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Chapter 1 of 7

Project Management and Network Theory

In the RRB JE Civil CBT-2 syllabus under Construction Management · 2 parts

Construction Planning & Project Management · Network Analysis — CPM

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📑 Contents (21 sections)

Part 1 of 2

Construction Planning & Project Management

Last reviewed 16 Sept 2026 · 6 min read

Construction projects

A project is a temporary endeavour with a defined beginning and end, undertaken to create a unique product, service or result within constraints of time, cost and quality.

Characteristics of construction projects

Unique — each site, design and set of conditions differ.
Temporary organisation assembled for the project.
Work carried out at the site, exposed to weather and ground uncertainty.
Involvement of many stakeholders — owner, consultants, contractors, subcontractors, suppliers, regulators, public.
Large capital, long durations, high risk.
Mix of skilled and unskilled labour, heavy equipment.

Project life cycle

Phase	Main activities
1. Conception / initiation	Identification of need, preliminary ideas, pre-feasibility
2. Feasibility study	Technical, financial, economic, environmental and social feasibility; alternatives; approximate cost
3. Detailed project report (DPR) and approvals	Surveys, investigations, preliminary design, cost estimate, financing plan, administrative approval, statutory clearances
4. Detailed design and engineering	Drawings, specifications, detailed estimates, technical sanction
5. Procurement / tendering	Tender documents, bidding, evaluation, award of contract
6. Construction (execution)	Mobilisation, site works, monitoring and control
7. Commissioning and handover	Testing, trial runs, completion certificate, as-built drawings
8. Operation, maintenance and closure	Defect liability period, final bill, project close-out, lessons learnt

The ability to influence cost is highest in early phases and decreases as the project advances, while the cost of changes increases with time.

Objectives of construction management

The traditional triple constraint — time, cost and quality (scope) — plus safety, environment and stakeholder satisfaction:

Complete the project within the scheduled time.
Within the budgeted cost.
To the specified quality and scope.
Safely, with minimum environmental and social impact.

Functions of management

Following classical management theory (Fayol and others):

Function	In construction
Planning	Deciding what, how, when, by whom — methods, sequence, schedules, resources, budgets
Organising	Dividing work, defining roles and authority, arranging resources and site layout
Staffing	Recruitment, placement and training of personnel
Directing (leading)	Instructions, motivation, communication, supervision
Coordinating	Harmonising the work of departments, subcontractors and agencies
Controlling	Measuring progress against plans (time, cost, quality) and taking corrective action

Part 2 of 2

Network Analysis — CPM

Last reviewed 16 Sept 2026 · 8 min read

Critical Path Method (CPM)

CPM was developed in the late 1950s (by DuPont with Remington Rand) for planning and scheduling projects with deterministic (known) activity durations. It is activity-oriented and widely used in construction, where durations can be estimated from experience; it also forms the basis of time–cost trade-off (crashing).

Network terminology

Term	Meaning
Activity	A task consuming time and resources (shown by an arrow in AOA)
Event (node)	The start or completion of activities — a point in time, consumes no time or resources
Dummy activity	Fictitious activity of zero duration and no resources, drawn as a dashed arrow — used to show logical dependency or to give unique identification to parallel activities
Predecessor / successor	Activities immediately before / after an activity
Burst event	An event from which more than one activity starts
Merge event	An event at which more than one activity ends
Duration	Time estimated for an activity
Critical path	The longest path through the network; determines project duration

Types of network diagrams

Activity on arrow (AOA)

Activities on arrows, events as nodes (circles); activity identified by $(i, j)$ — tail and head events.
Needs dummies for correct logic.

Activity on node (AON) / precedence diagram

Activities in nodes (boxes); arrows show dependencies only.
No dummies needed; easier to draw and modify; used by most software.
Allows relationships FS, SS, FF, SF with lags/leads.

Rules for drawing AOA networks

Each activity is represented by one arrow only.
No two activities may have the same tail and head events — use a dummy.
There should be one initial and one final event (in a basic network).
Arrows flow from left to right; no looping (circular logic).
No dangling — every activity except the last must have a successor, and every event except the first must have a predecessor.
Avoid redundant dependencies.
The length of the arrow has no significance (not to scale).

Fulkerson's rule for numbering events

Number the initial event 1.
Delete all arrows emerging from numbered events; this creates new initial events — number them 2, 3, …
Repeat until the final event is numbered.

Result: for every activity $(i, j)$ , $i < j$ (head number greater than tail number).

Common errors

Looping (cycling) — endless loop of activities.
Dangling — an activity disconnected from the end event.
Redundancy — unnecessary dummy or link where dependency is already implied.

Time computations

FormulaEvent times (AOA)

Forward pass — earliest event time:

E_{1} = 0, E_{j} = i max (E_{i} + t_{ij})

Backward pass — latest event time:

L_{n} = E_{n} (or scheduled date), L_{i} = j min (L_{j} - t_{ij})

Event slack $= L - E$

FormulaActivity times for activity (i, j) of duration t

Earliest start $E S T = E_{i}$ ; earliest finish $E F T = E_{i} + t$
Latest finish $L F T = L_{j}$ ; latest start $L S T = L_{j} - t$

Floats

FormulaFloats of activity (i, j)

Total float

T F = L S T - E S T = L F T - E F T = L_{j} - E_{i} - t

The maximum time an activity can be delayed without delaying the project.

Free float

F F = E_{j} - E_{i} - t = T F - (L_{j} - E_{j})

Time an activity can be delayed without delaying the earliest start of any succeeding activity.

