QBUS6320 S1 2025 Assignment 1

This is an individual assignment. It is worth 10% of your final grade. It consists of three questions. Each question is worth different marks. It is due on Friday 4 April at 11:59pm and must be submitted through Canvas using Turnitin.

The submission will comprise two separate parts:

1.   A typed  report (PDF please) that addresses all questions and contains images all of relevant tables, charts and decision trees within the report. The report must be able to be read as a standalone document.

2.   An Excel file with containing all the original tables, charts and decision trees. The Excel file is provided for backup and corroboration purposes.

Failure to submit both files by the due date will result in late penalties being applied. Additional instructions occur after the questions.

Question 1 (25 marks)

The Australian Institute of Sport (AIS) is considering whether to introduce mandatory drug testing for all athletes. Knowing that drug tests are not completely reliable, they want to use decision tree analysis to see whether the benefits outweigh the costs.

Probabilities:

If an athlete is tested for a particular drug, the test result will either be positive or negative. However, as these tests are not completely accurate some athletes who are drug free test positive (a false positive) and some athletes who are drug users test negative (a false negative). The best data we have available suggests that 8% of all athletes use drugs. 2.5% of all tests on drug free (DF) athletes result in false positives and 7.5% of all tests on drug using athletes result in false negatives.

Monetary Values:

The monetary values are difficult to assess but include the following:

•     The benefit B from correctly identifying a drug user and banning them.

•     The direct cost, C1, of a test.

•     The cost, C2, of violating a non-users privacy by performing the test.

•     The cost C3, of falsely accusing a non-user and banning them.

•     The cost C4, of not identifying a drug user and allowing them to participate.

We measure all benefits and costs relative to C1 (the direct cost of a test). We assign C1 a value  of  -1  to  indicate it represents a cost. All other monetary values are expressed as multiples of C1's magnitude. For example, a value of -2 represents a cost twice as large as the direct testing cost, while a value of +25 represents a benefit 25 times larger than the testing cost. The index values are shown in Table 1.1 on the following page.

Table 1.1

Questions:

1.   In Excel create two net benefit pay-off tables that map the net benefit of either testing (four different states) or not testing (two different states) against the decision to ban or not ban an athlete.  Include the pay-off tables in your report. Note: the first table should be expressed in index notation (+B, -C1, -C2  etc) while the second table should state the net benefit in numerical terms based on values indicted in table 1.1. For example, if a positive test is obtained for a non-drug user and this athlete is banned, there are three associated costs: Cost of the test (-1), the cost of violating the athlete's privacy (-2) and cost of falsely accusing the athlete (-20). (6 marks)

2.   Calculate the  relevant posterior probabilities. Include any Bayes tables generated in Excel in your report. (4 marks)

3.   Based  on the values  in the net benefit pay-off table and the Bayesian probabilities, create a decision tree using Precision Tree that will help the AIS decide whether they should implement mandatory drug testing. Note: Be careful to avoid double counting the costs (for example, do not include the C1, C2, C3, or C4 costs at multiple decision points if they have already been accounted for in earlier calculations). Include your decision tree in your report. (8 marks)

4.   For the given assumptions around the cost and benefit, outline the best strategy and its net benefit and discuss this solution. (2 marks)

5.   Conduct a brief sensitivity analysis giving reasons why you might change the relative index values. Discuss how this might impact the original solution. (5 marks)

Question 2 (35 marks)

The University of Sydney s procurement office has invited Intelligent Computing (iC) to tender on a new contract. The contract calls for the supply of 200 generic desktop computers and associated accessories which will be used for digital in-place exams. All vendors must fulfil the order within 6 weeks of contract award.

Despite the urgency the contract specifications are generic and so the university has informed all bidders that the low bid will win the contract. iC believes that the cost of preparing the bid will be $10,000 and the cost of supplying the computers will be $190,000.

The bids are sealed, so iC has no information about the value of the bids their competitors will submit. However, in the last 12 months iC has managed to poach several key employees away from vendors who are competing for the contract and so iC has a good understanding of how the competitors may behave. In summary iC believes that the size and probability of a low competitor bid will be:

Table 2.1

In addition, because of supply chain constraints, iC think there is a 30% chance there will be no rival bid.  Further assume iC s bid will never equal any competitor s bid.

Part A (20 marks)

A.1.             Based on this  information create a pay-off table in excel which outlines iC s

most logical bid prices given potential competitor bid options. Include relevant probabilities. (8 marks)

A.2.             Based on the pay-off table and any other relevant information use Precision

Tree to create a decision tree which sets out the problem. Include an image of the whole tree in your report. (10 marks)

A.3.             Using this decision tree, indicate the strategy that maximises EMV for iC. What

is that optimum value? (2 marks)

Part B (15 marks)

Use the sensitivity analysis function on the Precision Tree tool bar to vary the following inputs:

• Bid Preparation Costs: +/-10% in 1% increments

• Supply Cost: +/-10% in 1% increments

•     No  competing  bid  percentage:  A  minimum  of  0%  to  a  maximum  of  60%  in  5% increments

B.1.             Run a one-way sensitivity analysis on the entire decision tree model selecting

one of either the tornado graph or the spider graph. For the tornado graph: Show how each variable impacts the expected value. For the spider graph: Display variable values on the x-axis and expected value on the y-axis. Include an image of the chosen graph in your report and provide a short interpretation of the graph. (5 marks)

B.2.             Run a second one-way sensitivity analysis on the bid value decision node (not

the entire tree) and create a strategy region graph. Include an image of the graph - that  plots the probability of  no competing bids against  Expected Value -  in your report along with a short interpretation of the graph. (5 marks)

B.3.             Run a two-way sensitivity analysis on the bid value decision node and create

another strategy region graph including an image of the graph in your report along with a short interpretation. (5 marks)

Note: Precision Tree s sensitivity functionality has not been explicitly covered in lectures.  Part B provides an opportunity for students to explore this for themselves and differentiate the quality of their submissions based on their responses.

Question 3 (40 marks)

The following table outlines the potential pay-offs for three separate investments.

Table 3.1

Write a report for potential investors which ranks the three investments in terms of their attractiveness. Your report should be approximately 500 words. All diagrams and tables used to support your analysis should be generated in Excel using Precision Tree.

As you do not know the individual risk preferences of investors you should consider all risk types.

Write a report for potential investors which ranks the three investments in terms of their attractiveness. Your report should be approximately 500 words. All tables and risk profiles used to support your analysis should be generated in Excel using Precision Tree. As you do not know the individual risk preferences of investors, you might wish to consider multiple risk perspectives:

- Expected monetary value (EMV)

- Risk measures (variance, standard deviation)

- Risk attitudes (risk-neutral, risk-averse, risk-seeking)

- Potential for extreme outcomes (downside risk)

- Dominance

Other Instructions

Word count

1,200 words +/-10% excluding tables, decision trees and charts and references. Any words beyond 1,320 will not be marked. Submissions below 1,080 words may be penalised.

Style

This is a business report not an essay. The report should:

-     Have a suitable cover page.

-     Be divided into 3 distinct sections.

-    The text should be concise. Using bullet points is acceptable.

-     Be professionally and logically laid out with good grammar and spelling.

-     Marks will be deducted for submissions that do not meet these requirements.

Precision Tree

If Precision Tree is not used where required ,the best mark possible will be 50% of the available marks.

Rubric

There is general rubric relating to this assignment in the Assignment 1 Canvas module where this brief is located that provides detailed information regarding the quality expectations of the submission.

Late penalties

Reports submitted after the due date will incur a late penalty of 5% per day or part thereof. Reports more than 10 days late will not receive a mark.