First steps in mining resource-constrained project-scheduling stochastic models for new valuable insights in project management

Relató

rio

T

é

cnico

First

Steps

in

Mining

Resource

-

_Constrained

Project

-

_Scheduling

_Stochastic

Models

for New Valuable

Insights

in

Project Management

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Alencar

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Rodrigues

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Schmitz

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03

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First

Steps

in Mining

Resource

-

_Constrained

Project-Scheduling Stochastic Models for

Neu

Valuable

Insights in Project Management

Antonio Juarez Alencar1

,GelsonGuedes Rodrigues1_{,Eber AssisSchmitz-,}

ArmandoLeite Ferreira andSérgioJoséMecena

Y

4 _i

Instituteof Mathematics,Federal UniversityofRio_{de Janeiro},

P.O. Box68530,21941

-

590

-

Riode Janeiro

-

RJ,Brazil

2_{ElectronicComputerCenter,Federal University of Rio de Janeiro}

,

P.O.Box 2324,20001-970

-

Riode Janeiro

-

RJ

.

Brazil

*The COPPEAD School ofBusiness,Federal UniversityofRiode Janeiro,

P.O

.

Box 68514,21945

-

970

-

Rio de Janeiro

-

RJ, Brazil

Production

Engineering Department,Fluminense Federal University

.

Rua Passo da Pátrian(

' 156,24210

-

240

-

Niterói

-

RJ, Brazil

juarezalencar@br.inter.net, gelsongr@gmail.com,

eber@nce.ufrj.br, armando@coppead.ufrj.br, smecena@globo.com

Abstract

.

In this work we show how classification trees, a family of non

-parametric statistical methods, can he used together with RCPS (Resource

ConstrainedProject Scheduling)_{stochastic modeling and}simulationtoprovide

project managers with better insights into the project they run

.

Such insights

make iteasierformanagerstoanticipatechanges in planning that favorprojects

tohe delivered on time, within budget, andincompliance with available cash

flow and therequirementsthey were set to satisfy'. Also_, we discuss the impli

-cationsoftheseinsights for boththemanagement ofcomplex projectsand the

construction of effective business strategies

.

Resumo

.

Nesteartigo descrevemoscomo árvoresdeclassificação,uma família

de métodos estatísticos não

-

paramétricos, pode ser utilizada juntamentecom

modelagem e simulaçãoestocásticaparaoescalonamentode projetoscom re

-cursos escassos (_RPCS) _{com vistas afornecer} aosgerentes umentendimento

mais profundo dosprojetossobresuaresponsabilidade. Esteentendimento fa

-cilitaa implementação de mudanças no planejamentodas atividades, favore

-cendo a entrega de projetosdentro do prazo, de acordo com o orçamento e

fluxo_{de caixa},eem sintonia comosrequisitos que se comprometeram a satis

-fazer. Em adição discutimos as implicações das técnicas aqui apresentadas

para a gerência de projetosde grande complexidadee para a construção de

estratégiasde negócio.

I

jr_*

1. Introduction

Overthe last few decadestheenvironmentin which organizations do business has changed

considerably withenormousconsequencesfor project management. The business para

bytheinformation age,knowledge ageand technology revolution which we are currently

experiencing[Jonesetal. 2002]. For example,theexistenceof rigid production linesof

impersonalized tangible products that characterized the industrial revolution are being

successfully challenged by increasing demand for highly customized products and ser

-vices,decentralized workforce and intangibleproducts,openingnew vistas for industrial

andbusiness development [Hosni and Khalil 2004].The cell phone communication,com

-puternetwork

.

TV ondemand anddistance learning industriesarejust afew examples of

such vistas [Wagner 2005]

.

The increasing competition for market space in many industries worldwide has

become an important societal force of this time and age, putting extreme pressure on

organizationsto make their complex, customized outputsavailableas quickly as possi

-ble. Nowadays, response must come faster,decisions must be made sooner and results

must occur more quickly. Hence, time

-

to

-

market has become a critical success factor in

several areasofbusiness[ Meredithand Mantel2002]. On top of that, for companies to

be competitive, they have to reduce their costsand focus on satisfying theircustomers

[Frame 2002]. If you do notdeliver the productsand services yourcustomersvalue,for

the price they are willingtopay,

someone

elsewill.

Market pressure and the growing demand for new and more complex prod

-ucts and services have required organizations to practice creative destruction on a

non

-

stop basis by replacing old ways of doing business in order to create new ways

[Hamill 2000,Aroraetal. 2001]

.

