Benefit-Oriented Modelling for Project Appraisal, Selection, … · Chapter 2: An Integrated Benefit-Oriented Project Evaluation Framework: Appraisal, Monitoring and Performance Judgement

Benefit-Oriented Modelling for Project Appraisal, Selection,

Monitoring, and Performance Judgement

Elham Merikhi

Master of Philosophy

2018

Benefit-Oriented Modelling for Project Appraisal, Selection, Monitoring,

and Performance Judgement

By

Elham Merikhi

A thesis submitted for the degree of Master of Philosophy

of The Australian National University

February 2018

@Copyright by Elham Merikhi 2018

All Rights Reserved

ii

SIGNED STATEMENT OF ORIGINALITY

The work presented in this thesis is, to the best of my knowledge, my own work, except

as acknowledged in the text and declaration statement. The material has not been

submitted, either in whole, or in part, for a degree at this or any other university.

Elham Merikhi

iii

DECLARATION FOR A THESIS BY COMPILATION

In accordance with The Australian National University Program and Awards

Status-Research Awards Rule 2017, I hereby declare that this thesis contains no material

which has been accepted for the award of any other degree or diploma at any university

or equivalent institution and that, to the best of my knowledge and belief, this thesis

contains no material previously published or written by another person except where due

reference is made in the text of the thesis.

This thesis includes two papers that are going to be submitted in two Top Tier

Journals. The core theme on the thesis is the modelling of project evaluation and selection.

The papers are the result of original research conducted by the candidate during the course

of the study in the MPhil Program. The ideas, development and writing of all the papers

in the thesis were the principal responsibility of myself, the candidate, working within the

Research School of Management under the supervision of A/Prof Ofer Zwikael (Primary

supervisor and Chair of the supervisory panel) and A/Prof Arik Sadeh (Associate

supervisor of the supervisory panel).

In papers development, the candidate is the primary author and contributed greater

than 50% of the content. A substantial portion of the initial drafts of both papers were

written by the candidate and any subsequent editing with the guidance of the supervisory

panel was performed by the candidate. Among these papers, the first one is an extension

of a submitted paper to the 78th annual meeting of the Academy of Management (AOM),

and the second one is an extension of an accepted paper in the 77th annual meeting of the

AOM, presented at Atlanta, GA in August 2017.

iv

PAPERS’ DETAILS

This is an MPhil thesis by compilation in which the following two papers as Paper 1

and 2 (i.e. Chapter 2 and 3 respectively) are elaborated

Paper 1 (Chapter 2)

Initial explanation This paper is an extension of a submitted conference

paper with the following characteristics.

Full title

An integrated benefit-oriented project evaluation

framework: appraisal, monitoring and performance

judgement

Authors Elham Merikhi; Ofer Zwikael

Candidate’s contribution (%)

The candidate/primary author contributed greater

than 50% to the paper’s content and was responsible

for the following:

Reviewing the literature and extracting the

research gap

Proposing the model

Writing the substantial sections of the

manuscript

Addressing the co-author’s comments and

editing manuscript accordingly

Conference This paper was submitted to the 78th annual meeting

of the Academy of Management (AOM)

Volume / Number / page N/A

Status Submitted

Date submitted: 9 January 2018

v

Paper 2 (Chapter 3)

Initial explanation

This paper is an extension of one accepted and

presented conference paper with the following

characteristics.

Full title Customizing modern portfolio theory for the project

portfolio selection problem

Authors Elham Merikhi; Ofer Zwikael

Candidate’s contribution (%)

The candidate/primary author contributed greater

than 50% to the paper’s content and was responsible

for the following:

Reviewing the literature and extracting the

research gap

Proposing the mathematical model

Writing the substantial sections of the

manuscript

Addressing the co-author’s comments and

editing manuscript accordingly

Conference 77th annual meeting of the Academy of Management

(AOM)

Volume / Number / page 2017, 1, 13178

Status Accepted and presented at Atlanta, GA in August

2017

Date accepted: 17 March 2017

Candidate’s Declaration

I declare that the above-mentioned papers meet the requirement to be included in the

MPhil’s thesis.

Candidate name Candidate Signature Date

Elham Merikhi

15 February 2018

vi

ACKNOWLEDGEMENTS

For the exceptional supervision, expert advice, encouragement, and unrelenting

confidence in me, my utmost respect and appreciation goes to A/Prof Ofer Zwikael. He

merits special recognition for his outstanding contributions to my development as a

scholar. I am fortunate to have had the chance to work with him and will always be

grateful for his generous guidance and provision growth opportunities throughout my

candidature. My heartfelt thank goes to A/Prof Arik Sadeh for his valuable comments and

guidance in developing this thesis.

For the financial support and professional development sponsorship, I am highly

grateful to A/Prof Ofer Zwikael, Prof George Chen, Prof Byron Keating, CBE HDR

administration office- particularly, Mrs. Julie Fitzgibbon and Ms. Sarah Woodbridge- the

Australian department of Education and Training-Endeavour Postgraduate Scholarship

and the ANU College of Business and Economics.

For the excellent service, leadership, and support throughout my candidature, I

am grateful to the Research School of Management faculty and administration. For the

wonderful friendship, kindness, and constant reassurance, thanks to all my friends in the

Research School of Management.

My heartfelt thanks go to my siblings, Neda and Mehdi, for their love and

generosity and above all, I owe a debt of gratitude to my parents, Hamid and Mahnaz, for

their unconditional love and unyielding support in all of my endeavors.

vii

DEDICATION

This thesis is dedicated to my beloved GOD

“Thank you for all your unconditional love and support”

viii

ABSTRACT

Benefit-Oriented Modelling for Project Appraisal, Selection, Monitoring, and

Performance Judgement

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Philosophy

The Australian National University, 2018

Primary supervisor and Chair of the supervisory panel:

A/Prof Ofer Zwikael

Associate supervisor of the supervisory panel:

A/Prof Arik Sadeh

Although the realization of benefits is the main reason projects are funded, current project

evaluation (i.e. appraisal, monitoring and performance judgement) frameworks underplay

the importance of benefit realization, because they focus on delivering project’s outputs

on time, budget and to specifications. Moreover, the integration among the various

evaluation frameworks is poor because different evaluation tools are used at various

project phases. Altogether, to address the research gap, there is a need to develop an

ix

integrated project evaluation framework that takes benefits into consideration and can be

used throughout all project phases. Furthermore, because a project with very attractive

expected benefits-and consequently a very attractive expected return- but high risk might

expose the organization to a large loss, evaluation frameworks should consider the

combined analysis of projects’ returns and risks, as supported by utility theory.

In addition, after project appraisal, because resources are limited, organizations need to

select the best set of projects, i.e. project portfolio. Modern portfolio theory (MPT) in

(financial) portfolio selection problem suggests that in addition to the expected return and

risk, “risk interdependencies among projects” should also be considered, because they

lead to achieve a project portfolio with lowest level of risk for the same level of return.

However, there is gap in the literature as it is underdeveloped in providing a clear

approach to estimate risk interdependencies among projects.

In order to close these gaps, two papers are developed in this thesis: paper 1 tailors utility

theory to propose an integrated benefit-oriented framework for project evaluation on the

basis of its return and risk; and paper 2 tailors MPT to propose a risk-return mathematical

model for project portfolio selection. It is expected that the proposed project selection

model and evaluation framework improve the quality of portfolio selection decision in

organizations and help them ensuring the realization of projects’ intended benefits.

x

TABLE OF CONTENTS

SIGNED STATEMENT OF ORIGINALITY ........................................................................... ii

DECLARATION FOR A THESIS BY COMPILATION ....................................................... iii

PAPERS’ DETAILS ................................................................................................................... iv

ACKNOWLEDGEMENTS ....................................................................................................... vi

DEDICATION............................................................................................................................ vii

ABSTRACT ............................................................................................................................... viii

TABLE OF CONTENTS ............................................................................................................ x

LIST OF TABLES ..................................................................................................................... xii

LIST OF FIGURES .................................................................................................................. xiv

CHAPTER 1: INTRODUCTION .............................................................................................. 1

REFERENCES ..................................................................................................................... 6

CHAPTER 2: Paper 1 ................................................................................................................ 9

An Integrated Benefit-Oriented Project Evaluation Framework: Appraisal, Monitoring and

Performance Judgement ............................................................................................................ 9

CO-AUTHOR AUTHORIZATION FORM .................................................................... 10

ABSTRACT ........................................................................................................................ 11

1. INTRODUCTION ........................................................................................................ 12

2. LITERATURE REVIEW ............................................................................................ 15

2.1. Existing frameworks in project evaluation ........................................................ 15

2.2. Utility theory ......................................................................................................... 18

2.2.1. Principles ............................................................................................. 18

2.2.2. Indifference curves ............................................................................... 20

2.3. The application of utility theory in project evaluation ......................................... 21

3. THE DEVELOPMENT OF PROJECT EVALUATION FRAMEWORK ............ 23

3.1. Project evaluation map ........................................................................................ 23

3.1.1. The dimensions of the project evaluation map ......................................... 23

3.1.2. Indifference curves ............................................................................... 30

3.2. Project appraisal ................................................................................................... 31

3.2.1. The effect of risk mitigation actions on attractiveness contours ................. 32

3.3. Project monitoring ............................................................................................... 33

xi

3.4. Project performance Judgement ......................................................................... 34

4. A NUMERICAL EXAMPLE ........................................................................................ 36

4.1. Project appraisal ................................................................................................... 36

4.2. Project monitoring ............................................................................................... 39

4.3. Project performance judgement ......................................................................... 40

5. CONCLUSIONS ............................................................................................................. 41

REFERENCES ................................................................................................................... 43

CHAPTER 3: PAPER 2 ........................................................................................................... 57

Customizing Modern Portfolio Theory for the Project Portfolio Selection Problem ......... 57

CO-AUTHOR AUTHORIZATION FORM .................................................................... 58

ABSTRACT ........................................................................................................................ 59

1. INTRODUCTION ........................................................................................................ 60

2. LITERATURE REVIEW ............................................................................................ 63

2.1. The definition of “project portfolio selection problem” (PPSP) ...................... 63

2.2. PPSP models in the literature .............................................................................. 64

2.3. Modern Portfolio Theory (MPT) ........................................................................ 66

2.4. PPSP-MPT models ............................................................................................... 69

2.5. Limitations of the existing PPSP-MPT models .................................................. 71

3. DESIGN PRINCIPLES ............................................................................................... 72

4. MODEL DEVELOPMENT ........................................................................................ 76

4.1. Model assumptions ............................................................................................... 76

4.2. Threats and Opportunities Identification .......................................................... 77

4.3. The customized approach to estimate MPT’s parameters in PPSP ................. 78

4.4. Benefit, cost and technical interdependencies among projects ........................ 85

4.5. The optimization model ....................................................................................... 88

5. A NUMERICAL EXAMPLE ...................................................................................... 90

6. CONCLUSIONS .......................................................................................................... 98

REFERENCES ................................................................................................................. 101

CHAPTER 4: CONCLUSIONS ............................................................................................ 122

xii

LIST OF TABLES

Chapter 1: Introduction

-

Chapter 2: An Integrated Benefit-Oriented Project Evaluation Framework:

Appraisal, Monitoring and Performance Judgement

Table1 The differences between the approaches used by utility theory in asset

evaluation with those should be used in project evaluation

Table 2 Project E’s risk register in appraisal stage

Table 3 The return and cost of project “E” in different potential situations in

appraisal stage

Table 4 Candidate risk mitigation programs for project “E” in appraisal stage

Table 5 The updated risk register of project “E” at t=9 in monitoring stage

Chapter 3: Customizing Modern Portfolio Theory for the Project Portfolio Selection

Problem

Table 1 A comparison of PPSP definitions in the literature

Table 2 The similarities between PSP and PPSP

xiii

Table 3 The differences between the approaches used in PSP with those should be

used in PPSP

Table 4 Project 1’s risk register

Table 5 Project 2’s risk register

Table 6 The return of project 1 in different potential situations

Table 7 The estimated returns, risks and costs relevant to 15 project proposals

Table 8 The returns of projects 1 and 2 in their common potential situations

Table 9 Technical interdependencies among 15 project proposals

Chapter 4: Conclusions

-

xiv

LIST OF FIGURES

Chapter 1: Introduction

Figure 1 Project evaluation and selection in different projects’ phases

Chapter 2: An Integrated Benefit-Oriented Project Evaluation Framework:

Appraisal, Monitoring and Performance Judgement

Figure 1 The indifference curves in the return-risk plane

Figure 2 The project evaluation map

Figure 3 The project evaluation map of the numerical example

Chapter 3: Customizing Modern Portfolio Theory for the Project Portfolio Selection

Problem

Figure 1 The efficient frontier of risky assets with the optimal capital allocation

line, CAL (P), and P as the optimal portfolio

Figure 2 The design principles of project portfolio’s attractiveness evaluation

Figure 3 The efficient frontier of the numerical example

Chapter 4: Conclusions

-

1

CHAPTER 1: INTRODUCTION

2

Organizations fund projects to enhance their performance (Lewis, Welsh, Dehler,

& Green, 2002). To reach project success, projects should be systematically evaluated in

three stages (Frechtling, 2002; Lee, Son, & Om, 1996): (1) Ex-ante evaluation, i.e. project

appraisal, which is conducted in the project’s initiation phase to see what goals are

targeted; (2) Interim evaluation, i.e. project monitoring, which is applied through the

project’s planning, execution and benefit realization phases to find whether the intended

goals are being met; and (3) Ex-post evaluation, i.e. project performance judgement,

which is conducted after the project’s benefit realization phase to see whether the intended

goals have been met. Figure 1 depicts these three evaluation stages, i.e. appraisal,

monitoring and performance judgement and their position through the four project’s

phases (Zwikael & Meredith, 2018).

Figure 1

Project evaluation and selection in different projects’ phases

In each of the three stages of project evaluation, literature has traditionally focused

on the evaluation of output delivery (Atkinson, 1999). However, evaluation with a focus

on outputs delivery, i.e. output-oriented project evaluation, is insufficient because

3

delivering an output efficiently does not necessarily imply benefits realization for the

funding organization (Winter & Szczepanek, 2008). Accordingly, over the past few years

scholars have paid more attention to the realization of projects’ benefits. However, of

three stages of project evaluation, benefit-oriented evaluation frameworks have been

developed for only one (e.g. Angus, Flett, & Bowers, 2005; Zwikael & Smyrk, 2012) or

two (e.g. Barclay & Osei-Bryson, 2010) stages. As a result, these evaluation frameworks

are dispersed and incoherent, which means a framework applied for one stage of project

evaluation is useless for the others. Using a different framework for each stage of project

evaluation can also lead to inconsistency and waste of resources, e.g. time and money. To

address this research gap, there is a need to have a coherent evaluation framework

throughout the entire project’s life rather than having different incoherent frameworks for

each evaluation stage. Furthermore, in such a framework, the combined analysis of

projects’ benefits-and consequently projects’ returns- and risks is important because a

project with a very attractive expected return but high risk might expose the organization

to a large loss, whereas a low-risk project might secure the organization a lower but more

certain return (Hillson, 2002; Sefair, Méndez, Babat, Medaglia, & Zuluaga, 2017).

Altogether, paper 1 (chapter 2) of this thesis develops a coherent integrated project

evaluation framework which takes into account both projects’ returns and risks, from the

early phase of projects until after their completion. Considering the similar core concepts

between asset evaluation and project evaluation, in paper 1, I use principles of utility

theory, a well-acknowledged theory for asset evaluation in Finance discipline, and tailor

it to develop an integrated benefit-oriented project evaluation framework. Accordingly,

4

paper 1 aims to answer the following research question: “How can utility theory’s

principles be applied in the project context to develop an integrated benefit-oriented

project evaluation framework?”

Furthermore, after project appraisal, i.e. at the end of projects’ initiation phases

depicted in Figure 1, because resources are limited, not all suitable for funding project

proposals can be funded (Carazo, 2015). The selection of subset of projects to be funded

to optimize organizational performance given limited resources is known in the literature

as the “project portfolio selection problem” (PPSP) (Li, Fang, Tian, & Guo, 2015; Shou,

Xiang, Li, & Yao, 2014). A major limitation with most PPSP models is disregarding risk

interdependencies among projects. Risk interdependencies occur when two or more

projects have greater or lower risks if carried out simultaneously than if they were

accomplished at different times (Mutavdzic & Maybee, 2015). Such interdependencies

arise over time from overall social and economic changes and can affect multiple projects

(Gear & Cowie, 1980; Guo, Liang, Zhu, & Hu, 2008). Disregarding such

interdependencies, i.e. assuming that projects are independent, can leads to funding an

inappropriate project portfolio as the result of underestimating or neglecting an

appropriate project portfolio as the result of overestimating the risks of project portfolios.

