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