Tasks:

1.Prepare a decision tree for the decision problem Bright Tech, described below, including probabilities and consequences.

2. Apply expected value analysis to calculate the expected costs in the tree.

3. If Bright`s only objective is to minimise the expected cost of the maintenance task, what size team should be used, and under what circumstances, if any, should Bright use the equipment on Day 2?

Aaron Bright is the owner of Bright Tech, a company that maintains batteries for water turbines. Aaron is planning a maintenance task for a supplier. The maintenance is expected to take 2 working days (referred to here as Day 1 and Day 2). If it is not completed by the end of Day 2, Aaron must pay the customer a 200,000 penalty.

Aaron has to decide how many engineers to allocate to the task. Due to the nature of the work, maintenance teams operate in multiples of 10 people, and for this task, Aaron can choose to assign a team of either 10, 20, or 30 people. The cost per team member is 4,800, so if a team of 10 is used, the team cost will be 48,000, while a team of 20 will cost 72,000, and 30 will cost 144,000.

Based on experience, Aaron has the following expectations about the likelihood that a team will be able to complete the task within 2 working days:

1. Team of 10: 0.4 probability of completion within 2 days

2. Team of 20: 0.7 probability of completion within 2 days

3. Team of 30: 0.9 probability of completion within 2 days.

Once the size of team has been decided, it cannot be changed.

Aaron has access to equipment that can speed up the maintenance activity. Unfortunately, it will not be available until Day 2 of the maintenance activity, and it cannot be operated by a team of 10. Using the equipment incurs a cost of 50,000. If used, it would guarantee successful completion on time.

Team of 20: 1.0 probability of success if equipment used on Day 2

Team of 30: 1.0 probability of completion within 2 days.

Because the use of the equipment is costly, Aaron will review progress at the end of Day 1 to determine whether the maintenance team is on schedule of behind schedule. He believes that there is

A 0.5 probability that a team of 20 will be behind schedule at end of Day 1

A 0.2 probability that a team of 30 will be behind schedule at end of Day 1.

Finally, he has assessed the likelihood that the maintenance task will exceed the deadline if the equipment is not used.

Probability that deadline is exceeded, if equipment not used team of 20.

If behind schedule - 0.5

If not behind schedule - 0.1

Probability that deadline is exceeded, if equipment not used team of 30

If behind schedule - 0.2

If not behind schedule - 0.075.