Accordingly, literature (e.g. Gear & Cowie, 1980; Guo et al., 2008) calls to add risk

interdependencies among projects into the PPSP optimization model. For this purpose,

having considered the similar core concepts between “(Financial) portfolio selection

problem” (PSP) and PPSP, e.g. return, risk and risk interdependency, in paper 2 (Chapter

3), I use principles of Modern Portfolio Theory (MPT), a well-acknowledged theory to

5

PSP in Finance discipline, and tailor it to develop an optimization model of PPSP.

Accordingly, the paper 2 aims to answer the following research question: “How can MPT

principles be applied in the project portfolio context to improve the optimization model

of PPSP?”

This thesis contributes to the literature in two ways: (1) it proposes an integrated

benefit-oriented framework for project evaluation, and (2) it tailors MPT and utility

theories to make it suitable for investment decisions and evaluation that may also include

projects. Furthermore, in practice, this study enhances the quality of project appraisal,

selection, monitoring, and performance judgment in organizations and helps them

ensuring the realization of projects’ intended benefits.

The rest of this thesis is organized as follows. Chapter 2 is assigned to the

explanation of paper 1. Paper 2 is presented in Chapter 3 and finally, the conclusions are

drawn in Section 4.

6

REFERENCES

Angus, G. Y., Flett, P. D., & Bowers, J. A. 2005. Developing a value-centred proposal for

assessing project success. International Journal of Project Management, 23(6): 428-

436.

Atkinson, R. 1999. Project management: cost, time and quality, two best guesses and a

phenomenon, its time to accept other success criteria. International journal of project

management, 17(6): 337-342.

Barclay, C., & Osei-Bryson, K. M. 2010. Project performance development framework: An

approach for developing performance criteria & measures for information systems (IS)

projects. International Journal of Production Economics, 124(1): 272-292.

Carazo, A. F. 2015. Multi-criteria project portfolio selection. In J. Zimmermann & C.

Schwindt (Eds.), Handbook on project management and scheduling vol. 2: 709-728.

Switzerland: Springer International Publishing.

Frechtling, J. 2002. The 2002 User-Friendly Handbook for Project Evaluation.

Gear, T. E., & Cowie, G. C. 1980. A note on modeling project interdependence in research

and development. Decision Sciences, 11(4): 738–748.

Guo, P., Liang, J. J., Zhu, Y. M., & Hu, J. F. 2008. R&D project portfolio selection model

analysis within project interdependencies context. In Industrial Engineering and

Engineering Management, 2008. IEEM 2008. IEEE International Conference on (pp.

994-998). IEEE.

http://link.springer.com/chapter/10.1007/978-3-319-05915-0_3

7

Hillson, D. 2002. Extending the risk process to manage opportunities. International Journal

of project management, 20(3): 235-240.

Lee, M., Son, B., & Om, K. 1996. Evaluation of national R&D projects in Korea. Research

Policy, 25(5): 805-818.

Lewis, M. W., Welsh, M. A., Dehler, G. E., & Green, S. G. 2002. Product development

tensions: Exploring contrasting styles of project management. Academy of

Management Journal, 45(3): 546-564.

Li, X., Fang, S. C., Tian, Y., & Guo, X. 2015. Expanded model of the project portfolio

selection problem with divisibility, time profile factors and cardinality constraints.

Journal of the Operational Research, 66(7): 1132–1139.

Mutavdzic, M., & Maybee, B. 2015. An extension of portfolio theory in selecting projects to

construct a preferred portfolio of petroleum assets. Journal of Petroleum Science and

Engineering, 133: 518-528.

Sefair, J. A., Méndez, C. Y., Babat, O., Medaglia, A. L., & Zuluaga, L. F. 2017. Linear

solution schemes for Mean-SemiVariance Project portfolio selection problems: An

application in the oil and gas industry. Omega, 68: 39-48.

Shou, Y., Xiang, W., Li, Y., & Yao, W. 2014. A multiagent evolutionary algorithm for the

resource-constrained project portfolio selection and scheduling problem. Mathematical

Problems in Engineering, 2014: 1-9.

8

Winter, M., & Szczepanek, T. 2008. Projects and programmes as value creation processes:

A new perspective and some practical implications. International Journal of Project

Management, 26(1): 95-103.

Zwikael, O., & Meredith, J. 2018. Who’s who in the project zoo? The ten core project roles.

International Journal of Operations & Production Management (forthcoming).

Zwikael, O., & Smyrk, J. 2012. A general framework for gauging the performance of

initiatives to enhance organizational value. British Journal of Management, 23(S1).

9

CHAPTER 2: PAPER 1

An Integrated Benefit-Oriented Project Evaluation Framework: Appraisal,

Monitoring and Performance Judgement

11

ABSTRACT

The realization of benefits is the main reason projects are funded. However, current project

evaluation (i.e. appraisal, monitoring and performance judgement) frameworks underplay the

importance of benefit realization, as they focus on delivering project’s outputs on time,

budget and to specifications. Moreover, the integration among the various evaluation

frameworks is poor with different evaluation tools used at various project phases. Altogether,

there is a need to develop an integrated project evaluation framework that takes benefits into

consideration and is usable for all project phases. Furthermore, because a project with a very

attractive expected return but high risk might expose the organization to a large loss, such a

framework should consider the combined analysis of projects’ returns and risks. The

principles of such return-risk evaluation are well supported by utility theory. This paper

tailors utility theory to propose an integrated benefit-oriented framework for project

evaluation on the basis of its return and risk. It is expected that the proposed project

evaluation framework will help organizations ensuring the realization of projects’ intended

benefits. To demonstrate how to apply the proposed framework, we employ a numerical

example and report the results.

Keywords:

Project evaluation; project appraisal; project monitoring; project performance judgement;

utility theory; risk register; benefit management

12

1. INTRODUCTION

Projects are the fundamental drivers of enhanced performance from an individual

business through to national economies (Lewis, Welsh, Dehler, & Green, 2002). A successful

project can bring benefits to the organization, such as better utilization of resources and

enhanced productivity (Lientz & Rea, 2016). To reach project success, a conceptually

coherent framework is required to systematically evaluate projects in terms of what goals are

planned to meet and whether the goals are being or have been met (Frechtling, 2002). The

evaluation of projects is implemented continuously along the whole projects’ life in three

stages: ex-ante, interim, and ex-post evaluation (Lee, Son, & Om, 1996). Ex-ante evaluation,

i.e. project appraisal, is aimed to prioritize project proposals before one or several projects

are funded (Laursen, Svejvig, & Rode, 2017). Interim evaluation, i.e. project monitoring,

compares from funding until completion the ongoing performance of a project to its initial

goals, to understand what went right or wrong in order to improve the strategy or the

processes (Crawford & Bryce, 2003). Ex-post evaluation, i.e. project performance

judgement, measures the realized project performance at the end of the project’s life to judge

whether the initial goals have been achieved and enhance organizational learning in order to

achieve successful projects in future (Angus, Flett, & Bowers, 2005).

In each of the three stages of project evaluation, i.e. appraisal, monitoring and

performance judgement, literature has traditionally focused on the delivery of outputs, such

as products (Atkinson, 1999). For example, project performance judgement particularly

13

focuses on delivering outputs on time, on budget, and to a defined quality, which is often

articulated as adhering to the “iron triangle” (Andersen, 2010). Project monitoring uses

methods such as Earned Value Management to track whether the project is on track to achieve

each of the iron triangle dimensions (Ong, Wang, & Zainon, 2016). In project appraisal,

output-based methods such as ‘scope-schedule-cost plan’ are applied (Project Management

Institute, 2017).

However, evaluation with a focus on output delivery is insufficient because delivering

an output efficiently does not necessarily imply benefits realization for the funding

organization (Winter & Szczepanek, 2008). Thus, in a wider view on the management of

projects (Morris, 1997), we see a shift from a sole focus on output creation to a holistic focus

on both output creation and benefit realization (Winter, Andersen, Elvin, & Levene, 2006).

Accordingly, over the past few years scholars have paid more attention to the realization of

projects’ benefits to develop some frameworks for one (e.g. Angus et al., 2005; Zwikael &

Smyrk, 2012) or two (e.g. Barclay & Osei-Bryson, 2010) out of three stages of project

evaluation. However, these frameworks are dispersed and incoherent, which means a

framework applied for one stage of project evaluation is useless for the other stages. Using a

different framework for each stage of project evaluation can lead to inconsistency and waste

of resources, e.g. time and money. Thus, there is a need to have a coherent evaluation

framework throughout the entire project’s life rather than having different frameworks for

each evaluation stage.

14

Furthermore, in such integrated framework, the combined analysis of project’s

benefits- and consequently project’s return- and risk is important because a project with a

very attractive expected return but high risk might expose the organization to a large loss,

whereas a low-risk project might secure the organization a lower but more certain return

(Hillson, 2002; Sefair, Méndez, Babat, Medaglia, & Zuluaga, 2017). Altogether, there is a

need to develop a coherent integrated project evaluation framework which takes into account

both projects’ returns and risks, from the early phase of projects until after their completion.

The principles of such evaluation framework are well supported by “utility theory”, as is

discussed next.

Utility theory is widely acknowledged in the Finance discipline to support decision

making under uncertainty, for example in asset evaluation, which trades off between asset’s

return and risk regarding the risk aversion of investors (Bell, 1995). A core principle of utility

theory is that each investor can assign a utility score to competing assets on the basis of their

expected returns and risks, which represents the welfare each asset has to the investor (Bodie,

Kane, & Marcus, 2014), to make a decision that maximizes the utility. This theory suggests

that the indifferent relation of assets’ returns and risks is transitive, and this leads to

equivalence classes of indifferent elements or, equally, to indifference curves (Luce, 1956).

Having considered the similar core concepts between asset evaluation and project

evaluation, i.e. return, risk and risk aversion, in this paper, we employ utility theory to

develop the integrated project evaluation framework based on projects’ returns and risks.

15

This paper contributes to the literature by proposing an integrated benefit-oriented framework

for all three stages of project evaluation. The paper also enhances the quality of project

evaluation in organizations and helps them ensuring the realization of projects’ intended

benefits. These contributions are achievable through answering the following research

question: “How can utility theory’s principles be applied in the project context to develop an

integrated benefit-oriented project evaluation framework?”

The rest of this paper is organized as follows. Section 2 reviews existing frameworks

in project evaluation, describes utility theory and discusses applying utility theory in project

evaluation framework. The new framework of project evaluation is proposed in Section 3.

Section 4 presents a numerical example to demonstrate how the proposed project evaluation

framework should be used. Finally, the conclusions are drawn in Section 5.

2. LITERATURE REVIEW

2.1. Existing frameworks in project evaluation

The prerequisite step to develop any framework for project evaluation is to clarify

what a project is. There are two common views in the literature to define a project (Angus et

al., 2005). The first is output-oriented view, exemplified by Project Management Institute

(2017): “A project is a temporary endeavour undertaken to create a unique product, service,

or result” (p. 4). Building on the output-oriented view, various frameworks exist for the three

stages of project evaluation, for instance: (1) Project appraisal - ‘scope-schedule-cost plan’

16

is applied (Project Management Institute, 2017); (2) Project monitoring - earned value, and

earned schedule are employed (Ong et al., 2016; Project Management Institute 2017); and

(3) Project performance judgement - the “iron triangle” (or triple constraint) test of project

success is the most conventional framework whereby performance is judged by the delivery

of project’s outputs fit-for-purpose, on time and within budget (Dvir & Lechler, 2004).

However, output-oriented evaluation frameworks ignore the realization of project’s

benefits (Ashurst, Doherty, & Peppard, 2008; Müller & Turner, 2007). Benefits are the flows

of value, i.e. the project’s desired end-effects derived from utilizing the project's outputs,

which is perceived as positive by the project funder, i.e. the senior manager who commits

funds and/or approves allocation of labor to the project (Laursen & Svejvig, 2016; Zwikael

& Meredith, 2018). In other words, although the underlying rationale for all projects is that

they seek specific target benefits (Dvir & Lechler, 2004), benefits do not appear among the

project evaluation criteria used in the output-oriented view (Zwikael & Smyrk, 2012).

To address the limitation of the project’s output-oriented view, the benefit-oriented

view was introduced, where a project is a unique process undertaken to achieve target

benefits (Zwikael & Smyrk, 2012). Building on the benefit-oriented view, a number of

frameworks exist for the three stages of project evaluation, for example: (1) Project appraisal

- Remer and Nieto (1995) discuss some return representatives in project appraisal such as

“net present value”, “payback period”, and “cost-benefit analysis”; (2) Project monitoring -

Sapountzis, Yates, Kagioglou, and Aouad (2009) focus upon the requirements to manage

17

change, tangible and intangible benefits in primary healthcare infrastructures. Ashurst et al.

(2008) propose a conceptual model of a benefits realization capability drawing on the

resource-based view of the firm; and (3) Project performance judgement - Atkinson (1999)

suggests a square route model to elaborate our understanding of success criteria in projects

with dimensions such as benefits for organization and community. Ashley, Lurie, and

Jaselskis (1987) refer to project success as having results much better than expected or

normally observed in terms of cost, schedule, quality, safety and participant satisfaction. De

Wit’s (1988) view is that the project is considered an overall success “if there is a high level

of satisfaction concerning the project outcome among key people in the parent organization”

(p. 165). Zwikael and Smyrk (2012) developed a conceptual triple-test performance

judgement framework including project management evaluation, project ownership

evaluation, and project investment evaluation.

The analysis of existing benefit-oriented project evaluation frameworks reveals the

dispersion and incoherence of these studies because a framework applied to one stage of

project evaluation is useless in the other stages. Although there are rare studies which deal

with two stages of project evaluation, such as Barclay and Osei-Bryson (2010) that developed

a framework for project monitoring and performance judgement, there is still a need to

develop an integrated framework to coherently combine all three stages of project evaluation.

Moreover, in such integrated framework, the combined analysis of projects’ returns and risks,

particularly in project appraisal and monitoring, is important because a project with a very

18

attractive expected return but high risk might expose the organization to a large loss, whereas

a low-risk project might secure the organization a lower but more certain return (Hillson,

2002; Sefair et al., 2017). Thus by and large, it can be asserted that, there is a need to develop

a coherent integrated project evaluation framework which takes into account projects’ returns

and risks, from the early phase of projects’ lives until after their completion.

To close the gap, because such evaluation framework is well explained by “utility

theory” (a powerful theory in the Finance discipline for asset evaluation which considers both

assets’ returns and risks), we employ the principles of this theory to develop an integrated

benefit-oriented project evaluation framework. Next, we discuss utility theory and explain

how its principles can be applied in developing the new project evaluation framework.

2.2. Utility theory

2.2.1. Principles

According to Bodie et al. (2014), it is assumed that each investor can assign a welfare,

or utility, score to competing assets on the basis of the expected returns and risks of those

assets. Higher utility values are assigned to assets with more attractive risk–return profiles.

Assets receive higher utility scores for higher expected returns and lower scores for higher

risks. Here, we pick up the quadratic von Neumann–Morgenstern utility function which

assigns an asset with expected return and risk , the following utility score, U:

19

21

2U A (1)

Where:

A is an index of the investor’s risk aversion, and

and are estimated by the mean and standard deviation of the asset’s historical returns.

Accordingly, investors choosing among competing investment assets will select the

one providing the highest utility level. Equation (1) is consistent with the notion that utility

is enhanced by higher expected return and diminished by higher risk. Notice that the return

of a risk-free asset (e.g., the return of placing money in the bank) receives a utility score equal

to its (known) rate of return, fr , because it has no risk. As can be seen from Equation (1),

the extent to which the variance of risky assets lowers utility depends on A, the investor’s

degree of risk aversion. Regarding the degree of risk aversion, investors can be divided into

three major categories as follows:

Risk-averse investors (for whom A>0) penalize the expected rate of return of a risky

asset by a certain percentage (or penalizes the expected profit by a dollar amount) to

account for the risk involved. The more risk averse the investor, the larger parameter

A is.

Risk-neutral investors (with A=0) judge risky assets solely by their expected rates

of return. The level of risk is irrelevant to the risk neutral investors, meaning that

20

there is no penalty for risk. For these investors, an asset’s certainty equivalent rate is

simply its expected rate of return.

