Question

The duration and resource usage for each activity are showed in the table below.

Activity	Predecessor	Total Processing Time (days)	# of painters required/day
A	---	1	1
B	---	1	1
C	A,B	0.5	1
D	C	1	1

Assume the maximum number of painters is 1. Level the resources by following the rule "Delay the activity with the most positive slack first". How much slack time (in days) does acitivity C have after leveling recources?

Answer 1

First, I have prepared Network Diagram for given table and activities:

Network diagram is prepared using forward and backward path method

Based on the Network diagram, we see that we have two critical path, these are Start - A-C-D- End, Start-B-C-D-End, project will take at least 2.5 days to complete.

Based on the network diagram, i have prepared Gantt chart, as shown below:

Gantt chart before Resource leveling:

Activity	Duration	Resources	0.5	1	1.5	2	2.5
A	1	1	1	1
B	1	1	1	1
C	0.5	1			1	1	1
D	1	1
		Total Resources	2	2	1	1	1
		Allowable resources	1	1	1	1	1

Gantt chart after Resource leveling:

the rule "Delay the activity with the most positive slack first". but here, all activities have zero slack or total float, here, I have delayed activity B by 1 day.

After Resource levelling
Activity	Duration	Resources	0.5	1	1.5	2	2.5	3	3.5
A	1	1	1	1
B	1	1			1	1
C	0.5	1					1
D	1	1						1	1
		Total Resources	1	1	1	1	1	1	1
		Allowable resources	1	1	1	1	1	1	1

now project will take at least 3.5 days to complete.

Here, we have got only one path and all activities on this path would be critical path activities, project will take at least 3.5 days to complete.

After Resource leveling,

Total slack or float for activity C =Late start - Earliest start=Late finish - earliest finish = 2-2=2.5-2.5= Zero