A project consists of eleven activities (all times are given in days) and has worker requirements as indicated in the table. Assume that all four workers employed by this organization are generalists

Question

What schedule is attainable if the number of workers is not an issue? What is the fastest the project can be completed while constrained by the four worker limitation?

Activity Activity time Workers Needed Predecessor
A 10 1
B 4 2
C 7 3 A
D 4 1 A
E 8 2 B
F 9 3 C,E
G 13 1 D
H 14 2 E,G
J 13 3 F
K 10 1 H, J
L 5 2 K

Answer 1

With no worker constraint, the project can be completed in 56 days by adhering to an early start schedule.

Activity Duration Early Start Early Finish Late Start Late Finish
A 10 0 10 0 10
B 4 0 4 7 11
C 7 10 17 12 19
D 4 10 14 10 14
E 8 4 12 11 19
F 9 17 26 19 28
G 13 14 27 14 27
H 14 27 41 27 41
J 13 26 39 28 41
K 10 41 51 41 51
L 5 51 56 51 56

Unfortunately, this schedule fails the four worker constraint on days 11 & 12 with the need for six workers and again on days 28-39 when five workers are needed. Adjusting for the constraint will require shifting non-critical activities back. Activity C delays starting until day 13 rather than the ES of 11. Activity F starts on day 20 instead of its ES of day 18. This results in Activity H delaying by one day and starting on day 29, otherwise day 28 is overscheduled by one worker. Activity J begins on day 43 and concludes on day 55, which delays K to starting on day 56 since H and J are both predecessors. L begins on day 66 and concludes on day 70. The four worker constraint delays the project completion by 14 days, from 56 days of project work to a full 70 days of work.