Scheduling and Network Planning

Introduction

A project schedule is more than a list of dates. It is a time-based model of how scope, resources, dependencies, constraints, uncertainty, and decisions interact. A credible schedule enables a project team to answer questions such as: When can the project finish? Which activities control completion? What flexibility exists? Where will delay have the greatest consequence? Which assumptions deserve management attention?

Scheduling and network planning convert the work breakdown structure (WBS) into an executable sequence of activities. The process normally includes defining activities, establishing logical relationships, estimating durations, developing the network, identifying milestones, analysing the critical path or critical chain, assigning resources, establishing a baseline, and controlling change.

A schedule is therefore both an analytical model and a governance instrument. It supports coordination among teams, procurement and contracting decisions, progress measurement, forecasting, and communication with sponsors and stakeholders. However, a schedule is not a prediction with unlimited precision. Its reliability depends on the quality of scope definition, estimates, dependency logic, calendars, resource assumptions, and risk analysis.

Learning Objectives

By the end of this chapter, the learner should be able to:

1. Define activities, milestones, dependencies, calendars, constraints, and schedule baselines.
2. Construct an activity-on-node network from project information.
3. Calculate early and late dates, float, and the critical path.
4. Distinguish critical path scheduling from critical chain scheduling.
5. Represent a schedule using Gantt charts and scheduling software.
6. Assess schedule constraints, uncertainty, sensitivity, and resource effects.
7. Establish and govern a credible schedule baseline.
8. Interpret schedule information for managerial decision-making.

1. From Scope to a Time-Phased Model

The WBS decomposes project scope into deliverables and work packages. Scheduling requires a further transformation: work packages are decomposed into activities that can be estimated, sequenced, assigned, monitored, and accepted. An activity should be sufficiently specific to have a clear owner and completion condition, but not so small that administration overwhelms control.

For example, “implement customer portal” is usually too broad. It may be decomposed into configure authentication, develop interface, integrate payment service, conduct system testing, train users, and deploy production release.

Important schedule objects include:

An activity list should normally include an identifier, description, responsible party, estimated duration, predecessor and successor relationships, calendar, assumptions, and acceptance criteria. The activity list is not independent of the WBS: each activity should be traceable to a work package and ultimately to an approved deliverable.

2. Dependency Logic and Network Representation

A network diagram represents the logical order of work. The most common contemporary convention is activity-on-node (AON), in which a node represents an activity and an arrow represents a dependency. AON is especially suitable for project scheduling software.

Four relationship types are possible:

Finish-to-start is the dominant relationship, but the other types can be valid. A lag adds time between linked events; a lead permits overlap. For example, a successor may start two days after a predecessor finishes (FS + 2 days), or begin one day before the predecessor finishes (FS − 1 day). Leads should be used cautiously because they can conceal real work or create difficult-to-audit logic.

Dependencies may also be classified by origin. Mandatory dependencies arise from the nature of the work or technical requirements. Discretionary dependencies reflect preferred practice and may be changed. External dependencies depend on parties outside the project team, such as regulatory approval or supplier delivery. Internal dependencies are controlled within the project.

A sound network is logically complete: activities have appropriate predecessors and successors, except for the start and finish points; relationships reflect actual work; unnecessary constraints are avoided; and open ends are investigated. Circular logic is invalid because it implies that an activity depends, directly or indirectly, on itself.

Milestones

A milestone has no planned duration. It marks an event such as contract award, design approval, regulatory submission, completion of testing, or go-live authorization. Milestones improve governance because they translate detailed work into decision points. A milestone should have a clear completion criterion and an accountable owner. It should not be used to hide unfinished activities.

3. Deterministic Network Analysis

The critical path method (CPM) calculates schedule dates from activity durations and logical relationships. The following treatment assumes a finish-to-start network with no resource limits, fixed activity durations, and a common project calendar. More complex relationship types and calendars require corresponding software logic.

For activity i, define:

• ESᵢ: early start
• EFᵢ: early finish
• LSᵢ: late start
• LFᵢ: late finish
• Dᵢ: activity duration
• TFᵢ: total float

Using a time convention in which an activity starting at time 0 and lasting 4 days finishes at time 4:

The forward pass calculates the earliest feasible dates. For an activity with predecessors:

where j represents every immediate predecessor of activity i. For a start activity, ESᵢ is normally zero or the project start time. The maximum is required because the activity must wait for its latest-finishing predecessor.

