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Socio-Economic Planning Sciences 42 (2008) 3145

A multiobjective model for the selection and timing of public

enterprise projects

Andre s L. Medagliaa, Darrell Huethb,c,, Juan Carlos Mendietab, Jorge A. Sefaira,b

aCentro de Optimizacion y Probabilidad Aplicada (COPA), Departamento de Ingeniera Industrial, Universidad de los Andes;

A.A. 4976, Bogota, DC, ColombiabCentro de Estudios sobre Desarrollo Economico (CEDE), Facultad de Econom a, Universidad de los Andes; A.A. 4976,

Bogota, DC, ColombiacUniversity of Maryland, Department of Agricultural and Resource Economics, 2200 Symons Hall, College Park, MD 20742, USA

Available online 7 September 2006

Abstract

In theory, a public utility company improves the quality of community life through its projects and actions. However,

project selection and prioritization by these companies are highly complex processes. To assist company planning

managers in such processes, we propose a mixed integer programming model that selects, from a bank of projects, which

are worthy of investment. The question of timing is also addressed. The model maximizes a weighted sum of normalized

economic and financial net present values and a social impact index. It simultaneously satisfies a set of precedence relations

among projects, the earliest and latest project start dates, exogenous budget limits, and endogenous project cash flow

generation. We illustrate the models effectiveness using an example constructed from a case study of a major Latin

American water and sewage company.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Project selection; Multicriteria decision-making; Public sector decision-making; Public investment decisions; Mixed integer

programming

1. Introduction

Most public enterprisesincluding water, sanitation, transportation, and energy supply utilitiesface a

common problem: the current budget available for those investment projects that could potentially beundertaken during a planning horizon is insufficient to initiate all projects during the first year. Adding to the

complexity of the decision process are technical limitations such as earliest and latest start dates and

precedence relations between specific projects. Moreover, there may be substantial external political pressure,

and internal bureaucratic support, for specific projects.

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www.elsevier.com/locate/seps

0038-0121/$- see front matterr 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.seps.2006.06.009

Corresponding author. University of Maryland, Department of Agricultural and Resource Economics, 2200 Symons Hall, College

Park, MD 20742, USA.

E-mail address: [email protected] (D. Hueth).

URLs: http://copa.uniandes.edu.co, http://economia.uniandes.edu.co.
http://www.elsevier.com/locate/sepshttp://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.seps.2006.06.009mailto:[email protected]:http://copa.uniandes.edu.co,mailto:http://copa.uniandes.edu.co,mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.seps.2006.06.009http://www.elsevier.com/locate/seps

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Two additional considerations are as follows:

(1) Some projectsfor example, those related to potable water supplies and electricitymay be at least

partially self-financing in that consumers can be billed for them; while otherssuch as reforestation of

hillsides and wetland restorationsmust be funded from other sources. Thus, to some degree, the budget

is endogenous.(2) Unlike the private sector, in which maximizing net financial benefits or returns to shareholders is generally

the sole criterion, the public sector must also consider social equity, economic, and political criteria.

The question thus arises as to what types of decision support systems (DSS) are currently available for

public agency managers in such a complex environment. Theoretical and applied research in economics and

operations research has provided substantial guidance in this area.1 In economics, McGuire and Garn [1]

building on the project evaluation work of Eckstein [2], Marglin [3], and othersincorporated equity

considerations into a project selection model by assuming that one can construct weights for each projects net

benefits to each income group, where the weights depend on each groups income and employment levels. In

contrast, Freeman [4] proposed that public administrators past decisions be used to construct a societal

welfare function that would allow project selection based on the marginal social value of each affected groupsincome. However, as Just et al. [5, p. 41] correctly pointed out, little hope [apparently] exists for determining

a societal welfare function on which general agreement can be reached.2 Thus, as explained below, in the

current paper we do not attempt to specify societal preferences but, rather, adopt a weighted set of widely

accepted criteria as an objective function.

The operations research literature has naturally focused more on alternative models and solution

algorithms. For example, Benjamin [6] proposed a goal-programming model for public-sector project selection

in Trinidad and Tobago in which the goals are stipulated by the program manager. This model, which was

applied to the energy sector, included economic, financial, social, and political factors but did not address

project scheduling despite the authors recognition that scheduling is the second phase in public-sector

investment problems. Much earlier, Lee and Sevebeck [7] used goal programming in their aggregative model

for municipal economic planning. The model was applied to a small problem from the municipal government

of Blacksburg, Virginia. More recently, Chan et al. [8] used a goal-seeking methodology within a capital

budgeting framework in considering technology modernization by the US Army.