However, this processof destruction and construction

requires all sortof different specialized knowledge,e.g. marketing,emerging technolo

-gies, finance, logistic, businessstrategy, etc. Therefore, although invisible, knowledge

has emergedasoneof themoststrategicassetsfor organizations [ Kakabadseetal.2001].

All of thishas forced organizations worldw ideto increase both the quantityand

complexity of projects they run. To remain competitive organizations have to innovate

constantly. The introduction of every innovation in productsand services requires the

executionof oneor,morefrequently,_severalprojets

.

_{Asthe paceof innovation increases},

so doesthe numberof projects. On the other hand, the demand fornew and morecom

-plex products calls for the execution ofmorecomplex projects;requiring the coordination

of efforts from multidisciplinary teams with advanced technical and business skills, the

establishment of strategic alliances withexternal partners,theoutsourcingof projectac

-tivities,and theuse of recently developed technology.

Nevertheless,_{short time}

-

to

-

market and fierce competitionfor market space require

projectsto beexecutedfaster, with tighter budgetsand less marginforerrors

.

Undoubt

-edly such constrains tend to put projets managers under enormous pressure to produce

results

.

When the pressure to deliver becomes toogreat,common senseoften goesout

thewindow,crucialstepsin the project development areignored,the end result is shoddy,

and therework required to repair the damage is far more expensive than if it were caught

in theplanningstages [Info

-

Tech Research Group 2003].

Effective project management in a lean resource environment requires good

planning and timely information, allowing problems to be anticipated and dealt with

before the worse happens[Wrightet al. 1999 ]. With the view' of antecipating prob

-lemsthat frequently prevent projects from finishing successfully, over the years, man

-*

agers have resorted to planning methods such as Gantt Charts, CPM (Critical Path Method),PERT (_Performance Evaluation and Review Technique) and,more recently,

toRCPS(ResourceConstrained Project Scheduling)stochasticmodeling andsimulation

[Lewis2000,Kerzner 2003]

.

Although thestochasticmodelingand simulationofRCPS problemshas proved

tobe apowerfultools for project planning in constrained environments,theconstruction

and analysis ofRCPS activitynetworksrequireconsiderable experiencein quantitative

model building andadvancedknowledge ofboth mathematics and statistics.

This work showshow classification trees,a family ofnoil-parametric statistical

methods,canbe usedtogetherwith RCPSstochastic modelingand simulationtoprovide

valuableinsight intoproject planninginconstrainedenvironments,making it easier for managerstoforeseechangesin planning that favor projectstobe deliveredontime,within

budgetand incompliance with availablecash flow andthe requirements they were set to

satisfy.Also,wediscusstheimplicationofsuchinsights forboththe projectmanagement

ofcomplexprojets and the construction of effectivebusiness strategies.

2

.

ConceptualFramework

One ofthe main goalsofproject schedulingis toproducea detailed planofproject re

-latedactivitieswith theview of allowingmanagers todealwitha large varietyof prob

-lemsbefore the worsehappens. Amongtheseproblemsone may find lackof specialized

or experienced labor, incompatible start and finish dates among activities, insufficient

funding,activitiesbeing executed in sequence when they shouldbe executed in

paral-lel,unavailabilityofequipment, etc. However,themostfrequent problem managersuse

project schedulingtosolveistheminimization of makespan1,othercommonpossibilities

includeminimization ofcost,maximizationof financialresults,maximization of quality

measures,etc.[Zhuetal

.

2005]

.

2.1

.

Resource-ConstrainedProject Scheduling

Project schedules that are subjected to precedence and resource constraints are called

“Resource

-

Constrained Project Scheduling" _{in the literature, or RCPS for short}. _Not

surprisingly,thevastmajorityofprojects inthe real worldfaceRCPSproblems. Hence,

thegreat amount ofattentionthat theacademic worldand industryhavebeenpayingto

effortsin dealingefficiently with RCPSproblems

.

Over the years numerous methods have been proposed to solve RCPS

prob-lems,such as: implicit enumeration,branch-and

-

boundprocedure,schedule generation

schemes (SGS), X-pass

.

etc. A comprehensive review of these methods is found in

[Demeulemeester andHerroelen2002,Kolisch andHartmann 2006]. Despite the differ

-ences these methods may have, they can all be classified in just twocategories: exact

methodsandheuristicmethods [CastilloandMu/ /oz2004].

Exact methods are usedtofindtheprecisemaximum or minimum valueofavari

-able under consideration. Forexample,theminimumproject duration or its maximum

financialreturn. However,these methodshaveconsiderable limitationsthat becomeev

-ident when projects haveagreat number of activities or complex resourceconstraints.

