factors affecting cost performance of construction in india

1.

Editorial board Page CO2

2.

Transferring projects to their final users: The effect of planning and preparations for commissioning on project success Pages 257-265 Dov Dvir

3.

The effect of systemic errors on optimal project buffers Pages 267-274 Dan Trietsch

4.

Simulation-based estimation for correlated cost elements Pages 275-282 I.-T. Yang

5.

Factors affecting cost performance: evidence from Indian construction projects Pages 283-295 K.C. Iyer and K.N. Jha

6.

Cost estimation of a software product using COCOMO II.2000 model a case study Pages 297-307 R. Dillibabu and K. Krishnaiah

7.

Designbuild pre-qualification and tendering approach for public projects Pages 309-320 Khaled Al-Reshaid and Nabil Kartam

8.

Evaluation of stakeholder influence in the implementation of construction projects Pages 321-328 Stefan Olander and Anne Landin

9.

Framework for project managers to manage construction safety Pages 329-341 Evelyn Ai Lin Teo, Florence Yean Yng Ling and Adrian Fook Weng Chong

International Journal of Project Management Copyright 2006 Elsevier Ltd and the International Project Management Association (IPMA). All rights reserved

Volume 23, Issue 4, Pages 257-341 (May 2005)

The International Journal of Project Management is devoted to the publication of papers which advance knowledge ofthe practical and theoretical aspects of project management. The Journal aims to: provide a focus for worldwideexpertise in the required techniques, practices and areas of research; present a forum for readers to share commonexperiences across the full range of industries and technologies in which project management is used; cover all areas ofproject management from systems to human aspects; and link theory with practice by publishing case studies andcovering the latest important issues in special series.

Contributions Those wishing to submit full-length papers or case studies should send four copies to the editor,Professor J R Turner, at the address below. Contributors should refer to the Notes for Authors printed in this issueof the Journal. These are also available from the publishers.

INTERNATIONAL EDITORIAL BOARDProfessor D Arditi Professor and Chairman,Department of Civil and ArchitecturalEngineering, Illinois Institute of Technology,3201 South Dearborn StreetChicago, IL 60616-3793, USAE-mail: [email protected]

Professor Karlos A Artto Helsinki Universityof Technology, PO Box 9500FIN02015 HUT, FinlandE-mail: karlos.artto@hut.

Professor B Boeva University for National andWorld Economic Studies, Studentslei gradCh. Botev, 1100 Soa, BulgariaE-mail: [email protected]

Professor Sergey Bushuyev Kiev NationalUniversity of Construction and Architecture,31 Povitrootsky pr., Kiev 04037, UkraineE-mail: [email protected]

Dr Juan Luis Cano Department of Design andManufacturing Engineering, University ofZaragoza, Maria de Luna 3, 50015 Zaragoza,SpainE-mail: jlcano@[email protected]

Mr Giles Caupin Caupin & Associes,3 Rue Creuse, F-77710TREUZYLEVELAY, FranceE-mail: [email protected]

Dr L. Crawford 10 Amaroo Crescent,Mosman, NSW 2088, AustraliaE-mail: [email protected]

D H Curling Principal Consultant,LODAY Systems Ltd, 1786 Devlin Crescent,Ottawa, Ontario K1H 5T6, CanadaE-mail: [email protected]

Dr J D Frame UMT, Suite 3061925 N. Lynn StreetArlington, VA 22209, USAE-mail: [email protected]

Professor Qian Fupei PO Box 617, NorthwesternPolytechnical University, Xian, 710072,Peoples Republic of ChinaE-mail: [email protected] Roland Gareis ProjektmanagementAustria-Institute, Wirtschaftuniversitet,Franz Klein Gasse, 1190 Vein, AustriaE-mail: [email protected] Shlomo Globerson Faculty ofManagement, Tel Aviv University, POB 39010Ramat Aviv, Tel Aviv 69978, IsraelE-mail: [email protected] Joop Halman University of Twente,Faculty of Engineering Technology,Department Construction EngineeringManagement, PO Box 217 7500 AE EnschedeProfessor Francis Hartman Faculty ofEngineering, University of Calgary,2500 University DriveNW, Calgary, Alberta, CanadaE-mail: [email protected] M Elizabeth C Hull School ofComputing and Mathematical Sciences,University of Ulster, Newtownabbey,Co Antrim, BT37 0QB, N. Ireland, UKE-mail: [email protected] Adesh Jain Director in Charge,Centre for Excellence in Project Management,A-48, Sector V, Noida 201 301, IndiaE-mail: [email protected] Jon Lereim Institutt for Teknologile-delse, Elias Smiths vei 15, Postboks 580,1302 Sandvika, NorwayE-mail: [email protected] Rolf A Lundin JonkopingInternational Business School,Jonkoping University, PO Box 1026,WE-551 11 Jonkoping, SwedenE-mail: [email protected]

Professor Christophe Midler Centre deResearche de Gestion, Ecole Polytechnique1 rue Descartes, 75005 Paris, FranceE-mail: [email protected]

Professor Peter Morris Professor of Constructionand Project Management, The Bartlett Schoolof Graduate Studies, UCL The Faculty of theBuilt Environment, Torrington Place Site,Gower Street, London WC1E 6BT, UKE-mail: [email protected]

Professor Jerey Pinto School ofBusiness, Penn State Erie, Station Road,Erie PA 16563, USAE-mail: [email protected]

Professor Nigel J Smith Department of CivilEngineering, University of Leeds,Leeds LS2 9JT, UKE-mail: [email protected]

Hiroshi Tanaka Project Services Division,Yokohama World Operations Center,3-1, Minato Mirai 2-chome, Nishi-ku,Yokohama 220-6001, JapanE-mail: [email protected]

Willi Vonrufs Project and ProcessManagement, Larchenstrasse 20,CH-8903 Birmensdorf, SwitzerlandE-mail: [email protected]

Professor Terry M Williams Departmentof Management Science, Graham Hills Building,40 George Street, Glasgow, G1 1QEE-mail: [email protected]

Professor K-T Yeo Nanyang TechnologicalUniaversity, School of Mechanical andProduction Engineering, Nanyang Ave,Singapore 2263

EDITORProfessor J R TurnerProfessor of Project ManagementISGI-Groupe ESC LilleAvenue Willy BrandtF 59777 EURALILLEFrance

Postal Address: EuroProjExWildwoodManor CloseEast HorsleySurrey KT24 6SA, UK

E-mail Address: [email protected]

INTERNATIONAL JOURNAL OF

PROJECTMANAGEMENT

International Journal of Project Management is the ocial journal of the International Project Management Association. Thejournal is available to all members of the IPMA at a special membership rate. For details of membership or enquires regarding theassociation, please contact:Ms Nancy Dol, IPMA International Secretariat, International Project Management Association, P.O. Box 1167, NL 3860 BDNijkerk, The Netherlands.Members of associations aliated to IPMA should contact their National Association for subscription details

INTERNATIONAL JOURNAL OF PROJECT MANAGEMENT

NOTES FOR AUTHORS

Scope

The International Journal of Project Management is devoted tothe publication of papers which advance knowledge on prac-tical and theoretical aspects of project management. The list ofkey words at the end of this guide indicates the scope of thejournal. Papers are selected for publication based on their re-levance, clarity, topicality, the extent to which they advanceknowledge, and their contribution to inspiring further devel-opment and research. The journal strives to maintain a balancebetween papers derived from research and from practical ex-perience. Authors are encouraged to submit case studies de-scribing the project environment; criteria and factors forsuccess; responsibilities of participants; managerial arrange-ments; human factors; contract forms; planning and controlsystems; problem areas encountered and lessons learned.

