Question

The R&D department is planning to bid on a large project for the development of a new communication system for commercial planes. The accompanying table shows the activities, times, and sequences required:

ACTIVITY              IMMEDIATE PREDECESSOR          TIME (WEEKS)

A                                                 —                                             5

B                                                  A                                               4

C                                                  A                                              6

D                                                    A                                            6

E                                                     B                                           1

F                                                  C D                                           5

G                                                D F                                             6

H                                                  D                                              2

I                                                   E G H                                       4

b. What is the critical path? More than one answer can be selected.

A-C-F-G-I

A-B-E-I

A-D-H-I

A-D-F-G-I

c. Suppose you want to shorten the completion time as much as possible, and you have the option of shortening any or all of B, C, D and G each one week. Which would you shorten? More than one answer can be selected.

B

C

D

G

E

F

d-1. What is the new critical path? More than one answer can be selected.

A-C-F-G-I

A-B-E-I

A-D-H-I

A-D-F-G-I

d-2. What is the earliest completion time for the new critical path?

Completion time ________ weeks

Answer 1

ACTIVITY	TIME	ES	EF	LS	LF	SLACK	CRITICAL
A	5	0	5	0	5	0	YES
B	4	5	9	17	21	12
C	6	5	11	5	11	0	YES
D	6	5	11	5	11	0	YES
E	1	9	10	21	22	12
F	5	11	16	11	16	0	YES
G	6	16	22	16	22	0	YES
H	2	11	13	20	22	9
I	4	22	26	22	26	0	YES

FORWARD PASS

We calculate the ES and EF values using a forward pass where the ES of an activity is the maximum EF of all the predecessor activities.

BACKWARD PASS

We calculate the LS and LF values using a backward pass where the LF of the activity is the minimum of all the successor activities.

SLACK

Slack is the value which is determined by subtracting EF from the LF or ES from the LS.

CRITICAL PATH

Critical path is the chain in the project network where the slack value of all the activities is 0, what this means is that any delay in these activities would result in delaying the entire project.

CRITICAL PATH = A-C-F-G-I & A-D-F-G-I

DURATION OF PROJECT = 26

2. WE WILL SHORTEN C, D AND G BECAUSE THEY ARE ON THE CRITICAL PATH

3. A-C-F-G-I AND A-D-F-G-I

4. COMPLETION TIME = 24