The backward pass begins with the required project completion time T. For a terminal activity:

For an activity with successors:

where k represents every immediate successor of activity i. Then:

Total float is the amount of time an activity can be delayed without delaying the calculated project completion date:

All date quantities use the same unit, such as working days, and durations must be interpreted under the relevant calendar. In a simple unconstrained network, activities with zero total float form a critical path. In practice, multiple critical paths may exist, and software may display near-critical activities according to a chosen threshold.

Worked Example: A Small Network

Consider the following activities, with durations in working days:

Forward pass:

• A: ES = 0, EF = 0 + 3 = 3.
• B: ES = 3, EF = 3 + 4 = 7.
• C: ES = 3, EF = 3 + 5 = 8.
• D: ES = 7, EF = 7 + 6 = 13.
• E: ES = 8, EF = 8 + 2 = 10.
• F: ES = max(13, 10) = 13, EF = 13 + 3 = 16.
• G: ES = 16, EF = 16 + 2 = 18.

The earliest project completion is 18 working days. The path A–B–D–F–G has duration 3 + 4 + 6 + 3 + 2 = 18 days. The path A–C–E–F–G has duration 3 + 5 + 2 + 3 + 2 = 15 days.

Backward pass from T = 18:

• G: LF = 18, LS = 18 − 2 = 16.
• F: LF = 16, LS = 16 − 3 = 13.
• D: LF = 13, LS = 13 − 6 = 7.
• E: LF = 13, LS = 13 − 2 = 11.
• B: LF = 7, LS = 7 − 4 = 3.
• C: LF = 11, LS = 11 − 5 = 6.
• A: LF = min(3, 6) = 3, LS = 3 − 3 = 0.

The resulting total float is:

Thus, the critical path is A–B–D–F–G. The procurement and environment path has three days of float. This does not mean that C and E are unimportant: consuming their float can make the path critical, and their progress may affect resource decisions or risk exposure.

4. Float, Constraints, and Schedule Sensitivity

Total float concerns project completion; free float concerns the delay possible without delaying the early start of any immediate successor. For a finish-to-start relationship, a common expression is:

where k represents immediate successors. Free float cannot exceed total float under the usual CPM assumptions.

Constraints alter the flexibility suggested by pure network logic. A “must finish on” date, a contractual deadline, a fixed delivery date, a resource availability window, or a regulatory shutdown may restrict the schedule. Constraints are not inherently wrong, but hard constraints should represent real conditions, not compensate for weak logic or arbitrary managerial preference. Excessive constraints can create negative float, obscure the true driving path, and prevent meaningful forecasting.

Schedule sensitivity concerns how strongly completion responds to changes in durations, dependencies, resources, or external events. Useful indicators include:

• number of critical and near-critical paths;
• amount of float on important activities;
• sensitivity of the completion date to key duration assumptions;
• exposure to external dependencies;
• frequency with which the critical path changes during updates;
• resource bottlenecks and calendar dependencies.

A schedule with one critical path and substantial float elsewhere may be less structurally sensitive than a schedule with several paths whose durations are nearly equal. However, low sensitivity in the network does not eliminate uncertainty in estimates.

Probabilistic Duration Analysis

When duration uncertainty is material, three-point estimates may be used: optimistic a, most likely m, and pessimistic b. Under the traditional beta-based PERT approximation:

where tₑ is the expected activity duration. A commonly used approximation for activity variance is:

These expressions assume that the three estimates reasonably represent the distribution and that the beta approximation is suitable. They are not guarantees of actual duration. Network-level probability calculations also require assumptions about activity dependence; simply adding variances is inappropriate when durations are correlated.

Monte Carlo simulation can sample activity durations and recalculate the network repeatedly. It produces a distribution of completion dates rather than a single date. Its usefulness depends on credible input distributions, correlation assumptions, calendars, and logic. Simulation should inform decisions, not create false precision.

5. Critical Chain and Resource Feasibility

CPM generally focuses first on logical precedence and then adjusts the schedule for resources. Critical chain project management (CCPM) defines the critical chain as the longest sequence of dependent activities considering both precedence and resource constraints. It also emphasizes protection against uncertainty through buffers and discourages excessive multitasking.

Typical CCPM concepts include:

• project buffer: protection placed before the project completion date;
• feeding buffer: protection where a non-critical chain feeds the critical chain;
• resource buffer: an alert that a required resource must be ready;
• aggressive but achievable activity estimates, with uncertainty managed at aggregated buffer points.