It is important to note that the approaches taken in these earlier studies all demand that managers specify a

policy by explicitly setting goal levels for several criteria.3

Some researchers have used the analytical hierarchy process (AHP) to help managers identify their

priorities. For example, Barbarosoglu and Phinass [11] project selection tool for the Istanbul Water and

Sewerage Administration used AHP and mixed integer programming (MIP) to include social, political and

economic criteria. After first using AHP to quantify tangible and intangible attributes, and obtain an

aggregate weight for each project, they used the resulting weights in the objective function of the project

scheduling MIP model. Son and Min [12] also combined AHP and integer programming to solve a capital

budgeting problem in the US electrical power industry, taking financial and regulatory (environmental)

constraints into account.Whereas these AHP-based approaches can include hard-to-quantify factors, the methodologys demanding

pairwise comparisons tend to limit the size of the project bank. For instance, the above two experiments

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1The economics literature is now, however, somewhat dated. Economic research on public investment criteria peaked during the era of

large dam construction, which ended in the mid-1970s when the sites for such projects became scarce and environmental concerns brought

a halt to most U.S. Army Corps of Engineers projects.2The search for an acceptable social welfare function for use in public investment decisions has been long and largely unsuccessful. Such

investigation has been characterized by three major approaches: (1) the subjective proposal of a specific analytical form; (2) the axiomatic

construction of a social welfare function from widely accepted axioms; and (3) a moral justice-based approach that distinguishes between

an individuals personal and moral preferences.3Due to go-no-go decisions in some project selection problems, integer goal programming can be viewed as an alternative methodology

[9] to that adopted in the current paper. Extensive reviews of techniques and applications of goal programming are provided by

Schniederjans [9] and Tamiz et al. [10].

A.L. Medaglia et al. / Socio-Economic Planning Sciences 42 (2008) 314532

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considered only nine and three projects, respectively. Moreover, the authors made no attempt to quantify the

economic cost of including social, environmental, and political factors.

Regardless the approach, Chan [13] has shown limited adoption by government units of those project

selection and capital budgeting models proposed in the operations research literature. Specifically, he found

that only 25% of 484 Canadian municipal governmental units surveyed used some form of capital budgeting

procedure or payback analysis, a finding echoed in similar research for the US [13]. If such procedures are littleused in these two developed countries, their frequent use in developing countries would seem to be much less

likely. In particular, we have found little evidence of current use of capital budgeting models by Latin

American public utilities. Rather, these companies tend to conduct economic and financial evaluations project

by project, after which agency administrators meet and attempt to reach the greatest possible consensus on

project selection and scheduling in light of any additional information.

The decision-making scenarios outlined above present a number of obvious problems. First, the significant

amount of subjectivity in the scheduling process may allow more powerful department administrators

inordinate influence over outcome(s). For example, Zanakis et al. [14] argued that, in non-profit organizations,

selection criteria could be influenced by political issues to the exclusion of technical considerations. Moreover,

the replacement of technical criteria by intuition in the decision-making process can reduce organizational

competitiveness [15].

Second, a project-by-project assessment may fail to consider a project evaluations dependence on the startdate. That is, some projects whose economic evaluation in the current time period is unfavorable may, as a

result of expected population and income growth, fare much better at a later date. Third, the process includes

no logical incorporation of social considerations and little or no way to estimate the economic opportunity

cost of achieving stated social goals. Finally, and most importantly, in most cases, such a process fails to

provide the decision maker with a current and complete economic efficiency ranking of all projects under

consideration.

To address such problems, this research aims to expand the set of decision-making tools available to public

agencies for project selection and scheduling. Specifically, it provides a multiobjective mixed integer linear

program (MOMILP) that can be embedded in a user-friendly DSS to extend the available project selection

models in a number of directions.

First, rather than attempting to specify a particular social welfare function or specific goal levels, we use themore modest but widely accepted approach of allowing the decision maker to find the economically efficient

solution, and then assess the opportunity cost of achieving social or financial goals. Second, our model considers

precedence relations among projects, including the key feature of positive and negative precedence gapswhich

enables user modeling of soft precedence constraintsseemingly missing from the project selection literature.

