Schedule Planning and Network Analysis

Introduction and context

A project schedule converts scope into a time-based execution logic. It identifies what must be done, how long activities may take, the order in which work can proceed, the resources required, and the dates by which deliverables should be achieved. In operations management, scheduling is not merely the production of a calendar. It is a decision system for coordinating constrained people, equipment, suppliers, information, cash, and managerial attention.

A credible schedule must satisfy three tests. First, it must be logically valid: activities cannot begin before their predecessors permit them. Second, it must be resource-feasible: the organisation must possess or obtain the people, equipment, materials, and facilities required. Third, it must be sufficiently robust: reasonable variation in activity duration or resource availability should not immediately make the plan unusable.

Network analysis provides the analytical foundation for these tests. The critical path method (CPM) identifies activities that determine the minimum project duration under specified assumptions. Programme Evaluation and Review Technique (PERT) represents uncertainty in activity durations. Critical chain project management (CCPM) incorporates resource constraints and protects the plan with strategically placed buffers. Schedule compression, resource levelling, and milestone control then support managerial intervention when the baseline is infeasible or performance deviates from plan.

Learning objectives

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

1. Decompose project scope into activities, milestones, and work packages.
2. Estimate activity durations using suitable methods and document assumptions.
3. Construct precedence networks using activity-on-node notation.
4. Calculate early dates, late dates, critical path, and total float.
5. Apply PERT expected duration and variance calculations appropriately.
6. Explain resource loading, resource levelling, critical chain logic, and buffers.
7. Evaluate crashing and fast-tracking alternatives for schedule compression.
8. Develop and govern a feasible, measurable, and ethically defensible schedule.

From scope to a schedulable model

Work breakdown and activities

Scheduling begins with a work breakdown structure (WBS). The WBS decomposes the project deliverable into progressively smaller components until work packages are sufficiently defined for estimation, assignment, monitoring, and acceptance. A work package is not automatically an activity. It may contain several activities, each producing an identifiable intermediate result.

An activity should have a clear start condition, finish condition, responsible owner, expected output, and measurable completion criterion. Activities that are excessively large conceal risk and make progress difficult to assess; activities that are excessively small create administrative burden and false precision.

A practical activity register normally includes an identifier, description, predecessor(s), successor(s), duration estimate, calendar, resource requirement, cost information, assumptions, and risk notes. The register is the auditable link between the WBS, network model, schedule baseline, and actual performance data.

Milestones and dependencies

A milestone is a zero-duration event used to mark a significant decision, approval, handover, or deliverable. Examples include “design approved,” “permit received,” and “system accepted.” Milestones should represent meaningful control points rather than arbitrary reporting dates.

Dependencies may be:

• Mandatory: imposed by the nature of the work, such as testing after assembly.
• Discretionary: preferred sequencing chosen by the project team, such as completing one area before another.
• External: controlled outside the project, such as a regulator’s approval or a supplier’s delivery.
• Internal: controlled by the project team.

The standard logical relationships are shown below.

Lags add waiting time to a relationship; leads allow overlap. A lead should be used cautiously because it can obscure the real logic and increase coordination risk. Every lead or lag should have an operational explanation, such as curing time, statutory review, or staged access.

Duration estimation

Duration is elapsed calendar time, not necessarily labour effort. Eight person-days of effort may require one person for eight working days, two people for four working days, or a different elapsed duration if coordination and learning effects are present. Therefore, effort, duration, resource quantity, and calendar availability must be recorded separately.

Common estimating approaches include:

• Analogous estimating: uses actual duration from a similar completed project. It is fast but depends heavily on similarity and data quality.
• Parametric estimating: applies a measurable rate, such as hours per unit, to the quantity of work.
• Bottom-up estimating: estimates detailed activities and aggregates them. It is usually more accurate but requires greater definition.
• Three-point estimating: develops optimistic, most likely, and pessimistic estimates to represent uncertainty.
• Expert judgement: draws on specialist knowledge, ideally supported by historical evidence and independent review.

Estimates should state the assumed scope, productivity, calendar, resource skill, technology, constraints, and confidence level. A duration without assumptions is not a reproducible estimate.

PERT estimation

PERT uses three time estimates:

• a: optimistic duration under favourable conditions;
• m: most likely duration;
• b: pessimistic duration under adverse but credible conditions.