CCPM can make resource contention visible and encourage focus. Its limitations include difficulty in estimating appropriate buffers, cultural resistance, and the risk that teams misunderstand buffers as spare time. CCPM and CPM should not be treated as mutually exclusive ideologies: CPM provides a powerful logical model, while resource analysis and buffer management address practical execution uncertainty.

Resource leveling delays activities to resolve over-allocation, potentially changing the critical path and completion date. Resource smoothing attempts to use available float without changing the required completion date. The distinction is managerial: leveling may change the end date; smoothing seeks to preserve it.

6. Gantt Charts and Scheduling Software

A Gantt chart displays activities against a time scale. Bars show planned or actual duration, while links show dependencies and milestones. Gantt charts are effective for communication because they connect work packages with calendar time. They are less effective than network views for diagnosing complex logic, especially when many links cross the display.

A professional scheduling tool commonly supports:

1. WBS and activity coding;
2. calendars and exceptions;
3. relationship types and lags;
4. resource and cost assignment;
5. baselines and variance fields;
6. progress updates and data dates;
7. critical path and float calculations;
8. filters, layouts, dashboards, and reporting;
9. what-if scenarios and, in some systems, risk simulation.

Software does not create a sound schedule automatically. Before accepting a generated critical path, the scheduler should check calendars, date conventions, relationship logic, constraints, out-of-sequence progress, actual dates, remaining duration, and open ends. A visually attractive Gantt chart may still contain invalid logic.

A robust workflow is:

• create the WBS and activity list;
• define milestones and acceptance criteria;
• add logic without initially forcing dates;
• apply calendars and estimate durations;
• run forward and backward calculations;
• inspect critical and near-critical paths;
• resolve resource conflicts;
• review constraints and assumptions;
• obtain stakeholder validation;
• save the approved baseline;
• update using actual status at each data date.

7. Schedule Baselines and Control

A schedule baseline is the approved version against which actual performance and forecasts are compared. It should include planned dates, durations, logic, calendars, milestones, and—where relevant—resource and cost information. The baseline is not immutable. It is changed through formal change control when approved scope, strategy, contractual requirements, or major assumptions change.

During control, actual start and finish dates, remaining durations, physical progress, and revised logic are entered at the data date. The project team then analyses variance and forecast completion. A late activity does not automatically justify moving the baseline. Moving dates without approved change destroys trend information and makes performance appear better than it was.

Schedule performance can be integrated with earned value management. Planned value (PV), earned value (EV), and actual cost (AC) are often expressed in monetary units, although schedule analysis itself may use time. The schedule performance index is:

SPI is dimensionless. Values below 1 indicate less earned work than planned at the measurement point, but SPI should not be interpreted as a literal time ratio in every circumstance. It can be distorted near project completion and does not replace critical-path analysis. Time-based forecasts and milestone trends remain essential.

Governance should define who can approve baseline changes, how assumptions are recorded, how progress is evidenced, and how schedule forecasts are communicated. Auditability is especially important in regulated, public-sector, construction, defence, and contract environments.

8. Detailed Applied Case: Digital Service Launch

Background

The following is an illustrative case. A university plans to launch a digital student-advising service before the start of a semester. The project includes requirements, privacy review, configuration, data migration, integration testing, user acceptance, training, and launch approval.

Problem

The sponsor initially requests a launch in 30 working days. The team creates a Gantt chart with parallel bars but does not document dependencies. During review, the privacy officer explains that data migration cannot begin before privacy approval, and the vendor requires five working days for interface configuration. The team must determine whether the requested date is feasible and which activities drive it.

Analysis

The planner identifies the following network:

The paths are:

• A–B–D–F–G–H–I = 4 + 6 + 4 + 4 + 3 + 3 + 1 = 25 working days.
• A–C–E–F–G–H–I = 4 + 5 + 5 + 4 + 3 + 3 + 1 = 25 working days.

Both paths are critical under the stated assumptions. The requested 30-day date appears feasible, but the schedule has two equal critical paths. A delay in privacy approval or interface configuration can therefore affect launch. If training could occur in parallel with user acceptance, the logic might shorten; however, the sponsor decides that training materials must incorporate findings from acceptance, so the finish-to-start relationship is retained.