Third, the models inclusion of specific earliest and latest start dates simulates the impact of political

decisions. Fourth, the model allows for endogenous cash flow generation in addition to the exogenous budget,

an important feature in that early investment in some projects could generate sufficient resources to partially

fund future projects. Lastly, application of the model in a case study shows it to be computationally efficient

for portfolios containing a large number of projects.

The remainder of the paper is organized as follows: Section 2 presents a general multiobjective optimization

model for public utility project selection and scheduling; Section 3 briefly explains the data requirements, data

sources, and methods of data preparation for the general model; Section 4 presents the results of a series of

model runs using a numerical example built on our experience with the Empresa de Acueducto y

Alcantarillado de Bogota (EAAB) (Bogota Water and Sewer Utility Company);4 and Section 5 summarizes

the work, and suggests future extensions of the proposed model.

2. A general model for optimal selection and timing of projects

In this section, we present a general model that can be applied to any public enterpriseincluding water,

sanitation, transportation, and energy supply utilities. The proposed formulation includes a set of candidate

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4Due to non-disclosure agreements, we are not at liberty to report results of the runs of the EAAB case study. However, the portfolio of

water and sewer projects, on which this paper is based, contained 170 projects.

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projects, P; the minimum and maximum number of projects to be included in the portfolio, KL and KU,

respectively; and a set of precedence relations between the projects, A. That is, if project iAPprecedes project

jAP, then (i,j)AA, whose precedence gap is, in turn, represented by gij 2 Z1. If gij 0, the last investment

period of project i should be over before the investment cycle of project jbegins; ifgijo0, an overlap of up to

gij investment periods will be allowed; and, if gij40, the last investment period of project ishould be at least gij

periods away from the first investment period of project j.The life of project i is denoted by vi, and its investment life (i.e., the number of periods up to the last

investment period) by ui. Trepresents the planning horizon for investment decisions t 2 f0; . . . ;Tg, while l1,

l2 and l3 are the a priori weights given by the decision maker to the respective economic, financial, and social

factors, respectively 0pllp1;P3

l1ll 1. The normalized economic, financial, and social indices are,

respectively, I1it, I2it and I

3it if project iAP starts in year t t 2 ft

i ; . . . ; minft

i ;T ui 1gg. Finally, cik and bik

are the investment cost and benefit in period kfor project i k 2 f0; . . . ; vi 1g; ti and t

i are the earliest and

latest respective start dates for project i(iAP); and r0t is the available budget for year t t 2 f0; . . . ; Tg. Without

loss of generality, we assume that r0T 0.

The model identifies those projects to be selected, and the starting date of each. The binary decision

variable, yit, takes a value of 1 if project iAPstarts on year t t 2 fti ; . . . ;minft

i ; T ui 1gg and a value of

0, otherwise. The model requires an auxiliary set of binary decision variables, xikt, that take the value of 1 if

period k k 2 f0; . . . ; vi 1g for project iAP is assigned to year t in the planning horizont 2 fti ; . . . ; t

i vi 1g, and a value of 0, otherwise. Let rt X0 be the available resources in year t

t 2 f0; . . . ; T 1g. We assume, without loss of generality, that r0 0.

The proposed mixed integer program for optimal investment planning is outlined below:

maxX3

l1

ll

X

i2P

Xminfti ;Tui1g

tti

Ilityit, (1)

subject to

Xminfti ;Tui1g

tti

yitp1; i 2 P, (2)

KL X

i2P

Xminfti ;Tui1g

tti

yitpKU, (3)

yit xi;k;tk; i 2 P; k 2 f0; . . . ; vi 1g; t 2 fti ; . . . ; minft

i ;T ui 1gg, (4)

yjtpXtuigij

t0 ti

yit0 ; i;j 2 A; t 2 fti ; . . . ; t

i g, (5)

rt1 rt r0t X

i2P

X

k0;...;vi1

bik cik xikt; t 2 f0; . . . ;Tg, (6)

rtX0; t 2 f0; . . . ;T 1g, (7)

yit 2 0; 1f g; i 2 P; t 2 fti ; . . . ; minft

i ;T ui 1gg, (8)

xikt 2 f0; 1g; i 2 P; k 2 f0; . . . ; vi 1g; t 2 fti ; . . . ; t

i vi 1g. (9)

As shown in (1), the models objective seeks to maximize the weighted sum of the normalized economic,

financial, and social values of the portfolio. The group of constraints in (2) allows the model to select at most

one start date for each project. The bound constraints in (3) allow the number of selected projects to fall

between a lower and an upper bound. If these two bounds are equal, the number of projects to be selected is

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fixed. The group of constraints in (4) articulates decision variables y with auxiliary variables x. If a given

project starts at a specified date, the corresponding y variable takes the value of 1. Thus, the periods of that

project are assigned to given dates in the planning horizon through activation of the corresponding x

variables.