Submission of Papers

Authors are requested to submit their original manuscript andgures plus three copies to Professor .J. R. Turner, EuroProjex,Wildwood, Manor Close, East Horsley, Surrey, KT24 6SA,UK. (When sending revisions. only two copies are required.)The editorial oce does not have bulk photocopying facilitiesand so cannot receive papers by e-mail onlypaper versionsmust be sent by post.

Submission of a paper implies that it has not been publishedpreviously, that is not under consideration for publicationelsewhere, and that if accepted it will not be published else-where in the same form, in English or any other language,without the written consent of the Publisher.

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[1] Cooper DF. Chapman CB. Risk analysis for large projects:models, methods and cases. New York: Wiley, I987.

[2] Potter M. Procurement of construction work: The clientsrole: In: U J. Orams AM, editors. Proceedings of 7th AnnualConference on Construction Law and Management, KingsCollege, London, UK, 1995. p. 169194.

[3] Norwood SR,Manseld NR. Joint venture issues concerningEuropean and Asian construction markets of the 1990s. Inter-national Journal of Project Management 1999;17(2):8993.

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Please choose at least two key words from the following lists, asappropriate. This will assist the editor in choosing referees, aswell as helping with cataloguing.

General:

Implementing Strategy; Managing Programmes; ManagingProjects; Success and Strategy; Processes, Procedures; Systems.Project Oce; Audits, Health Checks; Systems Approach.

External Context:

PEST: Legal; Environmental; Value, Benet, Finance.

Implementation:

Functionality. Value; Conguration; Scope of Work; Organi-zation Resources; Quality; Cost; Time; Risk; Safety andHealth.

Life cycle:

Integration-Life Cycle; Start-up; Proposal and Feasibility;Design and Appraisal; Implementation; Progress; Commis-sioning and Close-out.

Commercial:

Value and Benet; Finance; Cash Flow Management; Taxa-tion; Insurance.

Contractual: Organization Design; Partnerships; Alliances;Procurement; Bidding; Contract Administration; Materials,Purchasing & Supply; Commercial Law; Claims; InternationalProjects.

People:

Management Structure; Teams; Individuals; Managing andLeading; Stakeholders; Competence; Culture; Ethics; Change.

General Management:

Human resource management: Marketing; Operations; In-formation technology; Finance and accounting; Strategy;Technology, Innovation.

nais

v D

versity

form

This paper examines the relationship between planning and preparing the project for transfer to its nal users and project success.

Four planning and preparation aspects are considered (development of operational & maintenance requirements, customer partic-

ipation in the development process, developers preparations for turning over the project to its nal users, and nal user preparations

out a project: extinction, addition, integration, and star-

unsuccessful or obsolete, may be terminated by starva-

tion, or in other words, by cutting out the funds for its

completion. Starvation is usually used when manage-

inclusion, integration, or extinction; a plan must be

sign responsibility for product support, if necessary [1].

Although the use of a termination manager for ensur-

ing that the project is complete and to deliver its out-

come (if successful) to its customers, is advocated by

several authors, and though project terminationE-mail address: [email protected].

International Journal of Project Manag


PROJECT0263-7863/$30.00 2005 Elsevier Ltd and IPMA. All rights reserved.vation [1]. Termination by extinction means the project

has been successful and achieved its goals: the new prod-

uct has been developed and handed over to the client; or

the building has been completed and accepted by the

purchaser. Projects terminated by extinction may have

been successful or unsuccessful. A project may be termi-

nated by institutionalizing it as a formal part of the

organization (addition) or by distributing the personnel,equipment and functions among the existing elements of

the parent organization (integration). Projects which are

developed to terminate it. The process of project termi-

nation is not an easy task. It is to be planned, budgeted

and scheduled like any other phase of the project life cy-

cle. Sometimes a special termination manager, whose

primary responsibility is to eectively and eciently

complete the termination process, is appointed. The du-

ties of a termination manager may include the following:

Ensure the project is complete, ensure delivery and clientacceptance, prepare a nal report, redistribute person-

nel, materials, equipment, and any other resources, as-for introduction into operational use), along with three measures of project success (project eciency, customer benets, and overall

success). The study is based on data from 110 defense projects performed in Israel and includes regression and correlation analysis

between the two sets of variables. The ndings suggest that customer participation in the development process and nal user prep-

arations have the highest impact on project success. Customer participation in the development process is highly correlated with

project eciency (0.45), while nal user preparations are highly correlated with customer benets (0.46).

2005 Elsevier Ltd and IPMA. All rights reserved.

Keywords: Project planning; Project commission & close out; Project success

1. Introduction

There are four fundamentally dierent ways to close

ment is reluctant to admit that the project actually

failed.

Regardless of a successful project is completed byTransferring projects to their and preparations for comm

Do

School of Management, Ben Gurion Uni

Received 20 April 2004; received in revised

Abstractdoi:10.1016/j.ijproman.2004.12.003l users: The eect of planningsioning on project success

vir

, P.O.B. 653, Beer Sheva 84105, Israel

22 June 2004; accepted 1 December 2004

www.elsevier.com/locate/ijproman

ement 23 (2005) 257265

MANAGEMENT

existing literature. Based on the review we propose four

rojechypotheses on the contribution of planning and prepar-ing the project for transfer to its nal users to project

success. A description of the research methodology is

presented in the next section followed by presentation

of the data structure and the reliability of the various

constructs. The next section contains the analysis of

the correlations between planning and preparations

variables and success variables, and the regression re-

sults between the three success measures and the plan-ning and preparing variables. We conclude with a

discussion of the ndings and their implications for

the practice of project management.

2. Theoretical background

The research body on project termination is rela-tively small in comparison to other research areas of

project management such as project planning, control,

success measurement, and risk assessment. Buell [3] in

an early article claims that the main reason for so little

information on the subject is simply because it is hard

to spell out specic guidelines for termination of

projects.

Most research on project termination focused onreasons for premature termination and not on the

introduction of the outcomes of successful projects into

use. Although, the decision to terminate a project may

be in certain situations more important than the deci-

sion to go on with the project, there is almost a unan-

imous agreement [1] that the termination stage of the

project rarely has much impact on technical success

or failure of the project. It has though, a great dealto do with residual attitudes toward the project constitutes a signicant part in the total project, it is of-

ten overlooked by project managers [2].

This paper examines the relationship between plan-

ning and preparing the project termination and com-

mission and project success. Our objective is to

analyze the relationship between the amount of eortinvested in planning and preparing the project for

transfer to its nal users and the degree of success

achieved, as seen from dierent points of view. The

analysis is based on data collected from 110 defense

R&D projects performed in Israel and includes four

planning and preparing for transfer aspects (develop-

ment of operational & maintenance requirements, par-

ticipation of the customer in the development process,developers preparations for turning over the project toits nal user, and nal user preparations for receipt of

the project and starting its operational use), along with

three measures of project success (project eciency,

customer benets, and overall success). The paper is

organized as follows: we begin with a review of the

258 D. Dvir / International Journal of Pthe taste left in the mouth of the client, senior man-agement, and the project team, which is important for

future projects, but of course have no impact on the

current one.