Usually,in these circumstances a solution cannot be found within reasonable computing

time. Heuristicmethods,on theother hand,usea schedule priority criteria toprovide an

approximate solution to RCPS problems

.

They are particularly useful when the use of

exactmethodsarenot feasible.

In theheuristicmethods every activity is initially a potential candidatetobesched

-uled. However,activitiescan _{only be scheduled if all its precedent activities have been}

completed and the

resources

required for its execution are fully available

.

Unfortunately,

wheneveractivities share resources, it may imply that they cannot be executed concur

-rently. Theuseofa heuristic is then necessarytodecidewheneach activity shouldreceive

its required resources and be executed as a result. When no real candidate activities are

available,theclock advancesuntil oneof the activitiesin progress is completed

.

At that

point in time resources are freed and the process is repeated, i.e. candidate activities are

identified,

resources

arechecked for availability and activities are scheduled. The total

duration of a project is the time required forthe completion of all its activities.

Thefollowingare examples ofheuristicsfrequently usedtodeal with RCPS prob

-lems: shortest processing time(SPT),most immediate successors(MIS), late start time

(LST),firstcome_{first served}(FCFS)

.

A thoroughaccountoftheseheuristics is provided

by[Goerlichand Olaguibel1989]. Asa mathematical problem RCPS belongs toa cat

-egory' where, in general,an optimal solution cannot be found in a linear or polynomial

timeframe,i.e. the NP

-

hardcategory [ Blazewiczetal

.

1983]. 2.2

.

ClassificationTrees

The _{techniques described in this article} to analyze RCPS stochastic models make

extensive use of classifications trees, a class of statistical inferential methods con

-ceived by Morgan and Sonquist in the 1960’_{s [ Morgan and Sonquist 1963] and later}

perfected by others, such as: [ Kass1980]_, [Breiman_etal

.

₁₉₈₄]_{, [Quinlan 1992],}

[ Loh and Vanichestakul 1988] and [ Loh and Shih 1997]

.

As an inferential method, classification trees seek toexplain the behavior of a

target _{variable by combining different values of a given set of predictive variables. To}

achieve this goal,the values of thepredictive_{variables aresuccessively combined insuch}

a way that an n

-

dimensionalspace is portioned into increasingly morehomogenoussets

of values with respect to thetarget variable. The way the portioning is doneallows the

final result to be presented asaflow

-

chart whoseformat resembles atree,so thenameof

thefamily ofmethods. Furthermore,the information presented in theflow

-

chart may be

easilytranslated into asetof rules thatindicate thelikelihood ofoccurrenceofvaluesin

the domain of the target variable for different circumstances

.

Classification trees are non

-

parametric methods, i.e. no restrictions are imposed

onthe_{distribution of values of predictive andtarget variables. Inaddition},these variables

are allow ed tohold all sort of relationshipsamongthemselves

.

All of thismakes iteasier

to use classification trees tosolve problems in the real word, where the distribution of

valuesof variables andtherelationships that they hold among themselves are frequently

unknown

.

Therefore,not onlyclassificationtreesare afamilyofrobust methods,but the

way theresultsarepresented makesunderstanding easierandfacilitates their dissemina

-tion amongall interested parties

.

-factory results even in the presence of noise and when little data is available; mak

-ing it a _{very attractive class of methods to be used in all sorts of different situations}

[Witten and Frank2005]

.

In formal terms, given asetof observationsO

₌

{

o\

.

o2

,

•• •,

om

}

, whereevery

Oj [i..m] O is a tuple (•/*],J:2 r

„

) and each tuple component x

,

_e[i..n] may take

value in adifferentdomain,thenlet p [j m bethevalue of the tuplecomponent

X,ofO j. In thesecircumstances,avariable _i 7)' in

O

isan undefinedvalueof the set

{

t

_’

i

.

i, i\%2,. .

.

, Moreover,let ir

„

be the target variable,whosebehavioronehopes to explain_{by combining the values of}?rj,w₂

.

•••

.

wn

_-\

.

Alsolet

w

„

takevalue in a_finite set J

.

In the classification tree paradigm theset of variablesin O is exhaustively exam

-ined for relations oftheform:

ifXi isa continuous variable

Xi

<

r

,

or

X, G

{

_ki

,

k2

,

k¿

.

• ••

.

k¡

}

.

ifXiis a discrete variable.

wherer and _[|.j_] belongthe domainof

xt .