The precedence conditions are accounted for in (5). The constraints in (6) are responsible for meeting the

exogenous budget and incorporate reinvestment of endogenous resources generated by other projects. Finally,the group of constraints in (7) establishes non-negativity conditions for the available resources at the end of

year t, while those in (8) and (9) force variables x and y to be binary.

3. Data sources and methodology

This section discusses the input requirements and methodology for the general model presented in the

previous section. The technical data for the projects, including precedence relations, gaps, earliest and latest

start dates, and project lifetimes, are available from the public utility. Data on the exogenous budget and

expected financial cash flows are also available from this source. Implementing the model requires the

construction of three sets of indiceseconomic I1it, financial (I

2it), and social I

3it.

Data for construction of the financial indices of net present values for each project and each possible start

date are readily available from the utility company. In addition, they can usually provide current population

figures, population projections, and current market interest rates.5

Construction of the economic net present value indices requires significantly greater effort than that needed

for the financial indices since private costs and benefits require adjustment to reflect those of society.

Estimation of the economic benefits and costs follows the same general principles and guidelines suggested

by the economic project evaluation literature [1618]. Thus, to begin, values of utility services produced must

be based on the consumers marginal willingness to pay rather than on government regulated utility rates.

Second, the prices of inputs in distorted markets (e.g., subsidies, tariffs and union power) must be adjusted to

their appropriate shadow prices. Third, the economic values of outputs of non-market goods (e.g., ecosystem

service flows and public health benefits) must be estimated following the non-market valuation techniques

found in [1921] and other sources.

Because time and money constraints normally preclude a detailed individual benefit cost analysis for each of

a large set of projects, maximum use of benefits transfer (BT) methodology [19,21] is recommended. In its

simplest form, this methodology, which has seen a rapid evolution in the literature, takes valuation estimation

results from one site and uses them, reasonably calibrated, for the site of that project or policy being

evaluated.6

Perhaps the best known of the growing number of available Internet sites giving BT information is the

Environmental Valuation Reference Inventory (EVRI) maintained by Environment Canada (http://

www.evri.ec.gc.ca/evri/), which provides free access to Canadian citizens and US academics. Unfortunately,

although this source contains a large database on environmental and health benefits, most of the empirical

results are from studies in the US, Canada, and other developed countries. Fortunately, the ENVAL database

created by the Environmental Protection Agency of New South Wales focuses on Australian and SoutheastAsian studies that contain more valuation results from the developing world (http://www2.epa.nsw.gov.au/

envalue/). For an inventory of benefits associated with water projects in particular, the interested researcher is

referred to the University of Californias Beneficial Use Values Database (http://buvd.ucdavis.edu).

The most subjective data we must consider in running our model are those for construction of the social

objective indices, which explicitly recognize equity considerations rather than economic efficiency. Possible

metrics for measuring social impact include: (1) The percentage of beneficiaries below the poverty line; (2) the

impact on income distribution, as measured by the well-known Gini coefficient [23, p. 30] for project location;

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5If the utility does not have census and population projection data, other government agencies will have to be consulted. These sources

may also need to be approached to build the social indices discussed below.6A more sophisticated approach to BT is to perform a meta-analysis [22] (i.e., a statistical regression analysis of a large number of

studies) and estimate the contribution of various variables to the projects benefit values.

http://www.evri.ec.gc.ca/evri/http://www.evri.ec.gc.ca/evri/http://www2.epa.nsw.gov.au/envalue/http://www2.epa.nsw.gov.au/envalue/http://buvd.ucdavis.edu/http://buvd.ucdavis.edu/http://www2.epa.nsw.gov.au/envalue/http://www2.epa.nsw.gov.au/envalue/http://www.evri.ec.gc.ca/evri/http://www.evri.ec.gc.ca/evri/

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(3) percentage of the project workforce that is unskilled; and (4) the percentage of project costs paid for by

people with personal income below the poverty line.