Risk-lover investors (for whom A<0) are happy to engage in fair games and

gambles. These investors adjust the expected return upward to take into account the

“fun” of confronting the prospect’s risk. Risk lovers will typically take a fair game

because their upward adjustment of utility for risk gives the fair game a certainty

equivalent that exceeds the alternative of the risk-free investment.

In project evaluation, most organizations are risk-averse and thus they will not

undertake a high-risk project unless the project delivers a high return (Singh, 1986).

2.2.2. Indifference curves

Assume a risk-averse investor identifies all assets that are equally attractive as asset

P, depicted in Figure 1. Starting at P, an increase in standard deviation, which lowers utility,

must be compensated by an increase in expected return. Thus, point Q in Figure 1 is equally

desirable to this investor as P. In other words, this investor will be equally attracted to assets

with high risk and high expected returns compared with other assets with lower risk but lower

expected returns. These equally preferred assets will lie in the “return-risk plane” on a curve

called the indifference curve (Bodie et al., 2014), which connects all assets points with the

same utility values. As a result, a higher indifference curve (e.g. the curve point O lies on in

Figure 1) represents more attractive assets than a lower one (e.g. the curve point P and Q lie

21

on in Figure 1) to this investor. Figure 1 exemplifies indifference curves of risk-averse, risk-

neutral and risk-lover investors.

------------------------------------

Insert Figure 1 about here

------------------------------------

2.3. The application of utility theory in project evaluation

Researchers (e.g., Luo, 2012; Sefair et al., 2017) have identified important similarities

between asset and project evaluation that justify the use of utility theory in project evaluation.

These similarities include: (1) Both assets and projects have expected returns; (2) These

expected returns have uncertainties, i.e. risks; and (3) Both investors and organizations have

their own levels of risk aversion.

Despite these basic similarities between asset and project evaluation, some

differences also exist between these evaluations. First, some critics say that in practice, few

companies use utility theory to help in decision-making as within the same organization, one

manager may typically champion risky projects, while another in a similar position may be

more conservative (Bailey, Couët, Lamb, Simpson, & Rose, 2000). This issue can be

resolved because in project evaluation, there is only one decision maker, i.e. the funder. Thus,

indifference curves in organizations should be drawn regarding the risk aversion level of the

funder. Second, Perlitz, Peske, and Schrank (1999) assert that usually there are not sufficient

historical returns available to calculate projects’ returns and risks. This problem can be

22

addressed through replacing historical returns by the effects of triggering events, i.e. threats

and opportunities, around projects (Merikhi & Zwikael, 2017). Third, Casault, Groen, and

Linton (2013) argue that unlike assets which only have monetary benefits, projects have both

monetary and non-monetary benefits. This difference can be addressed through converting

non-monetary benefits and disbenefits to monetary ones (dolor values) by using some

techniques such as Delphi (Abbassi, Ashrafi, & Tashnizi, 2014) which its explanation is out

of the scope of this paper. Last but not least, unlike assets, some mitigation actions exist in

projects to reduce their risks. The objective of risk mitigation actions is to increase the

probabilities or impacts of opportunities and decrease the probabilities or impacts of threats

(Fang & Marle, 2015), which can in turn result in changing projects’ returns. These

mitigation actions cause shifting a project to a different indifference curve.

Altogether, Table 1 summaries the approaches used by utility theory in asset

evaluation and those should be used in project evaluation which introduces some implications

for the proposed integrated project evaluation framework.

------------------------------------

Insert Table 1 about here

------------------------------------

The analysis of Table 1 shows that although utility theory provides a good foundation

for project evaluation, two additional elements that are unique to project evaluation should

be integrated to the proposed framework. According to Table 1, these elements includes: (1)

The effects of triggering events that can have either damaging impacts as threats or assisting

23

impacts as opportunities on the expected return of a project through some chain of

consequences (Zwikael & Smyrk, 2011); and (2) the effects of risk mitigation actions. Next,

we propose a utility-based framework for three stages of project evaluation.

3. THE DEVELOPMENT OF PROJECT EVALUATION FRAMEWORK

Here, we first discuss how the return-risk plane should be drawn for project

evaluation. We call this plane “Project evaluation map”, which is the foundation of the

proposed project evaluation framework. Then we explain the usage of this map in each

project evaluation stage.

3.1. Project evaluation map

To develop the “project evaluation map”, we are inspired by the Project Investment

Evaluation (PIE) map (Zwikael & Smyrk, 2012), which uses project worth and its riskiness

to make decision regarding project appraisal. In the following sections we discuss the

dimensions of the project evaluation map and two core indifference curves required to make

evaluation decisions.

3.1.1. The dimensions of the project evaluation map

24

In order to estimate projects’ returns and risks, according to Table 1, we need first to

identify the effects of threats and opportunities around projects. The risk register is an

effective project management tool that includes this information used as part of a business

case which is updated through the project’s life (Project Management Institute, 2017).

Because most projects include a risk register as a core management tool, the proposed

framework uses data included in this document to estimate projects’ returns and risks. There

are different formats for risk registers proposed by various studies. One of the most

comprehensive formats is that proposed by Merikhi and Zwikael (2017) that is used in this

paper and exemplified in Table 2, in which a risk register is a table where rows are associated

with threats/opportunities and columns are relevant to their attributes including their

likelihoods and damaging/assisting impacts. The advantages of implementing this format

here is taking into account all threats and opportunities with all their possible damaging (i.e.

benefit reduced, benefit delayed, disbenefit increased, disbenefit advanced, cost increased,

and cost advanced) and assisting impacts (i.e. benefit increased, benefit advanced, disbenefit

decreased, disbenefit delayed, cost decreased, and cost delayed) on the project. Furthermore,

to develop the evaluation framework, we assume that the organization is going to implement

projects in a fixed planning period of time [0 T] assuming all project proposals, if get funded,

start at time 0.

------------------------------------


------------------------------------

25

Employing the risk register introduced by Merikhi and Zwikael (2017), exemplified

in Table 2, the total number of potential situations can surround project i, im , is 2 in reached

from Equation (2) in which in is the number of threats/opportunities mentioned in the risk

register of project i.

... 20 1 2 3

iii i i i n

i

i

nn n n nm

n

(2)

Furthermore, we apply the “Modified Internal Rate of Return” (MIRR) as the

representative of a project’s rerun. MIRR (r in this paper) assumes that benefits/disbenefits

generated from a project are reinvested at the risk-free rate of return rather than at the

project’s internal rate of return (Lin, 1976). Equation (3) represents this assumption regarding

continuous compounding instead of discrete one.

rT

Futurevalue of benefits and disbenefitsPresent valueof costs

e (3)

Where: e is Euler's number which represents continuous compounding.

Thus, the return of project i in potential situation s, isr , is calculated as follows by

considering the fact that benefits and disbenefits have continuous flows, whereas costs are

discrete ones which only occur during the project’s life:

( )is is

is is isisis

FB FDLn

Ln FB FD Ln PCPCr

T T

(4)

26

( )

11

( )

11

1( )

(1 )

(1 )

(1 )

i

f

ik ikuB Bik iku

u s

f

i ik iku

B Bik ikuu s

f B Bik iku ik ikuu sf

KT r T t

is B BS S

k u s

r T tT

K B B

u s

S Sk f

r T S SB Br T Tu s

f

Where FB M M e dt

M M e

r

M M

e er

1

1

1

(1 )

1

i

i f B Bik iku ik ikuu s

K

k

K r T S SB B

u s

k f

M M

er

(5)

( )

11

( )

11

1( )

(1 )

(1 )

(1 )

i

f

il iluD Dil ilu

u s

f

i il ilu

D Dil iluu s

f D Dil ilu il iluu sf

LT r T t

is D DS S

l u s

r T tT

L D D

u s

S Sl f

r T S SD Dr T Tu s

f

FD M M e dt

M M e

r

M M

e er

1

1

1

(1 )

1

i

i f D Dil ilu il iluu s

L

l

L r T S SD D

u s

l f

M M

er

(6)

1

1

1i f C Cif ifu

u s

if ifu

F r S S

is C C

f u s

PC M M e

(7)

Where:

27

isFB is the total future value of benefits relevant to project i at time T if potential situation s

materializes,

isFD is the total future value of disbenefits relevant to project i if potential situation s

materializes,

isPC is the total present value of costs relevant to project i if potential situation s materializes,

iK is the total number of benefits relevant to project i,

iL is the total number of disbenefits relevant to project i,

iF is the total number of costs relevant to project i,

ikBM is the estimated/realized magnitude of kth benefit relevant to project i,

ikuBM is the estimated percentage of changes in the magnitude of kth benefit relevant to

project i if threat/opportunity u materializes,

ikBS is the estimated/realized scheduling for the realization of kth benefit relevant to project i,

ikuBS is the estimated percentage of changes in the scheduling for the realization of kth benefit

relevant to project i if threat/opportunity u materializes,

ilDM is the estimated/realized magnitude of lth disbenefit relevant to project i,

iluDM is the estimated percentage of changes in the magnitude of lth disbenefit relevant to


28

ilDS is the estimated/realized scheduling for the realization of lth disbenefit relevant to project

i,

iluDS is the estimated percentage of changes in the scheduling for the realization of lth

disbenefit relevant to project i if threat/opportunity u materializes,

ifCM is the estimated/spent magnitude of fth cost relevant to project i,

ifuCM is the estimated percentage of changes in the magnitude of fth cost relevant to project i

if threat/opportunity u materializes,

ifCS is the estimated/realized scheduling for the spending of fth cost relevant to project i, and

ifuCS is the estimated percentage of changes in the scheduling for the spending of fth cost

relevant to project i if threat/opportunity u materializes.

On the other hand, the likelihood of situation s materializing in project i, isp , is

calculated as the multiplication of the likelihoods of the threats/opportunities included in

situation s materializing and likelihoods of the others not materializing, demonstrated as

follows:

(1 )is u u

u s u s

p l l

(8)

Where: ul is the likelihood of threat/opportunity u materializing.

Thus, the estimation for return (i.e. mean, î ), risk (i.e. standard deviation, ˆ

i ), and

cost ( î ) of project i can be reached as follows:

29

1

ˆ (1 )im

is is is

i u u

s u s u s

Ln FB FD Ln PCl l

T

(9)

2

1

ˆ ˆ(1 )im

is is is

i u u i

s u s u s

Ln FB FD Ln PCl l

T

(10)

1

ˆ (1 )im

i u u is

s u s u s

l l PC

(11)

Since surplus budget is rarely left idle, we assume that the investor can always invest

unallocated budget in a risk-free asset with return fr (Findlay, McBride, Yormark, &

Messner, 1981). Thus, the estimated “overall expected return” and “overall risk” resulted

from funding project i (i.e. î and ˆ

i respectively, which constitute the project evaluation

map’s dimensions, i.e. and ), and its estimated attractiveness (i.e. utility, îU ) can be

reached as follows:

ˆ ˆˆ ˆ( ) ( )i i

i i fr

(12)

ˆˆ ˆ( )i

i i

(13)

21ˆ ˆ ˆ2

i i iU A (14)

Where: is the available budget to fund project i.

30

3.1.2. Indifference curves

We employ two types of indifference curves in project evaluation: (1) Funder

investment frontier; and (2) Attractiveness contours (Zwikael & Smyrk, 2011) discussed

next.

“Funder investment frontier” is an indifference curve with the utility equal to risk-

free rate of return, which represents all combinations of “overall returns” and “overall risks”

that a funder would be prepared to accept as a worst case. In the Funder’s point of view, the

risk-free rate of return can be for example placing money in the bank, the return of a well-

established production line or the like. Building on utility theory, this frontier is unique for

each funder according to how much risk averse he is and how much rate of return he considers

risk-free. Funders’ levels of risk aversion, “A”, can be extracted from analyzing their previous

decisions (see Bailey et al., 2000 for details). Having considered Equation (1), the function

of “Funder investment frontier” is reached as follows, depicted in Figure 2.

21

2fA r (15)

The “Funder investment frontier”, i.e. Equation (15), is applied in project appraisal

and project performance judgement explained later.

“Attractiveness contours” are indifference curves representing the attractiveness of

project proposals, depicted in Figure 2. The “Attractiveness contour” of project i with

attractiveness îU is as follows:

31

21 ˆ2

iA U (16)

Where îU is drawn from Equation (14).

Taken together, Figure 2 represents the “Project evaluation map” including “Funder

investment frontier” and “Attractiveness contours”.

------------------------------------


------------------------------------

3.2. Project appraisal

A project’s life consists of four phases: initiation, planning, execution, and benefit

realization (Zwikael & Smyrk, 2011). The decision whether a project gets funded is made at

the first phase of a project’s life, i.e. initiation. Accordingly, project appraisal is done in

initiation phase to prioritize project proposals before one or several projects are funded

(Laursen et al., 2017) based on their “overall returns” and “overall risks”, through applying

Equations (2), and (4) to (14).

According to Equation (15), all project proposals which their overall returns and

overall risks applies to this function will lie on the “Funder investment frontier” and their

attractiveness is equal to the known risk-free rate of return fr . As a result, project proposals

which lie bellow (and to the right of) “funder investment frontier” are unacceptable for

funding, while projects that lie above (and to the left of) this frontier are suitable for funding.

32

Furthermore, according to Equation (16), all project proposals lying on an

attractiveness contour represent the same attractiveness to the funder. The higher the location

of an attractiveness contour, the more attractive its corresponding project proposal is.

3.2.1. The effect of risk mitigation actions on attractiveness contours

Different risk mitigation actions, either to enhance the probabilities and impacts of

opportunities or decrease the probabilities and impacts of threats, can result in shifting a

project proposal from one attractiveness contour to one another, either higher or lower. A

risk mitigation action decreases the project’s risk and depending on its cost, increases or

decreases the project’s overall return and overall risk. Different combinations of candidate

risk mitigation actions construct candidate risk mitigation programs. Accordingly, here,

Equations (4) to (14) as well as Equation (16) should be again calculated based on the updated

risk register resulting from each candidate risk mitigation program and its corresponding cost.

Through this calculation, the cost of risk mitigation program should be considered as a new

project’s cost in Equation (7).

In Figure 2, if we assume “I0” as the location of project proposal i before applying

any mitigation programs, i.e. pre-risk mitigation program scenario, three possible post-risk

mitigation program scenarios are shown as “I1”, “I2” and “I3” where:

I1 is more attractive than I0 (because the cost of risk mitigation program is more than

adequately compensated for by the reduction in overall risk, I1 lies on a higher

33

attractiveness contour than I0). Such risk mitigation programme is cost effective and

can be considered for adoption.

I2 is equally attractive as I0 (because the cost of risk mitigation program is

compensated for by the reduction in overall risk, I2 lies on the same attractiveness

contour as I0). Such risk mitigation program makes no difference if it is adopted.

I3 is of less attractiveness than I0 (because the reduction in overall risk is only small

while the cost of the associated risk mitigation program is large, I3 lies on a lower

attractiveness contour than I0). Such risk mitigation programme is not cost effective

and so should not be adopted.

Regarding this argument, the best risk mitigation program for a specific project

proposal would be the one that moves the project proposal to the highest possible

“Attractiveness contour” given limited resources, as each risk mitigation program would

bring cost to the funder. Such highest attractiveness contour is called “Approved business

case contour”, depicted in Figure 2, which is the foundation of project monitoring and project

performance judgement explained in the following.

3.3. Project monitoring

Project monitoring, measures the ongoing performance of a project during planning,

execution and benefit realization phases, to understand whether the project is on the track of

its initial goals in order to improve the strategy or the processes (Crawford & Bryce, 2003).

34

During these phases: (1) Some threats/opportunities materialize, some new ones appear,

some become irrelevant, and some remain either with or without changes in their likelihoods

or impacts; and (2) Some benefits/disbenefits are realized and some costs are spent. All of

these changes result in an updated risk register for each project’s milestone. Thus, at different

project’s milestones, first, the project’ overall return and overall risk should be updated

according to its corresponding updated risk register and applying Equations (2), and (4) to

(14). Then, the corresponding point (i.e. the coordinate of updated “overall risk” and “overall

return”) should be located on the project evaluation map to see whether the project has been

shifted to a different attractive contour than the “approved business case contour”. If project

monitoring indicates project shifting to a higher attractiveness contour than or remaining on

the “approved business case contour”, demonstrated as scenarios X and Y respectively in

Figure 2, the project progresses better than or as expected. Otherwise, represented as scenario

Z in Figure 2, the appropriate corrective actions should be implemented to bring back the

project to the “approved business case contour”.

3.4. Project performance Judgement

Project performance judgement evaluates the realized project performance at the end

of the project’s life, through applying two tests: (1) Project business case judgement:

represented by the project’s performance in realizing the initial goals, i.e. “approved business

case contour”; and (2) Project investment judgement: represented by the project’s

35

performance in meeting the funder’s minimum preferences, i.e. “Funder investment frontier”

(Zwikael and Smyrk, 2012).