Each relation

RXi

_<ror

R

_.¡,e{k

^

-

Xi) that is

found allowsOtobe partitioned intotwosets,i.e.

_OR

andO^R

,

such that

ORHO

-,R

= {

}

and

_OR

U0-,R

=

O

.

In thiscase

.

OR

contains the observations in_{O for}which Rholds

and0~,_Rthe observationsforwhich the negation of Rholds.

A metric M is then used toevaluatehow diverse the data in O

,

_OR

andO^Rare

regarding the elements in Thedifference between M(O) and the weighted average

of M(

_OR

)and

M

(

O

_^R

)

indicates the contribution of relation Rfor the reduction in the

diversityoftheelements in J asaresultofpartitioning

O

into

_OR

and

O

-^R

.

Becauseone

wantsdiversitytobe reduced asfastas possible,therelation R that provides the biggest

reduction in diversity is initially used to partition

O. The

process is then successively

reapplied to

_OR

andO^R

,

until

no

gain in the reductionofdiversity is achieved

.

In the classification tree paradigm, when J has only two elements, one of the

most frequently used diversity metric istheGini diversity index. The index

was

initially

proposed _{by Corrado Gini [Gini 1939] and later adaptedby[Breimanetal. 1984] for the}

development of classification methods

.

In formal terms, fora given set of observations

Ö,Giniis calculated as

1(

0

) = 1-5, (1)

where5

₌

P( ji

_\

ö

)2 _f

°

r 3i J, and P(j

,

\

0) is the probability of occurrence of

objects j

,

inO

.

In thesecircumstances the reductionin diversity provided by a relationR

is given by

A1(0)

₌

1(

0

)- {¡(

_{O R}

) x p R4- I(

O

^R) X ]K R)

where PR and p^Rarerespectivelythe proportion of elements in

OR

andO_^R

.

(

2

)

3. Mining

RCPS

Stochastic

Models

with Classification

Trees

According toSeneca(4BC

-

AD65),the Roman philosopher:

“Rules make thelearner'_{s path long,w'hile examples make it short and}

Asa result, themining process presented in this article is introduced with the help of a

real

-

world inspired example.

Suppose that a chain of furniture stores decides to create a catalog to promote

someoftheproducts they sell toa largegroupof prospectsata special price. The proper

undertaking of this task requires that eight interdependent activities are efficiently exe

-cuted withina time frame,i.e.

1

.

Product Selection

-

that choosesthe productsthat will be advertised in the catalog;

2

.

Prospect Selection

-

that identifies the prospects to whom the catalogsare going

tobe mailed;

3. Pricing

-

that establishes thepromotional price of every product tobe advertised

in the catalog;

4. Catalog Design

-

where thegraphicand textual aspect of thecatalog,andaccom

-panyingadvertising material are conceived andputtogether;

5. Labe! Printing

-

where labels with prospects' _{names andaddressesare printedand}

organized:

6. StockControl

-

that makes sure that the productsadvertised in thecatalog will be

availablefor shippingwhen theyare ordered;

7

.

Catalog Printing

-

where theactualprint of thecatalog is done;

8. Catalog Labeling & Mailing

-

which labels the catalogs with prospects' _names

and addressesandsends them totheirintendeddestinationsover themail

.

Toughcompetition in the furniture business has brought down profit margins over the years,as a result the chain of furniture storesoperates witha skinny employee struc

-ture.Therefore,_{only two people have been selected}towork onthecatalog project.They

aregoingtobe named Mimi and Ed

.

Table1 shows the human resourcesrequired by each

of the project'_sactivities.

Table1.Resources required by each of the project’sactivities.

Activity ResourceRequired

Label Description

PdS Product Selection Mimiand Ed

PsS Prospect Selection Mimi

Pricing

P Mimi and Ed

CD Catalog Design Ed

LP Label Printing Mimior Ed

SC Stock Control MimiorEd

CP Catalog Printing Mimi or Ed

CLM Catalog Labeling & Mailing Mimiand Ed

Figure I presentstheproject'_{s networkof activities. In that figure Product Selec}

-tion is thefirst activity tobeexecuted and Catalog Labeling and Mailingthe last. More

-over,an arrow connectingtwoactivities suchas Product Selection

that the latter may onlystart when theformer has been completed and all thenecessary

resourcesare available.

