Question

A construction project consists of 7 activities. These activities, their connecting events, and the three PERT times (optimistic, likely, and pessimistic), in days, are listed in the table below. The project starts on 27th July 2026. Assuming no holidays for the entire duration of the project except 15th August 2026, the expected date of completion of the project will be August 2026 (mention the date in integer).

Activity	Connecting Events	Three PERT Times (in Days)
P	1 to 2	4 - 6 - 8
Q	1 to 3	5 - 6 - 13
R	2 to 5	6 - 8 - 22
S	2 to 3	8 - 11 - 14
T	3 to 5	2 - 4 - 12
U	3 to 4	4 - 8 - 18
V	4 to 5	5 - 7 - 15

Hint:

Find te = (a+4m+b)/6 for each activity, take the longest path 1-2-3-4-5 as the critical path (34 days), then count 34 working days from 27 July skipping the 15 August holiday.

Answer 1

Correct Answer: 30

Step 1: Build an earliest-event-time table instead of listing paths.
Using $t_e = \dfrac{a+4m+b}{6}$ for each activity: P = 6, Q = 7, R = 10, S = 11, T = 5, U = 9, V = 8 days.

Step 2: Work out the earliest occurrence time (EOT) of each event.
$$EOT_1 = 0$$
$$EOT_2 = EOT_1 + P = 0+6 = 6$$
$$EOT_3 = \max(EOT_1+Q,\ EOT_2+S) = \max(0+7,\ 6+11) = \max(7,17) = 17$$
$$EOT_4 = EOT_3+U = 17+9 = 26$$
$$EOT_5 = \max(EOT_2+R,\ EOT_3+T,\ EOT_4+V) = \max(6+10,\ 17+5,\ 26+8) = \max(16,22,34) = 34$$
So the earliest the project can finish is day 34 of the project, through the path 1-2-3-4-5, confirming the critical path found by direct listing.

Step 3: Convert the 34 day duration into a calendar date.
Lay out the calendar day by day from 27 July 2026 as day 1: the last 5 days of July are days 1 to 5, then August dates equal (day number minus 5) as long as no holiday intervenes.
Checking day 19: August date $= 19-5 = 14$, so day 19 is 14 August, and day 20 would be 15 August. Since 15 August is a declared holiday, no work happens that day, so it does not count towards the 34 required days: everything shifts one calendar day later from that point on.

Step 4: Locate day 34 on the shifted calendar.
Without the holiday, day 34 lands on 29 August ($34-5=29$). Adding the one lost day for the 15 August holiday moves the finish to 30 August 2026.

Final Answer:
The project is expected to finish on 30 August 2026.