After all benefits and disbenefits of a project are realized, all threats and opportunities

become irrelevant for the project and so we remain with the realized overall return, but no

risk (Zwikael and Smyrk, 2011). Regarding Figure 2, having located the corresponding point

(i.e. the coordinate of zero “overall risk” and realized “overall return”), achieved through

applying Equations (2), and (4) to (14), on the project evaluation map, three possible

scenarios are shown as “F”, “G”, and “H” where:

F lies on the overall return dimension bellow fr . In this situation, because F’s

corresponding attractiveness contour is bellow both the “approved business case

contour” and “funder investment frontier”, both project business case and investment

are judged as failures.

G lies on the overall return dimension between fr , and 1

ÎU (the attractiveness of the

“approved business case contour”). Here, project business case is judged as failure,

while project investment is judged as success.

H lies on the overall return dimension above 1

ÎU . In this situation, both project

business case and investment are judged as successes.

36

4. A NUMERICAL EXAMPLE

The purpose of this section is to employ a numerical example in order to illustrate

how the proposed project evaluation framework can be applied. Let us assume that a funder

with the risk aversion of 4 faces a hypothetic project proposal “E” for a period of 15 months,

the risk-free rate of return of 0.2% per month and a limited budget of $20,000. Table 2 depicts

the risk register developed for this project, which shows three threats, their pre-likelihoods

and -damaging impacts.

Regarding Equation (15), the “funder investment frontier” is drawn as follows, which

is depicted in Figure (3)

22 0.002

------------------------------------


------------------------------------

4.1. Project appraisal

Regarding Equation (2), as this project has three threats, there are eight potential

situations to materialize. Table 3 shows these potential situations, the likelihood of each

situation materializing ( Esp ) drawn from Equation (8), the return of project “E” in each

situation ( Esr ) calculated by Equations (4) to (7), and the total present value of the project’s

costs in each situation ( EsPC ) calculated by Equation (7).

37

------------------------------------


------------------------------------

Applying Equations (9) to (11), the estimated return, risk and cost of project “E”

before applying any risk mitigation programs are calculated as follows:

00.21 0.14

0.09

ˆ ( 0.0446) (0.09 0.0033) (0.21 0.0072) ( 0.0425)

( 0.057 0.06 0.141) ( 0.0072) ( 0.0 0.034) ( 0.0661)

0.0074 0.

06

74%

E

0

2 2 2

2 2

2 2

2 2

ˆ ( ) 0.09 ( 0.0033 )

0.21 (0.0072 ) ( )

(

0.21 0.0446 0.0074 0.0074

0.0074 0.14 0.0425 0.0074

0.09 0.0571 0.0074 0.06 0.0072 0.0074

0.14 0.0034 0.0074 0.06 0.0661 0.0074 0.0011867

) (

) ( ) 2

)

(

Ê

E

00.0344 3.44%

00.21 0.14

0

ˆ ( 14,841) (0.09 16,818) (0.21 14,841) ( 14,841)

( 16,818) ( 16,818.09 0.06 0.1) ( 14,841)4 0.06

15,43

( 16,818)

$ 4

E

Furthermore, according to Equations (12), (13) and (14), the overall return and overall

risk resulted from funding project “E” and its attractiveness are reached as follows:

0

15,434 20,000 15,434ˆ 0.0074 0.002 0.0062 0.62%

20,000 20,000E

0

15,434ˆ ( ) 0.0344 0.0266 2.66%

20,000E

38

0

21ˆ 0.0062 (4)(0.0266 ) 0.00482

EU

Thus, according to Equation (16), the attractiveness contour of project “E” is reached

as follows, depicted in Figure 3 as the curve point E0 (2.66%, 0.62%) lies on:

22 0.0048

In order to decrease the risk of project “E”, the funder faces three candidate risk

mitigation programs demonstrated in Table 4 as M1, M2 and M3.

------------------------------------


------------------------------------

Having applied Equations (4) to (14) on all three risk registers resulted from risk

mitigation programs M1, M2 and M3 and their corresponding costs, the estimated return, risk,

cost, overall return, overall risk and attractiveness of project “E” are calculated as: (1) For

M1- 0.57%, 3.16%, $18,034, 0.54%, 2.85%, and 0.0037; (2) For M2- 0.78%, 3.02%, $16,737,

0.68%, 2.53%, and 0.0055; and (3) For M3- 0.48%, 2.89%, $18,737, 0.46%, 2.71%, and

0.0031 respectively. Figure 3 represents the corresponding attractiveness contours of risk

mitigation programs M1, M2 and M3, achieved by Equation (16), as the curves points E1

(2.85%, 0.54%), E2 (2.53%, 0.68%), and E3 (2.71%, 0.46%) lie on respectively. As can been

seen the best risk mitigation program is M2 because E2 sits on the highest attractiveness

contour, which results in the “approved business case contour” of project “E”, depicted in

Figure 3. Furthermore, the cost of this mitigation action would be added to the risk register

39

as C4 with the magnitude of $1500 and scheduling for spending at time zero. Altogether, it

can be concluded that if the funder approves project “E” to be funded, he should apply the

risk mitigation program M2 and use the “approved business case contour” for the project

monitoring and performance judgement.

4.2. Project monitoring

The funder considers 14 milestones to monitor project “E” during its life with respects

to the “approved business case contour” (the 15th milestone coincides with project

performance judgement). As an example, we demonstrate the monitoring of project “E” in

Milestone t=9. The corresponding updated risk register is demonstrated in Table 5, in which

C4 has been added to the risk register as the cost of approved risk mitigation action M2.

------------------------------------


------------------------------------

As can be seen form Table 5, the likelihood of threat T02 has changed from 50% to

40%, threat T03 has become irrelevant for the project, and a new threat T04 has been added

to the risk register. Furthermore, cost C1 has been spent as expected (i.e. with the magnitude

of $5,000 at time 1, whereas cost C2 has been spent differently to what expected with the

magnitudes of $5,200 at times 4.5. Moreover, the project’s disbenefit, i.e. D1, has been

realized as expected at time 5 with the magnitude of $1,000. Having employed Equations (2),

and (4) to (14) on the updated risk register demonstrated in Table 5, the updated estimated

40

return, risk, cost, overall return, overall risk and attractiveness of project “E” at time t=9 are

calculated as 1.05%, 2.97%, $16,887, 0.92%, 2.51%, and 0.0079 respectively, which its

corresponding point is depicted in Figure 3 as V (2.51%, 0.92%). As can be seen this point is

above the “approved business case contour” and thus the project progresses better than

expected. Also, the ongoing attractiveness of the project has increased from 0.0055 to 0.0079.

4.3. Project performance judgement

To judge the project performance, assume that benefits B1, B2 and B3 have been

realized at times 11, 12 and 12 with the magnitudes of $2,900, $3,000 and $3,000

respectively. Also, the remaining cost, i.e. C3, has been spent at time 10 with the magnitude

of $5,300. Having employed Equation (2) and (4) to (14) on the realized benefits, disbenefit

and spent costs, the realized return, risk, cost, overall return, overall risk and attractiveness

of project “E” are achieved as 1.01%, zero, $16,838, 0.88%, zero, and 0.88% respectively,

which its corresponding point is depicted in Figure 3 as W (0, 0.88%). As this point is above

the “approved business case contour”, both project business case and investment are judged

as successes. Furthermore, the realized attractiveness, i.e. 0.0088 is higher than expected, i.e.

0.0055.

41

5. CONCLUSIONS

Project evaluation is a crucial topic in project management to appraise project

proposals, monitor projects during their lives and judge projects’ performances upon their

completions. In project evaluation, not only delivering the outputs is important, but also

realizing the projects’ benefits is crucial. Furthermore, as the intended benefits are affected

by some threats and opportunities around projects, it is crucial to incorporate such effects

into the project evaluation framework. Accordingly, we proposed a new project evaluation

framework to such incorporation inspired by utility theory, an effective framework for asset

evaluation in the Finance discipline.

Theoretically, this paper builds synthesized coherence (Locke & Golden-Biddle,

1997) across project evaluation and utility theory, which are not typically cited together, to

suggest an integrated benefit-oriented project evaluation framework. It also contributes to the

project evaluation literature by developing an integrated framework for all three stages of

project evaluation regarding projects’ returns and risks. In practice, having used risk registers

which are crucial, well established and practiced documents exist in most projects, the

proposed evaluation framework is asserted to be practical and effective in order to help

organizations ensuring the realization of projects’ intended benefits. To apply the proposed

integrated framework: (1) When developing a business case, one should ensure it includes a

risk register with different candidate risk mitigation programs; (2) When a funder approves

42

a project proposal, one should keep updating risk register in determined milestones; and (3)

When a project is completed, one should calculate the realized overall return of the project.

Our paper also has some limitations that need to be acknowledged. First, as we apply

projects’ risk registers as the source of information to develop the project evaluation

framework, adopting the limitation of this document is undeniable. As a result, the proposed

framework does not consider unknowns-unknowns, i.e. uncertainties which are not known at

the beginning of projects (Lechler, Edington, & Gao, 2012). Future research that takes into

account unknown-unknowns in the project evaluation framework can improve its quality.

Second, we use some sample data to demonstrate how our project evaluation framework

should be applied. Future studies can test the framework using data from real projects in

various industries, countries and cultures. Third, future research can investigate different

ways to incorporate non-monetary benefits and disbenefits into the project evaluation

framework. Finally, future research may explore the application of some other theories such

as “prospect theory” in the developing of the project evaluation framework.

43

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49

Table 1

The differences between the approaches used by utility theory in asset evaluation with

those should be used in project evaluation

# Parameter Asset evaluation Project evaluation

Implication for

the proposed

framework

1 The source

of risk

aversion

The risk aversion of

the individual investor

is considered.

The risk aversion of the funder

should be considered.

The investor is

replaced by the

funder.

2 Required

data

An appropriate amount

of reliable historical

returns is available.

Often there are not enough

historical returns or the accessible

historical returns are not reliable

enough. This is because the

triggering events, i.e. threats and

opportunities, faced by a project

can be unique and not possible to

generalize to other projects. The historical

returns are

replaced by the

effects of

triggering

events, i.e.

threats and

opportunities,

around projects.

3

Mean as

the measure

of expected

return

( )

Assets’ expected

returns are estimated

by using a “backward

approach”. In other

words, the mean of

historical returns

relevant to asset i are

used to estimate its

expected return.

Projects’ expected returns should

be estimated by using a “forward

approach”. In other words, some

forecasting techniques specific to

project management, i.e. taking

into account the effects of threats

and opportunities, should be

considered to estimate projects’

expected returns.

4

Standard

deviation as

the measure

of risk

( )

Assets’ risks are

estimated by the

standard deviations of

their historical returns.

Projects’ risks should be

estimated by using some


project management, i.e. taking

into account the effects of threats

and opportunities.

5 Benefit /

Disbenefit

Only monetary

benefits and

disbenefits, measured

in private terms, are

considered in assets’

expected returns.

Both monetary and non-monetary

benefits and disbenefits, measured

in organizational terms, should be

considered in projects’ expected

returns.

Out of the scope

of this paper

6 Mitigation

action

No risk mitigation

actions can be done to

decrease an asset’s

risk.

Various mitigation actions can be

applied on threats and

opportunities to decrease projects’

risks, which can cause shifting a

project to a different indifference

curve.

The effects of

risk mitigation

actions are

added.

50

Table 2

Project E’s risk register in appraisal stage

ID Threat / Opportunity

Pre

Lik

elih

ood

Pre damaging/assisting impact

Benefit Disbenefit Cost

B1 B2 B3 D1 C1 C2 C3

M

($) S

(Mo)*

M

(I)**

S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

3100 10 3600 11 3000 12 1000 5 5000 1 5000 5 5000 10

∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S

T01 Exchange rate increases 30% -20% +20% -30% -10% +10% -20% +30%

T02 Environmental

organization protests 50% -20% +30%

T03 City requirements

estimate deviates 40% -10%

Where:

“M” is the “estimated/realized magnitude” of benefits, disbenefits or costs in the absence of any threats and opportunities,

“S” is the “estimated/realized scheduling” for the realization of benefits or disbenefits or the spending of costs in the absence of any threats and opportunities,

“∆M” is the “estimated percentage of changes in the magnitude” of benefits, disbenefits or costs (in two directions: increased or decreased, represented by “+” and “–

” respectively) resulted from corresponding threat or opportunity materializing, and

“∆S” is the “estimated percentage of changes in the scheduling” for the realization of benefits or disbenefits or spending of costs (in two directions: delayed or

advanced, represented by “+” and “–” respectively) resulted from corresponding threat or opportunity materializing.

* Mo: Month

** I: Index (the unit of non-monetary benefits/disbenefits can be converted to monetary values by Delphi approach)

51

Table 3

The return and cost of project “E” in different potential situations in appraisal stage

Situation

(s)

Threat/opportunity

included in the

situation s

likelihood of situation s

materializing

(Esp )

Return

(Esr )

Total present

value of Costs

(EsPC )

1 N/A 21% 4.46% $14,841

2 T01 9%* -0.33%** $16,818***

3 T02 21% 0.72% $14,841

4 T03 14% 4.25% $14,841

5 T01 & T02 9% -5.71% $16,818

6 T01 & T03 6% -0.72% $16,818

7 T02 & T03 14% 0.34% $14,841

8 T01 & T02 & T03 6% -6.61% $16,818

* According to Equation (8): 0.3×(1-0.5)×(1-0.4) = 0.09 = 9%

** According to Equations (4) to (7):

0.002(15 10(1 0.20)) 0.002(15 11(1 0)) 0.002(15 12(1 0))

2

0.002(15 5(1 0.10))

2

2

3100(1 0.2)( 1) 3600(1 0.30)( 1) 3000(1 0)( 1)

0.002 0.002 0.002$26,610

1000(1 0)( 1)

0.002$10,611

$16,818***

E

E

E

E

e e eFB

eFD

PC

r

2

(26,610 10,611) (16,818)0.0033 0.33%

15

Ln Ln

*** According to Equation (7):

0.002 1(1 0) 0.002 5(1 0.2) 0.002 10(1 0)

2 5000(1 0) 5000(1 0.1) 5000(1 0.3)$16,818

EPC e e e

52

Table 4

Candidate risk mitigation programs for project “E” in appraisal stage

Ris

k m

itig

ati

on

pro

gra

m I

D

Th

reat

/ O

pp

ort

un

ity

ID

Cost of

mitigation

Post

Lik

elih

ood

Post damaging/assisting impact


B1 B2 B3 D1 C1 C2 C3

M

($) S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

3100 10 3600 11 3000 12 1000 5 5000 1 5000 5 5000 10

∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S

M1

T01 - - 30% -20% +20% -30% -10% +10% -20% +30%

T02 2600 0 30% -20% +30%

T03 - - 40% -10%

M2

T01 1500 0 20% -20% +20% -20% -10% +10% -20% +30%

T02 - - 50% -20% +30%

T03 - - 40% -10%

M3

T01 1500 0 20% -20% +20% -20% -10% +10% -20% +30%

T02 1200 0 40% -20% +30%

T03 800 0 30% -10%

53

Table 5

The updated risk register of project “E” at t=9 in monitoring stage

ID Threat /

Opportunity P

ost

Lik

elih

ood

Post damaging/assisting impact


B1 B2 B3 D1 C1 C2 C3 C4

M

($) S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

3100 10 3600 11 3000 12 1000 5 5000 1 5200 4.5 5000 10 1500 0

∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆M ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S

T01 Exchange rate

increases 20% -20% +20% -20% +30%

T02 Environmental

organization protests

parliament

40% -20% +30%

T03 City requirements

estimate deviates 0

T04 Project manager

leaves 10% +10% +10% +10%

54

Figure 1

The indifference curves in the return-risk plane

55

Figure 2

The project evaluation map

56

Figure 3

The project evaluation map of the numerical example

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 1 2 3 4 5

E0

E1

E2

E3

V W

Overall Return %

Overall

Risk %

Funder

Investment

Frontier

Approved

Business case

contour

57

CHAPTER 3: PAPER 2

CUSTOMIZING MODERN PORTFOLIO THEORY FOR THE PROJECT

PORTFOLIO SELECTION PROBLEM

59

ABSTRACT

Because an organization’s performance depends on the projects it implements, selecting

the most appropriate portfolio of projects given limited resources is a crucial decision.