The first two of these social impact metrics are likely to be correlated and thus have similar implications;however, the third and fourth indicators can vary from the others and might therefore be considered separate

objectives. In our case study, we measure social impact directly by the number of people below the poverty line

(BPL) who will benefit from the project.

Once construction of the social objective indices is complete, the database of normalized economic and

financial net present values, and the social indices, are ready for use as input to the proposed optimization

model.

4. A numerical example based on a case study

The numerical example provided in this section is based on our experience with the Bogota Water and Sewer

Utility Company (EAAB, for its acronym in Spanish). As mentioned above, because of legal considerationswe are unable to report the actual results of our case study here. The current example, however, demonstrates

typical model outputs as well as how public utility management can use the model for project selection and

scheduling.

We consider a public utility company with 10 projects (p1,y, p10), whose earliest and latest start dates are

shown in Table 1, and with a time horizon of 8 years. As Table 1 illustrates, projects p3, p5, p6, p7 and p9 have

no flexibility with regard to their start dates, whereas the remaining projects do. The yearly exogenous budgets

are given in Table 2. These data are carefully constructed to reflect representative infrastructure and wetlands

restoration projects for EAAB.

The projects precedence relations guarantee that the investment cycle of a given project cannot start before

that of another project. In this example, the investment cycle of project p10 must end before the investment

cycle of project p8 can begin, and projects p1 and p5 must precede project p4. The model allows for gapsbetween projects in the optimal solution.

The construction of the social index vector begins with the data shown in Table 3 on the impacted

population and number of people below the poverty line for each project.

Table 4 presents the economic and financial net present values for each project, assuming each begins on the

first year of the planning horizon.7 It should be noted that the economic and financial performance for each

project varies. For instance, from an economic standpoint, projects p1, p7 and p8 perform poorly but are

financially attractive, while from a social standpoint, the best projects are p1, p6 and p7. Obviously, decision-

making is complicated for the planning manager or analyst facing project selection and scheduling under such

multiple competing criteria.

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Table 1

Earliest and latest start dates

Project ti ti

p1 2004 2011

p2 2004 2011

p3 2004 2004

p4 2006 2011

p5 2005 2005

p6 2005 2005

p7 2004 2004

p8 2004 2007

p9 2005 2005

p10 2004 2006

7It should be noted that since the start date is flexible for a subset of projects (p1, p2, p4, p8 and p10), each possible start date in this

subset will have its own set of financial and economic indices.


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4.1. The optimal portfolio

It should first be noted that to produce the optimal solution to the MOMILP (see Fig. 1), the model uses a

precedence gap of zero (i.e., gij 0, i;j 2 A) between projects having precedence relationships. Not only does

the resulting solution show an ordering that satisfies both the earliest and latest start dates, but the decision

maker has chosen a portfolio containing all 10 projects KL KU 10, when equal weights are given to the

economic, financial, and social criteria (i.e., each l 33.3%).

Fig. 2 shows the budget and optimal investment for the entire planning horizon. It is worth noting that the

model allows for the accumulation of resources, that is, resources that are not invested in a given year are

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Table 2

Exogenous budget

Year Budget US$ millions

2004 2,500

2005 5,000

2006 5,500

2007 5,500

2008 9,000

2009 5,500

2010 6,500

2011 8,500

Table 3

Social performance

Project Population Population below

poverty line

% of population below

poverty line (%BPL)

p1 400,000 49,757 12.44

p2 120,000 12,838 10.70

p3 110,000 10,846 9.86

p4 450,000 54,832 12.18

p5 220,000 24,466 11.12

p6 720,000 91,979 12.77

p7 320,000 43,602 13.63

p8 345,000 36,355 10.54

p9 320,000 28,054 8.77

p10 320,000 28,054 8.77

Table 4Economic, financial, and social project evaluation

Project Economic

NPV

Financial

NPV

%BPL Economic

ranking

Financial

ranking

Social

ranking

Average

ranking

p6 2910.7 555.8 12.77 2 4 2 2.7

p4 382.4 1838.5 12.18 5 1 4 3.3

p7 6843.0 871.5 13.63 10 2 1 4.3

p5 13261.2 84.9 11.12 1 7 5 4.3

p1 143.8 117.2 12.44 7 6 3 5.3

p2 120.9 184.0 10.70 6 5 6 5.7

p8 4967.7 703.3 10.54 9 3 7 6.3

p3 1616.3 556.4 9.86 3 9 8 6.7

p9 1281.5 1308.3 8.77 4 10 10 8.0p10 188.6 247.4 8.77 8 8 9 8.3


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carried over to the next year. This carryover means that investment in a given year can exceed the amount of

exogenous budget allocated for that year.

