9.3 Operations Strategy – Operations Planning and Critical‑Path Analysis (CPA)
Learning Objective
Identify and describe the three basic elements of a network diagram (activities, dummy activities and nodes) and use them to calculate the critical path, total and free floats, and the minimum project duration. Relate the analysis to the wider operations‑strategy context (flexibility, ERP, lean production and functional‑area influences).
1. Why Operations Planning?
- Translates strategic goals (e.g., market‑launch dates, capacity utilisation) into a timed sequence of work.
- Ensures the right resources – people, plant, finance – are available when needed.
- Provides a basis for monitoring progress, spotting delays early and taking corrective action.
2. Operational Decisions that Shape the Plan
Operations planning does not happen in isolation. The following functional areas routinely influence the choice of activities, their durations and their sequencing.
| Functional Area | Key Influence on Operations Planning |
|---|
| Human Resources |
Availability of skilled staff, training programmes and shift patterns determine realistic activity durations; recruitment or training can appear as separate activities. |
| Marketing |
Launch dates, promotional campaigns and market‑research milestones become “must‑finish‑by” nodes that constrain the network. |
| Finance |
Budget limits may restrict the number of parallel activities; cost‑benefit analysis is required before “crashing” a critical activity. |
3. Flexibility, Innovation and Technology
- Volume flexibility – ability to change output levels quickly.
- Delivery‑time flexibility – ability to accelerate or delay delivery without major cost.
- Specification flexibility – ability to modify product features.
- Process innovation (e.g., modular design, 3‑D printing) often creates new activities or shortens existing ones, directly affecting the network diagram.
4. Enterprise Resource Planning (ERP) and Network Diagrams
An ERP system integrates data on inventory, capacity, labour and scheduling. In practice the ERP feeds the following information into the CPA:
- Estimated activity durations (based on historic capacity utilisation).
- Resource availability calendars (e.g., machine maintenance windows).
- Cost data for each activity (used when deciding whether to crash).
Typical ERP data flow:
ERP → Activity List → Network Diagram → CPA → Project Schedule → ERP (updated actuals)
5. Lean Production and Its Impact on CPA
Lean concepts such as Just‑In‑Time (JIT) and waste reduction influence the network diagram in two ways:
- Reduced buffers – fewer dummy activities and shorter lead times, which often lower total float.
- Improved sequencing – activities are arranged to minimise waiting, producing a more compact critical path.
6. Network‑Diagram Elements
A network diagram is built from three fundamental components. The symbols below follow the most common A‑Level convention (activity‑on‑arrow).
| Element | Purpose | Typical Symbol | Effect on Project Duration |
|---|
| Activities (real) |
Perform the actual work required to deliver the project. |
Solid arrow (or box) labelled with activity code, duration and optionally resources/cost. |
Adds directly to the total time; may become part of the critical path. |
| Dummy activities |
Preserve logical precedence when no work is performed. |
Dashed arrow, often labelled “D” or left blank. |
No time added; only clarifies sequencing. |
| Nodes (events) |
Mark the start or finish of an activity; serve as calculation anchors. |
Circle or rectangle, numbered sequentially. |
Used to compute earliest/latest times, floats and the critical path. |
7. Critical‑Path Analysis (CPA) Mechanics
7.1 Key Terms
| Term | Definition |
|---|
| Earliest Start (ES) | Earliest time an activity can begin, given that all predecessors have finished. |
| Earliest Finish (EF) | ES + duration. |
| Latest Start (LS) | Latest time an activity can start without delaying the project. |
| Latest Finish (LF) | LS + duration. |
| Total Float (TF) | LF − EF (or LS − ES). The amount an activity can be delayed without affecting overall project duration. |
| Free Float (FF) | EF − earliest start of the next activity. Delay that does not affect any successor. |
| Critical Path | The longest path through the network; activities on this path have TF = 0. |
7.2 Forward Pass – Calculating Earliest Times
- Set the ES of the start node to 0.
- For each activity, compute EF = ES + duration.
- The ES of a successor node = the highest EF of all its immediate predecessor activities.
7.3 Backward Pass – Calculating Latest Times
- Set the LF of the final node equal to the highest EF obtained in the forward pass (the project duration).
- For each activity, compute LS = LF – duration.
- The LF of a predecessor node = the smallest LS of all its immediate successor activities.
7.4 Identifying the Critical Path
- Calculate TF for every activity (TF = LS – ES).
- Activities with TF = 0 belong to the critical path.
- The sum of the durations on the critical path equals the minimum project completion time.
