Question

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Question 2 (20 Marks) a) Given the following project details, identify the project's critical path; Activity Predecessor A B Duration (Man Days) 5 10 12 8 6 15 D Ε F B, C GE CD G H 20 18 30 5 I,J к F, L M (10 Marks) Continued...

Answer 1

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	5	0	5	0	5	0
B	10	5	15	54	64	49
C	12	5	17	52	64	47
D	8	5	13	5	13	0
E	6	17	23	64	70	47
F	15	23	38	70	85	47
G	4	17	21	66	70	49
H	20	13	33	13	33	0
I	18	33	51	33	51	0
J	2	33	35	49	51	16
K	4	51	55	51	55	0
L	30	55	85	55	85	0
M	5	85	90	85	90	0

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 & DURATION

A + D + H + I + K + L + M = 90

2. CRASHING

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	12	0	12	0	12	0
B	8	12	20	13	21	1
C	9	12	21	12	21	0
D	6	21	27	21	27	0

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 & DURATION

A + C + D = 27

EXPLANATION

1. We calculate crash cost per period by using the formula:

CPP = (CRASH COST - NORMAL COST) / (NORMAL TIME - CRASH TIME)

2. If we have 1 critical path, we crash an activity from it with the least crash cost per day and can still be crashed.

3. We recalculate the critical path after the crash to see if the critical path is still the critical path, if there’s still 1 critical path, we repeat step 2, else we crash 1 activity from each chain, till we get the desired crashed period.

ACTIVITY	NORMAL TIME	CRASH TIME	NORMAL COST	CRASH COST	CRASH COST PER PERID	CRASH TIMES	CRASH #	COST
A	12	12	200	350	0			0
B	8	8	300	300	0			0
C	9	7	250	450	100	1	1	100
D	6	5	400	600	200	1	2	200

TOTAL POSSIBLE CRASHES = 2

TOTAL CRASH COST = 300