Exam January 2022 solutions

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Titolo presentazione sottotitolo • Milano, XX mese 20XX Exam 10th January 2022 Exercise 1 The manager of a company is responsible for the following project. Identify the critical path. Consider the possibility to crash the activities as shown in the following table. Identify the optimal solution according to a crashing program. A penalty of 30 000€ for each month of delay is applied in case the project is not concluded before month 9. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s (only Crashing ON/OFF can be applied). Activity Immediate Predecessor Duration (months) Duration Reduction (Crashing) Total Crashing Cost (€) A - 2 1 28000€ B - 5 3 10000€ C A 6 2 45000€ D A 5 4 150000€ E B 3 1 5000€ F C 4 1 20000€ G D 2 1 10000€ H D 4 2 6000€ I E,F,G,H 1 - - 2 75 D 3 81 0 55 B 4 94 5 83 E 9 124 2 86 C 2 80 8 124 F 8 120 The critical path is A-C-F-I. The project duration is 13 months. Solution 0 22 A 0 20 7 92 G 10 123 7 114 H 8 121 12 131 I 12 130 Solution For crashing, we focus only on activities belonging to the critical path. The activity providing the highest real benefit is activity F. Indeed, Crashing C would lead to a reduction of only 1 month of total duration reduction, due to the fact that a new critical path (A-D- H-I) would emerge. Moreover, crashing C + H would allow to achieve a duration reduction of 2 months, but the overall benefit is lower than crashing only F. Therefore, we start crashing F, see next slide. Activity Immediate Predecessor Duration (months) Duration Reduction (Crashing) Total Crashing Cost (€) Unitary Crashing Cost €) Real benefit A - 2 1 28000€ 28000€ 2000€ B - 5 3 10000€ 3333.33€ C A 6 2 45000€ 22500€ -15000€ D A 5 4 150000€ 37500€ E B 3 1 5000€ 5000€ F C 4 1 20000€ 20000€ 10000€ G…