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CMA Final · Strategic Cost Management

Network Analysis: PERT and CPM for CMA Final

Network analysis plans a project as a diagram of activities and events. CPM uses fixed times to find the critical path, the longest path that sets project duration. PERT uses three time estimates and probability. To solve a question, draw the network, run forward and backward passes, find float, then apply PERT or crashing as asked.

What this chapter covers

Network analysis is the tool for planning, scheduling and controlling a project made of many linked activities. You draw the activities as a network, estimate their times, and find which activities decide the project's finish date. The chapter covers the Critical Path Method (CPM), which uses a single time per activity, and PERT, which uses three estimates and treats duration as uncertain.

The chapter builds in layers. You start with diagram rules, then the forward and backward pass, then float. PERT adds probability on top of the same network. Crashing adds cost: you shorten the project by spending more on selected activities. Resource levelling and updating deal with how a plan is managed once the project is running.

In Strategic Cost Management this chapter sits with the decision-oriented topics. Crashing is a time-cost trade-off, so it links to cost behaviour, relevant costing and project cost control. Questions are numerical, so the chapter rewards practice more than reading.

Network analysis is mostly procedural, so a student who practises can score full marks on a numerical question, which is not true of many other topics. The same skills can appear in the compulsory MCQ section (for example, critical path length or float) and in the descriptive section as a full problem with a recommendation. The steps are mechanical, so you can learn them in a short time and apply them reliably under exam pressure. Because the chapter stacks, a firm grip on the early topics also makes the later, more complex ones easy.

Network Analysis - PERT, CPM: topics in the order to study them

  1. 1Network Analysis Basics: Activities, Events, DiagramsYou cannot do any calculation until you can draw a correct network with proper events, dummies and numbering.
  2. 2Critical Path Method (CPM) and Critical PathThe forward and backward pass and the critical path are the base for every later topic.
  3. 3Float and Slack: Total, Free, IndependentFloat is calculated from the earliest and latest times you just found, and it shows which activities have room to move.
  4. 4PERT: Three Time Estimates and ProbabilityPERT reuses the same network and critical path, adding expected time, variance and a normal-distribution probability.
  5. 5Project Crashing and Time-Cost Trade-offCrashing needs the critical path and float skills, then adds cost slopes and repeated decisions.
  6. 6Resource Levelling, Updating and ApplicationsThis is the management layer on top of the calculations, so it is best learnt last, once the core methods are secure.

How to prepare Network Analysis - PERT, CPM

Treat this chapter as a skill, not a reading task. Aim to solve each type of problem the same way every time.

  1. Learn the drawing rules first: one start event, one end event, no loops or cycles, and dummy activities only where needed. Redraw three networks from activity tables without looking at a solution.
  2. Fix a routine for the forward pass and backward pass. Write earliest and latest times on the diagram, and check that the last event has the same earliest and latest time.
  3. List every path and its length to confirm the critical path. This catches arithmetic slips in the passes.
  4. Calculate total float, free float and independent float for each activity, and keep the definitions written in one line each.
  5. For PERT, write the expected time and variance formulas from memory, then practise the probability step using critical-path variance only, with the normal table.
  6. For crashing, build a table of normal time, crash time, cost slope and maximum crash. Shorten the cheapest critical activity first, and recheck for new critical paths after each step.
  7. Finish with mixed timed questions and always end with a clear conclusion: project duration, critical path, cost or probability.

Common mistakes in Network Analysis - PERT, CPM

  • Drawing a network with missing or unnecessary dummy activities

    Fix: Check each activity's predecessors against the arrows you drew. Add a dummy when two activities would share the same head and tail events (so each activity has a unique identification), or when a dependency has to be shown for only some of the activities that share a node.

  • Errors in the backward pass

    Fix: At an event with several outgoing activities, the latest time is the minimum of (latest time of the head event − duration) over those activities. Then cross-check by listing all paths and their lengths.

  • Mixing up total, free and independent float

    Fix: Remember what each one protects. Total float is the delay an activity can take without delaying project completion. Free float is the delay possible without delaying the earliest start of the succeeding activity. Independent float is the delay possible when the predecessor finishes at its latest and the successor starts at its earliest. The order is IF ≤ FF ≤ TF, and a negative independent float is taken as zero.

  • Adding variances of all activities in PERT

    Fix: Add variances of critical-path activities only. Also use the expected times, not the most likely times, to find the critical path.

  • Crashing the wrong activity or crashing beyond what pays

    Fix: Only crash critical activities, within their maximum crash limit. After each step, recompute path lengths. When two paths are critical, crash both together or choose a common activity if it is cheaper.

  • Stopping at the numbers without a recommendation

    Fix: State the final project duration, the critical path, and for crashing the total cost and whether the saving or penalty justifies the extra spend.

Last-day revision: Network Analysis - PERT, CPM

  • Critical path is the longest path through the network and fixes the project duration.
  • Activities on the critical path have zero total float.
  • Forward pass gives earliest times; backward pass gives latest times.
  • Total float = latest finish − earliest start − duration.
  • Free float = earliest time of head event − earliest time of tail event − duration. This equals the earliest time of the head event − earliest finish of the activity.
  • Independent float = earliest time of head event − latest time of tail event − duration. A negative value is taken as zero. It assumes the tail event occurs at its latest time (the predecessor finishes as late as possible) and the head event at its earliest time (the successor starts as early as possible), so using it does not affect any other activity. Independent float is less than or equal to free float, which is less than or equal to total float (IF ≤ FF ≤ TF).
  • PERT expected time te = (to + 4tm + tp) ÷ 6.
  • PERT variance of an activity = ((tp − to) ÷ 6)².
  • Project variance is the sum of variances of critical-path activities only; standard deviation = √variance.
  • Z = (target time − expected project time) ÷ project standard deviation.
  • Cost slope = (crash cost − normal cost) ÷ (normal time − crash time).
  • Crash the critical activity with the lowest slope first, and recheck whether other paths become critical.

Network Analysis - PERT, CPM practice questions

Network Analysis - PERT, CPM in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Network Analysis - PERT, CPM: frequently asked questions

Is network analysis difficult for CMA Final?

It is procedural, so most students find it manageable with practice. The risk lies in arithmetic slips in the passes and in crashing. A fixed routine and cross-checking by path length reduce errors.

What is the difference between PERT and CPM?

CPM uses one fixed time for each activity and is used where durations are well known, often with a time-cost trade-off. PERT uses optimistic, most likely and pessimistic times to handle uncertainty and gives the probability of finishing by a given date.

Do I need the normal distribution table for PERT?

Yes, for probability questions you convert the target time to a Z value and read the probability from the standard normal table. Check whether the question supplies the table values, and practise reading them.

How should I answer a crashing question?

Calculate the cost slope for every activity, then shorten the cheapest critical activity one step at a time. After each step recheck all paths, track the total cost, and end with the best duration and its cost.