9.3 Operations Strategy – Operations Planning and Critical‑Path Analysis (CPA)
Learning objectives
- Construct a network (precedence) diagram for an operation.
- Carry out forward‑pass and backward‑pass calculations (ES, EF, LS, LF).
- Determine total float, free float and identify the critical path.
- Use the diagram to perform Capacity Planning and Analysis (CPA) and discuss its strategic implications (flexibility, innovation, ERP, lean production, benchmarking and quality).
- Explain how HR, marketing and finance decisions influence the network diagram.
Key concepts
- Operations planning – deciding what, how, when and where to produce.
- Capacity Planning and Analysis (CPA) – matching the organisation’s capacity with forecast demand.
- Network diagram (project/precedence diagram) – visual representation of activities, logical relationships and time required for each.
- Critical‑Path Analysis (CPA) – technique for calculating the longest sequence of activities (the critical path) and locating slack (float).
How operations decisions influence the network diagram
- Human‑resources (HR): staffing levels determine the realistic duration of labour‑intensive activities. A shortage of skilled workers lengthens the activity, potentially moving it onto the critical path.
- Marketing: product‑mix decisions affect the number and type of activities required (e.g., a new colour variant adds a coating step). Forecasted sales volumes from marketing set the demand level used in CPA.
- Finance: budget constraints may limit the amount of equipment that can be purchased, forcing a longer duration for a bottleneck activity or the use of overtime, both of which alter ES/EF values.
Link to wider operations‑strategy themes (Cambridge syllabus 9.3)
- Flexibility & innovation: identifying bottlenecks enables process‑innovation (new machinery, automation) or resource re‑allocation that increases volume, delivery‑time or specification flexibility.
- Enterprise Resource Planning (ERP): modern ERP systems store activity‑duration and resource‑requirement data, automatically generate and update network diagrams, and provide real‑time capacity information for CPA.
- Lean production: the critical path highlights non‑value‑adding steps; removing or streamlining these steps reduces waste and shortens the overall lead time.
- Benchmarking: total‑path duration and float values can be compared with industry best‑practice figures to assess relative performance.
- Quality control & assurance: inspection or testing activities on the critical path must be tightly controlled; any delay directly lengthens the project.
What is a network diagram?
A network diagram shows the logical flow of activities in a process. It is used to:
- Identify the activities that determine the overall project duration (critical path).
- Show parallel (concurrent) activities that can be performed at the same time.
- Calculate earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) times for each activity.
- Determine total float (TF) and free float (FF) – the amount of time an activity can be delayed without affecting the project finish or the start of a succeeding activity.
Steps to construct a network diagram
- List all activities required to complete the operation.
- Determine precedence relationships (which activities must finish before others can start).
- Assign an estimated duration (days, weeks, hours, etc.) to each activity.
- Draw the diagram – use circles or rectangles for activities (nodes) and arrows for dependencies. Number the nodes for easy reference.
- Perform the forward pass to obtain ES and EF for every activity.
- Perform the backward pass to obtain LS and LF for every activity.
- Calculate floats:
- Total float (TF) = LS – ES = LF – EF
- Free float (FF) = earliest ES of any immediate successor – EF
- Identify the critical path – activities with TF = 0.
- Use the diagram for CPA – convert activity times into resource‑hour requirements, spot bottlenecks and evaluate capacity options.
Forward‑pass / backward‑pass calculations
| Step | Formula | Explanation |
|---|
| Forward pass (left‑to‑right) |
ES = max(EF of all immediate predecessors)
EF = ES + duration |
Gives the earliest time an activity can start and finish. |
| Backward pass (right‑to‑left) |
LF = min(LS of all immediate successors)
LS = LF – duration |
Gives the latest time an activity can finish/start without delaying the project. |
Floats and the critical path
- Total float (TF) – amount an activity can be delayed without affecting the overall project finish.
- Free float (FF) – amount an activity can be delayed without affecting the start of any immediate successor.
- Activities with TF = 0 form the critical path. Any delay on these activities lengthens the whole project.
Using the diagram for Capacity Planning and Analysis (CPA)
CPA consists of three linked stages.
- Capacity forecasting – estimate future demand (units per month, quarter, …).
- Capacity evaluation – compare forecast demand with the capacity indicated by the network diagram:
- Critical‑path duration = total time required for one “unit” of output.
- Convert this duration into capacity‑hours (duration × number of resources required for each activity).
- Determine how many parallel lines, shifts or overtime slots are needed to meet demand.
- Capacity adjustment – decide on actions such as:
- Adding resources to bottleneck activities (extra machines, staff, overtime).
