Planning & Decision Making · Guided Practice
Multiple Control Measures
10 questions with answers and video solutions. Try each one before revealing the answer.
The probability of the first is and the probability of the second is .
Calculate the probability that neither happens.
Answer
The probability of the first is and the probability of the second is .
Calculate the probability that at least one of them happens.
Answer
Two independent events could cause a delay, with probabilities and .
Calculate the expected cost of a delay.
Answer
Two independent events could cause a delay, with probabilities and .
A control measure costing would remove the first risk completely.
Calculate the expected cost if this control measure is taken.
Answer
Two independent events could cause a delay, with probabilities and .
A control measure costing would remove the second risk completely.
Calculate the expected cost if this control measure is taken.
Answer
The expected cost with no control measure is .
Control measure 1 gives an expected cost of and control measure 2 gives an expected cost of .
Only one control measure may be used.
State which should be chosen, and justify your answer.
Answer
Its expected cost of is lower than for measure 2 and lower than with no measure at all.
Two independent events could cause a delay, with probabilities and .
(a) Calculate the expected cost of a delay.
(b) A control measure costing would remove the second risk completely. Calculate the expected cost if it is taken, and determine whether the company should use it.
Answer
, so .
(b) , so .
The company should use it, as is less than .
An electric vehicle charging company has been awarded a contract to install 500 charging points in a city. As part of the contract a number of tasks must be completed including ordering and receiving charger parts and installing electric cables.
If the installation is delayed the company faces a fixed penalty of £75,000.
The company has identified the following two reasons for a possible delay:
- a shortage in parts for the chargers
- the electric cables will not be in place in time.
There is a 0.325 probability one or both of these delays will happen.
(a) Calculate the expected cost of a delay.
The company is considering using the following control measures:
- Control Measure 1 - Import extra parts at a cost of £15,000.
- Control Measure 2 - Pay another firm to help lay the cables, at an additional cost of £16,000.
There is a 0.1 probability of a shortage in parts for the chargers.
There is a 0.25 probability that the electric cables will not be in place in time.
(b) Calculate the expected cost of a delay using:
(i) only control measure 1
(ii) only control measure 2.
The company will only use one control measure.
(c) Based on your calculations, explain which control measure the company should use in order to minimise expected costs.
Answer
(a) = £24,375
(b)(i) Expected cost = = £33,750
(b)(ii) Expected cost = = £23,500
(c) The company should use control measure 2 because it has the lowest expected cost.
An events management company has been awarded a contract to construct the stages for a music festival. If the construction of the stages is delayed the contract says that a penalty of £25,000 will be charged.
For the purposes of the cost-benefit analysis, the company has assumed only two events will cause a delay: a stage structure failing, or staff failing to attend the site. The probability of no delay is 0.76.
(a) Calculate the expected cost of a delay.
The company is considering using the following control measures:
- Control Measure 1: Pay another company to have staff on standby to attend the site in the case of their staff being unable to attend, at a cost of £1000.
- Control Measure 2: Have a spare stage on standby in case of a failure, at a cost of £1500.
The probability of staff failing to attend the site is 0.2.
The probability of a stage structure failing is 0.05.
(b) Calculate the expected cost if control measure 2 is taken.
The expected cost if control measure 1 is taken is £2250. The company will only use one control measure.
(c) Explain which control measure the company should use to minimise expected costs.
Answer
(a) £6000
(b) £6500
(c) Control measure 1 because it has the lowest expected cost.
A TV production company is responsible for the delivery of a new quiz show to a national television channel. If the production is delayed, the company will be charged an additional £10,000.
For the purposes of the cost benefit analysis, it is assumed that there are only two events that will cause a delay:
- 0.3 probability that a key member of staff will fall ill
- 0.1 probability that there will be equipment failure.
(a) Calculate the expected value of costs that should be considered for the cost benefit analysis.
It is possible to use the following control measures:
- Control Measure 1: Employ back up staff who can replace anyone unwell, at a cost of £1000.
- Control Measure 2: Spend £3000 on an equipment inspection to ensure all equipment is functioning correctly.
(b) Calculate the expected value of costs if control measure 1 is taken.
The expected value of costs if control measure 2 is taken is £6000.
(c) State which control measure(s) should be taken. Give a reason to support your recommendation.
Answer
(a) Probability of no issues:
Probability of at least one issue:
Expected penalty:
(b) Cost of measure 1 + Expected penalty from equipment failure:
(c) Control measure 1 should be taken as it has the lowest expected cost (£2000 vs £3700 with no measures and £6000 for measure 2).