Asthe project has tobecompleted withina time frame, it is crucial thatmanage

-mentis made aware of itsexpectedmakespan inrespect tothecurrentresource constraints

Prospect Selection Label Printing

t

Catalog L&M Stock Product

Selection Pricing Control

i

Catalog

Design

Catalog Printing

Figure 1.Theproject’_{snetworkofactivities.}

and thedurationofthe different project activities.However,becausetheseactivitieshave

notbeenexecutedyet, theirdurationcanonlybe estimated. Inthiscase,with thesupport

of other experiencedproject managers anda database of previously executedprojects,

a three point estimate hasbeenestablished for eachactivity,indicatingtheirminimum,

mostlikelyandmaximumexpectedduration.Table 2presentsthese figures.

Table 2. Minimum, maximumand most likelydurationof project activities.

Activity Activity Duration

Minimum Most Likely

w Maximum PcIS

—

3 6 PsS 3 6 8 P 4 6 7 CD I 8 10 LP 7 9 1 1 SC 5 6 7 CP 4 5 8 CLM I 2 4

Consideringthat theexactduration of each activity is unknownand that the avail-able resources may be insufficient to ensure that all activitiesare executed when their

precedentsare completed,a stochastic simulationmodel has been built to analyze the

project makespan.Inthismodel,theduration of each activity is described byatriangular

probability density function,oneofthemost widelyused functionstodescribe activity

duration[Chung2003].

Subsequently the stochastic model wassubjectedtoasimulationprocess,_w'here

resourceswere granted tothe first activity toplacearequest for them. During

simula-tion the durasimula-tion ofeach activity wasrecorded in the formofapercentageoftheir re

-spective timerange. Also,theactivity waiting timefor resourceallocationwasrecorded

togetherwith theoutcomeofeachsimulatedscenario,indicating whether the project

fin-ished withintheallowed time. Table 3 presentsthe figurescollected during simulation.

Table4describes the meaning ofthecolumns presented inTable 3. See[Chung 2003] for

F:_{orexample,asindicatedby variablesSenandCD,inthe first simulated scenario}

theexecutionofCatalog Designconsumed 25.4%ofits time range,i

.

e

.

,₁₄-0.254 x( 10—

1)=3.3 timeunits

.

Moreover,the variable

_Leo

shows thatthe necessaryresourcesforits executionwerebeingusedbyother activitiesat the timetheywererequestedand that 4.1 time units passed until theywerereleased

.

Itshouldalso be noted thatonlytwoactivities

had their waitingtime for resource allocationregistered

.

Thisisdue tothe fact that no otheractivities hadto wait forthe allocation of resources they needed

.

Figure2shows theproject makespanclassificationtreebuiltwiththehelpofthe

SPSS software(www.spss

.

com),usingthedatagenerated during thesimulationprocess

and the CRToption,anenhanced variation of[Breimanetal. 19X4]approach to classi

-fication

.

In that figure the box labeled Node 0 is the root ofthe classification tree

.

It

contains the total numberof observationsavailable foranalysis,i

.

e

.

5,000 inthis case

.

Also,itdisplaysthe number and proportion of the different scenariosinwhich thecatalog

projectfinishedand didnotfinishontime.

Forexample,initially,in60.7% ofthegenerated scenariostheproject finishedon

time,whilstin39.3% itdidnot.Itshouldbe noted that the relation that is usedtopartition

the initialsetof scenariosis Lip

_<

4.8,and that,as aconsequence, Node I contains the

4,110observations forwhich thisrelation holdsandNode2theremaining890

.

Becauseoftheincrementalway in which thetreeis constructed,all relations that

hold fortheobservations in anode also hold for the the observations in its descendants

nodes

.

For example,in thescenarios that are part of Node3the label-printing waiting

time for resource allocation is smaller thanor equal to4.8 time units (

_LLP

_<

4.8)and

Table 3. Simulation results connecting the duration ofprojectactivities and wait-ing time for resource allocation with the project’s outcome.

Sen PdS PsS P CD I P SC CP CLM

_Leo

_{L I P}

Rst 44.4 88.3 1.2 25.4 24.5 36.6 36.8 10.9 4.1 0.0 In 2 80.6 13.6 70.4 67.6 14.7 16.1 24.1 76.9 0.0 3.5 In 3 34.8 78.7 0.9 13.8 32.9 66.1 49.3 21.2 4.1 0.0 In 4 40.7 84.2 80.5 29.2 64.5 20.7 84.2 81.6 0.0 4.4 Out 38.5 92.2 27.3 84.6 45.2 49.1 85.8 31.3 0.0 4.6 Out n

Table 4. Meaning of the variables whose values were collected during the simu-lation process.

Variable Meaning

Sen

Scenarioidentifier

.

PdS

,PsS

.