The beta-distribution approximation gives the expected duration:

and the estimated variance:

Here, t_e is in time units and σ² is in squared time units. The standard deviation is σ = (b − a) ÷ 6. PERT assumes that the three estimates adequately describe uncertainty and that the weighted average is a useful approximation. It does not guarantee a beta distribution, and it should not be used to disguise weak estimating evidence.

Worked example. Suppose an approval activity has a = 2 days, m = 5 days, and b = 14 days.

t_e = (2 + 4×5 + 14) ÷ 6 = 36 ÷ 6 = 6 days.

The variance is ((14 − 2) ÷ 6)² = 4 days², and the standard deviation is 2 days. The wide range indicates material uncertainty, even though the expected duration is six days.

Precedence diagrams and network logic

The most common modern representation is activity-on-node (AON), in which each node represents an activity and arrows represent precedence relationships. A network should have a clear start and finish, no circular logic, and no unexplained dangling activities. Activities that can proceed in parallel should be shown in parallel; forcing a serial relationship increases the calculated duration without operational justification.

The critical path method generally uses a deterministic duration for each activity. For an activity with duration d_i, the forward pass calculates early start and early finish:

For a project start at time zero, an activity with no predecessors has ES_i = 0. Otherwise:

where the maximum is taken over all immediate predecessors j. The maximum is necessary because the activity must wait for its latest-arriving predecessor.

The backward pass begins with the project finish time T, normally the largest early finish. For a terminal activity, LF_i = T. For other activities:

where k denotes each immediate successor. Late start is:

Total float is:

All dates use the same project calendar. A zero-float activity is critical under the stated model. Negative float indicates that the imposed completion date cannot be achieved with the current logic and durations unless assumptions, resources, scope, or methods change.

Worked CPM example

Consider the following project network. Activities A and B start the project. C follows A; D follows B; E follows both C and D; F follows E.

Forward pass:

• A: ES 0, EF 4.
• B: ES 0, EF 3.
• C: ES 4, EF 9.
• D: ES 3, EF 9.
• E: ES max(9, 9) = 9, EF 11.
• F: ES 11, EF 14.

The project duration is 14 days. Backward pass:

• F: LF 14, LS 11.
• E: LF 11, LS 9.
• C: LF 9, LS 4.
• D: LF 9, LS 3.
• A: LF 4, LS 0.
• B: LF 3, LS 0.

Thus every activity has zero total float, and there are two critical paths: A–C–E–F and B–D–E–F. Multiple critical paths increase schedule risk because delay in either branch can delay the project. The result is not that every activity is equally risky; it means every activity has no timing flexibility in this baseline.

Float interpretation

Total float is the amount an activity can be delayed without delaying the calculated project completion date, assuming the rest of the network remains unchanged. Free float is the delay possible without delaying the early start of any immediate successor. For an activity with successors:

where k denotes immediate successors. Free float cannot exceed total float in a standard finish-to-start network. Float is a property of the current model, not a permanent resource owned by an individual manager. Consuming float may be acceptable, but it should be visible and governed.

Milestones, baselines, and schedule control

A schedule baseline is the approved version against which actual progress and forecast dates are compared. Baseline approval should follow validation of scope, logic, calendars, resources, assumptions, and stakeholder commitments. A baseline is not an immutable promise; changes should be controlled through documented change management.

Milestone trend analysis tracks forecast milestone dates over successive reporting periods. A milestone that repeatedly moves later may reveal unresolved dependencies, optimistic estimates, insufficient resources, or deliberate concealment of bad news. Good governance requires early escalation rather than retrospective reclassification of incomplete work as “nearly complete.”

Schedule performance may be integrated with earned value management. The schedule performance index is:

where EV is earned value—the budgeted value of completed work—and PV is planned value—the budgeted value of work scheduled to be completed. SPI = 1 indicates performance equal to the baseline in value terms; a value below 1 indicates less work has been earned than planned. SPI is not a direct measure of calendar delay and should be interpreted with milestone forecasts and network analysis.

Resource feasibility and levelling

A technically valid network may be infeasible when several activities require the same scarce resource simultaneously. Resource loading maps resource demand against time. If demand exceeds availability, the schedule must be changed through altered sequencing, additional capacity, different methods, outsourcing, or acceptance of a later completion date.

Resource smoothing uses available float to move activities while preserving the required completion date. Resource levelling resolves over-allocation even if the project finish date changes. The distinction matters: smoothing protects the date but may not eliminate all overload; levelling prioritises feasibility.