8. Worked Example – Product‑Launch Project
Activities, predecessors and durations are shown below.
| Activity | Predecessor(s) | Duration (days) |
|---|
| A | Start | 4 |
| B | A | 3 |
| C | A | 5 |
| D (dummy) | B, C | 0 |
| E | D | 2 |
| F | C | 4 |
| G | E, F | 3 |
Network diagram (activity‑on‑arrow)
(0) ──► A ──► B ──► D ──► E ──► G ( )
│ ▲ ▲
│ │ │
└──► C ────┘ │
│ │
└────► F ───────┘
Forward Pass
- Node 0: ES = 0
- A: ES = 0, EF = 4
- B: ES = 4, EF = 7
- C: ES = 4, EF = 9
- D (dummy): ES = max(EF B, EF C) = 9, EF = 9
- E: ES = 9, EF = 11
- F: ES = 9, EF = 13
- G: ES = max(EF E, EF F) = 13, EF = 16
Project duration = 16 days.
Backward Pass
- Node G: LF = 16, LS = 13
- E: LF = LS G = 13, LS = 11
- F: LF = LS G = 13, LS = 9
- D (dummy): LF = min(LS E, LS F) = 11, LS = 11 (duration 0)
- B: LF = LS D = 11, LS = 8
- C: LF = LS D = 11, LS = 6
- A: LF = min(LS B, LS C) = 6, LS = 2
Floats
| Activity | ES | EF | LS | LF | Total Float |
|---|
| A | 0 | 4 | 2 | 6 | 2 |
| B | 4 | 7 | 8 | 11 | 4 |
| C | 4 | 9 | 6 | 11 | 2 |
| D (dummy) | 9 | 9 | 11 | 11 | 0 |
| E | 9 | 11 | 11 | 13 | 0 |
| F | 9 | 13 | 9 | 13 | 0 |
| G | 13 | 16 | 13 | 16 | 0 |
Critical Path
Activities with zero total float: D → E → G. The 16‑day duration is dictated by this path.
9. Using the CPA Results
- Zero‑float activities are critical – any delay lengthens the whole project.
- Positive float offers flexibility:
- Delay start to free resources for critical work.
- Re‑sequence non‑critical activities to reduce idle time.
- Apply “crashing” (add resources) to a critical activity if the cost‑benefit analysis (Finance) justifies it.
- Float information supports risk assessment, stakeholder communication and contingency planning.
10. Benefits and Limitations of CPA
| Benefits | Limitations |
|---|
- Clear visualisation of sequence and dependencies.
- Identifies the minimum possible project duration.
- Highlights activities that must be closely monitored.
- Facilitates resource allocation, schedule compression and “what‑if” analysis.
|
- Assumes deterministic activity durations (no uncertainty).
- Ignores resource constraints – may suggest parallel work that is infeasible.
- Becomes cumbersome for very large projects.
- Does not directly incorporate cost, quality or sustainability considerations.
|
11. Linking CPA to the Wider Operations Strategy
- Flexibility – Activities with high free float can be used to absorb demand variability.
- ERP integration – Real‑time updates from ERP keep the network diagram current, allowing dynamic re‑planning.
- Lean focus – Reducing waste shortens or eliminates dummy activities, often shrinking the critical path.
- Innovation – New technologies may replace several activities with a single, shorter one, changing the network topology.
12. Summary Table – Network‑Diagram Elements
| Element |
Purpose |
Typical Symbol |
Effect on Project Duration |
| Activities (real) |
Perform the actual work required to deliver the project. |
Solid arrow (or box) with code & duration |
Adds directly to total time; may become part of the critical path. |
| Dummy activities |
Maintain logical precedence where no work is done. |
Dashed arrow, often labelled “D” |
No time added; only clarifies sequencing. |
| Nodes (events) |
Mark start or finish points; serve as calculation anchors. |
Circle or rectangle, numbered |
Used to compute ES, EF, LS, LF and to identify the critical path. |
13. Key Take‑aways
- Operations planning converts strategic objectives into a timed sequence of activities.
- A network diagram consists of real activities, dummy activities and nodes – each has a specific visual convention.
- CPA uses a forward‑pass and backward‑pass to obtain earliest/latest times; total and free floats follow directly.
- Zero‑float activities form the critical path and dictate the shortest possible project duration.
- Understanding floats enables managers to re‑allocate resources, manage risk, and compress schedules where justified.
- CPA should be interpreted alongside flexibility requirements, ERP data, lean principles and functional‑area constraints for a realistic operations‑strategy plan.