4.2. Sensitivity to objective weights (ls)

A primary goal in a public utility companys decision-making is the economically efficient use of public

funds. However, pursuing pure economic efficiency may negatively affect financial or social performance. On

the other hand, pursuing a better financial or social performance often implies an efficiency loss, measured by

the decrement in economic net present value resulting from the increased weight assigned to financial and

social factors. Therefore, studying the magnitude of these tradeoffs is of vital importance for the decision

makers in charge of public investment.

As Fig. 3 illustrates, various changes occur when the economic and social importance is varied but the

financial weight (l2 0) remains fixed. If the only objective is to achieve economic efficiency (point A), the

maximum economic net present value of 18 billion dollars is reached by benefiting a small number of people

below the poverty line (272,000). Increasing this number to 344,000 implies a sacrifice of 0.15 billion dollars in

economic efficiency (point B); that is, a cost of 2083 dollars/person. However, benefiting an additional 36,000

people implies an economic efficiency loss of 11 billion dollars (point C), or a per capita cost of 305,556

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Fig. 1. Optimal timing of the 10-project portfolio using a precedence gap of zero.

0

1

2

3

4

5

6

7

8

9

10

2004 2005 2006 2007 2008 2009 2010 2011

US$Millions

Investment Budget

Fig. 2. Budget and optimal investment.


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dollars. The controversial decision of moving from point B to point C may imply a harsh battle between those

interested in economic efficiency and those in favor of social efficiency.

The relation between the economic and financial net present values is shown in Fig. 4 using two different

levels for the social factor. The first level places no value on social performance (l3 0), whereas the second

assigns a weight of 50 percent to the social factor (l3 0.5). At point A (where only economic efficiency

matters), the economic and financial net present values reach 17.8 billion dollars and 75 million dollars,

respectively. At point B (where the financial factor is valued higher), the financial net present value reaches 1.3

billion dollars with an economic efficiency sacrifice of 1.2 billion. Moving from point B to point C implies an

increment in financial net present value of 0.6 billion dollars with an economic loss of 1.6 billion. The most

dramatic loss in economic efficiency occurs in a move from point C to point D, where a gain of 1.2 billion in

financial net present value is paid at a sacrifice of 11.6 billion dollars in economic efficiency. Reducing the

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-

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

230,000 280,000 330,000 380,000

Millions

Population BPL

Economic

NPV

2=0

(1=1, 3=0)

(1=0, 3=1)

Fig. 3. Tradeoff between economic efficiency and social impact.

-

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

- 500 1,000 1,500 2,000 2,500 3,000 3,500

Millions

Millions

Financial NPV

E

conomicNPV

3=0 3=0.5

(1=1, 2=0)

(1=0, 2=1)

(1=0, 2=0.5)

A

B

C

D

Fig. 4. Tradeoff between economic efficiency and financial profits.


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importance of the economic criterion (i.e., increasing the importance of the social criterion) implies a financial

gain from a loss in economic efficiency, a trend that explains the curvature of the relation, l3 0.5.

The relation between financial and social performance is shown in Fig. 5 with the importance of the

economic factor fixed (l1 0). First, the analysis gives full importance to the financial factor but none to the

social. The maximum financial net present value reaches 3.1 billion dollars, affecting 341,882 people below the

poverty line. Improving the life of 38,900 additional peoplethat is, providing additional public utility

services to 380,782 people below the poverty lineimplies a financial sacrifice of 1.7 billion dollars or 44,971

dollars per person, a price that the public utility will most probably be unwilling to pay.To more realistically explore the tradeoffs as the objective weights (~l) change, we next expand the bank of

projects to 100 and show the full set of efficient solutions for all feasible combinations of~l together with the

portfolios economic and financial values (shown in Figs. 6 and 7, respectively).

Figs. 6 and 7 illustrate the following important findings:

(1) Stepwise surface. Critical values exist for the parameters (~l) such that once they are reached, the optimal

timing and ordering changes significantly. This variation (represented graphically as stairs) is reflected in

abrupt changes in the economic and financial value of the portfolio resulting from small changes in the set

of~l.