A sound levelling process is:

1. Identify resource types, calendars, skills, and maximum availability.
2. Load resources against activities, including part-time and shared assignments.
3. Locate periods of over-allocation.
4. Reschedule noncritical activities within float where possible.
5. Reconsider priorities, split activities only when technically valid, and evaluate overtime or additional resources.
6. Recalculate the network because levelling can create a new critical path.
7. Obtain approval for any changed completion date, cost, risk, or quality consequence.

Resource-driven schedules should not assume that adding people always shortens duration. Communication overhead, scarce expertise, learning curves, and work-front limitations can produce diminishing or negative returns.

Critical chain and buffers

Critical chain project management extends critical-path thinking by considering both precedence and resource dependencies. The critical chain is the longest sequence of dependent activities after resource constraints are taken into account. CCPM commonly reduces protective safety embedded in individual activity estimates and places aggregated protection in buffers.

The principal buffers are:

• Project buffer: placed between the critical chain and the project completion date.
• Feeding buffer: protects the critical chain from delays on noncritical feeding chains.
• Resource buffer: signals that a key resource must be ready when required; it is generally an alert mechanism rather than time added to the network.

Buffer management monitors the rate at which buffer is consumed relative to work progress. CCPM can improve focus and reduce local multitasking, but its benefits depend on credible estimates, disciplined priority rules, reliable resource data, and organisational acceptance. It is not a licence to remove all contingency or to report optimistic durations as commitments.

Schedule compression

Schedule compression seeks a shorter duration without reducing project scope. It should be applied only after confirming that the delay is real, the logic is correct, and the quality and safety implications are understood.

Crashing

Crashing adds cost or resources to shorten activity duration. Candidates should be selected using incremental cost per unit of time saved:

The numerator is incremental cost and the denominator is time saved, so the unit is currency per day or other time unit. The formula assumes a meaningful linear approximation between normal and crash points. Real projects may have nonlinear costs, discrete staffing options, or quality limits.

Example. An activity normally costs 12,000 currency units and takes 10 days. It can be crashed to 7 days at 15,600 units. Its cost slope is (15,600 − 12,000) ÷ (10 − 7) = 1,200 currency units per day saved. Crashing is valuable only if the activity is on the current critical path and the resulting network remains critical after each intervention.

Fast-tracking

Fast-tracking overlaps activities that were originally sequential. It can reduce elapsed time without direct crash cost, but it increases rework, coordination, interface, and safety risk. For example, procurement may begin using an approved preliminary design, but later design changes may require rework. Fast-tracking should be supported by explicit decision rights, interface controls, and contingency planning.

A rational compression sequence is to identify the current critical path, assess feasible alternatives, compare incremental cost and risk, compress the lowest-cost acceptable critical activity, recalculate the network, and repeat until the target is achieved or no acceptable option remains. Compressing noncritical activities normally does not shorten the project.

Detailed applied case: illustrative warehouse automation project

Background

The following is a fictional illustrative case. A distribution company plans to install an automated picking system in an operating warehouse. The project must maintain customer service while integrating conveyors, software, safety controls, and operator training.

Problem

The initial plan promised completion in 30 working days, but the resource-loaded schedule showed that the controls engineer was assigned simultaneously to software integration, safety testing, and commissioning. In addition, the supplier’s acceptance test was treated as an informal dependency rather than a milestone.

Analysis

The project team created the following high-level activities:

The precedence-only forward pass gives: A 0–4, B 4–12, C 4–14, D 12–18, E 18–23, F 23–26, G 14–18, and H 26–30. The planned duration is therefore 30 days, with A–B–D–E–F–H as the critical path. G has two days of float because H waits for F at day 26.

Resource analysis showed that the same controls engineer was needed for E, F, and H. This did not create an issue in the pure precedence model because those activities are sequential, but the engineer was also required for a two-day supplier support task not included in the network. The omitted work made the schedule incomplete. The team also discovered that safety inspection required a regulator appointment with a five-day booking lead time.

Approach and solution

The team added the supplier support activity, represented the regulator appointment as an external milestone, and separated “inspection requested” from “inspection completed.” They then evaluated three options:

1. Baseline: retain the 30-day logic and accept a high risk of missing the inspection window.
2. Crashing: hire an additional commissioning technician for 3,000 currency units, reducing commissioning by one day.
3. Fast-tracking: begin operator training using a simulator before final software configuration, reducing the training interface delay but increasing change-management risk.

