Question

Colonial State College is considering building a new multipurpose athletic complex on campus. The complex would provide a new gymnasium for intercollegiate basketball games, expanded office space, classrooms, and intramural facilities. The following activities would have to be undertaken before construction can begin:

				Immediate		Time
Activity		Description		Predecessor		(weeks)
A		Survey building site		—		11
B		Develop initial design		—		10
C		Obtain board approval		A, B		16
D		Select architect		C		10
E		Establish budget		C		9
F		Finalize design		D		10
G		Obtain financing		D, E		11
H		Hire contractor		F, G		12

1. Which project network is correct?
   

   (i)		(ii)
   (iii)		(iv)

   
   
   
2. Identify the critical path.
   
   B-C-D-G-H
   
3. Develop the activity schedule for the project. If your answer is zero, enter “0”.
   
   

   Earliest

   Latest

   Earliest

   Latest

   Critical

   Activity

   Start

   Start

   Finish

   Finish

   Slack

   Activity

   A

   B

   C

   D

   E

   F

   G

   H

4. Does it appear reasonable that construction of the athletic complex could begin one year after the decision to begin the project with the site survey and initial design plans? What is the expected completion time for the project?
   
   
   
   Project Completion Time is  weeks.

Answer 1

a.

Project network

Below is the project network (Options are not shown in the Question)

b.

Critical path is A-C-D-G-H

(detailed approach and calculation is given under point c.)

c.

We will use below approach:

Earliest Start Time (ES) = the earliest time that an activity can begin

Earliest Finish Time (EF) = the earliest time that an activity can be completed

EF = ES + duration of activity        

Latest Start Time (LS) = the latest time that an activity can begin without lengthening the minimum project duration

Latest Finish Time (LF) = the earliest time than an activity can be completed without lengthening the minimum project duration

LF = LS + duration of activity   

Duration of the project = the difference between the maximum value of the "lastest finish time" of projects and the minimum value of the "earliest start time" of projects

Project duration = max(LF) - min(ES)     

Slack = the amount of time that a project can be delayed without increasing the duration of the project

Slack = LF- LS or EF - ES

Critical path is the path with Slack = 0

Activity	Description	Immediate Predecessor	Time (weeks)	Early Start (ES)	Early Finish (EF)	Latest Start (LS)	Latest Finish (LF)	Slack	Critical Activity
A	Survey building site	—	11	0	0+11=11	11-11=0	11	11-11=0	Y
B	Develop initial design	—	10	0	0+10=10	11-10=1	11	11-10=1
C	Obtain board approval	A, B	16	11	11+16=27	27-16=11	27	11-11=0	Y
D	Select architect	C	10	27	27+10=37	37-10=27	37	27-27=0	Y
E	Establish budget	C	9	27	27+9=36	37-9=28	37	28-27=1
F	Finalize design	D	10	37	37+10=47	48-10=38	48	38-37=1
G	Obtain financing	D, E	11	37	37+11=48	48-11=37	48	37-37=0	Y
H	Hire contractor	F, G	12	48	48+12=60	48	60	48-48=0	Y

d.

Project Completion time in weeks = 60 weeks

It does not appear reasonable that construction would begin in one year (~52 weeks) considering total completion time for assessment is much higher at 60 weeks.

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