Independent float

I F = E_{j} - L_{i} - t = F F - (L_{i} - E_{i})

Delay possible when predecessors finish as late as possible and successors start as early as possible (if negative, taken as zero).

Interfering float $= T F - F F =$ head event slack $(L_{j} - E_{j})$

Relationship: $I F \leq F F \leq T F$ .
Critical activities have zero total float (when the project's scheduled completion equals its earliest completion). Negative float indicates the schedule cannot meet a target date.
The critical path joins critical activities from start to end; there may be more than one critical path.

Worked example 1 — AOA network

Worked ExampleCPM computations

Activity	(i–j)	Duration (days)	Predecessor
A	1–2	3	—
B	2–3	4	A
C	2–4	2	A
D	3–5	5	B
E	4–5	3	C
F	5–6	2	D, E

Forward pass: $E_{1} = 0$ ; $E_{2} = 3$ ; $E_{3} = 7$ ; $E_{4} = 5$ ; $E_{5} = max (7 + 5, 5 + 3) = 12$ ; $E_{6} = 14$

Backward pass: $L_{6} = 14$ ; $L_{5} = 12$ ; $L_{3} = 7$ ; $L_{4} = 12 - 3 = 9$ ; $L_{2} = min (7 - 4, 9 - 2) = 3$ ; $L_{1} = 0$

Activity	t	EST	EFT	LST	LFT	TF	FF
A	3	0	3	0	3	0	0
B	4	3	7	3	7	0	0
C	2	3	5	7	9	4	0
D	5	7	12	7	12	0	0
E	3	5	8	9	12	4	4
F	2	12	14	12	14	0	0

Check for C: $F F = E_{4} - E_{2} - 2 = 5 - 3 - 2 = 0$ ; interfering float $= 4 - 0 = 4$ (slack of event 4). For E: $F F = 12 - 5 - 3 = 4$ ; $I F = E_{5} - L_{4} - 3 = 12 - 9 - 3 = 0$ .

Critical path: A–B–D–F; project duration = 14 days.

Worked example 2 — using a dummy

Worked ExampleDrawing logic with a dummy

Activities: A and B start the project; C depends on A; D depends on both A and B.

Solution (AOA). Draw A (1–2) and B (1–3). C starts from node 2. D must follow both A and B: draw D from node 3 and add a dummy from node 2 to node 3 (so D waits for A), while C remains dependent only on A. Without the dummy, C would wrongly depend on B, or D would not depend on A.

Precedence diagram relationships (AON)

Relationship	Meaning
Finish-to-start (FS)	Successor starts after predecessor finishes (most common)
Start-to-start (SS)	Successor starts after predecessor starts (with lag) — e.g. plastering starts 3 days after brickwork starts
Finish-to-finish (FF)	Successor finishes after predecessor finishes
Start-to-finish (SF)	Successor finishes after predecessor starts (rare)
Lag / lead	Waiting time (e.g. curing) / overlap

AON node boxes typically show ES, EF, LS, LF, duration and total float.

Advantages of CPM

Shows interdependencies; identifies critical activities needing close control.
Computes floats — flexibility for resource allocation.
Basis for crashing, resource levelling, cost control and updating.
Effect of delays on the project can be analysed.

Frequently tested points

CPM: deterministic durations, activity-oriented, used for time–cost trade-off; PERT: probabilistic, event-oriented.
Dummy: zero time, zero resources, dashed arrow — logic or unique identification.
Fulkerson's rule numbers events so that $i < j$ for every activity.
Errors: looping, dangling, redundancy.
$E_{j} = max (E_{i} + t)$ ; $L_{i} = min (L_{j} - t)$ .
TF = L_j − E_i − t; FF = E_j − E_i − t; IF = E_j − L_i − t; interfering float = TF − FF = head slack.
IF ≤ FF ≤ TF; critical activities TF = 0; critical path = longest path; may be several.
AON needs no dummies; FS, SS, FF, SF relationships with lags.

Common MistakeCommon mistakes

Taking the minimum instead of the maximum at merge events in the forward pass (and vice versa in the backward pass).
Calling the shortest path the critical path.
Assuming free float equals total float for every activity.

Revision SummaryChapter summary

CPM is a deterministic, activity-oriented network technique identifying the critical path and floats.
Networks may be activity-on-arrow (with dummies and Fulkerson numbering) or activity-on-node (precedence diagrams).
Forward and backward passes give earliest and latest event and activity times.
Total, free, independent and interfering floats measure scheduling flexibility; critical activities have zero total float.
Precedence relationships (FS, SS, FF, SF) with lags model real construction logic.

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Activity	t	EST	EFT	LST	LFT	TF	FF
A	3	0	3	0	3	0	0
B	4	3	7	3	7	0	0
C	2	3	5	7	9	4	0
D	5	7	12	7	12	0	0
E	3	5	8	9	12	4	4
F	2	12	14	12	14	0	0

Activity	t	EST	EFT	LST	LFT	TF	FF
A	3	0	3	0	3	0	0
B	4	3	7	3	7	0	0
C	2	3	5	7	9	4	0
D	5	7	12	7	12	0	0
E	3	5	8	9	12	4	4
F	2	12	14	12	14	0	0

Activity	t	EST	EFT	LST	LFT	TF	FF
A	3	0	3	0	3	0	0
B	4	3	7	3	7	0	0
C	2	3	5	7	9	4	0
D	5	7	12	7	12	0	0
E	3	5	8	9	12	4	4
F	2	12	14	12	14	0	0