Critical path analysis

Sample questions

Original practice questions written in the style of the exam.

1. Question 17 marks

   A project consists of the activities in the precedence table. Durations are in days.

   Activity	Duration	Immediately preceded by
   A	4	–
   B	6	–
   C	3	A
   D	5	A
   E	7	B, C
   F	4	B, C
   G	6	D, E
   H	3	F
   I	2	D

   (a) Find the earliest start time and latest finish time of each activity.

   (b) State the critical path and the minimum project duration.

   (c) Find the total float on activities $B$ and $D$.

   (d) Calculate a lower bound for the number of workers needed to complete the project in the minimum time.

   Mark scheme

   • (a) M1 Forward pass: earliest starts A 0, B 0, C 4, D 4, E 7, F 7, G 14, H 11, I 9 (1)
   • M1 Backward pass from 20 (1)
   • A1 Latest finishes A 4, B 7, C 7, D 14, E 14, F 17, G 20, H 20, I 20 (1)
   • (b) Critical path $A$–$C$–$E$–$G$ (1)
   • Minimum duration 20 days (1)
   • (c) Float on $B = 7 - 0 - 6 = 1$ and on (1)