(2) Robustness. There exist some stable areas in which changes on the importance of the criteria (economic

and financial) do not affect the optimal timing and ordering of projects. It is useful for the decision maker

to know, that changing the values of~l in these areas (valleys) do not generate changes on the optimal

timing and ordering nor on the economic or financial values of the portfolio. This illustrates how the

model could be used as a negotiation tool in a political environment.

4.3. Sensitivity to technical constraints

By relaxing the constraints on the earliest and latest start dates, projects are free to move within the

planning horizon. Projects find their optimal placement in time according to their best contribution to the

objective function. Due to political pressure, projects are often started near the beginning of the planning

horizon. By advancing the latest start date, the model understands that the project must be accomplished

sooner. Hence, the model looses flexibility by being more constrained, and there is a sacrifice on the value of

the objective function.

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500

1,000

1,500

2,000

2,500

3,000

3,500

330,000 340,000 350,000 360,000 370,000 380,000 390,000

Millions

Population BPL

FinancialNPV

1=0

(2=1, 3=0)

(2=0, 3=1)

A

B

Fig. 5. Tradeoff between financial profits and social impact.


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To illustrate this principle using the 10-project example, we free the latest start date for projects p3 and p9

previously, scheduled to begin in 2004 and 2005, respectivelyso they are postponed and scheduled to start in

2010 and 2008, respectively (see Table 1). After this change, the objective function increases in 6.6%. For this

scenario, we set the precedence gap to zero.

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Fig. 6. Normalized economic value surface and contours with varying ~l (where l3 1 l1 l2) for the 100-project example.

Fig. 7. Normalized financial value surface and contours with varying ~l (where l3 1 l1 l2) for the 100-project example.


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Finally, as shown by the circle in Fig. 8, changing the precedence gap between projects p5 and p4 (from 0

to 1) allows the investment periods of the two projects to overlap while all other precedence relations remain

definitive (with a gap of 0). Allowing this overlap increases the objective function in 1.7%.

4.4. Sensitivity to budget changes

In this experiment, we assume that the exogenous budget for 2006 is cut dramatically from 5.50 million

dollars to 0.55 million dollars. As Fig. 9 shows, neither the original budget nor the partial cumulative budget

(which picks up the slack of uninvested resources) is able to cope with the aggressive investment plan.

Under a purely economically efficient scenario, allowing endogenous resources translates into a net benefitof 18.06 million, a positive effect of the financial cash flows from earlier projects enabling p2 to start in 2005

rather than being pushed later along the planning horizon (i.e., 2007).

5. Concluding remarks and future research

In this paper, we have introduced a new multiobjective mixed integer programming model for optimal

project selection and scheduling that is especially geared toward public sector companies. This model provides

a much-needed decision support tool for public company planning managers who must decide which projects

to select from an existing project bank and when to invest in them. The proposed model maximizes a weighted

sum of normalized economic and financial net present values and a social impact index (i.e., the percentage of

people below the poverty line). Moreover, it simultaneously satisfies the following important criteria: a set of

precedence relations among projects, earliest and latest project start dates, exogenous budget limits, and

endogenous project cash flow generation.

We have illustrated the model using a case study based on our experience with a major water and sewage

company in Colombia, South America. We conducted a sensitivity analysis that: measured the impact of

changes of the weights on normalized economic and financial net present values, as well as on the social index;

measured the impact of relaxing the earliest and latest start dates on the optimal timing; and measured the

impact of endogenous resource generation in a low-budget scenario on the optimal investment plan. We also

explored the opportunity cost of decisions made because of political pressure, a common occurrence for public

utility companies in Latin America.

The models value as a support tool for public utility company planning managers is evidenced by several

characteristics First, it permits optimal selection and ordering in an ex ante scenario, Second, it not only

allows planning managers to defend the investment strategy that best suits the utilitys goals, but it

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Fig. 8. Effect of changing the precedence gaps of projects p5 and p4.


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quantitatively measures the opportunity cost of political decisions. Finally, it greatly facilitates the planning

process of public companies that must invest public resources using a social welfare orientation.The model also provides several avenues for future research. For example, extended models might capture

the essence of different utility companies, such as those that want to incorporate risk into their decisions. The

authors of this paper have developed project selection models for the private sector that incorporate risk

[2426], much work on this aspect remains to be done for the public sector.

