Exam July 2022 solutions

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Titolo presentazione sottotitolo • Milano, XX mese 20XX Exam July 2022 Exercise 1 The manager of a company is responsible for the following project. Using the PERT algorithm identify the critical path. Compute the probability that paths A-C-H and A-E-H are concluded after month 30. Consider the possibility to crash the activities as shown in the following table. Identify the optimal solution according to a crashing programme. A penalty of 30 000€ for each month of delay is applied in case the project is concluded after month 20 (>20 month) . In addition, a market opportunity equal to 45 000€/month is achieved in case the project is reduced by month 20 to month 18. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s. Activity Immediate Predecessor Time Optimistic (months) Average Time (months) Time Pessimisti c(months) Std. deviation Duration Reduction (months) Total Crashing Cost (€) A - 6 7 14 4 2 74 000€ B - 2 4 12 3 3 45 000€ C A 5 7 15 7 3 45 000€ D A 3 4 5 1 2 1 000€ E A 9 10 11 1 5 80 000€ F B 5 6 7 1 5 10 000€ G B 5 6 19 6 3 9 000€ H C,D,E,F,G 3 5 19 4 - - Solution Activity Immediate Predecessor Time Optimistic (months) Average Time (months) Time Pessimistic (months) Expected duration (months) Std. deviation Duration Reduction (months) Total Crashing Cost (€) A - 6 7 14 8 4 2 74 000€ B - 2 4 12 5 3 3 45 000€ C A 5 7 15 8 7 3 45 000€ D A 3 4 5 4 1 2 1 000€ E A 9 10 11 10 1 5 80 000€ F B 5 6 7 6 1 5 10 000€ G B 5 6 19 8 6 3 9 000€ H C,D,E,F,G 3 5 19 7 4 - - 8 168 C 10 182 0 55 B 5 105 8 124 D 14 186 8 1810 E 8 180 5 116 F 12 187 The critical path is A-E-H. The project duration is 25 months. Solution 0 88 A 0 80 5 138 G 10 185 18 257 H 18 250 Solution ➢ Path A-C-H: P(Duration > 30 ) = P(z > 30−23 16+49+16) = 𝑃…