Among the studies on project termination we can

nd for example a study by Dean [4], who provides,

based on a small-scale survey, the frequencies of fac-tors reported as reasons for termination of R&D pro-

jects. Balachandra and Raelin [5,6] performed a

discriminant analysis of variables aecting R&D pro-

jects termination. De et al. [7,8] did a detailed quanti-

tative work on taking abandonment decisions from a

nancial point of view at dierent contexts. Shafer

and Mantel [9] developed a decision support system

(DSS) for project termination. The DSS is able to ana-lyze the sensitivity of various parameters of project ter-

mination, but the requirement for an extensive

database on projects of dierent types, limits its use

in practice. Archibald [10] prepared a check-list for

project termination. Stallworthy and Kharbanda [11]

categorized the problems involved in project termina-

tion into emotional and intellectual problems. Several

other studies on the same issue are those of Pintoand Mantel [12], Green et al. [13], Broockho [14],

Black [15], and Chi et al. [16].

Another stream of research closely related to the re-

search on project premature termination is the research

on project critical success factors (CSF). The list of crit-

ical success factors is often used as a yard stick for

assessing the chances of a project to end successfully

when encountering problems. Pinto and Slevins work[17,18] and other lists of critical success factors devel-

oped over the years, can be used for that purpose. When

several CSFs do not exist in a project, management mayconsider terminating it in order to cut the potential

loses.

Only few researchers see project commission, when

the projects outcome is handed over to its customersfor use, as an integral part of the project life-cycle. Thatis probably the reason for the lack of research on that

issue. The importance of the transfer phase to the suc-

cess of projects (not only the residual attitudes toward

the project), is indirectly evident from some of the stud-

ies on critical success factors of projects which have

identied the act of selling the project to its nal users

as one of the critical success factors [19,20]. Kleinsch-

midt [21], who studied the dierences in project manage-ment practices between Europe and North America,

noticed that in Europe project managers more actively

encourage customer involvement in the project execu-

tion than in the US. Customer involvement is clearly

one of the most important ingredients that contribute

to an ecient and smooth transfer of the project out-

come to its users.

Hadjikhanis [22] perception that every project is anepisode in project marketing is one of a few exceptions.

t Management 23 (2005) 257265The goal of marketing is dened as repetitive selling to

rojecthe same buyer. Following Hyden [23] who dened pro-

jects life to begin when one rm draws up a contractwith another rm, and it is dissolved at the end of the

operation phase when the transaction is completed,

Hadjikhani focused his study on the management of

the relationship left after project completion and thedevelopment and marketing activities after project sell-

ing. His hypothesis was that every project leaves sedi-

ment, and accordingly studied cases focused on the

phases before negotiation and after project completion.

This view is also shared by Faulkner and Anderson [24]

who claim that a project cannot be regarded as isolated

from former projects; projects are connected to each

other somehow.In summary, there are many studies on project termi-

nation, but only few of them deal (implicitly) with the

impact of the termination activities on the project suc-

cess. The act of selling the project to its future users

and customer involvement in the project execution were

already identied as factors contributing to project suc-

cess. It is obvious that the main reason for customer

involvement is to increase the chances that the projectsoutcome will meet the customer requirements and de-

sires. But why sell the project to the customer who al-

ready paid for it. The answer is probably that there are

other factors that help the customer to accept and start

using the new product. Furthermore, in our studies of

projects we have seen other activities that were meant

to improve the orderly transfer of projects to their nal

users and not only to establish successful and lastingrelations with the customer. Active involvement in the

development process and preparations made by the con-

tractor for turning over the project to its users are exam-

ples for such activities.

Some of these activities are aimed at improving the

eciency of the project execution, but most of them

are done to ensure that the customer will get the product

he needs and will start using it as soon as possible. Basedon the literature review and our own observations, we

propose the following hypotheses:

1. User involvement in the development of operational

& maintenance requirements is positively contribut-

ing to the overall success of the project and the cus-

tomer benets from its outcomes.

2. The involvement during the project execution of anescorting team representing the customer, positively

contributes to the eciency of the project and to

the customer benets from its outcomes.

3. The developers support for turning over the projectto its nal user positively contributes to the customer

benets from the project.

4. The nal user preparations for receipt of the project

and starting its operational use positively contributeto the customer benets from the project and to its

D. Dvir / International Journal of Poverall success.3. Research methodology

Correlation analysis is often used when it is necessary

to relate a set of variables to other sets of variables.

When one set or both contain a large number of vari-

ables, it is dicult to interpret the results and to ndcausal relationships among the variables. To simplify

the analysis, factor analysis is very often employed to

represent the large data set by fewer, easy-to-interpret

factors. The current study follows that methodology.

First, we employ factor analysis to reduce the large

number of planning variables pertaining to the hand-

over of the project to its nal users. The resultant factors

are correlated with the three main success dimensions(which were found in an earlier study to be more impor-

tant than the other dimensions [25]) and the results are

analyzed and discussed. Regression analysis is used to

enhance our understanding of the relationship between

the planning and preparing variables and success

dimensions.

3.1. Data

Data on 110 defense projects performed in Israel over

the last two decades were gathered using structured

questionnaires [26]. The questionnaires were lled out

by at least three key personnel related to the project

and representing the various stakeholders (the customer,

project management and procurement organization).

The projects in the sample were performed by a vari-ety of rms in the areas of electronics, computers, aero-

space, mechanics and others. The respondent

population included many types of defense projects:

new weapon systems, communication, command and

control systems, electronic warfare equipment, and sup-

port equipment development projects. The sample in-

cludes almost all defense development projects

performed under the hospices of the Israeli Ministry ofDefense at that period. Since the processes and proce-

dures used in the Israeli defense industry are similar to

those used in the US, the sample is probably a good rep-

resentation of that population too, nevertheless, it might

not be a good representation of defense projects per-

formed in other countries.

The questions solicited subjective evaluations on a

seven-point scale. For example, the level of involve-ment of the team escorting the development and inte-

gration of the project was determined by asking the

respondent the following question: According to your

assessment, how active was the escorting team in devel-

opment, integration and testing activities during the

project execution? The answer was given on the scale:

1 (not active at all) to 7 (extremely active). The ques-

tionnaires were administered in face to face sessionsby specially trained interviewers, all of whom had been

t Management 23 (2005) 257265 259previously involved with this type of projects in various

rojeccapacities. Most of the interviewers were retired ocers

from the Israeli Defense Forces with technical back-

ground and the others were MBA students in the man-

agement of technology track. For each project there

were three respondents: the project manager (or a se-

nior representative from the project oce); a represen-tative from the customer or end-users community; and

a representative from the government sponsoring orga-

nization. Although an eort was made to locate the

most informed interviewees for each project, it did

not always succeed. In some cases, instead of the pro-

ject manager, only a team member could be located

and interviewed, in other cases the contracting ocer

was replaced with a new ocer whose knowledge onthe project was only second hand. To compensate for

the less reliable answers, the interviewer, who became

well acquainted with the project history, completed a

separate questionnaire integrating the three sets of re-

sponses, giving a lower weight to the less reliable re-

sponses. The analysis presented here is based on the

integrative questionnaire.

