Question

Activity	Duration(hours)	Depends on :	Numbers of workers
A	5		4
B	2		2
C	4		5
D	6	A,B	1
E	2	A,B,C	6
F	2	B,C	3
G	5	F	4
H	8	E,F	2
I	3	G	7
J	5	H,I	3
K	6	J	4
L	8	I	3

1. Calculate a lower bound for the number of workers required to complete the project in 26 days. [2 ????]
2. Use the precedence table to draw an activity-on-arc network. Include the early and late times for each event. [8 ?????]
3. Which activities are critical [2 ?????]?
4. Find the critical path for the network. [2 ?????]
5. Calculate the float of each activity [6 ?????]
6. What is the total float activity? [3 ?????]
7. Draw a Cascade (Gantt) charts to represent the project [5 ?????]
8. . It is possible for 4 workers to complete activity C in 5 hours. [2 ?????]
9. Would you recommend this approach? Fully explain your answer. [2 ?????]

Answer 1

Answer:

a. As per given information, the longest chain of activities will take 26 hours with the allocated no. of workers, i.e. 44 no. The question reads as “number of workers required to complete the project in 26 days”. Is it 26 days? If so, then only one worker would be able to complete the job within such time frame. And if it is 26 hours, then workers have to be engaged phase by phase for set of activities which could be simultaneously operated.

Here the longest track is E-H-J and F-G-I-J. The maximum no, of allocation at any activity within this path are 6 and 7 respectively. Therefore, minimum 13 worker can perform the job by doing continuously.

b. The Network Diagram

Table of event timing

Activity	Duration (hours)	Depends on :	Numbers of workers	Early Time	Late Time
A	5		4	5	5
B	2		2	2	2
C	4		5	4	4
D	6	A,B	1	11	13
E	2	A,B,C	6	7	13
F	2	B,C	3	6	8
G	5	F	4	11	13
H	8	E,F	2	15	21
I	3	G	7	14	16
J	5	H,I	3	20	26
K	6	J	4	26	32
L	8	I	3	22	24

c. The critical activities are:

A – E – H – J – K

The activities have longest overall duration. Together these activities define the minimum required time to complete the entire project, as the other activities can be accomplished simultaneously beside these specific activities.

d. Critical path is already marked in red color in the above diagram.