The selected solution combined a modest crash with controlled fast-tracking. Training materials were prepared from a configuration freeze, while hands-on training began only after a validated simulator test. The regulator appointment was booked before installation began. A two-day project buffer was added after internal acceptance, not as a substitute for regulatory compliance.

Outcome

The revised schedule completed internal acceptance on day 29 and regulatory handover on day 31. The organisation did not achieve the original day-30 operational target, but it avoided unsafe commissioning and uncontrolled rework. The additional cost was lower than the estimated cost of service disruption and emergency contractor mobilisation.

Learning points

• A network is only as complete as the work it represents.
• External dependencies require explicit milestones and owners.
• Resource feasibility must be tested after precedence analysis.
• Fast-tracking is a risk trade-off, not free time.
• A buffer should protect a defined uncertainty and should not conceal missing scope.
• Safety and regulatory activities cannot be compressed by administrative pressure.

Challenges, limitations, and governance

Network calculations are exact only relative to their assumptions. Common limitations include uncertain scope, biased estimates, hidden dependencies, calendar inconsistency, omitted work, excessive use of constraints, and treating probability-based forecasts as guarantees. A mathematically elegant schedule can therefore be operationally false.

Schedule governance should establish a schedule owner, coding standards, calendars, status dates, update rules, baseline approval authority, change thresholds, and escalation routes. Progress rules must be objective. “Started” is not the same as “complete,” and percentage-complete claims should be based on observable outputs or an approved earned-value method.

Ethically, schedule pressure must never justify unsafe work, falsified progress, suppression of adverse forecasts, unpaid excessive overtime, or deliberate underestimation intended to secure approval. Managers should distinguish a challenging target from an impossible commitment and should communicate uncertainty transparently.

Digital scheduling systems can calculate networks, test scenarios, integrate resource data, and produce dashboards. Artificial intelligence can assist with anomaly detection, duration benchmarking, and risk forecasting, but its outputs require human validation. Historical data may encode past bias, omit failed projects, or reflect different operating conditions. AI-generated schedules should be explainable, traceable to source data, and subject to approval by accountable professionals.

Best-practice checklist

Before approving a schedule, the project team should verify that:

• scope and WBS are complete enough for control;
• every activity has an owner, output, duration, calendar, and assumption;
• dependencies are evidence-based and leads/lags are justified;
• the network has been forward- and backward-calculated;
• critical and near-critical paths are understood;
• resource demand does not exceed credible availability;
• external approvals and supplier commitments are represented;
• uncertainty, buffers, and contingency are visible;
• compression alternatives include cost, quality, safety, and rework effects;
• baseline changes are authorised and traceable;
• progress measurement rules are agreed before execution.

Chapter Summary

Schedule planning transforms project scope into an executable model of activities, dependencies, durations, resources, milestones, and uncertainty. AON networks and CPM forward and backward passes determine early dates, late dates, project duration, and float. PERT incorporates optimistic, most likely, and pessimistic estimates, but its statistical outputs remain dependent on the quality of those estimates and the suitability of its assumptions.

A precedence-feasible schedule may still be impossible when resources are over-allocated. Resource smoothing uses float to protect a required date, whereas resource levelling prioritises feasible allocation even when completion is delayed. Critical chain management adds resource dependencies and uses project, feeding, and resource buffers. Crashing trades additional cost for shorter duration; fast-tracking trades overlap for increased coordination and rework risk. Both require repeated network recalculation.

Effective schedule management combines quantitative analysis with professional judgement, transparent governance, ethical reporting, and continuous forecast review. The best schedule is not the one with the most optimistic date; it is the one whose logic, resources, risks, assumptions, and decision consequences are understood and controllable.

Key Terms

Activity: A defined piece of project work with a measurable start and finish.

Activity-on-node: Network notation in which nodes represent activities and arrows represent relationships.

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

Buffer: Deliberate time protection allocated to absorb specified uncertainty or delay.

Crashing: Shortening activity duration by adding resources or incurring additional cost.

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

Critical path: The sequence of activities determining the minimum calculated project duration.

Duration: Elapsed time required to complete an activity under stated assumptions.

Fast-tracking: Overlapping activities that were previously planned in sequence.

Float: Schedule flexibility available before a defined date or successor is delayed.

Forward pass: Calculation of early start and early finish dates.

Lag: Waiting time inserted into a dependency relationship.

Milestone: A zero-duration event marking an important decision, approval, or deliverable.