• • •,

CLM

Duration of activities PdS

.

PsS

.

,CLM expressed as a percentageoftheirrespectivetime range

.

Leo

aid

_LLP

Waitingtimeforresourceallocation of activitiesCDandLP

.

Rsl Theoutcomeofagiven scenario,where Inindicates that the projectfinishedwithin the allowed time and

Out

indicatesoth

4 Node 0 Category % n n Out 39.3 1964 607 3036 iOut

_*

I In

'

i I in I Total 100.0 5000 I

1

>4,8 <=4.8 Node2 Category % Node 1 Category % n n 69.8 621 30,2 269 32.7 1343 67.3 2767 Out Out In In Total 17,8 890 82.2 4110 Total

EJ

CD >08 <_*0.8 Node 4 Category % Node 3 Category % n n 52.3 944 477 860 17 3 399 82 7 1907 Out BOut In In 36.11804 Total 46 1 2306 Total

Î

>41 <=41 Node 8 Category % Node7 Category % n n 46.3 132 537 153 Out 13.2 267 86,8 1754 Out In In 5.7 285 Total 40 4 2021 Total EJ EJ

.

LP CP >0.6 <= 0.6 <= 0.6 >0.6 Node16 Category % Node15 Category % Node13 Category % Node 14 Category % n n n n 77.0 67 23.0 20 mOut 32.8 65 67.2 133 Out 9.7 173 90,3 1611 &Out 397 94 60,3 143 Out In In In In 1.7 87 4.0 198 Total Total 4.7 237 Total Total 357 1784

the time spent in the design ofthe catalog issmaller thanorequalto80% of its estimated time range (_{C D}

_<

_0.8). Table 5 shows all the relations that hold forthe leaves of the

tree presented in Figure 2, i.e. for the nodesthat have nodescendants,together with the

proportionof In'_{sand Out}’_s.

Table 5_{. Rules indicating in which circumstances the catalog project is more} likelytobe finished ontime.

Node Rule _Outcome

Out In

LLP

>

4.8 2 _{30.2% 69.8%} 4

_LLP

_<

4.8and

C D >

0.8 47.7% 52.3%

LLP

<

4.1 and

C D

<

0.8and C P

<

0.G 13 _{90.3% 9.7%}

LLP

<

4.1 and

C D

_<

0.8and

C P

> 0.0 14 _{60.3% 39.7%}

15

_LLP

>

4.1 and

_{L u}

>

<

4.8andC D

<

0.8 andL P

<

0.6 67.2% 32.8%

LLP

>

4.1and LL p

<

4.8andC D

<

0.8 and L P

>

0.6

16 _{23.0% 77.0%}

It should be noted thataccordingto_{the information displayed in Figure 2}, ifthe

project manager can ensure that the label

-

printing waiting time for resource allocation issmaller than or equal to4.8time units (

_LLP

_<

4.8), then the chances of the project

finishingon timegoesfrom 60.7%to67.3%. However, ifthey can also ensure that the

time spenton the catalog design is smaller than orequal to80% ofitstime range(C D

<

0.8), _{then the chances of the project being delivered on time increases even further to}

82.7%

.

In addition,ifthe label

-

printing waitingtimeforresourceallocation is shortened

to at most4.1 time units (

_{LP <}

4.1) and the catalog printing is carried outin less than

orequal to_{60% of its estimated time range(C P}

_<

_0.6),then thechances of the project

beingfinished asplannedgoesto90.3%

.

4

. Discussion

At the outset of this articlewe undertook tosuccessfully mine RCPS stochastic models

with the view of making it easierfor managers toanticipate tactical changes in project

planning. Bellow weanswersome key questions about the implications of theinsights

provided by classificationtreesfor both project management and the construction of ef

-fective business strategies.

4.1. What are the necessary steps leading to the successful mining of RCPS stochastic models?

Tosuccessfully mine RCPS stochastic models with the view’of helping managers toan

-ticipate changes in project planning _{that increase the chances of finishing the projecton}

timeonemaytakethe followingsteps:

1. Build a stochastic model that properly representstheproject'

_s

_{activities,theirin}

-terdependencyrelations and the resource constrainsto whichthey are subjected;

2

.

Run a simulation process that, for each scenario, collects the project outcome

indicating_{whether it finished on time or not. In these circumstances a scenario is}

composedof_{the duration of all project activities as percentage of itstimerange},

3

.

Use the datacollected during thesimulation process toconstruct aclassification

treethat hasthe projectoutcomeasits target variable;

4

.