Out of the data collected by this questionnaire, rele-vant data to project success and planning and prepara-

tion activities for the transfer of the project to its nal

users were used in this study to examine the relationship

between the development of the project operational and

logistic requirements, the eort invested in escorting the

development, the developer support for transferring the

project to its users and the user preparations for receiv-

ing the product and starting using it, and projectsuccess.

3.2. Measures

3.2.1. Success criteria

Project success was measured along three criteria

(two constructs measuring success from two dierent

points of view and an overall success measure) that werevalidated in previous research by Lipovetsky et al. [25].

1. Meeting planning goals (project eciency).

2. Customer benets (success from the customers pointof view).

3. Overall success (an integrative measure of project

success).

Table A.1 in Appendix A describes the responses to

the questionnaire items that addressed the two dimen-

sions of success used in this study.

3.2.2. Overall success measure

In addition to the two sets of success measures de-

scribed above, the questionnaire included an item

reecting the overall success of the project. Overall suc-cess was also measured on a 1 to 7 scale, where 1 repre-

260 D. Dvir / International Journal of Psents a complete failure and 7 represents outstandingsuccess. There were 108 responses, ranging from 1 to

7, with an average of 4.85 and a SD of 1.54.

3.2.3. Planning the Transfer of the project to its nal users

Twenty-two variables were used for estimating the

investment in planning and preparing for transfer ofthe project to its nal user. Factor analysis with Vari-

max rotation on all items was carried out in order to val-

idate previous grouping of the variables into four factors

and examine their internal consistency. The results of

the factor analysis closely resemble the original grouping

of variables in the questionnaire and include only vari-

ables with loadings of 0.55 or higher (Table A.2 in the

Appendix A). The independence of the four factors isdemonstrated by the low loadings of the variables com-

prising each factor on the other factors. Cronbachscoecient a was also calculated for each group. Thefour resultant factors are listed below. A short title for

each dimension and Cronbachs coecients are inparenthesis.

1. Development of operational & maintenance require-ments (O&M requirements, a = 0.76).

2. Escorting the development process (escorting,

a = 0.82).3. Developers support for turning over the project to its

nal user (developer support, a = 0.90).4. Final user planning and preparing for introduction

into operational use (user preparations, a = 0.95).

While the names of factors 1, 3, and 4 are self-

explanatory, the term escorting the development

process, needs some explanation. In many projects,

customer participation is a common practice; usually

representatives of the nal user are taking part in the

project denition phase and in the nal testing. Here,

in addition to representatives of the nal users, techni-

cal experts knowledgeable in the specic technologicalareas related to the project were an integral part of

the contractors development team. The main purposeof building such a team is to gain in-depth knowledge

of the nal product to enable maintaining and even

improving the product by the user organization with-

out any external help.

The list of items comprising each factor and their

descriptive statistics are shown in Tables A.3A.6 inAppendix A.

3.3. Data analysis and results

The central part of the data analysis consists of exam-

ining the correlations between the four composite mea-

sures of planning and preparing for transfer of the

project to its nal users with the three measures of pro-ject success. The factors scores were computed as the

t Management 23 (2005) 257265average scores of all measures comprising a specic fac-

Table 1

Correlations between average planning and preparing for transfer to nal user scores and average success scores

Escorting Developer support User preparation Project eciency Customer benets Overall success

O&M requirements Corr. 0.37 0.08 0.26 0.22 0.22 0.33

Sig. 0.000 0.531 0.053 0.093 0.031 0.001

N 102 64 58 101 92 101

Escorting Corr. 0.19 0.30 0.45 0.27 0.28

022

52

000

D. Dvir / International Journal of Project Management 23 (2005) 257265 261tor. The results of the correlation analysis appear in Ta-

ble 1.

There are 21 correlation coecients, and it is possible

that some will appear to be statistically signicant due to

the compounded eect of Type I error. Consequently,we have adjusted the critical signicance level to the

rather conservative value of 0.001. This means that the

compounded Type I error, i.e., the probability that

Sig. 0.127 0.

N 64 58

Developer support Corr. 0.

Sig. 0.

N 57

User preparations Corr.

Sig.

N

Project eciency Corr.

Sig.

N

Customer benets Corr.

Sig.

N

Bold font represents p 6 0.001.one of the 21 correlations will appear to be statistically

signicant while in fact it is not, is about 0.021, well be-

low the commonly applied threshold of 0.05.

Several interesting results emerge from the correla-

tions presented in Table 1. First, there is a high correla-tion between escorting and O&M requirements. There is

also a high correlation between user preparations and

developer support. But, there is no correlation at all be-

tween the developer support and preparation of O&M

requirements and no signicant correlation with escort-

ing. On the other hand there is a correlation (although

not signicant at the 0.001 level) between user prepara-

tions and O&M requirements and escorting. Althoughthe four dimensions are almost independent (as dis-

cussed earlier), the correlations between some of the

dimensions is not surprising. For example, the developer

Table 2

Multiple step-wise regression results (N = 56)

Success dimension Intercept point O&M requirements Escorting

Project eciency 2.138 0.372

Customer benets 3.714

Overall success 4.033

Bold font represents p < 0.05.support is a complementary activity to the user prepara-

tions; it is not likely that the user (probably via the

escorting team) will make preparations for introduction

into use without the developers support. These activitiesare dierent but performed with the same goal in mind.

Each of the three success measures is highly and sig-

nicantly correlated only with one of the planning and

preparations factors. The project eciency dimension

0.001 0.009 0.005

101 93 101

0.30 0.23 0.17

0.024 0.070 0.168

65 62 65

0.38 0.46 0.28

0.003 0.000 0.032

59 59 59

0.62 0.57

0.000 0.000

94 105

0.71

0.000

95is correlated with escorting (0.45), customer benets

dimension is correlated with user preparations (0.46)

and overall success is correlated with O&M require-

ments (0.33). Furthermore, project eciency is also cor-

related, though to a lesser extent with the developersupport and user preparations (0.30 and 0.38, respec-

tively). Customer benets dimension and overall success

are positively, but not signicantly, correlated with all

other planning and preparation factors.

Finally, all three success measures (project eciency;

customer benets; and overall project success) are highly

inter-correlated, implying that projects perceived to be

successful are considered successful by all their majorstakeholders.

Table 2 presents the results of a step-wise regression

analysis between the three success dimensions and the

Developer support User preparations p Adjusted R2

0.269 0.0003 0.239

0.447 0.0006 0.185

0.272 0.0424 0.057

User preparations are positively and signicantly cor-

related with all three success dimensions. This result is

rojecalso supported by the regression analysis (Table 2).

User involvement in development of O&M require-

ments is positively and signicantly correlated with the

overall success of the project as hypothesized and posi-tively correlated but to a signicance level of only

0.031 with customers benets.Escorting the development process by a dedicated

team positively and signicantly contributes to project

eciency as hypothesized while the contribution to the

customer benets and overall success, although positive,

is only signicant to the level of 0.009 and 0.005, respec-

tively. The positive relationship between escorting andproject eciency is also supported by the regression

analysis.