One characteristic of this model is that it takes all prices as exogenous for each project. In some settings, the

size of utility company projects can be sufficiently large to affect input or output prices and in these cases we

would need to have demand and supply relationships incorporated in the model rather than point estimates of

prices. These considerations would create market interdependencies among projects in addition to the

technical interdependencies we have modeled here. We leave these considerations to further research.

Acknowledgments

The constructive comments of the Editor-in-Chief, Dr. Barnett R. Parker, and two anonymous reviewers

greatly improved the paper. As always, any and all errors are fully attributable to the authors. We thank

Dawn Mazzanti, from Dash Optimization for providing us with access to Xpress-MPs optimization products

under the Academic Partner Program. Finally, we express our appreciation to Diego Rentera, Ne stor Botero,

Oscar Pardo, and the planning team from the Gerencia de Planeamiento y Control at Empresa de Acueducto

y Alcantarillado de Bogota for many helpful comments along the way.

References

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Systems and Information Engineering Design Symposium; 2005.

Andre s L. Medaglia is Associate Professor of Industrial Engineering, Universidad de los Andes, Bogota , Colombia and director and

founding member of the Centro de Optimizacio n y Probabilidad Aplicada (COPA; the Center for Applied Optimization and Probability).

He received a B.S. in industrial engineering from Universidad Javeriana, Bogota , Colombia, an M.Sc. in industrial engineering from

Universidad de los Andes, and a Ph.D. in operations research from North Carolina State University, Raleigh. Prior to his current position,

Professor Medaglia was an optimization specialist, Supply Chain Center, SAS Institute Inc., Cary, NC. His current research interests

include multiobjective evolutionary optimization and optimization applications to logistics and project selection. Professor Medaglias

research has appeared in Annals of Operations Research, Automation in Construction, European Journal of Operational Research, Fuzzy Sets

and Systems, and Interfaces. He currently serves as Associate Editor of Journal of Industrial and Management Optimization and

International Journal of Management Science and Engineering Management; and as regional VP for Central and South America for the

Institute of Industrial Engineers.

Darrell Hueth is Professor of Resource Economics, University of Maryland, College Park, and Profesor titular, Universidad de Los Andes,

Bogota , Colombia. He holds a B.S. in accounting and M.S. in applied economics, both from Montana State University, Bozeman, and a

Ph.D. in agriculture and resource economics from the University of California, Berkeley. Professor Hueth has held academic

appointments at Oregon State University, University of California (Berkeley), and the University of Rhode Island. His research areas

include environmental and resource economics, project and policy evaluation, and the economics of biotechnology. His most recentpublication is Welfare Economics of Public Policy: A Practical Approach to Project and Policy Evaluation with Richard Just and Andrew

Schmitz (Edward Elgar Publishing, 2004). The predecessor to this book won the Publication of Enduring Quality Award from the

American Agricultural Economics Association (AAEA). Professor Hueths research has appeared in such journals as American Economic

Review, Quarterly Journal of Economics, American Journal of Agricultural Economics, Western Journal of Agricultural Economics,

Economic Inquiry, American Economic Review, and Journal of Agricultural and Resource Economics He has served as co-editor of the

Western Journal of Agricultural Economics.

Juan Carlos Mendieta is Instructor and Research Associate, Centro de Estudios para el Desarrollo Econo mico (Center for Studies in

Economic Development, CEDE), School of Economics, Universidad de los Andes, Bogota , Colombia. He received a B.Sc. in agronomic

engineering from Universidad Nacional Agraria de Nicaragua, Managua, and an M.Sc. in environmental and resources economics from

the Joint Program between the University of Maryland, College Park, and Universidad de los Andes. His research interests include non-

market valuation and transportation economics.

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http://www.fs.fed.us/rmhttp://www.fs.fed.us/rmhttp://dx.doi.org/10.1016/j.ejor.2005.03.068http://dx.doi.org/10.1016/j.ejor.2005.03.068http://www.fs.fed.us/rmhttp://www.fs.fed.us/rm

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Jorge A. Sefair is Research Assistant of Industrial Engineering, Universidad de los Andes, Bogota , Colombia. He received a B.Sc. in

Industrial Engineering from Universidad de los Andes, and is a B.A. student in Economics and M.Sc. student in Industrial Engineering at

the Universidad de los Andes. He is engaged in several research and consultancy projects at the Centro de Estudios para el Desarrollo

Econo mico (CEDE) and the Centro para la Optimizacio n y Probabilidad Aplicada (COPA). His research interests include project

selection problems and optimization applications in industrial engineering.

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