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Spec mapping: AQA 7138 Unit 3.3.4 — Change (refer to the official AQA specification document for exact wording). This lesson develops Network Analysis (also called Critical Path Analysis or CPA) at A-Level depth — the project-management technique for planning, scheduling and managing complex projects by mapping activities, dependencies and durations into a network diagram, calculating Earliest Start Times (EST) and Latest Finish Times (LFT), identifying the critical path (the longest dependency chain that determines minimum project duration) and computing float time (the slack on non-critical activities). Network analysis (Annex 8 sophisticated concept #a4) is the explicit lesson anchor. The float-time formula (Annex 7 formula 38 = LFT − duration − EST) is the standard quantitative test. The 9-mark Assess prompt for this lesson asks whether network analysis is genuinely useful for managing change projects in contemporary organisational contexts or whether it is largely an exam-question artefact whose practical utility has been overstated. Phase 2 depth here requires moving beyond mechanical EST-and-LFT calculation to engage the project-management application — how network analysis informs resource allocation, risk management and change-implementation sequencing.
Connects to:
Definition: Network analysis (Annex 8 sophisticated concept #a4), also called Critical Path Analysis or CPA, is a project-management technique developed in the late 1950s (DuPont's CPM method; US Navy PERT for the Polaris programme) for planning projects with multiple interdependent activities. The project is represented as a network diagram — nodes (events) connected by arrows (activities). The technique calculates each activity's earliest start time and latest finish time. The critical path is the longest dependency chain; critical-path activities have zero float and any slip delays the entire project. Off-critical-path activities have positive float, allowing some delay without affecting completion.
Three features make network analysis strategically loaded: (i) it surfaces hidden dependencies — the diagrammatic discipline catches sequencing constraints that intuitive planning misses; (ii) the critical-path identification directs management attention — in a complex project with dozens of activities, management attention is scarce, and the critical-path concept tells managers which activities must be managed intensively; (iii) the float concept enables resource flexibility — activities with float can be re-scheduled or re-resourced to accommodate competing demands, making float the operational input to dynamic resource allocation.
Before constructing a network diagram, the standard terms must be defined precisely:
| Term | Definition |
|---|---|
| Activity | A task or job that consumes time and (typically) resources. Represented by an arrow in activity-on-arrow diagrams. |
| Event (node) | The instantaneous point marking the start or end of one or more activities. Represented by a circle or rectangle containing the event number and timing values. |
| Duration | The time required to complete an activity, typically expressed in days, weeks or months. |
| Predecessor | An activity that must be completed before another activity can begin. |
| Earliest Start Time (EST) | The earliest point at which an activity can begin, given the completion times of its predecessors. Calculated by a forward pass through the network. |
| Latest Finish Time (LFT) | The latest point at which an activity can finish without delaying the project. Calculated by a backward pass through the network. |
| Critical path | The longest sequence of dependent activities through the network. Determines the minimum project duration. Activities on the critical path have zero float. |
| Float (total float) | The amount of time an activity can be delayed without delaying overall project completion. Formula: Float = LFT − Duration − EST. |
| Dummy activity | A zero-duration logical-dependency activity, shown as a dotted arrow, used to maintain network logic without consuming time. |
Each node is divided into three sections:
The convention: event number on top; EST on the bottom left (forward-pass output); LFT on the bottom right (backward-pass output). When EST equals LFT for a node, that node sits on the critical path.
A medium-sized UK insurance firm is implementing a new digital underwriting platform as part of a major change programme. The implementation project has nine activities:
| Activity | Description | Duration (weeks) | Predecessor |
|---|---|---|---|
| A | Requirements analysis | 4 | — |
| B | Platform architecture design | 6 | A |
| C | Data-migration planning | 3 | A |
| D | Platform build and configuration | 5 | B |
| E | Data-migration build | 3 | C |
| F | Platform testing | 4 | D |
| G | User training programme | 6 | C |
| H | Migration cut-over | 3 | E, F |
| I | Go-live and stabilisation | 2 | G, H |
Start at node 1 (time 0) and work forwards. At each node with multiple incoming paths, take the highest EST value (the activity cannot start until every predecessor is finished).
| Node | Calculation | EST (weeks) |
|---|---|---|
| 1 | start of project | 0 |
| 2 | via A: 0 + 4 | 4 |
| 3 | via B: 4 + 6 | 10 |
| 4 | via C: 4 + 3 | 7 |
| 5 | via D: 10 + 5 | 15 |
| 6 | max(via E: 7 + 3 = 10; via F: 15 + 4 = 19) | 19 |
| 7 | max(via G: 7 + 6 = 13; via H: 19 + 3 = 22) | 22 |
| 8 | via I: 22 + 2 | 24 |
Minimum project duration: 24 weeks.
