First of all, the imperfect information sampling value (ISP) is calculated: IISV = EMV - EMVPP = 41170 - 41000 = $170 m3 Therefore, the current cost is adequate as it implies the lower cost of $170/part. The perfect information value (PIV) is: PIV = MLU-EMV = 42800 - 41000 = $1,800 Thus, up to $1,800 is paid for perfect information. 7.12 Antidoping Tests The sporting authorities of ADESA University are considering setting up an an- tidoping test programme for university interschool athletes. Nevertheless, one of the Sports Committee members and a Quantitative Methods teacher have some doubts as to the use of such tests with student athletes given the possible social costs incurred by a false-positive test. The teacher has decided to conduct a mathematical study of the test process by taking into account the costs and reli- ability of such tests, and the costs relating to negative and positive errors. If the antidoping test programme is set up, student athletes will be expected to do an antidoping test. The test result may be positive (suggests a potential user of performance-enhancing drugs) or negative (does not suggest a potential user of performance-enhancing drugs). If the test result is negative, no follow-up action will be taken; yet if the test is positive, follow-up action will be taken to determine whether the athlete or student actually uses performance-enhancing drugs. The difficulty in this decision model lies in assigning costs to several possi- bilities. The teacher proposes employing the following potential costs: Cost of a test with a false-positive result, Ci. Cost of a user of performance-enhancing drugs who has not been identified, C2. . Cost of someone innocent who has to do the doping test and it proves negative, C3. Costs of properly identifying a user of performance-enhancing drugs, and the cost of an innocent athlete not doing the test is considered 0. No quantitative values have been assigned to C1, C2 and C3, but a hierarchy of values have been established. In relative terms, CI is the highest cost and C2 is higher than C3. So: C1 > C2 > C3. 7.12 Antidoping Tests 247 By assuming that test reliability is 95 % and that 5 % of athletes use perfor- mance-enhancing drugs, considering the ADESA University Sporting Commit- tee's objective of minimising expected costs helps the teacher solve the decision model. (a) Draw the corresponding decision tree and indicate with a letter per branch the associated probability or the associated cost (depending on the case) (b) Solve the tree and obtain the most economic solution