Modern portfolio theory in (financial) portfolio selection problem suggests that in

addition to the expected return, risk should also be considered. Because projects are

unique and lack of historical data, Modern portfolio theory needs to be tailored to the

“risk-return optimization” of project portfolio selection problem. A core element in risk-

return optimization is “risk interdependencies among projects” leading to achieving a

project portfolio with lowest level of risk for the same level of return. However, the

literature is underdeveloped in providing a clear approach to estimate risk

interdependencies among projects. In order to fill this gap, we substitute the historical

data in MPT with projects’ risk registers and propose a new risk-return optimization

model for. To demonstrate how to apply the proposed new model, we employ a numerical

example and report the results.

Keywords:

Project portfolio selection problem; risk-return optimization; Modern portfolio theory;

risk register; risk interdependency

60

1. INTRODUCTION

Senior executives approve project proposals that have the potential to enhance

organizational performance (Lewis, Welsh, Dehler, & Green, 2002; Zwikael & Smyrk,

2012). However, because resources are limited, not all project proposals can be funded

(Carazo, 2015). Selecting the most appropriate set of projects is a crucial organizational

decision (Ghasemzadeh, Archer, & Iyogun, 1999) because a wrong decision can result in

two destructive consequences: (1) resources are wasted on inappropriate projects that

have been funded (type II error), and (2) the benefits that could have been realized from

allocating such resources to better projects are lost (type I error) (Christensen & Knudsen,

2010; Martino, 1995). The selection of subset of projects to be funded to optimize

organizational performance given limited resources is known in the literature as the

“project portfolio selection problem” (PPSP) (Li, Fang, Tian, & Guo, 2015; Shou, Xiang,

Li, & Yao, 2014). The combined analysis of portfolio’s return and risk is important in

this problem since a portfolio with a very attractive expected return but high risk might

expose the organization to a large loss, whereas a low-risk portfolio might secure the

organization a lower but more certain return (Hillson, 2002; Sefair, Méndez, Babat,

Medaglia, & Zuluaga, 2017).

A major limitation with most of the existing PPSP models is disregarding risk

interdependencies among projects. Risk interdependencies occur when two or more

projects have greater or lower risks if carried out simultaneously than if they were

accomplished at different times (Mutavdzic & Maybee, 2015). Such interdependencies

arise over time from overall social and economic changes and can affect multiple projects

61

(Gear & Cowie, 1980; Guo, Liang, Zhu, & Hu, 2008). For example, a potential increase

in the exchange rate can increase the expected return of a project which its final product

would be exported (an opportunity), and simultaneously reduce the expected return of a

project that its raw material should be imported (a threat). Considering such

interdependency in the optimization model of PPSP to reach the optimal project portfolio

is crucial as it provides the condition to reach a project portfolio with lowest level of risk

for the same level of return (Mutavdzic & Maybee, 2015). Disregarding such

interdependencies, i.e. assuming that projects are independent, can leads to funding an

inappropriate project portfolio as the result of underestimating or neglecting an

appropriate project portfolio as the result of overestimating the risks of project portfolios.

Accordingly, literature (e.g. Gear & Cowie, 1980; Guo et al., 2008) calls to add risk

interdependencies among projects into the PPSP optimization model through applying

financial principles of (financial) portfolio selection problem (PSP) in which the concept

of such interdependency is well analyzed.

PSP is one of the most studied topics in finance (Chien, 2002), and is concerned

with the allocation of limited capital to a number of potential assets for a profitable

investment strategy (Lwin & Qu, 2013). An effective optimization model to PSP is

“Modern portfolio theory” (MPT) - for which its pioneer, Harry Markowitz, was awarded

a Nobel Prize (Varian, 1993). MPT views PSP as a mean-variance optimization problem

with regard to two criteria: to maximize the portfolio’s return and to minimize its risk,

measured by the mean and standard deviation of its return respectively (Markowitz,

1952). The underlying principle of MPT is that assets should not be selected solely based

62

on their individual returns and risks, so it is concerned with quantifying how each asset’

return changes in relation to other assets in the portfolio, i.e. assets’ correlations, in the

overall market fluctuations (Casault, Groen, & Linton, 2013). This crucial principle also

applies to the projects in a portfolio as their expected returns are affected by some threats

and opportunities such as overall social and economic changes, which in turn can result

in risk interdependencies among projects.

Having considered the similar concepts between PSP and PPSP, i.e. return, risk,

correlation/risk interdependency and the available budget, as well as the importance of

analyzing the risk interdependencies among projects, researchers tried to apply MPT into

PPSP (e.g., Esfahani, Sobhiyah, & Yousefi, 2016; Luo, 2012; Sefair et al., 2017).

However, there is a research gap in these studies as they disregard some fundamental

differences exist between the characteristics of financial portfolios and those of project

portfolios (Casault et al., 2013). The major difference is based on the fact that unlike

financial assets, because each project is unique (Westerveld, 2003), often there is not

enough projects’ historical data, or the accessible historical data is not reliable enough to

estimate projects’ returns and risks as well as risk interdependencies among them.

Thus, although MPT provides a good foundation for considering risk

interdependencies among projects in the project portfolio selection model, some other

customizations in the model of MPT are required to make it suitable to be used in PPSP.

Such research gap will be addressed by this paper in which first the essential differences

between PSP and PPSP are distinguished and then some customizations in the MPT

model are proposed in order to make it suitable to be used in PPSP. Accordingly, the

63

paper aims to answer the following research question: “How can MPT principles be

applied in the project portfolio context to improve the optimization model of PPSP?” Our

paper contributes to the literature in two ways: (1) the proposed optimization model

expands PPSP models by incorporating the effects of threats and opportunities around

projects into the optimization model, and (2) it expands MPT to make it suitable to

investment decisions that may also include projects with no historical data to allow a

reliable estimation of their return and risk levels. Furthermore, in practice, this paper may

improve the quality of portfolio selection decision in organizations.

The rest of this paper is organized as follows. Section 2 reviews different

definitions and models have been used by the researchers into PPSP, describes MPT,

exemplifies studies that have applied MPT in PPSP, and discusses their limitations. The

principles of designing the optimization model are clarified in Section 3. Section 4

proposes the optimization model of the problem which customizes MPT to PPSP. A

numerical example is presented in Section 5 to demonstrate how the proposed model

should be applied and finally, the conclusions are drawn in Section 6.

2. LITERATURE REVIEW

2.1. The definition of “project portfolio selection problem” (PPSP)

The literature has suggested multiple definitions for PPSP. Table 1 compares the

leading definitions in their objectives and constraints. As can be seen from this table,

there is an agreement that the objective of PPSP is to optimize organizational

performance and that there are limited resources available to the decision maker. After

64

considering the similarities and the consensus in the literature, the following definition

for PPSP will be used in this paper: “The selection of subset of project proposals to be

funded to optimize organizational performance given limited resources”.

------------------------------------

Insert Tables 1 about here

------------------------------------

2.2. PPSP models in the literature

Since the mid-1950s researchers have developed various models to formulate and

solve PPSP (Lorie & Savage, 1955). These models can be categorized into four distinct

groups. The first group of models proposes one-criterion optimization models in which

only one criterion is considered to assign a score to each project. Thus, projects are

selected from the highest to the lowest score of this criterion until the budget available is

spent. For instance, Lorie and Savage (1955), Myers (1972) and Weingartner (1962)

apply economic assessment measurements (e.g., net present value and internal rate of

return) to calculate the project score.

Multi-criteria models form the second group of models. As the sphere in which

decisions are taken in any organization is usually characterized by a set of competing

criteria (Carazo, 2015), this category of methods presents different multi-criteria models

in order to incorporate the decision maker’s preferences into the process. For example,

Gear, Lockett, and Muhlemann (1982), Melachrinoudis and Rice (1991) as well as

Vepsalainen and Lauro (1988) apply “comparative models” such as analytical hierarchy

process (AHP) to combine different criteria to a single objective criterion and then

65

compare one project to either another project or some subsets of alterative projects. Albala

(1975), Cooper (1978) and Krawiec (1984) use “Scoring models” to combine the merit

of each project with respect to a small number of decision criteria to specify its desirability

score and then rank projects according to their scores. Benjamin (1985), Golabi,

Kirkwood, and Sicherman (1981) as well as Neely, North, and Fortson (1977) apply

“mathematical programing models” to maximize objectives such as profit, revenue and

utility or minimize others like resource use, cost and runtime simultaneously.

The third group of models includes projects’ interdependency models. As there

may be technical (e.g. complementarities), cost and benefit interdependencies (i.e.

synergies produced by sharing resources and benefits respectively) among projects

derived from conducting more than one project at the same time (Czajkowski & Jones,

1986; Fox, Baker, & Bryant, 1984), this group of solutions incorporates one or more

categories of these interdependencies into the optimization model. For example,

Carraway and Schmidt (1991) propose a model by formulizing the benefit and cost

interdependencies among pairs of projects quantitatively. Klapka and Piños (2002), Lee

and Kim (2000), Santhanam and Kyparisis (1995) as well as Schmidt (1993) suggest

different models which reflect benefit, cost and technical interdependencies among the

sets of two or three projects. Doerner, Gutjahr, Hartl, Strauss, and Stummer (2006),

Santhanam and Kyparisis (1996) as well as Yu, Wang, Wen, and Lai (2012) developed

various models that allowed the technical, benefit and cost interdependencies among any

numbers of projects.

66

A major limitation of the above-mentioned models is disregarding the risk

interdependencies among projects that arise over time from overall social and economic

changes (Gear & Cowie, 1980; Guo et al., 2008). Such interdependencies can affect a

portfolio’s risk in a way that it is inferior or superior to the weighted average sum of the

risks of all its projects (Mutavdzic & Maybee, 2015). Disregarding such

interdependencies, i.e. assuming that projects are independent, can be catastrophic and

leads to funding an inappropriate project portfolio as the result of underestimating or

neglecting an appropriate project portfolio as the result of overestimating the risks of

project portfolios.

The resolution of this limitation resulted in the advent of the fourth group of

models, which tries to consider the risk interdependencies among projects in addition to

the projects’ returns and risks in their optimization models. To reach this objective,

models in this group employ MPT. Next, we discuss the suitability and structure of MPT

and summarize some of its implementations in PPSP, i.e. PPSP-MPT models.

2.3. Modern Portfolio Theory (MPT)

One of modern finance theory’s main tenets is MPT which led to Markowitz’s

Nobel Prize in Economics in 1990. Markowitz (1952) originally formulated the

fundamental theorem of mean-variance portfolio model for risk-return optimization in

PSP, which trades off between expected return and risk of a portfolio (represented by

mean and standard deviation of that portfolio’s return respectively) to reach the optimal

portfolio of various assets. The underlying principle of MPT is that assets should not be

67

selected solely based on their individual returns and risks, so it quantifies assets’

correlations which represent how each asset’ return changes in relation to other assets in

the portfolio in overall market fluctuations (Casault et al., 2013). Such correlation is

called “risk interdependency” in project portfolio. Having considered the correlation

among assets, MPT argues that by the same level of expected return, portfolio’s risk can

be reduced by creating a diversified portfolio of unrelated assets, i.e. with lowest

correlation coefficients (Moriarty, 2001). Then, a portfolio is considered “efficient” if for

a given level of expected return there are no portfolios with a lower risk, or conversely

for a given level of risk there are no portfolios with a higher expected return. The complete

set of these efficient portfolios forms the efficient frontier that represents the best trade-

offs between return and risk (Markowitz, 1952, 1959; Markowitz, Todd, & Sharpe, 2000).

Accordingly, the mean-variance optimization model is as follows (Bodie, Kane, &

Marcus, 2014):

P f

P

P

rMax S

(1)

1

N

p i i

i

Where X

(2)

2

1 1

N N

p i j i j ij

i j

X X

(3)

1

1N

i

i

Subject to X

(4)

0 1 1,2,...,iX i N (5)

Where:

pS is the slope of capital allocation line (CAL), called “Sharpe ratio” (Sharpe, 1994),

68

p is the expected return of portfolio p,

fr is the risk-free rate of return (e.g., the return of placing money in the bank),

p is the standard deviation of return relevant to portfolio p,

i is the expected return of asset i,

i is the standard deviation of return relevant to asset i,

ij is “Pearson correlation coefficient” between assets i and j,

N is the number of available assets, and

iX is the decision variable of the budget proportion invested in asset i.

To estimate two parameters i and i , MPT uses the historical data relevant to

asset i, e.g. as follows:

1

îM

i is is

s

p r

(6)

22

1

ˆ îM

i is is i

s

p r

(7)

Where:

î and ˆ

i are the estimates of i and i respectively,

iM is the number of historical situations available for asset i,

isr is the return of asset i in historical situation s, and

isp is the proportion of happening historical situation s.

Figure 1 depicts the “optimal capital allocation line”, CAL (P), which is tangent

to the “efficient frontier” at the “optimal portfolio” (P).

69

------------------------------------


------------------------------------

Having summarized the structure of MPT, that is both well-constructed in its

theoretical foundations and successful in its applications in PSP (Chien, 2002), we can

now turn to PPSP-MPT models.

2.4. PPSP-MPT models

A few researchers have identified important similarities between PSP and PPSP

(e.g., Boasson, Cheng, & Boasson, 2012; Luo, 2012; Sefair et al., 2017). Table 2

summarizes these similarities in relation to four concepts, i.e. return, risk, correlation

among assets/risk interdependencies among projects, and available budget. This analysis

suggests strong similarities between PSP and PPSP and encourages the implementation

of a strong financial theory, i.e. MPT, to deal with the research limitation of the first three

groups of PPSP models discussed earlier.

------------------------------------


------------------------------------

Building on the similarities, PPSP-MPT models applies the mean-variance

foundation of MPT in forming optimal risk-return project portfolio. These models can

further be divided into two distinct subgroups.

The first subgroup belongs to those models that use projects’ historical data or not

propose an approach how to estimates different MPT’s parameters, i.e. projects’ returns

70

and risks as well as risk interdependencies among them. For instance, Boasson et al.

(2012) apply MPT to municipal financial and capital budgeting decisions by considering

the historical data relevant to benefits and cost of the similar projects. Esfahani et al.

(2016) apply MPT to PPSP considering the historical returns of similar projects and

proposed the harmony search algorithm to solve it. Findlay, McBride, Yormark, and

Messner (1981) apply MPT to indivisible assets/projects to develop a quadratic integer

programming model without explaining how the projects’ return, risk as well as risk

interdependencies can be estimated. Sefair et al. (2017) developed a linear solution for

the Mean-SemiVariance PPSP in the oil and gas industry by considering the historical

data relevant to the net present value of the similar projects.

The second subgroup of models implementing MPT for PPSP addresses the lack

of projects’ historical data through considering a few common elements among projects.

For example, Luo (2012) concentrated on the risk-side control for Research and

Development (R&D) project portfolio and developed a method for optimal diversification

of R&D project portfolio incorporating market and technology risk. Ball and Savage

(1999) explain five sources of risk interdependencies among projects including prices,

places, profiles, politics and procedures and declare that simulation or decision tree model

can be used to calculate return, risk and risk interdependencies among production and

exploration projects in oil industry. Mutavdzic and Maybee (2015) consider the same five

sources of correlation and propose a two-way data table to estimate the risk

interdependencies and constructed a preferred portfolio of petroleum assets.

71

2.5. Limitations of the existing PPSP-MPT models

An analysis of models applying MPT in PPSP suggests that they ignore some core

differences that exist between PSP and PPSP, discussed below. Boasson et al. (2012) and

Casault et al. (2013) argue that unlike financial assets which only have monetary benefits,

projects have both monetary and non-monetary benefits. Mutavdzic and Maybee (2015)

assert that usually there is not sufficient historical data available to calculate the risk

interdependencies among projects. This argument highlights the main difference between

financial portfolios and project portfolios. In projects, given the lack of historical data,

the effects of triggering events on the return of multiple projects determine risk

interdependencies among them. A triggering events’ effect can be either a damaging

impact as a threat or an assisting impact as an opportunity through some chain of

consequences (Zwikael & Smyrk, 2011). As the threats and opportunities that surround a

project can be unique, one cannot use projects’ historical data or limit the source of risk

interdependencies to some certain elements such as prices, places, profiles, politics and

procedures to estimate MPT’s parameters in PPSP. This means that historical data

employed by MPT in PSP should be substituted by the effects of threats and opportunities

in PPSP. However, the existing PPSP-MPT models are underdeveloped in estimating

MPT’s parameters appropriately, i.e. taking into consideration the effects of threats and

opportunities.

Table 3 compares the approaches used in PSP with those should be used in PPSP,

which introduces some initial guidelines for the proposed design principles.