Start at the final node and work backwards. At each node with multiple outgoing paths, take the lowest LFT value (every successor activity must be able to start on time).
| Node | Calculation | LFT (weeks) |
|---|---|---|
| 8 | end of project | 24 |
| 7 | via I: 24 − 2 | 22 |
| 6 | via H: 22 − 3 | 19 |
| 5 | via F: 19 − 4 | 15 |
| 4 | min(via G: 22 − 6 = 16; via E: 19 − 3 = 16) | 16 |
| 3 | via D: 15 − 5 | 10 |
| 2 | min(via B: 10 − 6 = 4; via C: 16 − 3 = 13) | 4 |
| 1 | via A: 4 − 4 | 0 |
The critical path passes through every node where EST equals LFT. From the calculations:
| Node | EST | LFT | On critical path? |
|---|---|---|---|
| 1 | 0 | 0 | Yes |
| 2 | 4 | 4 | Yes |
| 3 | 10 | 10 | Yes |
| 4 | 7 | 16 | No |
| 5 | 15 | 15 | Yes |
| 6 | 19 | 19 | Yes |
| 7 | 22 | 22 | Yes |
| 8 | 24 | 24 | Yes |
Critical path: A → B → D → F → H → I (duration: 4 + 6 + 5 + 4 + 3 + 2 = 24 weeks).
These activities must complete on time or the entire 24-week project slips.
Total float tells the project manager how much an activity can slip without delaying the project. The standard formula (Annex 7 formula 38):
Total Float = LFT (end node) − Duration − EST (start node)
| Activity | EST | Duration | LFT | Total Float |
|---|---|---|---|---|
| A | 0 | 4 | 4 | 0 |
| B | 4 | 6 | 10 | 0 |
| C | 4 | 3 | 16 | 9 |
| D | 10 | 5 | 15 | 0 |
| E | 7 | 3 | 19 | 9 |
| F | 15 | 4 | 19 | 0 |
| G | 7 | 6 | 22 | 9 |
| H | 19 | 3 | 22 | 0 |
| I | 22 | 2 | 24 | 0 |
Activities with zero float (A, B, D, F, H, I) are on the critical path. Activities C, E and G each have 9 weeks of float — they can be delayed by up to nine weeks without delaying project completion. Float is path-dependent: if Activity C is delayed by 5 weeks (within its 9-week float), the remaining float on C, E and G is reduced correspondingly. Float is a shared resource across activities on the same non-critical path, not an independent allowance.
Network analysis is more than a calculation exercise — it supports several specific change-implementation decisions:
Resource allocation. The critical-path identification tells the project manager where to concentrate resources. If Activity F (testing, critical path) faces capacity pressure, resource can be re-deployed from Activity G (training, 9 weeks float) without delaying completion.
Risk management. The critical path is the risk-concentration; critical-path activities deserve disproportionate risk-management attention — more frequent progress reviews, contingency planning, senior-management oversight. The risk vs uncertainty (Annex 8 sophisticated concept #d10) framing matters: activity durations are forecast as point estimates but real-world completion is uncertain. The PERT extension (developed for the US Navy Polaris programme) computes each duration as a weighted average of three estimates (optimistic, most likely, pessimistic) and outputs an expected project duration with associated standard deviation, supporting probabilistic statements about project completion. A-Level CPA treats durations deterministically; PERT is the contemporary refinement.
What-if analysis. What if Activity B slips by a week? Recalculate; check critical-path effect. What if Activity C is delayed by 10 weeks? It exceeds the 9-week float; the critical path shifts through C; overall duration extends by one week.
Cash-flow forecasting. Each activity has resource and cost implications; linking the network analysis to cash-flow forecasting tells the firm when capital outflows occur over the timeline, supporting working-capital planning and milestone-payment scheduling.