Finally, developer support is positively but not signif-

icantly correlated with project success. Counter to our

hypothesis, the highest correlation is with project e-

ciency (0.30) and not with customer benets or overall

success.

4. Discussion and conclusions

Planning is considered a central element of modern

project management. Commonly accepted professional

standards, such as the PMI Guide to the Project Man-

agement Body of Knowledge, recommend investing in

project management processes and procedures thatsupport planning in order to reduce uncertainty and

increase the likelihood of project success. Nevertheless,

planning of the termination phase, especially planning

for commissioning, has not received proper attention.

As we have seen in the literature review, most studies

on project termination focus on premature termination

and even those who see projects as somehow con-

nected to each other [22,24] focus on the managementof the relationship with the customers left after projectplanning and preparations factors. Only signicant be-

tas are presented (p < 0.05).

User preparations factor is the only factor that comes

out signicant in all three regression analyses. The

escorting factor is also signicant in the regression anal-

ysis of the planning variables with project eciency. Theregression analysis of the overall success with the plan-

ning and preparation variables has very little explana-

tory power while the other two are explaining each

about 20% of the variability of project eciency and

the customer benets from the project.

Referring now to the hypothesized relationships be-

tween the planning and preparation variables and pro-

ject success, we can see that only hypothesis 4 is fullysupported by the study results while hypotheses 2, 3

and 4 were only partially supported.

262 D. Dvir / International Journal of Pcompletion or on the development and marketingactivities after project selling and their eect on project

success.

Our study focuses on the planning and preparing the

introduction of the project into use. It shows that the ef-

fort invested in these activities directly aects project

success both from the eciency point of view and fromthe customer benets perspective.

From the correlations table we can see that all plan-

ning and preparation eorts positively aect project suc-

cess, the escorting team and the nal user preparations

have the greatest impact. Project eciency is signi-

cantly aected by the involvement of an escorting team

and by the nal user preparations for introduction of the

project into use, while customer benets are mainly theresult of the nal user preparations. These ndings are

in line with Dvir et al. [27] conclusions that studied

the eect of planning at large on project success and rec-

ommended that end-user involvement should start at the

rst stage of the project execution and continue until its

successful end. Kleinschmidts [21] observation that inEurope customers are more actively involved in the pro-

ject execution than in the US, represents probably anintuitive understanding of the crucial role of customersinvolvement in project success.

The current study goes one step further and helps to

understand specically how to improve the chances for a

successful commission. By establishing a team that will

escort the development and a team that will plan and

prepare the project commission, the nal user can di-

rectly improve the chances for success, his eorts havea greater inuence on project success than the activities

done by the developer himself.

Furthermore, these nal user activities have a much

larger eect than the up-front formulation and deni-

tion of operational and maintenance requirements.

The main conclusion of this study is that projects per-

formed under contract for a specic customer, either an

external customer or an internal one, should devote con-siderable eorts for planning and preparing in advance

the hand-over of the project to its nal users. Customer

involvement in all phases of the project can highly con-

tribute to the project success, especially to its ecient

execution.

The term we use in this paper defense projects is

somehow misleading and limiting the applicability of

the study results. Defense projects are usually associatedwith weapon systems which their eectiveness is mainlydetermined by their functional performance and to a les-

ser extent by the way they were introduced into service.

However, defense projects also include command and

control systems, electronic warfare systems, communica-

tions systems and logistic and support devices. These

types of systems are complicated, require continuous

maintenance, and it takes time to learn how to use themeciently, and therefore they can benet from proper

t Management 23 (2005) 257265planning and preparing their introduction into service.

Members of the contracting oce are ideal candidates

for the escorting team due to their technical skills. They

can contribute to the project denition, participate in

the development, integration and commissioning and as-

sist in future improvements of the product.

There are many other types of projects, not necessar-ily defense projects that can benet from adopting this

approach. Projects performed within an organization

(i.e., production improvement projects, improving logis-

tic procedures, and IT projects) or government, munici-

pal and state contracted projects are examples.

This study is of an exploratory nature; the limited sam-

ple size, the homogeneity of projects types and the focus

on Israeli defense projects,may limit its applicability. Fur-ther research should be done in other countries and in dif-

ferent industries to study the termination and hand over

phase of projects in order to develop better ways for intro-

ducing projects into service and ensuring their nal users

satisfaction,which is the ultimate proof of project success.

Appendix A

Descriptive statistics for the Project Success Items and

Factor loadings and descriptive statistics of the 22 Plan-

ning and Preparations variables (see Tables A.1A.6).

Table A.1

Descriptive statistics for the project success items

technological

specications

Table A.2

Factor loadings of the 22 planning and preparations variables

Variable Factor 1 Factor 2 Factor 3 Factor 4

Criteria for operational

eectiveness dened

0.24 0.37 0.62 0.22

User representatives

involved in

requirement denition

0.06 0.04 0.83 0.00

Combat mode of

operation dened

0.34 0.12 0.72 0.19

Logistic support

requirements dened

0.02 0.22 0.67 0.39

Human engineering

specications

0.13 0.31 0.59 0.17

Representative of the

nal user

active in the project

escorting team

0.25 0.55 0.05 0.08

Escorting team actively

involved in the

development process

0.09 0.79 0.03 0.05

Key escorting personnel

stayed for

the whole duration of

the project

0.11 0.79 0.19 0.06

Escorting team capable

to maintain

and improve the

operational system

0.11 0.70 0.32 0.01

Escorting team

committed to project

during operation

0.11 0.76 0.11 0.02

Prociency level of

escorting team

0.19 0.79 0.18 0.15

Developer prepared

detailed training

program

0.53 0.01 0.12 0.73

Quality of training by

the developer

0.51 0.03 0.01 0.74

Simulators were used for

operational training

0.01 0.23 0.13 0.57

Quality of training

documentation

0.29 0.28 0.34 0.67

Developers teamssupported

introduction

to operation

0.33 0.06 0.18 0.80

Developers teamsavailable in case of

problems at all times

0.45 0.15 0.04 0.61

Existence of professional

team to escort

introduction to

operational use

0.87 0.05 0.12 0.08

Systematic monitoring

of the introduction to

operation process

0.91 0.23 0.04 0.15

Adaptation of the

introduction process

due to lessons learned

0.93 0.06 0.02 0.19

Evaluation of the

introduction process

after completion

0.84 0.16 0.11 0.37

Formal introduction to

operation program

0.84 0.12 0.10 0.17

D. Dvir / International Journal of Project Management 23 (2005) 257265 263Meeting schedule 103 1 7 3.89 1.78

Meeting budget

goals

102 1 7 4.22 1.74

Meeting

procurement goals

82 1 7 4.62 2.30

Customer

benets

Satisfying customer

operational need

93 1 7 5.56 1.66

Project end-product

is in use

90 1 7 4.83 2.45

Systems delivered to

end user on time

83 1 7 4.24 2.16

System has

signicant usable life

expectancy

86 1 7 5.24 1.99

Performance level

superior to previous

release

75 1 7 6.08 1.47

End user capabilities

signicantly

improved

74 1 7 4.96 2.01

End user satised

from project end-

75 1 7 4.79 2.03Success

dimensions

Success measures N Min. Max. Mean SD

Project

eciency

Meeting functional

requirements as

dened

103 1 7 5.82 1.23

Meeting 101 1 7 5.69 1.31product prepared by user

ce re

9

0

5

7

7

rting

264 D. Dvir / International Journal of Project Management 23 (2005) 257265Table A.3

Descriptive statistics for the development of operational & maintenan

Measures N

Criteria for operational eectiveness dened 9

User representatives involved in requirement denition 10

Combat mode of operation dened 9

Logistic support requirements dened 8

Human engineering specications 8

Table A.4

Descriptive statistics for the escorting the development process (esco

Measures

Representative of the nal user active in the project escorting team

Escorting team actively involved in the development process

Key escorting personnel stayed for the whole duration of the projectReferences

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Escorting team capable to maintain and improve the operational system

