Engineering Management 1

Lecture 2: Project Scheduling I

Ruel EllisDepartment of Mechanical and Manufacturing Engineering

� Network Scheduling

� Critical Path Method

Program Evaluation & Review Technique�

� Issues in Network Scheduling

Net w or k S chedul ing

Net w or k S chedul ing P has es

Activity Definition Do what?

Activity Sequencing Activity relationship?

Duration Estimating Duration?

Project SchedulingI n what order?

Schedule ControlAdj us t schedule per formance?

Act ivi t y Def in i t ion:S t ar t ing P oint

Mus t define all activities needed to complete proj ectWhat are natural s tar ting points for activity definition?Outputs of activity definition phase

Activity l is tS uppor ting documentationT he Work Breakdown S tructure (WBS )

Act ivi t y S equencing:Def in ing R elat ions hips

Activities typically have interdependencies

Precedence cons traints

Nature of precedence requirements

Act ivi t y S equencing:Def in ing R elat ions hips

ApproachesExper ienceHierarchicalYellow s ticky

Defining precedence relationships challenging in complex projects

Dur at ion/ Cos t E s t imat ion S t r at egies

Top-Down Estimating Bottom-up Estimating Level of Effort Standard Costs and Time Historical Relationships Simpson’s Rule

T op-Dow n E s t imat ing

I dentify large “blocks” of effor t from the WBS (task/subtask level)Es timate cos ts and time

S imilar work/exper t as ses sment/cos t es timating relations hips

S trength Quick

WeaknessMay be inaccurate and/or les s precise

L e ve l 2

L e ve l 1

L e ve l 3 L e ve l 3 L e ve l 3

L e ve l 2 L e ve l 2

L e ve l 1

P ro je ct

B ot t om-U p E s t imat ing

I dentify small “blocks” of effor t from the WBS (work package/activity level)

S um for higher level cos t es timates

S trength Greater confidence in “small increment” es timation

Weakness More time consumingMay s tack-up “contingency” planning by es timator s

L evel of E f f or t

ApproachPer form at high levelI dentify individuals needed

Number and j ob clas s ificationEs timate per iod each individual needed

How long wil l each individual be needed

L evel of E f f or t

S trength Quick

WeaknessFocus on people NOT tasks needed doneMay be inaccurate and/or les s precise

S t andar d Cos t s and T ime

Known/Repeatable activities and s tandard operationsLittle var iance in s imilar operations Not dependent on par ticular proj ect

S t andar d Cos t s and T ime

S trengthAccuracy increased, var iance decreased

Weakness Assumes s tandard activitiesAssumes his tor ical record available and cur rent

H is t or ical R elat ions hips

Stable ratios may exist -- for example: documentation, known activities, or prior efforts(C1/C2)=(Lines of code1/Lines of code2)n

Cost Estimating Relationships -- duration may vary as a function of some $ variable

cost = f(weight of spacecraft)cost=f(square feet of interior space)

Future = f(past) or f(parameter)

S imps on’s R ule f or E s t imat ion

T ime or cos t may vary from nominalCan les sen “anx iety” about es timatingUses nominal, minimum, and mos t likely values to es tablish es timate

Xexp Xmin + 4Xnom + Xmax

6=

P r oj ect S chedul ing

What is the purpose of proj ect scheduling?

T he WBS gives no sequencing of the different work packagesT he WBS gives no relationship between the work packagesMus t develop the logical relationships between work activities

By hand - - - computer s?

P r oj ect S chedul ing Appr oaches

Most common approachesMilestone ChartGanttCPM (Critical Path Method)PERT (Prog Eval and Rev Technique)PDM (Precedence Diagramming Method)

Other approaches - (sim, GERT,TOC)

Miles t one and Gant t Char t s :

Miles tone Char tsDepict pr incipal proj ect miles tones (events )Good Overview T oolGreat for ‘progres s repor ts ’

Miles t one and Gant t Char t s :

Gantt Char ts (aka Bar Char ts )S how activity s tar t and s top timesDo not show precedence relationships

May but becomes cumbersome

Great management presentation tools

P r oj ect Net w or ks

Net w or k Analys is

T wo approachesActivity on Ar row (AOA)Activity on Node (AON)

More typical definition CPM - determinis tic proj ect schedulePERT - probabilis tic proj ect schedule

Act ivi t y on Node:F undament al R elat ions hips

A B C

X

Y

Z

J

K

L

M

J

K

L

M

Act ivi t y on Ar r ow :F undament al R elat ions hips

2 7A

2 7

3

6

14

A

D

B F7

3

6

3

6

A

B

F

R

Net w or k S chedul ing –Cr i t ical P at h

Met hod ( CP M)

P r oj ect Net w or ks :B as ic R ules

Flow from left to r ightActivity cannot begin until connected activities have completedAr rows indicate precedence & flowEach activity has unique I DLooping (or cycling) not allowedConditional s tatements not allowedHave unique s tar ting point