Approach and Solution

The team validates each dependency with its owner, assigns a shared working calendar, and adds a milestone for “launch readiness approved.” It creates a baseline at the approved 25-day plan, leaving five working days between planned completion and the semester start as management reserve outside the activity estimates. The reserve is explicitly governed rather than hidden in arbitrary activity durations.

A weekly update records actual progress and remaining duration. The planner monitors both critical paths, the external vendor interface, and privacy approval. A scenario is prepared in which interface configuration takes seven days. This would add two days to one critical path, reducing the reserve to three days. A second scenario examines a two-day delay in privacy approval, producing the same effect on the other path.

Outcome

The service launches before the semester. The project team avoids a misleading single-path interpretation and directs management attention to two independent drivers. The baseline also enables the sponsor to distinguish normal progress variance from an approved change in launch scope.

Learning Points

1. A Gantt chart is not a substitute for verified network logic.
2. Parallel critical paths increase schedule sensitivity.
3. External and approval dependencies require named owners and explicit assumptions.
4. Reserve should be visible and governed, not concealed in inflated durations.
5. A baseline is valuable only when updates preserve actual history.

9. Contemporary Tools, Automation, and AI

Cloud scheduling platforms improve shared access, version control, and integration with issue, finance, procurement, and collaboration systems. Automated schedule quality checks can identify missing predecessors, excessive constraints, negative float, invalid dates, and unusually long lags. These checks are useful because they expose structural defects that visual inspection may miss.

AI-assisted tools may classify activities, suggest dependencies from historical projects, estimate durations from organizational data, detect patterns in schedule updates, or generate narrative reports. Their outputs require professional validation. Historical data may encode obsolete methods, biased estimates, or inconsistent definitions of completion. Confidential project data also raises privacy, security, intellectual property, and contractual concerns. An AI-generated dependency should be treated as a proposal, not as an approved project decision.

10. Challenges, Limitations, and Best Practice

Common scheduling failures include starting with imposed dates, omitting work required for quality or governance, using summary activities as substitutes for detailed logic, confusing effort with duration, ignoring calendars, overusing hard constraints, and updating percentages complete without assessing remaining work.

Best practice includes:

• derive activities from approved scope and deliverables;
• use clear, measurable completion criteria;
• distinguish mandatory from discretionary dependencies;
• prefer logic-driven dates over manually imposed dates;
• document assumptions, calendars, lags, and external commitments;
• analyse critical and near-critical paths;
• test resource feasibility before approving the baseline;
• use progressive elaboration without erasing the original baseline;
• review schedule quality with subject-matter experts;
• integrate risk analysis when uncertainty is significant;
• preserve actual dates and approve changes transparently.

Ethically, project professionals should not manipulate logic or progress data to create favourable reports. Concealing a critical dependency, inflating float, backdating actuals, or repeatedly rebaselining without approval undermines governance and may create contractual or regulatory consequences. A credible schedule communicates inconvenient information early enough for responsible action.

Chapter Summary

Scheduling translates project scope into a time-phased model of activities, dependencies, resources, constraints, milestones, and decisions. Activity-on-node networks represent logical relationships, with finish-to-start, start-to-start, finish-to-finish, and start-to-finish relationships available where appropriate. CPM uses forward and backward passes to calculate early dates, late dates, float, and critical paths. The critical path is not necessarily permanent: resource constraints, actual progress, revised logic, and uncertainty can change it.

Gantt charts communicate planned and actual timing effectively, while network views are stronger for logical diagnosis. Critical chain methods add resource constraints and buffers to the analysis. Schedule sensitivity should be assessed through critical and near-critical paths, float, external dependencies, alternative scenarios, and, where justified, probabilistic simulation. A schedule baseline provides an approved reference for control, but it must be protected from unauthorized date changes and revised only through governance.

Professional scheduling requires more than software competence. It requires judgement about scope, dependency validity, uncertainty, resources, ethics, and the evidence needed to support progress claims. The most useful schedule is not the most detailed or visually impressive; it is the one that represents how the project can actually be delivered and supports timely managerial action.

Key Terms

Activity: A defined piece of project work with a duration and completion condition.

Activity-on-node: A network convention in which activities are represented by nodes and relationships by arrows.

Baseline: The formally approved version of the schedule used for performance comparison.

Calendar: Rules defining working time, non-working time, holidays, and shifts.

Critical chain: The longest resource- and logic-dependent sequence of activities.

Critical path: The sequence of activities with the controlling duration and normally zero total float.