Escorting team committed to project during operation

Prociency level of escorting team

Table A.5

Descriptive statistics for the developers preparations for turning over the p

Measures N

Developer prepared detailed training program 64

Quality of training by the developer 62

Simulators were used for operational training 61

Quality of training documentation 60

Developers teams supported introduction to operation 60Developers teams available in case of problems at all times 61

Table A.6

Descriptive statistics for the nal user planning for receipt of the project a

Measures

Formal introduction to operation program prepared by user

Existence of professional team to escort introduction to operational use

Systematic monitoring of the introduction to operation process

Adaptation of the introduction process due to lessons learned

Evaluation of the introduction process after completionquirements (O&M requirements) items

Min. Max. Mean SD

1 7 4.75 1.77

1 7 5.80 1.42

1 7 4.38 1.82

1 7 3.99 1.85

1 7 4.34 1.89

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77 1 7 3.99 2.00

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100 1 7 5.6 1.21

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1 7 5.23 1.80

1 7 5.03 1.72

1 7 2.87 2.01

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1 7 4.72 1.83

1 7 5.70 1.45

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D. Dvir / International Journal of Project Management 23 (2005) 257265 265

rs

rie

l Hall

form

cost

d dam

a mo

e leve

as a data-based fraction of the estimated project duration or budget. We also introduce a new approach for collecting data and

estimating the parameters necessary to implement the model. This approach places a smaller burden on decision makers than tra-

cost control. For example, to prevent wasting earliness,

a project buer is placed at the end of the project sche-

analysis.

buer is the dierence between the due date and the ex-

pected completion time. Similar analysis is directly

the serial structure, if we assume that earliness is uti-lized, then the expected duration of the project is equal

to the sum of the expected durations of the activities.

Our result for the serial structure can serve to develop

insights for more realistic project networks, where such

* Tel.: +649 373 7599x87381; fax: +649 373 7430.

E-mail address: [email protected].

International Journal of Project Manag


PROJECT0263-7863/$30.00 2005 Elsevier Ltd and IPMA. All rights reserved.dule. Similarly, where chains of activities merge withthe critical path, feeding buers may be inserted. Note

that to specify such buers is mathematically equivalent

to deciding when to start each chain of activities. Yet the

size of these buers is usually specied as an arbitrary

fraction of the estimated chain duration. The purpose

of this paper is to provide a rst step towards optimizing

such buers based on plausible theory and relevant data

applicable to the determination of a cost buer as well,by the simple substitution of the due date by a project

budget. The main cost of a typical project is the sum

of the individual activity costs, although it also includes

overhead charges and holding costs that depend on the

project duration. Therefore, at least approximately, we

can say that cost is additive and not sensitive to the pro-

ject network structure. Similarly, due to the simplicity ofditional PERT: they provide single point estimates for means, while variance elements and bias correction are computed electron-

ically using historical data.

2005 Elsevier Ltd and IPMA. All rights reserved.

Keywords: Time; Cost; Operations

1. Introduction

Recent developments in the practice of project sched-

uling focus attention on the correct specication of

safety buers. Time buers are used to protect the sche-

dule, and, similarly, budget contingencies are used for

In this paper we study the most basic case: the opti-mal buering of projects with n (not necessarily indepen-

dent) activities in series, and without intermittent idling.

Thus there is only one chain of activities and it is neces-

sarily also the critical path. Assuming that either the due

date or the start time is a decision variable, the projectThe eect of systemic erro

Dan T

ISOM Department, University of Auckland, Old Chora

Received 7 September 2004; received in revised

Abstract

Existing mathematical models for setting buers for time or

tistically independent. This leads to a highly counterintuitive an

negligible for projects with long chains of activities. We present

caused by estimation bias. We show that if relatively high servicdoi:10.1016/j.ijproman.2004.12.004on optimal project buers

tsch *

, 7 Symonds Street, Auckland City 1001, New Zealand

22 October 2004; accepted 3 December 2004

in project management assume that project activities are sta-

aging conclusion that project buers should become relatively

del that considers the statistical dependence between activities

ls are desired, this imposes a positive lower bound on the buer

www.elsevier.com/locate/ijproman

ement 23 (2005) 267274

MANAGEMENT

assumption is that planned idling should not occur with-

in the critical path or within any chain of activities.

Nonetheless, it is incorporated where such chains merge

Project Management 23 (2005) 267274chains are often embedded. In such a case, the (serial)

project buer becomes a feeding buer for non-critical

chains feeding other project activities; e.g., feeding the

critical path. Such chains are sub-projects with a serial

structure. A useful approach for extending the results

we obtain here to more complex project networks isby simulation, but this is beyond our scope.

Henceforth, we will discuss time buers, keeping in

mind that the results also apply to contingency budget-

ing. For this, we need to know the cumulative distribu-

tion function of the project completion time, which, in

turn, is a function of the individual activities distribu-tions. In Malcolm et al. [1], the PERT developers dis-

cussed the need for stochastic estimation of activitydurations. Nominally, they proposed tting a beta dis-

tribution. Practically, they required a triplet of estimates

for each activity {min, mode, max} and then arbi-

trarily set standard deviation = (max min)/6 andmean = (min + 4 mode + max)/6. Assuming indepen-

dence, they noted that the sum of a serial chain of activ-

ities is approximately normal by the central limit

theorem. Although they recommended it for tractability,the team recognized that the use of the most likely crit-

ical path is optimistic: it ignores the statistical depen-

dence between paths that share activities. They already

had a computationally intensive remedy: Clark [2] pro-

vided approximate but unbiased calculations for the

project duration distribution. Finally, they highlighted

a major concern about systemic bias which is at the

heart of this paper and we will discuss it later. Armedwith 20/20 hindsight, one may criticize invoking the beta

distribution, considering that it was not really utilized,

but this is harmless. More seriously, it is dicult, per-

haps impossible, to obtain reliable triplets from process

owners. Anecdotal evidence to this eect, related to

work place politics, was given by Woolsey [3]. To this

we must add systemic human error as studied by Tver-

sky and Kahneman [4]; e.g., they observed that 98%condence intervals estimated by experts tend to fail in

about one third of the cases (i.e., experts tend to grossly

underestimate the true variance).

