Multiple Control Measures

Video coming soon3 worked examples

Theory

In reality, very few projects are delayed by just one single issue. There are usually multiple different risk factors impacting a project, and consequently, a business will have multiple different control measures available to choose from.

1. Dealing with Multiple Probabilities

When a project can be delayed by Event A or Event B or both, you must find the combined probability of a delay occurring before you can calculate the expected penalty.

Because we are dealing with multiple sequential or simultaneous probabilities, tree diagrams are the best mathematical tool to use to find the overall chance of a delay.

Exam Shortcut:

Remember the "At Least One" rule from Section 7! Instead of calculating all the combinations of things going wrong, simply calculate the probability of everything going perfectly (e.g., No Delay × No Delay) and subtract your answer from 1.

2. Evaluating Multiple Control Measures

When a company is choosing between several different control measures (e.g., Option 1, Option 2, or doing both), you must conduct a separate cost-benefit analysis for every single option.

The Golden Rule: When you pay for a specific control measure, it usually only eliminates that specific risk. The other risks will still exist, and you must factor their remaining expected penalty into your calculation.

\text{Expected Cost of Option 1} = \text{Upfront Cost of Option 1} + (\text{Remaining Probability of Delay} \times \text{Financial Penalty})

To make your final decision, you must compare all your answers and recommend the option that results in the lowest overall expected cost.

Worked examples

Example 1

Example 1: Calculating the Combined Probability of a Delay

A catering company is supplying food for a large corporate event. If they are late, they will face a contractual penalty of £4,000. The company has identified two independent reasons for a possible delay:

Their industrial oven breaks down (Probability = 0.1).
Their delivery van breaks down (Probability = 0.2).

(a) Calculate the probability that the catering company is delayed.

(b) Calculate the expected cost of taking no control measures.

(a) A delay happens if the oven breaks, the van breaks, or both. We use the shortcut: find the probability of a completely perfect day and subtract it from 1.

$P(\text{No oven break}) = 1 - 0.1 = 0.9$
$P(\text{No van break}) = 1 - 0.2 = 0.8$
$P(\text{Perfect day}) = 0.9 \times 0.8 = 0.72$
$P(\text{Delay}) = 1 - 0.72 = 0.28$

(b) Expected cost (doing nothing):

$\text{Expected Cost} = 0.28 \times \text{\pounds}4000 = \text{\pounds}1,120$ .

Example 2

Example 2: Evaluating Single Control Measures

Following on from the scenario in Example 1, the catering company is considering two separate control measures:

Measure A: Rent a backup oven for the day at a cost of £300.
Measure B: Rent a backup delivery van for the day at a cost of £400.

(a) Calculate the expected cost of taking only Control Measure A.

(b) Calculate the expected cost of taking only Control Measure B.

(a) Measure A (Backup Oven): This eliminates the oven risk, but the van could still break down (P = 0.2).

$\text{Expected Cost} = \text{Cost of Measure} + (\text{Remaining Risk} \times \text{Penalty})$

$\text{Expected Cost} = \text{\pounds}300 + (0.2 \times \text{\pounds}4000) = \text{\pounds}300 + \text{\pounds}800 = \text{\pounds}1,100$ .

(b) Measure B (Backup Van): This eliminates the van risk, but the oven could still break down (P = 0.1).

$\text{Expected Cost} = \text{Cost of Measure} + (\text{Remaining Risk} \times \text{Penalty})$

$\text{Expected Cost} = \text{\pounds}400 + (0.1 \times \text{\pounds}4000) = \text{\pounds}400 + \text{\pounds}400 = \text{\pounds}800$ .

Example 3

Example 3: Making a Final Recommendation (Exam Style)

A software development firm faces a penalty of £12,000 if their new app is not launched on time. The project manager identifies two independent risks:

The lead developer falls ill (Probability = 0.15).
The server crashes during the upload (Probability = 0.08).

(The probability of one or both of these delays happening is calculated to be 0.218).

The manager has three options:

Option 1: Hire a temporary assistant developer for £1,000 to eliminate the illness risk.
Option 2: Pay £800 to upgrade the server and eliminate the crash risk.
Option 3: Do both.

Determine which option, if any, the manager should choose to minimise their financial risk. Give a reason to support your recommendation.

We must calculate the expected cost for all possible scenarios to find the lowest value.

Do Nothing: $0.218 \times \text{\pounds}12,000 = \text{\pounds}2,616$ .
Option 1 (Assistant only): Server crash risk (0.08) remains.
Cost = $\text{\pounds}1000 + (0.08 \times \text{\pounds}12,000) = \text{\pounds}1000 + \text{\pounds}960 = \text{\pounds}1,960$ .
Option 2 (Server only): Illness risk (0.15) remains.
Cost = $\text{\pounds}800 + (0.15 \times \text{\pounds}12,000) = \text{\pounds}800 + \text{\pounds}1800 = \text{\pounds}2,600$ .
Option 3 (Both): No risk remains.
Cost = $\text{\pounds}1000 + \text{\pounds}800 = \text{\pounds}1,800$ .

Conclusion: The manager should choose Option 3 (Do both), as this provides the lowest overall expected cost (£1,800) compared to doing nothing or using just one measure.

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10 Multiple Control Measures questions with answers and video solutions