- Shortening the critical path by re‑sequencing, process innovation or faster technology.
- Shifting work to non‑critical activities that have slack.
Scenario (what‑if) analysis
- What if the duration of a non‑critical activity is reduced? (Check impact on free float.)
- What if an additional resource is added to a bottleneck? (Re‑calculate the critical path.)
- What if demand rises by 20 %? (Determine the extra number of parallel lines or shifts required.)
Worked example – Production of a smartphone
| Activity |
Description |
Duration (days) |
Predecessor(s) |
| A | Component procurement | 4 | – |
| B | Assembly line setup | 2 | A |
| C | Phone assembly | 5 | B |
| D | Software installation | 3 | C |
| E | Quality testing | 2 | C |
| F | Packaging & dispatch | 1 | D, E |
1. Network diagram (textual description)
(A) → (B) → (C) → splits to (D) and (E) → both converge to (F). The critical path is shown in bold in the tables below.
2. Forward‑pass (ES / EF)
| Activity | ES (days) | EF (days) |
|---|
| A | 0 | 4 |
| B | 4 | 6 |
| C | 6 | 11 |
| D | 11 | 14 |
| E | 11 | 13 |
| F | 14 * (max of 14 & 13) | 15 |
3. Backward‑pass (LF / LS)
| Activity | LF (days) | LS (days) |
|---|
| F | 15 | 14 |
| D | 14 | 11 |
| E | 14 (F cannot start before 14) | 12 |
| C | 11 (minimum of LS of D and E) | 6 |
| B | 6 | 4 |
| A | 4 | 0 |
4. Floats
| Activity | Total Float (TF) | Free Float (FF) |
|---|
| A | 0 | 0 |
| B | 0 | 0 |
| C | 0 | 0 |
| D | 0 | 0 |
| E | 1 (LS‑ES = 12‑11) | 1 (next ES‑EF = 14‑13) |
| F | 0 | 0 |
5. Critical path
Activities with zero total float: A → B → C → D → F. Critical‑path duration = 15 days.
6. Capacity evaluation (example)
- Forecast demand = 30 smartphones per month (≈ 1 unit per day).
- Critical‑path time for one unit = 15 resource‑days.
- Required capacity = 30 units × 15 days = 450 resource‑days per month.
- If the plant works 20 days/month, average daily capacity needed = 450 / 20 = 22.5 resource‑days.
- Assuming one assembly line provides 5 resource‑days per day, the firm needs at least 5 parallel lines (22.5 / 5 ≈ 4.5 → round up).
7. Scenario analysis
- What‑if the quality‑testing activity (E) is reduced from 2 days to 1 day?
New EF for E = 12, LF unchanged at 14 → TF for E becomes 2 days, but the critical path (A‑B‑C‑D‑F) remains 15 days. No capacity gain.
- What‑if an additional machine cuts the assembly time (C) from 5 days to 3 days?
Re‑calculate forward pass: EF of C = 9, EF of D = 12, EF of F = 13 → new critical‑path duration = 13 days.
Capacity requirement falls to 13 × 30 = 390 resource‑days → only 4 parallel lines may now be sufficient.
Advantages of using network diagrams
- Clear visual of the whole operation and its logical sequence.
- Identifies the critical path and bottlenecks for targeted improvement.
- Provides quantitative data (ES, EF, LS, LF, floats) for realistic CPA.
- Facilitates “what‑if” scenario analysis and supports strategic decisions on flexibility, lean redesign, benchmarking and ERP integration.
Limitations
- Accuracy depends on the reliability of activity‑duration estimates.
- Very large or highly complex processes can produce diagrams that are difficult to read.
- Network diagrams show time but not cost; additional tools (e.g., cost‑benefit analysis) are required for full financial assessment.
- Quality information must be added explicitly; the diagram itself does not capture defect rates or re‑work.
Exam‑style checklist (what the examiner looks for)
- List all activities and their logical order (predecessors).
- Assign realistic durations.
- Draw a clear network diagram (nodes + arrows, numbered).
- Perform the forward‑pass to obtain ES and EF for every activity.
- Perform the backward‑pass to obtain LS and LF for every activity.
- Calculate total float (TF) and free float (FF) for each activity.
- Identify the critical path (activities with TF = 0) and state its total duration.
- Convert the critical‑path duration into capacity‑hour requirements and compare with forecast demand.
- Discuss at least two capacity‑adjustment options (e.g., add resources, re‑sequence, introduce new technology).
- Link the analysis to wider strategic themes – flexibility/innovation, ERP support, lean production, benchmarking and quality control.