Britney [5] presented optimal buers for stochastic

project activities on a one-by-one basis. Planned idling

occurs between activities unless the preceding buer is

exceeded. He did not, however, optimize the project as

a whole. Also, he did not consider the possibility ofcombining serial buers. The combined buer approach

was used by Yano [6], who obtained the optimal single

buer for a project (or supply chain) composed of inde-

pendent serial activities. Yano [7] inserted individual

buers between the serial activities. Ronen and Trietsch

[8], Kumar [9], and Chu et al. [10], independently, opti-

mized the ordering times of n parallel project (or supply

chain) items with stochastic lead times, where the latestone determines the completion time; i.e., they showed

268 D. Trietsch / International Journal ofhow to coordinate n parallel feeding buers.(yielding feeding buers). The size of protective buers is

determined as an arbitrary fraction of the expected

chain leading to the buer (e.g., 50%). Leach [12] sug-

gested the maximum of a buer based on the traditionalindependence assumption and the arbitrary fraction.

Leach [15] listed 11 reasons why projects are typically

longer than expected. He then proposed a larger buer

based on the sum of the two elements mentioned before.

Although Clarks approximation can handle depen-dent activities, none of the existing mathematical models

for buer setting accounts for systemic error. We intro-

duce an elementary model for this purpose and showthat it yields dependency between activities. We show

that if relatively high service levels are desired, this im-

poses a positive lower bound on the project buer as a

data-based fraction of the expected duration. In con-

trast, the independence assumption leads to a highly

counterintuitive and damaging conclusion that project

buers should become relatively negligible for projects

with long chains of activities. We also recommend anapproach for collecting data and estimating the param-

eters necessary to implement our model. This approach

places a smaller burden on users than traditional PERT:

single point estimates are required instead of triplets.

Variance and bias estimates can then be computed by

a decision support system that uses historical data,

and we show how.

The remainder of the paper is organized as follows.After introducing the main notation, Section 2 presents

the [existing] basic buer optimization model subject to

a given project distribution. Section 3 introduces our

model with the bias-induced correlation. Section 4 ad-

dresses the estimation of the necessary model inputs.

Section 5 provides numerical illustrations. Section 6 is

the conclusion.

2. Notation and basics

B the bias of time or cost estimates of project

activities (a random variable)

b E(B), where E() is the expected value functionV b r2b V(B), where V() is the variance functionC the cost to postpone the due date (per timeThis idea using planned project- and feeding buers

to achieve improved reliability and avoid [implicit] pro-

ject delay penalties had recently been popularized un-

der the title Critical Chain, and many practitioners

nd it useful. Reviews and discussions of this modern

development abound; e.g., Herroelen and Leus [11],Leach [12], Raz et al. [13], Trietsch [14]. The basicunit)

ties are independent by nature, their estimated durations

are often subject to the same estimation error. Thus,

ProjD the nominal project duration/due date (a deci-

sion variable)

P time unit cost during delay, including penalty

(where P > C)

nj the number of activities in project j

(j = 1, . . ., J). (Here and elsewhere, j is usedexclusively to index projects, and may be sup-

pressed)

SL service level, the probability of meeting or beat-

ing the due date

Yij the duration of activity i in project j

(i = 1, . . ., nj; j = 1, . . ., J) a random variablewith the realization yij

Yj the set {Yij} for all i in project jYj

PYij, the true project duration

Fj(t) the cumulative distribution function of Yjlij E(Yij)rij the standard deviation of Yijrj the standard deviation of the completion time

of project j

Xij a random variable that models Yij (but not nec-

essarily correctly)Xj the set {Xij} for all i in project j

eij the nominal estimate of lij, assumed propor-tional to E(Xij)

We assume that we have to determine a project due

date, D, or that one is given with enough slack to make

possible a delayed start. The time from the project start

to the due date is the planned duration. For conve-nience, we will treat the start as time zero, so the

planned duration is equal to D. We also assume that

there is an economic cost per time unit, C, which pro-

vides an incentive to reduce the planned duration; e.g.,

the customer is more likely to award us the contract if

we quote an early (but reliable) due date. If the customer

is not likely to pay before the due date when the project

is early, C should also include any xed charge the pro-ject incurs while on the books. Any delay beyond D in-

curs a cost (including penalty) of P(Y D)+, whereY =

PYi and h

+ = max{0, h}. P > C, or it would be

optimal to set D = 0 and pay P as long as necessary.

The objective is to minimize the expected total cost

(TC),

ETC CD EP Y D(By dening P 0 = P C and subtracting CY from bothsides of the equation a value which is not a function

of D we can show that minimizing this objective func-tion is equivalent to minimizing

ECD Y P 0Y D:Thus both earliness and tardiness have economic losses

associated with them.)

Denote the optimal probability of meeting or beating

D. Trietsch / International Journal ofthe due date, i.e., the service level, by SL* (we will usewhen the same optimist estimates many activities, they

will all tend to be underestimated. Equivalently, pres-

sure by management may inuence people to give too

short estimates that cannot be met later. Similarly, badweather during the project or the loss of a key employee

may impede several activities. A booming economy may

increase queueing time for more than one activity, etc.

The same or similar causes also apply in the reverse

direction; e.g., pessimists will tend to overestimate dura-

tions (and severe punishment for missing due dates in

the past will turn optimists to pessimists). The result is

a systemic bias across a project. But the magnitude ofthis bias is a random variable and even its orientationasterisks to denote optimality in general). For continu-

ous distributions, a straightforward application of the

newsboy model shows that SL* = (P C)/P. Thus,D* = arg{SL* = F(D*) = (P C)/P}, where F(t) is theproject duration distribution. For discrete due dates,

where it is possible to hit the due date exactly and thusbe neither early nor late, we must set D such that the

probability of delay will not exceed C/P and the proba-

bility of earliness will not exceed (P C)/P. Either way,we need F(t). The technical focus of this paper is obtain-

ing a correct duration distribution (or expenditure distri-

bution) based on the estimates we have for each activity,

but subject to systemic error.

3. Modeling positive dependence due to systemic error

It is well known that project activities are sometimes

statistically dependent. Nonetheless, with one exception,

the literature on setting buers assumes statistical inde-

pendence. This includes academic papers and practi-

tioner books. But if we increase the number ofactivities along the critical path, the independence

assumption leads to so-called optimal project buers

that, as a fraction of the mean, approach zero asymptot-

ically. Because this is a highly counterintuitive conclu-

sion, the practical approach has always been to set the

buer, or the contingency, as a fraction of the antici-

pated duration; e.g., see OBrien [16]. In addition toleading to such a highly counterintuitive conclusion,and to ying in the face of experience, the independence

assumption should be challenged on theoretical grounds

as well. Leach [15], after citing empirical evidence dem-

onstrating that the independence assumption is not valid

in practice, identies positive bias as the culprit. He then

provides 11 causes of positive bias mostly related to

large projects with multiple paths. Our focus here is

on a single cause of positive or negative bias that applieseven to serial projects and that, arguably, explains the

bulk of the problem. The crux is that even when activi-

ect Management 23 (2005) 267274 269is not known in advance. This introduces a strong

Projdependence as far as deviations from plan are concerned.

But, operationally, the only variation that concerns us is

relative to plan!

