Assignment 1 Brief

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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 comprehensive    net   benefit    pay-off   tables   showing   the consequences of all possible decision combinations. The tables should systematically map every possible state (test/no test, positive/negative results, drug user/drug free tatus)  against  every  possible  action  (ban/don't  ban),  regardless  of  the  logical consistency of the decision path. (8 marks)

Notes: 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 the values shown in table 1.1 above. 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).

While you can have different formats for payoff tables to aid marking please create payoff tables with decisions as the rows and states as the columns.

2.   Calculate the  relevant posterior probabilities. Include any Bayes tables generated in Excel in your report. (2 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 costs C1, C2, C3, or C4  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  by  discussing  how  changing  the  relative  index values or prior probabilities/data likelihoods could lead to a different  best strategy outcome.  (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 $5,000 and the cost of supplying the computers will be $95,000.

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 all  relevant probabilities in the table. (8 marks)

Note: Think carefully about bid prices that give iC certainty about whether they will win or lose against each competitor scenario.

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)

-    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.