Show through sample network constructions in
A-O-A and A-O-N modes how a dummy could be used to
(a) Generate a single source and sink in the network.
(b) Permit uniqueness of activity representation.
(c) Represent correct network logic.
(d) Represent a redundancy.
: A project of ten jobs has the following precedence
relations
| Job |
Predecessors |
| a |
c,e,f |
| b |
d,g |
| c |
d,g |
| d |
h,i |
| e |
h,i |
| f |
j |
| g |
j |
| h |
j |
| i |
--- |
| j |
--- |
|
Draw an
- A-O-A network
- A-O-N network
- Adjacency matrix
- Node arc incidence matrix for the project.
- Fundamental loop and cutset matrices for any chosen tree
.
Is there a redundancy in the above predecessor list?
If all jobs are of equal duration determine the critical
path and the four floats for all jobs.
A work project consists of 12 activities, labeled
A to L. When the work manager was asked to specify the order
in which jobs have to be done, he answered as follows: Job A
comes first and precedes B,C and D. Both B and C must be done
before E starts, and C and D must precede F, but G and H can
start as soon as D is completed. Job I succeeds D,E,F and G;
and jobs J and K can start when G, H and I are all completed.
Job L comes after J and K.
(a) Using a precedence matrix, assist the works manager to eliminate
redundancy in his list of precedence relationships. List the
immediate predecessors for each job.
(b) Draw an AON diagram, using as few precedence arrows as necessary
to show correct precedence relationships.
(c) Draw an arrow-diagram representation of the same project,
using as few dummy jobs as necessary to show correct precedence
relationships and unique node identification of activities.
Phil Moody, project manager was interested in
developing a network for a 20-job project under his responsibility.
He labeled the jobs A to T and for each job listed all its predecessors
as best as he could determine;
| Job |
Immediate
Predecessors |
Job |
Immediate
Predecessors |
| A |
-- |
K |
G |
| B |
-- |
L |
F,G,K |
| C |
-- |
M |
H,I |
| D |
A,B |
N |
H,I,J,L |
| E |
A,B,C |
O |
J,K,L |
| F |
A,B,C |
P |
M,N |
| G |
C |
Q |
O,P |
| H |
D,E |
R |
J,K,L,O |
| I |
D,E,F |
S |
N,Q,R |
| J |
F,G |
T |
O,S |
|
Moody suspected that some predecessors
he listed were redundant, and he was not sure how to develop
a network from his list of jobs and predecessors.
(a) Which (if any) predecessors shown could be eliminated without
affecting the network logic?
(b) Assist Mr. Moody by drawing an arrow diagram for this project,
using as few dummies as possible.
(c) Draw an AON diagram from the original project list (including
redundant predecessors), and determine to your satisfaction
that the redundant predecessor arrows could be removed without
changing the network logic.
In the table below, each activity of a project
is listed in the first column, and those activities which must
follow the given job are listed in the second column. From this
information draw the Roy network and the CPM network for the
project.
| Activity |
Must
Follow |
| A |
P,N,M |
| B |
P |
| C |
A,B |
| D |
I,J,C |
| E |
I,J,C |
| F |
D,E |
| G |
-- |
| H |
G |
| I |
H |
| J |
H,B,A |
| K |
G |
| L |
G |
| M |
L |
| N |
K,O |
| O |
L |
| P |
Q,O |
| Q |
K |
|
The jobs of the following network have the indicated
time estimates
| Job |
Optimistic |
Most
Likely |
Passimistic |
| (1,2) |
3 |
6 |
15 |
| (1,2) |
2 |
5 |
14 |
| (1,2) |
6 |
12 |
30 |
| (1,2) |
2 |
5 |
8 |
| (1,2) |
5 |
11 |
17 |
| (1,2) |
3 |
6 |
15 |
| (1,2) |
3 |
9 |
27 |
| (1,2) |
1 |
4 |
7 |
| (1,2) |
4 |
19 |
28 |
|
(a) Draw the project network
(b) Calculate the length and variance of the critical path
(c) What is the probability that the jobs on the critical path
will be completed by the due date of 41 days?
(d) What is the probability that the jobs on the next critical
path will be completed by due date?
(e) What is your estimate that the entire project will be completed
by due date?
(f) Under standard PERT assumptions, what is the probability
of completing the project - before 30 days?
- between 15 and 35 days?
- After 38 days?
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