72

------------------------------------


------------------------------------

According to substantial differences between PSP and PPSP highlighted in Table

3, in particular the lack of reliable projects’ historical data rooted in different threats and

opportunities exist around projects, as well as benefit, cost and technical

interdependencies among projects, it can be concluded that despite the similar concepts

between two problems mentioned in Table 2, direct application of MPT to PPSP is

problematic and thus some other customizations are also required to capture such

characteristics in the evaluation of project portfolio. To do such customization, in this

paper, we substitute the historical data in MPT with the effects of threats and opportunities

and propose a new risk-return optimization model for PPSP.

3. DESIGN PRINCIPLES

This section develops the core design principles of the model. Design principles

are prescriptive statements that show how to do something in order to achieve a goal

(Gregor & Jones, 2007). As the basis of any selection problem is the evaluation of

different alternatives (Dey, 2006; Oral, Kettani, & Lang, 1991), here, design principles

elaborate “how to evaluate the attractiveness of project portfolios” that play the crucial

role in developing the PPSP’s optimization model. These “know how” are developed in

the rest of this Section.

The evaluation foundation of a portfolio is well-developed in MPT, which tells a

single investor how to combine individual assets into a portfolio in order to accomplish

73

the goal of maximizing portfolio attractiveness, i.e. Sharpe ratio (Smith & Smith, 2005).

MPT uses assets’ historical returns to investigate their behaviors in different market

fluctuation to estimate assets’ individual returns and risks as well as correlation

coefficients among them (Bodie et al., 2014). However, as the threats and opportunities

exist around a project can be unique and not possible to generalize to other projects, one

cannot use projects’ historical returns to estimate the individual projects’ returns and risks

as well as risk interdependencies among them. In other words, the effects of threats and

opportunities on projects determine the individual projects’ returns and risks as well as

risk interdependencies among them. Thus, we propose the following design principles:

Design principle 1 (P1). The attractiveness of a project portfolio is evaluated

based on its return and risk.

Design principle 2 (P2). Project portfolio’s return is evaluated based on the

individual returns of its projects.

Design principle 3 (P3). The individual returns of projects are evaluated based

on the effects of threats and opportunities on those projects.

Design principle 4 (P4). Project portfolio’s risk is evaluated based on the

individual risks of its projects and the risk interdependencies exist among those

projects.

Design principle 5 (P5). The individual risks of projects and risk

interdependencies among them are evaluated based on the effects of threats and

opportunities on those projects.

74

While MPT is significant to provide the context of how the individual returns and

risks of projects and risk interdependencies among them should be evaluated based on

the effect of different threats and opportunities exist around those projects, it is not

sufficient to explain some other interdependencies among projects including benefit, cost

and technical interdependencies. This type of evaluation is well developed in the third

group of PPSP models, i.e. projects’ interdependency models. According to these models,

a portfolio’s return is calculated by considering the individual returns of its projects as

well as three more elements, i.e. projects’ benefit, cost and technical interdependencies,

which influence this calculation in a way that the portfolio’s return is inferior or superior

to the sum of the individual returns of all its projects (Spradlin & Kutoloski, 1999; Carazo,

2015). Benefit interdependencies derive from two or more projects producing greater or

less benefits when carried out simultaneously than if they were accomplished at different

times (Carazo, 2015). For example, suppose that the objective of one project is to develop

a new product feature that would make an existing product more attractive to a certain

demographic group and would have the effect of increasing sales by some amount as the

benefit. Suppose the objective of another project is to develop a second feature that would

make the same product more attractive to a different demographic group and would also

increase sales as the benefit. If both projects were funded and successful, sales may show

a net increase that is less than the sum of the two increases. In other words, it is possible

that the introduction of both new features would make the product less attractive to the

demographic groups than expected when considering the two features independently (Fox

et al., 1984). Cost interdependencies originate when the simultaneous implementation of

75

two or more projects require less or more resources than if they were carried out

separately. It implies that the required cost of a project portfolio is inferior or superior to

the sum of the costs of all its projects (Carazo, 2015). For example, two products might

share development resources, so that the cost of developing both might be less than the

sum of the individual projects’ costs (Spradlin & Kutoloski, 1999). Technical

interdependencies take place when the accomplishment of a determined project

necessarily involves the total or partial accomplishment or non-accomplishment of

another project or projects (Chien, 2002). For example, a project may be technologically

infeasible unless several enabling projects are undertaken to close existing technology

gaps (Czajkowski & Jones, 1986). Accordingly, it can be asserted that:

Design principle 6 (P6). Project portfolio’s return is also evaluated based on the

benefit, cost and technical interdependencies exist among the projects of that

portfolio.

Figure 2 demonstrates the above-mentioned six design principles of project

portfolio’s attractiveness evaluation, upon which an optimization model will be

developed in the next Section.

------------------------------------


------------------------------------

76

4. MODEL DEVELOPMENT

Here, we first introduce our model’s assumptions and the threat and opportunities

identification, then propose a customized approach to estimate MPT’s parameters as well

as benefit, cost and technical interdependencies in PPSP and finally develop the

optimization model.

4.1. Model assumptions

To develop the optimization model, we consider the following model assumptions

which are common in most PPSP models (Sefair et al., 2017; Ball & Savage, 1999;

Mutavdzic & Maybee, 2015):

Funding period is fixed. The output of the model would be the best subset

of project proposals to be funded in a planning period of time [0 T]

assuming all projects start at time 0.

Projects are not divisible. The decision variables are binary, representing

the selection, or not, of each project proposal. In other words, one cannot

fund a proportion of a project (e.g. building half a bridge).

Projects are considered before mitigation actions. The returns and risks

of projects before any risk mitigation actions are implemented to reflect the

available information during the project selection decision point in time.

Only new project proposals are considered. The selection decision takes

into account new project proposals, but does not deal with project

adjustments and terminations.

77

4.2. Threats and Opportunities Identification

According to design principles depicted in Figure 2, to develop our model, we

first need to identify threats and opportunities. The risk register is an effective project

management tool that includes this information used as part of a business case (Project

Management Institute, 2017). Because most projects include a risk register as a core

management tool, this paper uses data included in this document to estimate MPT’s

parameters in order to customize MPT for PPSP. There are different formats proposed by

various studies and standards for developing a risk register. One of the most

comprehensive formats is that proposed by Zwikael and Smyrk (2011), in which a risk

register is a table where rows are associated with threats and columns are relevant to their

attributes. Through applying the third model assumption, we use the first four columns of

their proposed format as follows:

1) Threat ID

2) Threat title: description of the triggering event

3) Likelihood of the threat in the absence of the proposed mitigation action

4) The damaging impacts of the threat on the project’ return in the absence of the

proposed mitigation action as at least one of the six potential effects: benefit

reduced, benefit delayed, disbenefit increased, disbenefit advanced, cost

increased, and cost advanced.

Furthermore, in order to generalize our formulation, we apply some modifications

in the above-mentioned risk register’s format. We consider both threats and opportunities

78

to cover both negatives and positive triggering events. Thus, the third column

demonstrates the likelihood of corresponding threat or opportunity materializing.

Moreover, there are six additional potential assisting impacts of opportunities: benefit

increased, benefit advanced, disbenefit decreased, disbenefit delayed, cost decreased, and

cost delayed, in addition to the above-mentioned potential damaging impacts of threats

in the fourth column.

Accordingly, Table 4 exemplifies the required part of a risk register that is used

in estimating MPT’s parameters explained in the rest of this section.

------------------------------------


------------------------------------

4.3. The customized approach to estimate MPT’s parameters in PPSP

Here, we elaborate how projects’ risk registers can be applied to estimate MPT’s

parameter, i.e. projects’ returns and risks as well as risk interdependencies among them.

In the course of a project’s life, any number of the threats and opportunities mentioned in

its risk register can materialize. Thus, the total number of potential situations can surround

project i, im , is 2 inreached from Equation (8) in which in is the number of threats and

opportunities mentioned in the risk register of project i.

... 20 1 2 3

iii i i i n

i

i

nn n n nm

n

(8)

79

On the other hand, we employ “Modified Internal Rate of Return” (MIRR) to

extract a proper representative for projects’ returns, in which benefits and disbenefits can

be both monetary and non-monetary. MIRR, assumes that benefits/disbenefits generated

from a project are reinvested at the risk-free rate of return rather than at the project’s

internal rate of return (Lin, 1976). Equation (9) represents this assumption regarding

continuous compounding instead of discrete one, in which non-monetary

benefits/disbenefits can be converted to monetary ones (dolor values) by using some

techniques such as Delphi (Abbassi, Ashrafi, & Tashnizi, 2014) which its explanation is

out of the scope of this paper.

.MIRR T

Futurevalue of benefits and disbenefitsPresent valueof costs

e (9)

Where: e is Euler's number which represents continuous compounding.

Regarding the fact that the return of a project portfolio should be obtained by

proportionate combination of projects’ return (Findlay et al., 1981), here we consider

.MIRR Te as the representative of a project’s return. Furthermore, according to Table 4, each

threat and opportunity can affect the “magnitude” or “scheduling for realization” of

different benefits, disbenefits or costs. Thus, the return of project i in potential situation

s, isr , is calculated as follows by considering the fact that benefits and disbenefits are

continuous flows, whereas costs are discrete ones which only occur during the project’s

life:

is isis

is

FB FDr

PC

(10)

80

( )

11

( )

11

1( )

(1 )

(1 )

(1 )

i

f

ik ikuB Bik iku

u s

f

i ik iku

B Bik ikuu s

f B Bik iku ik ikuu sf

KT r T t

is B BS S

k u s

r T tT

K B B

u s

S Sk f

r T S SB Br T Tu s

f

Where FB M M e dt

M M e

r

M M

e er

1

1

1

(1 )

1

i

i f B Bik iku ik ikuu s

K

k

K r T S SB B

u s

k f

M M

er

(11)

( )

11

( )

11

1( )

(1 )

(1 )

(1 )

i

f

il iluD Dil ilu

u s

f

i il ilu

D Dil iluu s

f D Dil ilu il iluu sf

LT r T t

is D DS S

l u s

r T tT

L D D

u s

S Sl f

r T S SD Dr T Tu s

f

FD M M e dt

M M e

r

M M

e er

1

1

1

(1 )

1

i

i f D Dil ilu il iluu s

L

l

L r T S SD D

u s

l f

M M

er

(12)

1

1

1i f C Cif ifu

u s

if ifu

F r S S

is C C

f u s

PC M M e

(13)

Where:

isFB is the total future value of benefits relevant to project i at time T if potential situation

s materializes,

81

isFD is the total future value of disbenefits relevant to project i if potential situation s

materializes,

isPC is the total present value of costs relevant to project i if potential situation s

materializes,

iK is the total number of benefits relevant to project i,

iL is the total number of disbenefits relevant to project i,

iF is the total number of costs relevant to project i,

ikBM is the estimated magnitude of kth benefit relevant to project i,

ikuBM is the estimated percentage of changes in the magnitude of kth benefit relevant to


ikBS is the estimated scheduling for the realization of kth benefit relevant to project i,

ikuBS is the estimated percentage of changes in the scheduling for the realization of kth

benefit relevant to project i if threat/opportunity u materializes,

ilDM is the estimated magnitude of lth disbenefit relevant to project i,

iluDM is the estimated percentage of changes in the magnitude of lth disbenefit relevant

to project i if threat/opportunity u materializes,

ilDS is the estimated scheduling for the realization of lth disbenefit relevant to project i,

iluDS is the estimated percentage of changes in the scheduling for the realization of lth

disbenefit relevant to project i if threat/opportunity u materializes,

ifCM is the estimated magnitude of fth cost relevant to project i,

82

ifuCM is the estimated percentage of changes in the magnitude of fth cost relevant to


ifCS is the estimated scheduling for the spending of fth cost relevant to project i, and

ifuCS is the estimated percentage of changes in the scheduling for the spending of fth cost

relevant to project i if threat/opportunity u materializes.

On the other hand, the likelihood of situation s materializing in project i, isp , is

calculated as the multiplication of the likelihoods of the threats/opportunities included in

situation s materializing and likelihoods of the others not materializing, demonstrated as

follows:

(1 )is u u

u s u s

p l l

(14)

Where: ul is the likelihood of threat/opportunity u materializing.

After placing Equations (8), (10) and (14) in Equations (6) and (7), the final

customized estimation for return ( î ) and risk (standard deviation, ˆ

i ) relevant to project

i can be reached as follows:

2

1

ˆ (1 )

ni

is isi u u

s u s u s is

FB FDl l

PC

(15)

22

2

1

ˆ ˆ(1 )

ni

is isi u u i

s u s u s is

FB FDl l

PC

(16)

Where isFB , isFD and isPC are calculated by Equations (11), (12) and (13) respectively.

Furthermore, the estimated cost of project i, î , can be calculated as follows:

83

2

1

ˆ (1 )

ni

i u u is

s u s u s

l l PC

(17)

Having calculated returns and risks of projects, in the following, we propose a

methodology to calculate risk interdependencies among projects in a portfolio. Each one

of the projects in the pairs of projects has two categories of threats/opportunities:

particular threats/opportunities (which are specific to each one) and common ones (which

are common in the two projects). It should also be mentioned that a threat for a project

can be a threat or opportunity to another project. To estimate the risk interdependencies,

i.e. correlation coefficient, between projects i and j, îj , we first estimate their covariance,

îj , as follows:

2 2

1 1

2 2 2 2 2 2

1 1 1 1

2 2

1 1

ˆ ˆ ˆ( , )

,

,

,

n nji

n n n n nnij ij ji j jii

ij ij ij ij ji ji ji ji

ij ij ji ji

n ni ji

ij ij ji ji

ij ji

ij i j

is is js js

s s

ic ic ia ia jc jc ja ja

c a c a

ic ic jc jc

c c

COV

COV p r p r

COV p r p r p r p r

COV p r p r

2 2 2

1 1

2 2 2

1 1

2 2 2 2

1 1

,

,

,

j

n n nij j ji

ij ij ji ji

ij ji

n nn ij jii

ij ij ji ji

ij ji

n n nn ij j jii

ij ij ji ji

ij ji

ic ic ja ja

c a

ia ia jc jc

a c

ia ia ja ja

a a

COV p r p r

COV p r p r

COV p r p r

(18)

Where:

84

ijn is equal to jin and is the number of common threats and opportunities in projects i

and j,

ijc and jic are the cth common situations in projects i and j respectively,

ijicp and jijcp are the likelihoods of common situations

ijc and jic materializing in projects

i and j respectively,

ijicr and jijcr are the returns of projects i and j in common situations

ijc and jic

respectively,

ija is the ath particular situation in project i when it is compared to project j,

ijiap is the likelihood of particular situation ija materializing in project i, and

ijiar is the return of project i in particular situation ija .

As we can see in Equation (18), there are four terms which should be calculated

to reach the total covariance between projects i and j. By considering some assumptions

as there is no covariance among particular threats/opportunities of project i and those of

project j, and there is no covariance among common threats/opportunities in project i and

particular ones in project j and vice versa, the second, third and fourth terms of Equation

(18) are equal to zero. These assumptions of independence are justified because no

explicit relationships exist among these combinations of threats/opportunities. In other

words, if one occurs in project i, it does not give us any new information on occurrence

of the other one in Project j (Bakhshi & Touran, 2012). for the same reason, in the first

term of Equation (18), only the likelihoods of common threats and opportunities

materializing in projects i and j should be considered in calculating ijicp and

jijcp , which

85

makes these two likelihoods equal to each other. On the other hand, if there are no

common threats/opportunities in projects i and j, their covariance would be equal to zero.

Accordingly, the final formulation of covariance between projects i and j is as follows:

2 2

1 1

2 2 2

1 1 1

ˆ ,

0 /

n nij ji

ij ij ji ji

ij ji

n n nij ij ji

ij ij ij ij ji ji ji

ij ij ji

ij ic ic jc jc

c c

ic ic ic ic jc jc jc

c c c

COV p r p r

If nocommon threats pportunities exist between

projects i and j

p r p r r p r Oth

erwise

(19)

Having considered the relationship between correlation coefficient and covariance

as demonstrated in Equation (20), the final formulation of risk interdependency between

projects i and j is drawn from Equation (21).