Opportunity cost. The opportunity cost (Annex 8 sophisticated concept #d6) dimension matters in resource allocation. Critical-path zero-float activities have higher opportunity cost than float-rich activities — an hour of project-manager attention applied to a critical-path activity has higher marginal value. Network analysis quantifies the opportunity-cost asymmetry that ad-hoc allocation ignores.
| Benefit | Why it matters |
|---|---|
| Identifies the critical path | Focuses management attention on activities that determine overall completion |
| Quantifies minimum duration | Enables realistic scheduling and customer commitment |
| Highlights float | Supports flexible resource allocation |
| Improves coordination | Forces explicit dependency identification, informing cross-team coordination |
| Supports what-if analysis | Enables evaluation of contingency scenarios and resource-reallocation moves |
| Aids cash-flow forecasting | Links spending to timeline, supporting working-capital planning |
| Limitation | Why it matters |
|---|---|
| Duration estimation is uncertain | The technique assumes durations are forecastable; in practice they are uncertain, particularly for novel activities |
| Complexity at scale | Projects with hundreds of activities require software support |
| Does not capture resource constraints | Parallel activities may require the same scarce resource; resource-levelling is a separate technique |
| Static representation | The diagram captures a moment in time; the network must be re-built as conditions change |
| Quality-of-input dependency | The analysis is only as good as the activity list and duration estimates |
| Over-reliance risk | Project managers may defer to the diagram rather than exercising judgement on emerging issues |
flowchart TD
Start["Project planning<br/>required"] --> List["List all activities,<br/>durations, predecessors"]
List --> Draw["Construct network diagram"]
Draw --> Forward["Forward pass:<br/>calculate ESTs<br/>(highest at each node)"]
Forward --> Backward["Backward pass:<br/>calculate LFTs<br/>(lowest at each node)"]
Backward --> Critical["Identify critical path<br/>(EST = LFT nodes)"]
Critical --> Float["Calculate float<br/>(LFT − Duration − EST)"]
Float --> Apply{"Apply for which<br/>purpose?"}
Apply -- "Resource allocation" --> Resource["Concentrate resource<br/>on critical-path activities"]
Apply -- "Risk management" --> Risk["Intensify oversight on<br/>critical-path activities"]
Apply -- "What-if scenarios" --> Whatif["Recalculate under<br/>scenario assumptions"]
Apply -- "Cash-flow planning" --> Cash["Link to spending<br/>schedule"]
Resource --> Iterate{"Project conditions<br/>changed?"}
Risk --> Iterate
Whatif --> Iterate
Cash --> Iterate
Iterate -- "Yes" --> Rebuild["Rebuild network<br/>with new data"]
Rebuild --> Forward
Iterate -- "No" --> Continue["Continue<br/>execution"]
style Critical fill:#1d4ed8,color:#fff
style Float fill:#15803d,color:#fff
style Rebuild fill:#b45309,color:#fff
The diagram captures the list-draw-forward-backward-identify-apply workflow of network analysis, with the iteration loop that distinguishes dynamic project management from one-off planning.
Branscombe Healthcare Group is a hypothetical UK private-healthcare provider founded 1995, headquartered in Bristol, with 2024 revenue of £165m at operating margin of 8 %. The firm operates 14 outpatient clinics across the South-West and South Wales. The board has approved a major change programme to consolidate four ageing IT systems (electronic patient records, appointment scheduling, billing, clinical-quality reporting) into a single integrated cloud-based platform — a project critical to enabling AI-augmented clinical-decision support, multi-site clinician scheduling, and regulator-required clinical-quality reporting (CQC moving to continuous-reporting in 2027). The programme is budgeted at £14m over 18 months with go-live targeted for end-Q2 2026.
The project comprises eight high-level activities:
Activity Description Duration (weeks) Predecessor P Vendor selection and contracting 8 — Q Detailed requirements design 10 P R Data-migration planning 6 P S Platform build and configuration 20 Q T Data-migration build and test 12 R U Clinician training programme 16 Q V Integration testing 8 S, T W Go-live cut-over and stabilisation 4 U, V The board has commissioned a network analysis. Initial CPA calculation shows critical path P → Q → S → V → W with project duration 50 weeks. Activities R (planning), T (migration build) and U (training) each have positive float (R: 8 weeks; T: 4 weeks; U: 6 weeks). External context: a regional competitor has just announced its own integrated-platform deployment; the CQC continuous-reporting deadline of 2027 is fixed; the clinician workforce is already operating under capacity pressure and is concerned that the training programme (Activity U) will absorb fee-earning time.
The CFO has raised a question for the board: "Is the formal network analysis genuinely useful for managing this project, or are we constructing critical-path diagrams that change every three weeks as reality intrudes?" The COO disagrees, arguing that the network analysis is essential to coordinating four parallel work-streams across the 18-month programme.
Figures and company are fabricated for illustrative purposes; not affiliated with any actual business.
Assess whether formal network analysis is genuinely useful for managing Branscombe Healthcare Group's integrated-platform programme. (9 marks)
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