Question

Operations Research

4- Consider the (simplified) list of activities and predecessors that are involved in building a house: Description Predecessors Duration (Days) Build foundation Activity Walls and ceilings A Roof Electrical wiring B Put in windows B Put in siding Paint house 10 6 C,F Construct the network for this project, identify the critical path using the (IC,TC,IL,TL, and H) method.

Answer 1

Network diagram is following: Finish

Three are three paths in the network. These are:

A-B-D	18
A-B-C-G	26
A-B-E-F-G	26

Paths A-B-C-G and A-B-E-F-G have the longest duration. Therefore, these are the critical path.

Draw the table listing ES, LS, EF, LF and Slack time of each activity Earliest Start (ES) is calculated by forward pass method as latest of the predecessors Earliest Finish (EF) Latest Finish (LF) is calculated using backward pass method as earliest of the successors Latest Start (LS). Earliest Finish (EF) Earliest Start (ES) + Activity Duration Latest Start (LS) = Latest Finish (LS)-Activity Duration Slack Latest Finish-Earliest Finish, or Latest Start-Earliest Start

Activity	Predecessor	Normal Time	ES	LS	EF	LF	Slack
A		5	0	0	5	5	0
B	A	8	5	5	13	13	0
C	B	10	13	13	23	23	0
D	B	5	13	21	18	26	8
E	B	4	13	13	17	17	0
F	E	6	17	17	23	23	0
G	C,F	3	23	23	26	26	0

Critical path can also be identified by 0 slack time in the above table.