ˆˆ

ˆ ˆ

ij

ij

i j

(20)

2 2 2

1 1 1

1

0 & /ˆ

ˆ ˆ

n n nij ij ji

ij ij ij ij ji ji ji

ij ij ji

ij

ic ic ic ic jc jc jc

c c c

i j

If i j

If i j Nocommon threats opportunities exist between

projects i and j

p r p r r p r

Otherwise

(21)

4.4. Benefit, cost and technical interdependencies among projects

86

Benefit interdependency between projects i and j, ijB , represents the difference

between the benefits of project i, when it is funded along with project j and when it is

funded in the absence of project j, calculated as follows:

( )

( )

( )

1

f

ijBij

f

ij

Bij

f Bij ijf

f Bij ij

T r T t

ij BS

r T tT

B

Sf

r T SB r T T

f

r T SB

f

B M e dt

M e

r

Me e

r

Me

r

(22)

Where:

ijBM is the estimated magnitude of benefit interdependency between projects i and j, and

ijBS is the estimated scheduling for the realization of benefit interdependency between

projects i and j.

Cost interdependency between projects i and j, ijC , represents the difference

between the costs of project i, when it is funded along with project j and when it is funded

in the absence of project j, calculated as follows:

f Cij

ij

r S

ij CC M e

(23)

Where:

ijCM is the estimated magnitude of cost interdependency between projects i and j, and

ijCS is the estimated scheduling for the realization of cost interdependency between

projects i and j.

87

Technical interdependencies among projects are added to the optimization model

as constraints (Carazo, 2015; Guo et al., 2008), which can be divided into three main

categories as follows:

Mutual exclusion technical interdependency: This type of technical

interdependency occurs when projects i and j cannot be funded simultaneously,

which is represented by Equation (24).

1i jX X (24)

Where:

iX and jX are binary decision variables, representing the selection, or not, of

projects i and j respectively.

Prerequisite technical interdependency: This type of technical interdependency

implies the situation in which project i cannot be funded unless project j also be

funded. In other words, if project j is rejected, project i have to also be rejected.

Equation (25) indicates prerequisite technical interdependency between projects i

and j.

0i jX X (25)

Compulsory technical interdependency: This kind of technical interdependency

occurs in three situations: (1) when project i is required to be funded, (2) when

project i is required to be abandoned, and (3) when project i is funded if and only

if project j is funded, that is, projects i and j should be both either funded or

abandoned simultaneously. These three types of Compulsory technical

interdependency are demonstrated in Equations (26), (27) and (28) respectively.

88

1iX (26)

0iX (27)

0i jX X (28)

4.5. The optimization model

Here, we develop an optimization model by summarizing the following model

parameters:

ˆpS : The estimated “attractiveness”, i.e. the Sharpe ratio, of project portfolio p

ˆp : The estimated expected return (mean) of project portfolio p

ˆp : The estimated risk (standard deviation) of project portfolio p

fr : The risk-free rate of return (e.g., the return of placing money in the bank or the return

of a well-established production line),

î : The estimated expected return of project i drawn from Equation (15)

î : The estimated risk (standard deviation) of project i achieved by Equation (16)

ijB : The benefit interdependency between projects i and j reached by Equation (22)

ijC : The cost interdependency between projects i and j achieved by Equation (23)

îj : The estimated risk interdependency between projects i and j drawn from Equation

(21)

M i : The set of projects with which project i has mutual exclusion technical

interdependencies

89

P i : The set of projects that are the prerequisites of project i

F : The set of projects required to be funded

A : The set of projects required to be abandoned

C i : The set of projects with which project i should be either funded or abandoned

simultaneously

: The total available budget

î : The estimated cost of project i drawn from Equation (17)

N : The number of project proposals

iX : Binary decision variable, representing the selection, or not, of project i

Furthermore, since surplus budget is rarely left idle, we assume that the investor

can always invest unallocated budget in a risk-free asset with return fr T

e (Findlay et al.,

1981). Thus, we add the following decision variable to the optimization model.

oX : The decision variable of the budget proportion invested in a risk-free asset

Accordingly, the final non-linear optimization model of customizing MPT to

PPSP is developed as follows:

ˆˆ

ˆ

fr T

p

p

p

eMax S

(29)

0

1 1

1 ˆˆ ˆ f

N Nr T

p i i i j ij

i j

Where X X B X e

(30)

2

21 1

1 ˆ ˆ ˆˆ ˆ ˆN N

p i j i j i j ij

i j

X X

(31)

90

0

1 1

ˆN N

i i j ij

i j

Subject to X X C X

(32)

1 ; , 1,2,...,i jX X j M i i N (33)

1 ;iX i F (34)

0 ;iX i A (35)

0 ; , 1,2,...,i jX X j P i i N (36)

0 ; , 1,2,...,i jX X j C i i N (37)

1

1N

i

i

X

(38)

0,1 ; 1,2,...,iX i N (39)

0 0X (40)

Where: the objective function, i.e. Equation (29), maximizes the attractiveness of project

portfolio. Constraint (32) maintains the total available budget. The projects’ technical

interdependencies are guaranteed in Equations (33) to (37). Constraint (38) assures the

selection of at least one project. Equation (39) and (40) denotes the domains of the

variables.

5. A NUMERICAL EXAMPLE

The purpose of this section is to employ a numerical example in order to illustrate

how the optimization model proposed in Section 4 should be applied. Let us assume that

an organization considers 15 project proposals for a period of 24 months regarding the

91

risk-free rate of return of 0.5% per month. With a limited budget of $160,000, the

organization wants to select the best set of projects to fund. Each project proposal includes

a business case with a risk register. Tables 4 and 5 depict two relevant data of the risk

registers developed for projects 1 and 2 respectively. As can be seen, the projects have

two common triggering events, as P1.T01/P2.T01 (“Exchange rate increases”) with the

likelihood of 0.3, and P1.T02/P2.O03 (“Iron import law is passed by the government”)

with the likelihood of 0.2. Furthermore, it is derived that the former plays the role of threat

for both projects, while the latter has a role of threat for project 1 and that of opportunity

for project 2.

------------------------------------


------------------------------------

We demonstrate how to calculate the return and risk of project 1. Regarding

Equation (8), as this project has three threats/opportunities, there are eight potential

situations to materialize. Table 6 shows these potential situations, the likelihood of each

situation materializing ( 1sp ) drawn from Equation (14), the return and cost of project 1

in each situation ( 1sr and 1sPC respectively) calculated by applying Equations (10) to (13).

------------------------------------


------------------------------------

Applying Equations (15), (16) and (17), the estimated return, risk and cost of

project 1 are calculated as follows respectively:

92

1ˆ ( ) (0.216 11.82) (0.126 14.03) ( 14.28)

(

0.504 14.97 0.056

0.054 11.09 0.024 0.014 13.35 0.006 10.46 13.) ( 11.19) ( ) ( ) 79

1

2 2 2

1

2 2

2 2

2 2

ˆ ( ) 0.216 (11.82 )

0.126 (14.03 ) ( )

0.504 14.97 13.79 13.79

13.79 0.056 14.28 13.79

0.054 11.09 13.79 0.024 11.19 13.79

0.014 13.35 13.79 0.006 10.46 13.79 2.1876

ˆ 1.

( ) ( )

( )

8

)

4

(

1 0.504 0.056 14,608

0.054 15,86

ˆ ( 14,608) (0.216 15,867) (0.126 14,608) ( )

( ) ( ) ( ) ( )

$

7 0.024 15,867 0.014 14,608 0.006 15,867

14,986

Similarly, the estimated return, risk and cost of project 2 are 17.24, 1.71 and

$18,595 respectively. Table 7 shows the estimated returns, risks and costs of projects 1

and 2 plus the assumed those of the other 13 project proposals, which can be reached by

applying the same approach.

------------------------------------


------------------------------------

To extract the risk interdependency between projects 1 and 2, we consider their

two above-mentioned common threats/opportunities. According to Equation (8) there are

four common situations in these two projects. Table 8 shows these common situations,

the likelihood of each situation materializing (121cp ) drawn from Equation (14), and the

returns of projects 1 and 2 in each common situation (as represented by 121cr and

212cr

respectively) have been calculated in the previous step.

------------------------------------

93


------------------------------------

According to Equations (19), (20) and (21), the estimated covariance and risk

interdependency between projects 1 and 2 are calculated as follows:

12 12

12

21 21

21

4

1 1

1

4

2 2

1

( ) (0.24 11.82) (0.14 14.03) ( 11.09) 13.85

( ) (0.24 15.41) (0.14 19.00) ( 16.68) 17.2

0.56 14.97 0.06

0.56 17.73 0.06 8

c c

c

c c

c

p r

p r

12 21ˆ ˆ ( )( )

(11.82 13.85)(15.41 17.28)

(14.03 13.85)(19.0

0.56 14.97 13.85

0 17.28

17.73 17.28

0.24

0.14

0

)

(11.09 13.85)(16.68 17.. 28) 1.0 346

12 21

1.34ˆ ˆ 0.53

1.48 1.71

By the same way, assume that the risk interdependency matrix relevant to all 15

project proposals are as follows:

1 0.53 0 0.30 0.02 0 0.03 0 0 0.08 0 0 0.23 0 0.10

0.53 1 0 0.1 0 0 0.21 0 0.41 0.07 0 0.27 0 0.1 0.10

0 0 1 0 0 0.10 0 0.22 0 0.09 0 0 0.12 0 0.03

0.30 0.1 0 1 0 0.05 0 0.12 0 0.19 0 0 0 0.26 0

0.02 0 0 0 1 0 0.03 0.13 0.21 0 0.14 0 0.27 0 0

0 0 0.10 0.05 0 1 0 0.19

0.11 0.09 0.21 0.06 0.03 0.18 0

0.03 0.21 0 0 0.03 0 1 0.30 0.13 0 0 0.12 0 0.22 0.41

0 0 0.22 0.12 0.13 0.19 0.30 1 0 0.19 0.08 0.20 0 0 0.11

0 0.41 0 0 0.21 0.11 0.13 0 1 0.10 0.10 0 0.09 0.10 0.08

0.08 0.07 0.09 0.19 0 0.09 0 0.19 0.10 1 0.21 0.05 0

.05 0.12 0.14

0 0 0 0 0.14 0.21 0 0.08 0.10 0.21 1 0 0.11 0 0.13

0 0.27 0 0 0 0.06 0.12 0.20 0 0.05 0 11 0 0.04 0

0.23 0 0.12 0 0.27 0.03 0 0 0.09 0.05 0.11 0 1 0.14 0.09

0 0.1 0 0.26 0 0.18 0.22 0 0.10 0.12 0 0.04 0.14 1 0

0.10 0.10 0.03 0 0 0 0.41 0.11 0

.08 0.14 0.13 0 0.09 0 1

94

Furthermore, the organization develops the magnitude and realization scheduling

Matrixes of benefit interdependency relevant to 15 project proposals, i.e. BM and BS

respectively, as the following,

0 1000 0 0 0 0 3500 700 0 0 0 0 0 0 0

1000 0 0 200 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 100 0 0 0 0 0 0 0

0 200 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1000 0 0 0 0 0 0 0

0 0 0 0 0 0 2000 0 450 0 0 0 0 0 0

3500 0 0 0 0 2000 0 0 700 0 0 0 0 0 0

700 0 100 0 1000 0 0 0 0 0 0 0 500 0 0

0 0 0 0 0 450 700 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

BM

0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 500 0 0 0 0 0 0 3000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 3000 0 0

0 12 0 0 0 0 12 20 0 0 0 0 0 0 0

12 0 0 10 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 18 0 0 0 0 0 0 0

0 10 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 15 0 0 0 0 0 0 0

0 0 0 0 0 0 18 0 13 0 0 0 0 0 0

12 0 0 0 0 18 0 0 10 0 0 0 0 0 0

20 0 18 0 15 0 0 0 0 0 0 0 11 0 0

0 0 0 0 0 13 10 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

BS

0 0 0

0 0 0 0 0 0 0 11 0 0 0 0 0 0 14

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 14 0 0

And the magnitude and realization scheduling Matrix of cost interdependency

relevant to 15 project proposals, i.e. CM and CS respectively, as follows:

95

0 500 0 0 0 0 1000 0 400 0 0 0 0 0 0

500 0 200 0 0 0 0 0 0 0 0 0 0 0 0

0 200 0 0 0 0 0 0 0 320 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 150 0 0 0 0 0 0 0

0 0 0 0 0 0 700 0 0 0 0 0 120 0 0

1000 0 0 0 0 700 0 0 0 0 0 0 1000 0 0

0 0 0 0 150 0 0 0 80 0 0 0 280 0 0

400 0 0 0 0 0 0 80 0 0 0 0 0 0 0

0 0 320 0 0 0 0 0 0

CM

0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 90 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 120 1000 280 0 0 0 0 0 0 500

0 0 0 0 0 0 0 0 0 0 90 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 500 0 0

0 5 0 0 0 0 6 0 10 0 0 0 0 0 0

5 0 7 0 0 0 0 0 0 0 0 0 0 0 0

0 7 0 0 0 0 0 0 0 5 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 11 0 0 0 0 0 0 0

0 0 0 0 0 0 8 0 0 0 0 0 8 0 0

6 0 0 0 0 8 0 0 0 0 0 0 5 0 0

0 0 0 0 11 0 0 0 7 0 0 0 11 0 0

10 0 0 0 0 0 0 7 0 0 0 0 0 0 0

0 0 5 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 9 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 8 5 11 0 0

CS

0 0 0 0 5

0 0 0 0 0 0 0 0 0 0 9 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 5 0 0

As an example, we calculate the benefit and cost interdependencies between

projects 1 and 2 through applying Equations (22) and (23) respectively as follows:

0.005(24 12)

12

0.005 5

12

1000( 1)$12,367

0.005

500 $ 488

eB

C e

Through using the similar approach, the benefit and cost interdependencies

matrixes relevant to all 15 projects are reached as follows:

96

0 12367 0 0 0 0 43286 2828 0 0 0 0 0 0 0

12367 0 0 2900 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 609 0 0 0 0 0 0 0

0 2900 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 9206 0 0 0 0 0 0 0

0 0 0 0 0 0 12182 0 5089 0 0 0 0 0 0

43286 0 0 0 0 12182 0 0 10151 0 0 0 0 0 0

2828 0 609 0 9206 0 0 0 0 0 0 0 6716 0 0

0 0 0 0 0 5089 10151 0 0 0 0

B

0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 6716 0 0 0 0 0 0 30763

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 30763 0 0

0 488 0 0 0 0 970 0 380 0 0 0 0 0 0

488 0 193 0 0 0 0 0 0 0 0 0 0 0 0

0 193 0 0 0 0 0 0 0 312 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 142 0 0 0 0 0 0 0

0 0 0 0 0 0 673 0 0 0 0 0 115 0 0

970 0 0 0 0 673 0 0 0 0 0 0 975 0 0

0 0 0 0 142 0 0 0 77 0 0 0 265 0 0

380 0 0 0 0 0 0 77 0 0 0 0 0 0 0

0 0 312 0 0 0 0 0 0 0 0 0 0

C

0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 86 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 115 975 265 0 0 0 0 0 0 488

0 0 0 0 0 0 0 0 0 0 86 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 488 0 0

Furthermore, the organization extracts technical interdependencies among the

project proposals as demonstrated in Table 9.

------------------------------------


------------------------------------

Having considered the non-linear optimization model presented in Equations (29)

to (40), we employed the global solver of the optimization modeling software “Lingo 17”

97

to reach the optimal portfolio. Accordingly, the optimal project portfolio, P, consists

funding projects 1, 2, 5, 6, 7, 9, 11 and 13 that requires a budget of $145,930 out of

$160,000 total available budget. The rest of the budget, i.e. $14,070 is invested in the

risk-free asset. Accordingly, the estimated expected return, risk and attractiveness of

optimal portfolio P are reached as 13.77, 0.46 and 27.64 respectively. Figure 3 shows the

optimal project portfolio P and efficient frontier of the discussed numerical example.

In order to compare our model with those that do not consider either risk

interdependencies or benefit and cost interdependencies among projects, we solved the

numerical example disregarding the benefit, cost and risk interdependencies among

projects. Disregarding the risk interdependencies among projects, the optimal project

portfolio, W, consists funding projects 1, 2, 5, 6, 7, 11, 14 and 15 as well as investing $3,698

in the risk-free asset. Furthermore, the estimated expected return, risk and attractiveness

of optimal portfolio W are reached as 13.69, 0.51 and 24.82 respectively. Disregarding

the benefit and cost interdependencies among projects, the optimal project portfolio, Y,

consists funding projects 2, 5, 6, 9, 12, 13 and 15 as well as investing $12,961 in the risk-

free asset. Moreover, the estimated expected return, risk and attractiveness of optimal

portfolio Y are reached as 11.96, 0.44 and 24.54 respectively. Finally, Disregarding the

risk, benefit and cost interdependencies among projects, the optimal project portfolio, Z,

consists funding projects 1, 5, 6, 7, 9, 11, 13 and 15 as well as investing $5,898 in the risk-

free asset. Moreover, the estimated expected return, risk and attractiveness of optimal

portfolio Z are reached as 13.26, 0.51 and 23.64 respectively. Optimal project portfolios

W, Y and Z are depicted in Figure 3.