PERT: A technique using three duration estimates to model expected time and uncertainty.

Precedence relationship: A logical rule governing the order of activities.

Resource levelling: Rescheduling to eliminate resource over-allocation, potentially changing completion date.

Resource smoothing: Adjusting activities within float to reduce variation while preserving the required date.

Schedule compression: Reducing project duration without reducing scope.

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

WBS: Hierarchical decomposition of project scope into manageable deliverables and work packages.

Review Questions

Short Answer Questions

1. Distinguish effort from duration and explain why the distinction matters in scheduling.
2. What is the difference between a mandatory dependency and a discretionary dependency?
3. Define total float and explain what a zero-float activity indicates.
4. State the main difference between resource smoothing and resource levelling.
5. Why should a schedule baseline be subject to change control?

Long Answer Questions

1. Explain how a WBS is converted into an activity register and then into an AON network.
2. Describe the CPM forward and backward passes, including the assumptions behind the calculations.
3. Explain PERT estimation, including its equations, interpretation, and limitations.
4. Compare crashing, fast-tracking, and critical chain buffers as methods of schedule risk management.
5. Discuss the governance and ethical responsibilities involved in reporting schedule performance.

Analytical / Application Questions

1. Activities A and B start at time zero. A takes 6 days and precedes C, which takes 4 days. B takes 5 days and precedes D, which takes 7 days. E takes 2 days and follows both C and D. Calculate the project duration and identify the critical path.
2. An activity has optimistic, most likely, and pessimistic durations of 3, 6, and 15 days. Calculate its PERT expected duration and variance, and interpret the result for schedule risk.
3. A project is two days late because a noncritical activity has consumed all its float, while a critical activity remains unchanged. Analyse whether crashing that noncritical activity will recover the project completion date, and recommend the information needed before deciding.

Multiple Choice Questions with Answers

Question 1

In an AON network, the early start of an activity with several immediate predecessors is normally determined by which operation?

A. The minimum of predecessor early finishes

B. The maximum of predecessor early finishes

C. The average of predecessor late starts

D. The sum of predecessor durations

Correct Answer: B. The maximum of predecessor early finishes

Question 2

Using PERT, what is the expected duration when a = 2 days, m = 5 days, and b = 14 days?

A. 4 days

B. 5 days

C. 6 days

D. 7 days

Correct Answer: C. 6 days

Question 3

Which statement best describes total float?

A. Time that can always be transferred to another project

B. Delay permitted without delaying the calculated project completion date, assuming other activities remain unchanged

C. The duration of all noncritical activities combined

D. Time added automatically to every critical activity

Correct Answer: B. Delay permitted without delaying the calculated project completion date, assuming other activities remain unchanged

Question 4

What is the principal purpose of resource levelling?

A. To eliminate resource over-allocation, even if the project finish date changes

B. To make every activity critical

C. To remove all project contingency

D. To calculate earned value

Correct Answer: A. To eliminate resource over-allocation, even if the project finish date changes

Question 5

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

A. Start-to-start

B. Finish-to-finish

C. Finish-to-start

D. Start-to-finish

Correct Answer: C. Finish-to-start

Question 6

An activity normally costs 12,000 units for 10 days and can be crashed to 7 days for 15,600 units. What is its cost slope?

A. 600 units per day saved

B. 1,000 units per day saved

C. 1,200 units per day saved

D. 3,600 units per day saved

Correct Answer: C. 1,200 units per day saved

Question 7

Which technique shortens a schedule by overlapping activities that were previously sequential?

A. Crashing

B. Fast-tracking

C. Resource smoothing

D. Milestone trending

Correct Answer: B. Fast-tracking

Question 8

In critical chain project management, what primarily protects the project completion date from delays on the critical chain?

A. Project buffer

B. Resource histogram

C. Free float

D. A mandatory lead

Correct Answer: A. Project buffer

Question 9

If an activity has an early finish of day 12 and its successor has an early start of day 15, what is the activity’s free float in a standard finish-to-start network?

A. 2 days

B. 3 days

C. 12 days

D. 15 days

Correct Answer: B. 3 days

Question 10

What does an SPI value below 1 generally indicate in earned value analysis?

A. More work has been earned than planned

B. The project has no critical path

C. Less budgeted work has been earned than was planned by the status date

D. The project is necessarily over budget

Correct Answer: C. Less budgeted work has been earned than was planned by the status date