Decision-making models: decision trees and expected values, critical path analysis (CPA), and cost-benefit analysis, including their construction, use and limitations.

What this dot point is asking

WJEC Unit 3 covers three quantitative decision-making models: decision trees (and expected values), critical path analysis (CPA) and cost-benefit analysis. The marks reward correct calculation (especially expected value and the critical path), interpretation, and a realistic view of each model's limitations - above all that they rely on estimated data and ignore qualitative factors.

The answer

Decision trees and expected values

To use a tree, calculate each option's expected value, subtract any cost of taking that option, and choose the option with the highest net expected value. The model forces the firm to quantify risk and to weigh the chance of each result, not just the best case. Its weakness is that the probabilities and values are estimates that may be wrong, and it ignores qualitative factors.

Critical path analysis (CPA)

Float (slack) is the spare time on non-critical activities (LFT - duration - EST). CPA helps a firm finish a project in the shortest time, allocate resources efficiently and identify which activities must not slip. Its limits are that activity times are estimates and it cannot account for unexpected problems.

Cost-benefit analysis

Cost-benefit analysis (CBA) weighs all the costs of a decision against all its benefits, including not just private financial costs and benefits but external (social) ones such as pollution, congestion or community gains. If the benefits outweigh the costs, the decision is worthwhile. CBA is widely used for large projects with wider social effects (a new road, a factory). Its weakness is that putting a money value on social and environmental effects is difficult and subjective.

Examples in context

Example 1. CPA on a construction project. A firm building a new unit uses CPA to schedule activities (foundations, walls, roof, fit-out), find the critical path and so the minimum completion time, and see which tasks have float and can be delayed without holding up the project. This lets it allocate workers efficiently and focus attention on the critical activities. The example shows CPA turning a complex project into a manageable, time-minimised plan.

Example 2. Cost-benefit analysis of a new factory. A council deciding whether to approve a new factory uses cost-benefit analysis, weighing private benefits (jobs, output) and costs against external effects such as extra traffic, noise and pollution against community gains. Because some social costs are hard to value in money, the analysis is partly judgemental. The example illustrates CBA's strength (it captures wider social effects) and its weakness (valuing those effects is subjective).

Try this

Q1. Define the term expected value. [2 marks]

• Cue. The sum of each possible outcome multiplied by its probability; the probability-weighted average financial result of a decision.

Q2. A decision has a 50% chance of a £80,000 gain and a 50% chance of a £20,000 gain. Calculate the expected value. [2 marks]

• Cue. EV = (0.5 x £80,000) + (0.5 x £20,000) = £40,000 + £10,000 = £50,000.