INDE 6332ENGINEERING PROJECT MANAGEMENT
SCHEDULING LECTURE 1
University of HoustonDept. of Industrial Engineering
Houston, TX 77204-4812(713) 743-4195
AGENDA
Scheduling Solving Network
SCHEDULING
Background… Network Techniques…
SCHEDULING BACKGROUND
Conversion of project plan into operating timetable Used to monitor and control project activity Based on WBS Does not need to be developed for all work packages Determines expected completion date Illustrates critical activities that cannot be delayed Illustrates slack activities that can be delayed
NETWORK TECHNIQUES
PERT… CPM… Terminology… Network representation… Constructing AON Networks…
PERT
Program Evaluation and Review Technique US Navy, Booz-Allen Hamilton, Lockheed Polaris Missile Program, 1958 Research and Development oriented
CPM
Critical Path Method DuPont, late 1950’s Construction industry oriented
TERMINOLOGY
Activity… Event… Network… Path… Critical…
ACTIVITY
Specific task or set of tasks required by the project Consume resources Take time to complete May have
Successors, but no predecessors Predecessors, but no successors Both predecessors and successors
EVENT
Result of completing one or more activities End state at a particular time Do not use resources
NETWORK
Arrangement of activities Illustrate logical sequence Represented by arcs and nodes Flow represented by arrows generally left to right
PATH
Series of connected activities between 2 events
CRITICAL
Activities, events or paths if delayed, will delay the completion of the project
Critical Path Sequence of critical activities and events from start to end
which cannot be delayed without delaying the project
NETWORK REPRESENTATION
Activity on Node (AON) Activities are represented by nodes Does not require dummy nodes Used by most software packages
Activity on Arc (AOA) Activities are represented by arcs May require dummy nodes
CONSTRUCTING AON NETWORKS
Table Network
TABLE
Task Precedence Time in Days
A None 5
B None 4
C A 6
D B 2
E B 5
F C,D 8
NETWORK
Start
a
b
c
d
e
f End
SOLVING A NETWORK
Small project Ten activities Optimistic estimates
Rarely less than Most likely estimate Pessimistic estimates
Rarely longer than Predeccessors
TABLE 8-1
Activity Optimistic Likely Pessim. Predecces.
A 10 22 22 --
B 20 20 20 --
C 4 10 16 --
D 2 14 32 A
E 8 8 20 B, C
F 8 14 20 B, C
G 4 4 4 B, C
H 2 12 16 C
I 6 16 38 G, H
J 2 8 14 D, E
NETWORK
Start
NETWORK
Start
a
NETWORK
Start
a
b
NETWORK
Start
a
b
c
NETWORK
Start
a
b
d
c
NETWORK
Start
a
b
d
c
e
NETWORK
Start
a
b
d
f
c
e
NETWORK
Start
a
b
d
f
gc
e
NETWORK
Start
a
b
d
f
gc
e
h
NETWORK
Start
a
b
d
f
gc
e
h
i
NETWORK
Start
a
b
d
f
g
j
c
e
h
i
NETWORK
Start
a
b
d
f
g
j
End
c
e
h
i
CALCULATING ACTIVITY TIMES
99 percent accurate estimates a=optimistic estimate b=pessimistic estimate m=most likely estimate, the mode Possible situations
a=m or m=b or If a and b are the same as m then TE=m
For some unknown reason project times follow beta dist. One formula (assumes std is 1/6th range for beta dist.)
TE=expected time=(a+4m+b)/6 Variance=((b-a)/6)^2
MAKE CALCULATIONS
Assuming beta distribution with std equal to 1/6 range Expected duration
E(A)=(10+4*22+22)/6 E(A)=20
Variance Var (A)=((22-10)/6)^2 Var (A)=4
TABLE 8-2
Activity TE VAR
A 20 4
B 20 0
C 10 4
D 15 25
E 10 4
F 14 4
G 4 0
H 11 5.4
I 18 28.4
J 8 4
INSERTING TIME ON NETWORK
Label each node with Expected duration Variance
NETWORK
Start
a 20,4
b20,0
d15,25
f14,4
g4,0
j8,4
End
c10,4
e10,4
h11,5.4
i18,28.4