E xample:T he E ngineer ing Cent er

D ura tio n(da ys )

A Application approval N one 5B C onstruction p lans A 15C Traffic study A 10D Service availability check A 5E Staff report B ,C 15F C ommission approval B ,C ,D 10G C enter C onstruction F 170H Occupancy E,G 35

A c tivity D e s c riptio n P re de c e s s o rs

I mplement ing CP M:Act ivi t y on Ar r ow

Will i l lus trate AOA CPM on the Engineer ing Center exampleT ake special note of:

Dummy act ivi t yForward and backward passEar lies t/lates t S tar t timesEar lies t/lates t F inish timesConcept of s lack (float)Concept of cr itical pathAssumption of unlimited resources

Act ivi t y on Ar r ow Not at ion

1 2A(ES ,EF)

Dur (LS ,LF)

AOA vs . AON:A Mat t er of P r ef er ence

Advant agesNo dummy activitiesEvents not usedEasy to drawActivity emphas is

Advant agesPath tracing easyEas ier to draw for complex proj ectsHighlights key events

AON** AOA

AOA vs . AON:A Mat t er of P r ef er ence

Dis advant agesPath tracing difficultNetwork drawing may be complex

Dis advant agesMay require dummy activitiesDetracts from activities

AON** AOA

P r ogr am E valuat ion

and R eview T echnique

( P E R T )

P E R T ver s us CP M CPM is det er min is t ic

One duration for each proj ect activityProj ect duration therefore determinis tic – one value

PERT is pr obabi l is t icT hree duration for each proj ect activity to es tablish “expected” durationProj ect duration therefore probabilis tic – a range of pos s ible values for proj ect duration

P E R T ver s us CP M

Both develop a “cr itical path”Both as sume unlimited (uncons trained) res ourcesPERT provides for s tatis tical analys is of proj ect durations

P E R T :Not hing is Cer t ain

S imilar ity to CPM methodApproach to activity duration es timationRole of the cr itical pathProj ect duration s tochas tic

Use of the CLT to as sume normalityDetermining mean and var iance

Calculating P(proj ect duration > X)Under lying as sumptions

Analys is of t he P E R T

Net w or k -E XAMP L E

P E R T Analys is E xample • Will demonstrate concepts using

example

1 2

3

4

5 6

Activity a m b E(duration) Std Dev (duration)

1-2 17 29 47 30 5 2-3 6 12 24 13 3 2-4 16 19 28 20 2 3-5 13 16 19 16 1 4-5 2 5 14 6 2 5-6 2 5 8 5 1

(a + 4m + b)/6

Activity a m b E(duration) Std Dev (duration)

1-2 17 29 47 30 5 2-3 6 12 24 13 3 2-4 16 19 28 20 2 3-5 13 16 19 16 1 4-5 2 5 14 6 2 5-6 2 5 8 5 1

(b-a)/6

Activity a m b E(duration) Std Dev (duration)

1-2 17 29 47 30 5 2-3 6 12 24 13 3 2-4 16 19 28 20 2 3-5 13 16 19 16 1 4-5 2 5 14 6 2 5-6 2 5 8 5 1

P E R T CP at h Var iance• I F YOU AS S UME I NDEPENDENCE

the var iance of any path = sum of activity var iances for all activities on that path

• NORMALLY DI S T RI BUT ED• Var iance of the PROJECT =

var iance of the CRI T I CAL PAT H• I f more than one cr itical path,

PROJECT VARI ANCE= larges t of CRI T I CAL PAT H VARI ANCES

P E R T Var iance

S ince NORMALLY DI S T RI BUT EDcan es timate probability of completing project on timecan es timate probability of completing project by any target date

if cr itical path expected = 64, S T D DEV= 6T arget= 70 Z = (70-64)/6 = 1probabil ity = 1 - .84 = .16

P E R T E s t imat esS o what do you mean by

optimis tic, pes s imis tic?value you expect to be exceeded at a

probability level and not exceeded at 1-αα probability

• PROBLEM: es timating the MOS T LI KELY duration of mos t things is hard

• Asking es timator s to come up with “What won’t be exceeded 95% of the time” is a guess at bes t.

I s s ues in Net w or k

S chedul ing

S hor t E xer cis e Net w or k S cheduling

I dentify three cr itical is sues , as sumptions , or l imitations in the use of network diagrams as a project management tool?

P r oj ect S chedul ing I s s ues

A typical project has les s than 10% of activities which are identified as cr iticalPoint vs . probabilis tic es timates

P r oj ect S chedul ing I s s ues

CPM or PERT : Research on PERT /CPM proj ects

T echnical per formance - - No s ignificant differenceProbability of cos t & schedule over runs - - S ignificant difference

Adequacy of es timates & WBSUncons trained resources