Notably, the need to account for estimation bias by

some calibrating program has been on the agenda from

the earliest PERT days. Malcolm et al. [1] stated that theproblem had been raised by many. They then suggested

a program of comparing estimates with actual perfor-

mance over a period of time to permit calibration ofthe estimators. Alas there is no evidence that such cal-

ibration was ever implemented on a wide scale, if at all.

Instead, subsequent papers about bias focused mostly

on the optimistic bias due to ignoring near-critical

parallel paths that may become critical in reality; e.g.,Klingel [17], Schonberger [18]. Thus, the clear recom-

mendation that the PERT team expressed in [1] was

ignored, while an issue that they considered more minor

and for which [2] had already provided an approxi-

mate remedy was highlighted.

Furthermore, [1] stated objective with respect to bias

was to calibrate the estimates to make them accurate.

But there is also a statistical dependence issue thatarises. For example, suppose we suspect that there is a

random bias error of 25%, and we nd that the rst se-

ven activities took 85% of their combined estimated

time, then we would probably consider it likely that

the next activities will also tend to consume around

85% of their estimate in other words, we form an infor-

mal estimate of 85% for the necessary calibration. This

means that we perceive a correlation between the rstfew activities and the ones that are yet to follow. This,

by denition, is a case of statistical dependence (because

independent variables are not correlated). In practice,

we need to know not only the average bias but also its

impact on the covariance of activities. Our purpose here

is to address both the need for calibration and the mag-

nitude of the correlation that is involved, so we can draw

conclusions for the optimal combined buer (includingelements for bias correction and for safety).

Let the true activity times compose the random vec-

tor Y = {Yi}. If decision makers would have the distri-

bution of Y, there would be no need for this paper. In

reality, however, decision-makers never know Y, so they

must use some estimate that acts as a model of Y.

Accordingly, let X = {Xi} be a vector of the decision-

makers models of the actual activity durations, {Yi}.So Xi is a random variable that represents another ran-

dom variable. Estimates are based on X, and not directly

on Y. Systemic error arises because X is not a perfect

model of Y. Mathematically, perhaps the simplest possi-

ble model for systemic error involves the introduction of

an additional independent random variable, B, that

multiplies X to obtain Y. In this paper, we limit our-

selves to this basic model. Other potential approachesexist, however, and further research may be justied to

270 D. Trietsch / International Journal ofidentify the best one. We will use b and V b r2b to de-note the mean and variance of B. We assume that ei,

the nominal (single point) estimate of Yi, is proportional

to E(Xi). For example, if a particular provider of esti-

mates includes a hidden 100% buer in her estimates,

then ei = 2E(Xi). Nonetheless, for simplicity (and with-

out loss of generality), we will set ei = E(Xi). As longas the assumption that ei is proportional to E(Xi) holds,

there always exists a B that corrects any deviation intro-

duced by this simplication.

In broad terms, the randomness of Xi relates to

chance events that are specic to Yi (as perceived),

e.g., problems with raw materials or power supply. X

also includes some (but not all the) eects of random-

ness in estimation, since estimates are the result of pro-cesses that are not deterministic. Even with the same

data, dierent people at dierent times typically come

up with dierent estimates. For example, they may for-

get or neglect dierent aspects of the job. Random esti-

mation errors are operationally equivalent to random

deviation from plan. Because perceived activity-specic

chance events and some estimation errors are con-

founded with each other, they must be represented bythe same random variable, Xi. In contrast, B models ef-

fects that are common to all activities, such as pressure

to produce attractive estimates quickly (leading to opti-

mistic bias and omissions), personal safety buers,

weather, economic conditions, etc. Note that B is impor-

tant even if b = 1; i.e., if we take steps to remove bias onaverage, as suggested by [1], and thus achieve accuracy,

B would still capture important information about sys-temic imprecision. Specically, those estimation errors

that are not confounded with activity-specic chance

events.

To present the most basic model, we assume that the

elements of X are independent of each other. This

assumption is often realistic, by which we mean that

decision makers typically estimate the elements of Y

(by the elements of X) as if they are independent andtherefore the elements of X are indeed independent

after all, X is a model only. (Modeling dependence into

X may be useful for some purposes, but requires further

research.) Because B and X are independent of each

other, li = b ei, but the multiplication by the same real-ization of B introduces [positive] dependence between

the elements of Y even if the elements of X are indepen-

dent. Specically, r2i b2 V X i V X i V b V b e2i ,and COV(Yi, Yk) = Vb ei ek; "i 6 k. We can separater2i to two parts, b

2 V(Xi) + V(Xi) Vb and V b e2i . Theformer equals E(B2) V(Xi) and the latter is a specialcase of Vb ei ek. Thus the covariance matrix of Y isthe sum of a diagonal matrix with elements V(Xi) E(B

2)

and a full symmetric matrix with elements Vb ei ek;"i, k (i.e., the vector product {rb ei}{rb ei}T). To cor-rect for the average bias we add a bias correction of(b 1)Pei to the nominal makespan estimate

Pei. Thus

ect Management 23 (2005) 267274we obtain a relative bias correction of b 1. If B = 1, we

note the covariance matrix of Y, and let 1 be a column

vector in Rn with elements of 1, then the result is

Projobtained directly by the matrix product 1TV1. To study

the eect of the standard deviation on the optimal

buer further, let q1(e) = E(B2) P

"iV(Xi), and let

q2(e) = (rb P

"iei)2, where e={ei}, then

maxfq1e

p;q2e

pg 6

q1e q2e

p

6q1e

p

q2e

p:

The central element in the inequality is r.pq2 is propor-

tional to the nominal makespan estimate (before the

bias correction),Pei. So there exists a fraction of this

estimate, namely rb, that acts as a lower bound on r.Therefore, if we wish to specify a safety buer against

random variation of kr for some k > 0, this safety bueris bounded from below by k rb

P"iei, which consti-

tutes a fraction of k rb of the nominal makespan esti-mate. Furthermore, when n!1 then q1/q2! 0 so thesame bound serves as the approximate optimal safety

buer. Recall that Leach [12] and Leach [15] suggest rel-

ative buers that are associated with Max{pq1,

pq2}

andpq1 +

pq2, respectively, so for a positive k these

values provide a lower- and an upper bound for the cor-

rect result. (There is no theoretical reason to limit our-

selves to k > 0, so we do not limit our analysis to this

case. Nonetheless, most project managers are uncom-

fortable with negative buers and the low service levels

they entail.)

4. Estimating model parameters

A tempting approach is to estimate Xi by the classical

3-point method of PERT, thus yielding ei and V(Xi). It

would then only remain to estimate B. However, there

are major diculties with this approach (as discussed

in Section 1), even without the new requirement to dis-tinguish consciously between systemic bias and individ-

ual activity variation causes. Therefore we propose to

limit the information elicited from process owners to

single point activity estimates, ei, and obtain all the

other necessary estimates from historical data with theobtain the classic model with independence. Similarly, if

V(B) = 0 but b 6 1, then after the bias correction weagain obtain the classic model. Therefore, our model

generalizes the classic approach. Finally, monitoring a

project over time during its execution always involves

estimating the bias that applies to it, either explicitlyor implicitly.

Bias correction is the rst response to bias, but the

standard deviation of the project completion time is vital

for rational determination of the safety buer. Since the

e

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