Examine the treecarefully looking for waysto improve the chances of finishing

theprojectontime;

5

.

Makethe necessary adjustments in the project planning of activities;

6. If any adjustments are made, then the stochastic model ought to reflect these

changes,thesimulationprocessshould be rerun andtheclassification treerebuilt.

4.2. Howdo usersofRCPSstochastic models benefitfromclassification trees?

One of the main benefits of building an RCPSstochastic model is the insight itcan po

-tentially provide on the dependency relations thatexists among the duration of project

activities,the waiting timefortheirresourceallocationandthe projectoutcome. Theun

-derstanding of these relations allows the identification ofactivitiesthat moststrongly in

-fluencethe outcomeofaproject,prompting changesin planningthat increasethechances

ofprojects being deliveredon time.

However, even theconstruction and analysis of small RCPS stochastic models

require considerable knowledge of mathematics and statistics, including the use of prob

-ability densityfunctionsfor both discrete and continuous variables,sampling,randomly

generatedscenarios,measuresof central tendency and spread,estimation,etc. Asa result,

many project managers are unabletoenjoythe benefitsofusing this trulypowerful tool,

because they just lack the necessarytechnical skills.

In addition,thetwostatisticalmethods that aremostfrequently employedtoiden

-tifycauseand effect relationshipsamong variablesin RCPSstochasticmodelsarelinear

correlation and regression. The proper useof these methods toanalyze the relationship

that existsamong theduration of project activities, waiting timefor resource allocation

and projectoutcomerequirestheserelationstobelinear,whichmostoften isnot thecase.

Moreover, linear regression requires predictive variables to be independent, i.e.

thevalue that oneof thesevariables may take may not depend upon the value that other

predictive variables take. Unfortunately, there is a natural tendency that the duration of

project activities depend upon each other. For example, in many industries time spent

on planningand designingtendstostrongly influence timespent on testing and delivery.

Therefore,situations in which the proper use of linear regression is welcomedo notcome

by as frequently as one may hope for.

Finally,both correlation and linear regression do not dealeasily withcategorical

variables. Linear regression requires thesevariablestobetransformed into asetof inde

-pendent variables

.

Linear correlation requires variables tobe of ratio scale, while rank

order correlation requires them to take value in an ordinal set

.

Furthermore, linear re

-gression requires the target variable tobecontinuous. See [ McClave and Sincich 2005]

for an introduction toregression and correlation, and [Kurpiusand Stafford 2005] fora

discussionabout measurementscales

.

Although, classification trees cannot make the construction of RCPS stochastic

models any easier, they do help w'ith theanalysis of the simulation process, particularly

with the extraction of information that favorstactical changes in project planning. The

use

of classification treesdoes not require predictive variablesto be independent nor to

despite its scale ofmeasurement being nominal, ordinal, scalar or ratio. All ofthis not

only greatly facilitates the analysisof RCPS stochastic models, but also makes it faster

and lesspronetoerrors

.

4.3. Are_{there anv additional benefits for users of RCPS stochastic models?}

While correlation uses a number that varies within well defined bounds,typically from

-

1 to I, to indicate the intensity of a relation that holds between two variables, linear

regression uses a polynomial equation to describe the relationship that holds between

a set of predictive variables and a target variable. Although the interpretation of these

resultsare not particularlydifficult,they dorequiresomeknowledge of mathematics and statistics

.

On the other hand, classification trees yield simple logical expressions that de

-scribe the dependencyrelation that hold among predictive variablesanda target variable.

Suchexpressions areeasytoreadand understand,even by those with a restricted knowl

-edge of mathematics andstatistics. Moreover,they do indicate,clearlyand incrementally,

themostcritical values that predictive variableswithdiscrimination powermaytake,i.e.,

values that most strongly influence a project'_{s outcome}

. This makes it easier for project

managers and theirteamstoidentify what needstobe doneandwhen itneedsto bedone,

before theworst happens.

4.4. Can the techniquesdescribed in thisarticle be used toanalyze otheraspects of

project management besidesmakespan?

Althoughalltheexamplesthathave beenused throughout this

article

have been concerned

with project makespan,there is noreason whyclassification trees cannotbe successfully

combined_{with stochastic modeling and simulationtoanalyze differentaspectsof project}

management,suchas cost,financing, budgetandcash flow compliance,operational risk,

human resourcehiring and allocation,quality conformity,etc.

Each of theseaspectsis more easily and effectivelyanalyzed with the right choice

of predictive and target variables

.