Data date: The date up to which actual project status has been recorded.

Dependency: A logical relationship that governs the order or timing of activities.

Early finish: The earliest calculated completion time of an activity.

Early start: The earliest calculated start time of an activity.

Float: Allowable schedule flexibility under defined conditions.

Gantt chart: A time-scaled bar chart showing activities and their planned or actual timing.

Lag: A positive waiting period inserted into a dependency relationship.

Lead: An intentional overlap that allows a successor to begin before its predecessor is complete.

Milestone: A zero-duration event marking a significant achievement or decision.

Network diagram: A graphical representation of activities and logical relationships.

Resource leveling: Adjusting activity timing to resolve resource over-allocation, potentially changing completion.

Schedule sensitivity: The degree to which schedule outcomes respond to changes in assumptions, durations, logic, or resources.

Total float: Delay allowable without delaying the calculated project completion date.

Work breakdown structure: A hierarchical decomposition of the total project scope.

Review Questions

Short Answer Questions

1. What is the difference between an activity and a milestone?
2. Name the four standard dependency types and briefly define each.
3. Why is the maximum predecessor early finish used in a forward pass?
4. What is the purpose of a schedule baseline?
5. How does resource leveling differ from resource smoothing?

Long Answer Questions

1. Explain how a WBS is transformed into a logically complete network schedule.
2. Describe the forward-pass and backward-pass procedures in CPM, including the meaning of float.
3. Compare CPM and critical chain project management in terms of assumptions, resources, and uncertainty.
4. Discuss how constraints can improve realism but also distort schedule analysis.
5. Explain the governance requirements for updating and changing a schedule baseline.

Analytical / Application Questions

1. Construct a network for a project in which design precedes procurement and construction, while testing requires both construction and system configuration. Calculate the critical path using reasonable durations of your choice and justify your assumptions.
2. A project has two paths with durations of 28 and 27 working days. Analyse why the second path should be treated as near-critical and propose controls for schedule sensitivity.
3. A manager asks the scheduler to change actual completion dates to match the baseline. Evaluate the ethical and governance implications and recommend an appropriate response.

Multiple Choice Questions with Answers

Question 1

In an activity-on-node network, what does an arrow normally represent?

A. An activity duration

B. A logical dependency

C. A project milestone

D. A resource calendar

Correct Answer: B. A logical dependency

Question 2

Activity B has an early start of day 8 and a duration of 5 working days. Using the chapter’s time convention, what is its early finish?

A. 3

B. 8

C. 13

D. 40

Correct Answer: C. 13

Question 3

If an activity has immediate predecessors with early finishes of 10 and 14, what early start should be used under finish-to-start logic?

A. 4

B. 10

C. 12

D. 14

Correct Answer: D. 14

Question 4

Which relationship means that a successor cannot start until its predecessor finishes?

A. Finish-to-start

B. Start-to-start

C. Finish-to-finish

D. Start-to-finish

Correct Answer: A. Finish-to-start

Question 5

An activity has ES = 6 and LS = 9. What is its total float?

A. 2 days

B. 3 days

C. 6 days

D. 15 days

Correct Answer: B. 3 days

Question 6

What is the principal purpose of a schedule baseline?

A. To eliminate all project uncertainty

B. To replace the WBS

C. To provide an approved reference for performance comparison

D. To ensure every activity has zero float

Correct Answer: C. To provide an approved reference for performance comparison

Question 7

Which statement best describes a critical chain?

A. The longest sequence based only on contractual milestones

B. The shortest path after resource smoothing

C. A sequence containing only externally dependent activities

D. The longest sequence considering precedence and resource constraints

Correct Answer: D. The longest sequence considering precedence and resource constraints

Question 8

In the illustrative digital-service case, why were two paths critical?

A. They had equal total durations of 25 working days

B. They contained the same activities

C. They used identical resources throughout

D. They both had negative float

Correct Answer: A. They had equal total durations of 25 working days

Question 9

Which practice most directly protects the integrity of schedule performance data?

A. Moving actual dates to match planned dates

B. Rebaselining after every minor variance

C. Recording actual status at a defined data date

D. Removing all constraints from the schedule

Correct Answer: C. Recording actual status at a defined data date

Question 10

Under the three-point PERT approximation, with a = 2, m = 5, and b = 8 days, what is the expected duration tₑ?

A. 4 days

B. 5 days

C. 6 days

D. 15 days

Correct Answer: B. 5 days