sequence and inter-relationships of project activities. Their historical development includes the Gantt chart, bar charts, milestone charts and, finally, network techniques such as CPM and PERT.

The Gantt chart was developed by Henry L. Gantt during World War I for production scheduling. The Gantt chart was later adapted into bar charts, which became important in project and production scheduling. Bar charts are activity-oriented and do not show interdependencies or identify the critical activities; milestone charts are event-oriented and show important dates. Network techniques overcome these limitations by explicitly showing precedence relationships and enabling critical path analysis.

Network Construction

A network is the graphical representation of project activities arranged in logical sequence and showing all inter-relationships. A network consists of activities and events.

Activity

An activity is a physically identifiable part of a project that consumes time and resources. In network diagrams an activity is usually represented by an arrow (in Activity-on-Arrow, AOA) or by a node (in Activity-on-Node, AON).

In arrow diagrams the head of an arrow represents the finish of the activity and the tail represents its start. The activity description and its estimated duration are shown along the arrow.

Common ways to identify an activity in a network:

• By numbers of its tail and head events (for example, 10-20).
• By a letter code (for example, A, B, C).

Predecessor activities are those that must be completed before the activity under consideration can start. Successor activities are those that must follow the activity under consideration.

An activity provided only to maintain precedence relationships during the construction of the network is called a dummy activity. A dummy is shown by a dotted arrow and consumes no time or resources. An unbroken chain of activities between any two events is called a path.

Event

An event (also called a node) represents the completion of one or more activities or the occurrence of a milestone. In network diagrams the beginning and end of activities are shown as events (nodes). An event does not consume time or resources. Each network begins with an initial event and ends with a terminal event.

Numbering Nodes - Fulkerson's Rule

Nodes (events) are numbered to establish a consistent ordering. Fulkerson's rule for numbering events is as follows:

1. Number the initial event (which has outgoing arrows and no incoming arrows) as 1.
2. Delete all arrows coming out of the node just numbered; some nodes will then become initial events-number these in ascending order (2, 3, ...).
3. Continue the process until the final node (which has only incoming arrows and no outgoing arrows) has been numbered.

To allow insertion of new events without renumbering, it is customary to use spaced numbers (for example, 10, 20, 30, ...).

Rules for Drawing a Network Diagram

• Each activity must be represented by one and only one arrow (or node, depending on system).
• No two distinct activities may share the same pair of end events.
• All precedence relationships among activities must be maintained.
• Use dummy activities only when necessary to preserve precedence; minimise their use.
• Loops (cyclic dependencies) among activities must be avoided.

Rule 5: Looping among the activities must be avoided.

Critical Path Method (CPM)

The Critical Path Method (CPM) is a deterministic network analysis technique. For each activity a single, definite duration is estimated. CPM is activity-oriented and is especially suitable where activity times are known with reasonable certainty. CPM permits evaluation of project duration, identification of critical activities, and time-cost trade-off (crashing) analysis.

1. A CPM network diagram is activity-oriented.
2. CPM is frequently used for time-cost optimisation. Direct cost and indirect cost are balanced to find an optimum project duration and cost.
3. Each activity has a single time estimate (deterministic).
4. CPM assumes the activity will be completed in the estimated duration (probability effectively 100% for the estimated value).
5. CPM is based on a deterministic approach (unlike PERT, which uses probabilistic time estimates).
6. CPM is suitable for repetitive or routine works where durations are well known.
7. Activity durations often follow the normal distribution when many small independent factors influence time.

Activity time parameters and calculation procedure

To compute the critical path and activity floats, two passes are carried out on the network: a forward pass to determine earliest event times and activity earliest start/finish, and a backward pass to determine latest event times and activity latest start/finish.

Definitions and formulae

Earliest start time (EST) - the earliest time at which an activity can start, given its predecessors.

Earliest finish time (EFT)

EFT = EST + activity duration

Latest finish time (LFT) - the latest time by which an activity must finish without delaying the project.

LFT = latest time of the head event

Latest start time (LST)

LST = LFT - activity duration

Forward and backward pass (procedure)

Forward pass (to compute earliest times):

Begin at the initial event with time 0.

For each activity, compute EFT = EST + duration.

When several activities converge to a common event, assign the event's earliest time as the maximum of incoming EFT values.

Proceed through the network until all EST and EFT values are determined.

Backward pass (to compute latest times):

Start at the terminal event with its latest time equal to its earliest time (project duration).

For each activity, compute LST = LFT - duration.

When several activities leave a common event, assign the event's latest time as the minimum of the LST values of those outgoing activities.

Proceed backward through the network until all LST and LFT values are determined.

Float (Slack)

Float denotes the allowable variation in activity timing without delaying completion of the project or affecting other activities depending on that activity. Common types of float are described below.

• Total float (F_T)
  F_T = LST - EST
  F_T = LFT - EFT
  
• Free float (F_F)
  Free float is the amount by which an activity can be delayed without delaying the earliest start of any immediate successor.
  

  Where S_j denotes the slack of the head event.

• Independent float (F_ID)
  Independent float is the amount of time an activity can be delayed assuming all predecessor activities finish as late as possible and all successors start as early as possible.
  

  Where S_i denotes the slack of the tail event.

  Classification by F_T:

  • F_T = 0 - activity lies on the critical path.
  • F_T > 0 - activity is on a subcritical path (has some slack).
  • F_T < 0 - indicates schedule infeasibility or a constraint that causes the project to be behind; usually must be resolved.
• Interfering float (F_IN)
  Interfering float is another name often used for the head event slack (difference between head event latest and earliest times).
  

The critical path is the longest duration path through the network. Activities on the critical path have zero total float and any delay in these activities will delay the project completion date. Identification of the critical path helps prioritise resources and control activities that determine project duration.

CPM Systems

Two common ways to represent activities in CPM networks are:

1. A-O-A (Activity on Arrow) - Activities are shown on arrows. The tail and head of the arrow represent the start and finish of the activity respectively. Dummy activities are frequently required to show certain precedence relationships.
   

   Activity on Arrow (AoA) Network Diagram
2. A-O-N (Activity on Node), also called the precedence diagram - Activities are represented by nodes and the arrows show dependency relationships. Events are not shown as separate numbered nodes. When several activities start together, a dummy start node (for example DEBUT D₀) with zero duration can be used; similarly a finish node (F₀) with zero duration can be used when several activities finish together.

Applications and Notes

• CPM is used for schedule planning, monitoring and control, identification of critical activities, resource allocation and time-cost trade-off (crashing) studies.
• While CPM assumes deterministic durations, actual projects often have uncertainty; PERT (probabilistic) or hybrid approaches are used when duration uncertainty is significant.
• When building networks, aim to minimise dummy activities and avoid loops; use clear numbering (for example, spaced numbers) to permit future insertions and revisions.
• Regularly update the network during execution to reflect progress, changes in durations, and revised constraints; use the updated network to re-compute critical path and floats and reallocate resources where necessary.

Activity on Arrow (AoA) Network Diagram