For example, for project cost analysis it is usual to

choose the estimatedcostof each activity as predictivevariablesandtheproject totalcost

as the target variable. However, because project cost may also be influenced by many

other factors,as for example the existence of penalties for late delivery, _{loss of qualified}

and experienced labor,sudden change in the interest and exchange rates, lack of proper

resources,equipment malfunction etc

.

, it is not uncommon that project cost analysis is

improved by the inclusion of a multitude ofothervariables related to both financial and

non

-

fmancialaspectsof project management.

Whateverthesituation, the right combination of predictive andtarget variablesis

bound to yield rules that help managers to keep their project on track, making tactical

changes in planning where andwhentheyareshown tobenecessary.

4.5. Can the combinationofclassificationtreesand RPCSstochastic modeling and simulation be used asa negotiation tool?

Despite all the efforts that project managers may place on their tasks, projects are full

of uncertainties that make planninga difficultendeavor. Not only are projects concerned

activities have been completed, _{they will not be executed in the future exactly the same}

way as in thepast. Therefore,reliableactivitycostandtime span estimation arenoteasily

achieved. Also, it isnot unusual that projects will have people workingtogetherfor the

first time; not to mention that many projects are influenced by a variety of economic,

social and political factors suchas interest rate, flow of importsand exports, change in

consumerbehavior,_{proximity to the electoral period},_{introduction of new technology},etc.

Hence,projects are very unlikelytorunasplanned,requiringfrequent adjustments

in the courseof time. Themorecomplex and lengthy the project, the moreadjustments

it is likely to require. While some projects many not need adjustments involving over

budget investmentsand deadlineextensions,othersgo the otherway around.

Because the rulesgenerated byclassification treesare conjunctions of logical ex

-pressions that are easy to read and understand, and can be presented to non

-

technical

personnel,they may be used asanawareness tool tomake senior managementmore con

-scious of critical aspectsof a project; in particular of thoseaspects where further invest

-ment is necessary. In thissense, the incremental w'ay in which the rulesare presented

makes it easier for project managers to indicate where the extra funding should go,as

well asthe consequent increase in the likelihood offinishingtheprojectontime.

For example, in the catalog project _{iffunding is made available to ensurecom}

-pliance with

_<

4.8and C D

<

0.8, thechancesof having the project finished on

time go from 60.4% to82.7%. However, ifadditional funding is made available to also

ensure that L

<

4.1 andC l}

<

0.G,then thechancesoffinishingthe project on time

increaseto90.3%. SeeNode 13inFigure 2. Therefore,notonly classification trees make

theanalysis of

RCPS

stochastic modeleasier, but they

can

also be usedasa negotiation

tool with stakeholderstoensure that a project receivesthe resources it needs in a timely

L P

manner

.

4.6. _{What are the implications of the insights prov ided by classification trees to}

project management and business strategy?

In the extremely competitive world that has emerged as a consequence of the advent of

the Internet and the globalization of theworld economy,organizations in many lines of

businesses have found themselves underenormous pressureto innovate,improving con

-stantly the quality ofthe products and services they market

.

Becauseinnovation depends

upon theexecutionof projects,thenumberand complexity of projectsthatorganizations

run annually have increased considerably.

Acombination of toolssuchas classificationtreesand RCPSstochastic modeling

and simulation that helps to increase the chances of projects being delivered on time,

within budget and according to the quality aspectsthat wereagreed upon, is certain to

favormoreeffective project management w ith positive impacton thenumberof projects

thataresuccessfullycompletedand,asa result,on thecompetitive aspect of business.

5. Conclusion

In this article we have demonstrated the viability of successfully combining classifica

-tion treeswith RCPSstochasticmodeling and simulation toprovide managers with the

meansto anticipatechanges in project planning that favor projects beingfinishedsuccess

project managementincludingproject makespanandcost,with many advantages ofmore

classical methods.

Classificationtreesarenotdifficulttobuildaspredictivevariablesarenot required

tohave any particulardistributionof valuesor holdanykindofrelationshipamongthem

-selves. Moreover,the rules generated byclassificationtreesareeasytoread, understand

and communicate toall interested parties, helping toavoid mis

-

communication among

team members and also w ith the identification of most needed adjustments in project

planning. c

Furthermore, easy to understand rules favor the involvementof senior manage

-ment with critical aspects of project planning and execution,making iteasier for project

managers to ensure that the necessary investmentsare made where and when they are

most needed

.

All of this makes classification trees a verv attractive toolm/ to be used in

combination with RCPSstochastic modeling and simulationtosupport themanagement ofcomplex projects in the real world.

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