98

------------------------------------


------------------------------------

As can be seen from Figure 3, our model reaches better results than those models

which do not consider either the risk interdependencies or the benefit and cost

interdependencies among projects in the optimization model of PPSP.

6. CONCLUSIONS

PPSP is a key decision that allows organizations achieving their strategic goals.

As a project portfolio with a high expected return may also expose the organization to a

large loss, the combined analysis of return and risk (“risk-return optimization”) should be

considered in the optimization model of PPSP. A similar approach is applied in PSP, i.e.

the leading financial theory “MPT” (Markowitz, 1952, 1959). Furthermore, project

portfolio’s returns and risks are influenced by some threats and opportunities. These

threats and opportunities may affect the returns of one or more projects simultaneously

and cause risk interdependencies among projects. Thus, it is crucial to incorporate the

effects of threats and opportunities into the optimization model of PPSP. Accordingly,

we proposed a new model to such incorporation inspired by MPT and customized to PPSP

through considering critical information that is not discussed in other PPSP models, i.e.

particular and common threats/opportunities exist around projects.

Theoretically, this paper builds synthesized coherence (Locke & Golden-Biddle,

1997) across PPSP and MPT to take into account the risk interdependencies among

projects to the PPSP model. Moreover, the paper contributes to the PPSP literature by

99

incorporating the effects of threats and opportunities around projects into the optimization

model through customizing MPT to PPSP. It also expands MPT to portfolio decisions

where some projects are also considered and make it suitable in the project environment

by taking into account the effects of threats and opportunities. In practice, having used

risk registers which are crucial, well established and practiced documents exist in most

projects, the proposed solution is asserted to be practical and effective in order to improve

the quality of portfolio selection decision in organizations.

Our paper also has some limitations that need to be acknowledged. First, as we

apply projects’ risk register as the source of information to develop the optimization

model, adopting the limitation of this document is undeniable. As a result, this paper does

not consider unknowns-unknowns, i.e. uncertainties which are not known at the

beginning of the project (Lechler, Edington, & Gao, 2012), in the model. Finding a way

to take into account unknown-unknowns in the optimization model can improve its

quality. Second, we assume that all projects start at the same time. Expanding our study

to the scheduling of projects in the portfolio and also scheduling of activities in projects

can enrich the generalizability of the model. Third, this paper applies the characteristics

of projects before doing any mitigation actions, so other research can investigate the

effects of candidate mitigating actions on the proposed model. Fourth, we only consider

the selection decision of new project proposals in model development. Future studies can

incorporate project adjustment to the optimization model. Fifth, we use some sample data

to demonstrate how our model should be applied. Future studies can test the model and

design principles using data from real projects. Finally, future research can investigate

100

different ways to incorporate non-monetary benefits/disbenefits to the optimization

model.

101

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109

Table 1

A comparison of PPSP definitions in the literature

Source PPSP definition Objective of PPSP Constraints of

PPSP

Ghasemzadeh

& Archer

(2000)

Project portfolio selection is the

periodic activity involved in

selecting a portfolio of projects,

that meets an organization's

stated objectives without

exceeding available resources or

violating other constraints.

Selecting a portfolio

of projects, that meets

an organization's

stated objectives

Without

exceeding

available

resources or

violating other

constraints

Shou et al.

(2014)

Given a set of project proposals

and constraints, the traditional

PPSP is to select a subset of

project proposals to optimize the

organization’s performance

objective.

To select a subset of

project proposals to

optimize the

organization’s

performance

objective.

Given a set of

constraints

Carazo

(2015)

The problem of selecting a

project portfolio arises from the

everyday dilemma faced by

organizations in finding the best

possible way to distribute a

limited budget among candidate

projects to fulfil the needs of the

organization.

Finding the best

possible way to

distribute … budget

among candidate

projects to fulfil the

needs of the

organization.

distribute a

limited budget

Li et al.

(2015)

The problem of how to select a

portfolio that meets a

firm’s/organization’s objectives

without violating indispensable

constraints is called a project

portfolio selection problem

(PPSP).

To select a portfolio

that meets a

firm’s/organization’s

objectives

without

violating

indispensable

constraints

110

Table 2

The similarities between PSP and PPSP

# Similar concepts between

PSP and PPSP Explanation

1 Assets’/projects’ return Both assets and projects have their own expected returns.

2 Assets’/projects’ risk There are uncertainties in the expected returns of both

assets and projects.

3

Correlations among assets/

risk interdependencies

among projects

The expected returns of both assets and projects are affected

by some threats and opportunities like the exchange rate

changes, which in turn can result in correlations among

assets or risk interdependencies among projects. For

example, a change in the exchange rate can increase the

expected return of an asset or project and simultaneously

lower that of another asset or project.

4 Available budget Both investors and organizations have a limited budget to

distribute among a set of assets or projects.

111

Table 3

The differences between the approaches used in PSP with those should be used in PPSP

# Parameter PSP PPSP

1 Required data

An appropriate amount of

reliable historical data is

available.

Often there is not enough historical

data or the accessible historical data is

not reliable enough, as the threats and

opportunities faced by a project can be

unique and not possible to generalize

to other projects.

2

Mean as the

measure of

expected return

( i )

Assets’ expected returns are

estimated by using a

“backward approach”. In

other words, the mean of

historical returns relevant to

asset i is used to estimate its

expected return.

Projects’ expected returns should be

estimated by using a “forward

approach”. In other words, some


project management should be used to

estimate the expected return relevant

to project i.

3

Standard deviation

as the measure of

risk ( i )

Assets’ risks are estimated

by the standard deviations

of their historical returns.

Projects’ risks should be estimated by

using some forecasting techniques

specific to project management.

4

Correlation

coefficient among

assets / risk

interdependencies

among projects

( ij )

The correlations among

assets are calculated by

using “Pearson correlation

coefficient formula” for

their historical returns.

The risk interdependencies among

projects should be calculated by

considering the common threats and

opportunities around them.

5 Benefit / Disbenefit

Only monetary benefits and

disbenefits, measured in

private terms, are

considered in assets’

expected returns.

Both monetary and non-monetary

benefits and disbenefits, measured in

organizational terms, should be

considered in projects’ expected

returns.

6 Benefit

interdependency

There are not any benefit

interdependencies among

assets.

Benefit interdependencies among the

projects of a portfolio should be

considered in that portfolio’s return

calculation. Such interdependencies

occur when two or more projects

producing greater or less benefits if

carried out simultaneously than if they

were accomplished at different times.

112

7 Cost

interdependency

There are not any cost


assets.

Cost interdependencies among the

projects of a portfolio should be



originate when the simultaneous

implementation of two or more

projects require less or more resources

than if they were carried out

separately. It implies that the required

cost of a project portfolio is inferior or

superior to the sum of the costs of all

its projects.

8 Technical

interdependency

There are not any technical


assets.

Technical interdependencies among

the projects of a portfolio should be



take place when the accomplishment

of a determined project necessarily

involves the total or partial

accomplishment or non-

accomplishment of another project or

projects.

113

Table 4

Project 1’s risk register


Lik

elih

ood

The damaging/assisting impacts of the threat/opportunity


B1 B2 B3 D1 C1 C2 C3

M

($) S

(Mo)*

M

(I)**

S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

6000 10 3000 11 9000 12 1000 5 5000 1 5000 5 5000 10

∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S

P1.T01 Exchange rate increases 30% -15% +10% -30% -10% +10% -8% +16%

P1.T02 Iron import law is

passed by the parliament 20% -20% +20%

P1.T03 Design changes 10% -9%

Where:

“M” is the “estimated/realized magnitude” of benefits, disbenefits or costs in the absence of any threats and opportunities,

“S” is the “estimated/realized scheduling” for the realization of benefits or disbenefits or the spending of costs in the absence of any threats and opportunities,

“∆M” is the “estimated percentage of changes in the magnitude” of benefits, disbenefits or costs (in two directions: increased or decreased, represented by “+” and

“–” respectively) resulted from corresponding threat or opportunity materializing, and

“∆S” is the “estimated percentage of changes in the scheduling” for the realization of benefits or disbenefits or spending of costs (in two directions: delayed or

advanced, represented by “+” and “–” respectively) resulted from corresponding threat or opportunity materializing.

* Mo: Month

** I: Index (the unit of non-monetary benefits/disbenefits can be converted to monetary values by Delphi approach)

114

Table 5

Project 2’s risk register


Lik

elih

ood

The damaging/assisting impacts of the threat/opportunity


B1 B2 D1 D2 C1 C2 C3

M

($)

S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

(I)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

M

($)

S

(Mo)

9000 9 15000 10 800 7 500 5 15000 1 2000 4 2000 7

∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S ∆M ∆S

P2.T01 Exchange rate increases 30% -20% -20%

P2.O02 Project manager leaves 10% +7% -5% -12% -15%

P2.O03 Iron import law is

passed by the parliament 20% +10% -15%

P2.T04 Customer requirement

changes 20% +12% -10% +15%

115

Table 6

The return of project 1 in different potential situations

Situation

(s) Threat/opportunity

included in the situation s

likelihood of situation s

materializing

(1sp )

Return

(1sr )

Cost

( 1sPC )

1 N/A 50.4% 14.97 $14,608

2 P1.T01 21.6%* 11.82** $15,867***

3 P1.T02 12.6% 14.03 $14,608

4 P1.T03 5.6% 14.28 $14,608

5 P1.T01 & P1.T02 5.4% 11.09 $15,867

6 P1.T01 & P1.T03 2.4% 11.19 $15,867

7 P1.T02 & P1.T03 1.4% 13.35 $14,608

8 P1.T01 & P1.T02 & P1.T03 0.6% 10.46 $15,867

* According to Equation (14): 0.3×(1-0.2)×(1-0.1) = 0.216

** According to Equations (10) to (13):

0.005(24 10(1 0.10)) 0.005(24 11(1 0)) 0.005(24 12(1 0))

12

0.005(24 5(1 0.10))

12

12

6000(1 0.15) ( 1) 3000(1 0.30) ( 1) 9000(1 0) ( 1)

0.005 0.005 0.005$208,015

1000(1 0) ( 1)

0.005$20,482

$15,867***

e e eFB

eFD

PC

12

208,015 20,48211.82

15,867r

*** According to Equation (13):

0.005 1(1 0) 0.005 5(1 0.08) 0.005 10(1 0)

12 5000(1 0) 5000(1 0.1) 5000(1 0.16)$15,867

PC e e e

Table 7

116

The estimated returns, risks and costs relevant to 15 project proposals

Project number

( i )

Estimated Return

( î )

Estimated Risk

( î )

Estimated cost

( î )

1 13.78 1.48 $14,986

2 17.24 1.71 $18,595

3 13.58 1.19 $21,644

4 17.34 2.70 $16,499

5 12.39 1.38 $18,925

6 11.36 1.16 $17,568

7 13.67 1.25 $22,297

8 12.96 1.64 $31,467

9 15.78 1.77 $20,478

10 17.32 2.95 $15,445

11 12.49 1.46 $16,404

12 14.15 1.87 $22,031

13 9.53 1.10 $23,880

14 9.21 1.00 $26,799

15 13.44 1.16 $24,817

117

Table 8

The returns of projects 1 and 2 in their common potential situations

Situation

( 12c )

Threat/opportunity

included in the

situation

likelihood of situation

s materializing

(121cp )

Return of

project 1

(121cr )

Return of

project 2

(212cr )

1 N/A 56% 14.97 17.73

2 P1.T01/P2.T01 24%* 11.82 15.41

3 P1.T02/P2.O03 14% 14.03 19.00

4

P1.T01/P2.T01

&

P1.T02/P2.O03 6% 11.09 16.68

* According to Equation (14): 0.3×(1-0.2) = 0.24

118

Table 9

Technical interdependencies among 15 project proposals

Type of technical interdependencies Sets

Mutual exclusion

(1) 3

(3) 1

(4) 8

(8) 4( ) 2,5,6,7,9,10,11,12,13,14,15

M

M

M

MM i i

Prerequisite

(1) 11

(3) 10

(7) 5( ) 2,4,5,6,8,9,10,11,12,13,14,15

P

P

PP i i

Compulsory

(9) 13

(13) 9( ) 1,2,3,4,5,6,7,8,10,11,12,14,15

FAC

CC i i

119

Figure 1

The efficient frontier of risky assets with the optimal capital allocation line, CAL (P), and P as

the optimal portfolio-Source: Bodie et al. (2014, p. 221)

120

Figure 2

The design principles of project portfolio’s attractiveness evaluation

P6

P5

P3

P2

P1

P4

Threats & Opportunities

Individual projects’ risks

Risk interdependencies

among projects

Project portfolio’s risk

Project portfolio’s

attractiveness

Project portfolio’s return

Individual projects’

returns

Benefit interdependencies

among projects

Cost interdependencies

among projects

Technical interdependencies

among projects

121

Figure 3

The efficient frontier of the numerical example

0

2

4

6

8

10

12

14

16

18

20

22

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8σ

μ

CAL (P)

Y

PZ

Efficient Frontier

W

122

CHAPTER 4: CONCLUSIONS

123

Because an organization’s performance depends on the projects it implements,

project evaluation and PPSP have become two crucial topics in project management to

appraise and select project proposals, monitor projects during their lives and judge projects’

performances upon their completions. In project appraisal, as the first stage of project

evaluation which is conducted in the initiation phase, those project proposals that are

unacceptable for funding are removed. In project selection (PPSP), which is conducted at the

end of the initiation phase, the best portfolio of project proposals is selected to optimize

organizational performance given limited resources. In project monitoring, as the second

stage of project evaluation which in conducted in the planning, execution and benefit

realization phases, the ongoing performance of a selected project is compared to its initial

goals, to understand what went right or wrong in order to improve the strategy or the

processes. In project performance judgement, as the third stage of project evaluation which

is conducted after benefit realization phase, the realized project performance of a selected

project is measured to judge whether the initial goals have been achieved and enhance

organizational learning in order to achieve successful projects in future.

In project evaluation and selection, not only delivering the outputs is important, but

also realizing the projects’ benefits is crucial. Furthermore, as the intended benefits are

affected by some threats and opportunities around projects, it is crucial to incorporate such

effects into the project evaluation framework and project portfolio selection model. To do

such incorporation, I proposed (1) a new project evaluation framework inspired by utility

124

theory, and (2) a new PPSP model inspired by MPT. Thus, the two research questions

developed in Chapter 1 can now be answered: (1) For paper 1 - the principles of utility theory

are applied to introduce a “project evaluation map”, as the foundation of the integrated

benefit-oriented project evaluation framework, including “Attractiveness contours”,

“Approved business case contour” and “Funder investment frontier”; and (2) For paper 2 -

the principles of MPT are applied to add risk interdependencies among projects into the PPSP

model through substituting the projects’ historical data with information from their risk

registers and introducing a new approach to estimate risk, return and risk interdependencies

among projects.

Theoretically, this thesis contributes to the project management literature by

developing an integrated framework for all three stages of project evaluation regarding

projects’ returns and risks. Furthermore, it contributes to the PPSP literature by incorporating

the effects of threats and opportunities around projects into the optimization model through

customizing MPT to PPSP. It also expands MPT to portfolio decisions where some projects

are also considered and make it suitable in the project environment by taking into account

the effects of threats and opportunities. In practice, the proposed evaluation framework and

PPSP model can improve the quality of portfolio selection decision in organizations and in

turn lower their resource wastes, as well as help them ensuring the realization of projects’

intended benefits.

125

As the project management discipline is now also taking into consideration projects’

benefits as the underlying rationale for all projects, this thesis opens a new horizon in benefit-

based project evaluation and selection for future studies. An extension of this thesis can also:

(1) take into account unknown-unknowns in the project evaluation framework and PPSP

model; (2) test the framework and model in various industries, countries and cultures; (3) add

project adjustment, the effects of risk mitigation actions, scheduling of projects in the

portfolio, and scheduling of activities in projects to the proposed PPSP model; and (4),

investigate different ways to incorporate non-monetary benefits and disbenefits into the

project evaluation framework and PPSP model.

Documents

Benefit-Oriented Modelling for Project Appraisal, Selection, … · Chapter 2: An Integrated Benefit-Oriented Project Evaluation Framework: Appraisal, Monitoring and Performance Judgement