Analyzing Academic Writing

Isaac Perry

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Water Utility Efficiency Assessment Using a Data Envelopment Analysis

Procedure

Abstract

This paper employs data envelopment analysis (DEA) of US EPA Community Water

System Survey data to compare the relative efficiencies of potable water utilities. Three

ownership types (private for-profit, private not-for-profit, and public) and two types of supply

sources (ground and surface) are compared. Statistically significant results indicating the

efficiency advantage of certain utility types were found, and clear trends towards certain utility

types were identified. The findings indicate that public utilities are most efficient overall,

followed by private not-for-profit utilities, with private for-profit utilities being least efficient.

Except for a few cases of very large supply demands, utilities employing ground water sources

were generally more efficient than those using surface water sources. A brief investigation into

the marginal return on information obtained from using additional measurement variables to

measure utility performance is presented. Additional ranking information can be obtained by

using more discrete measurement variables, but with diminishing marginal returns. This

efficiency evaluation of public water utilities should prove useful as a tool for guiding ownership

policy and water source development.

1 Graduate Research Assistant, Department of Civil and Environmental Engineering, University of

Michigan, 1208A ERB, 2200 Bonisteel Blvd., Ann Arbor, Michigan, 48109-2099.

2 P.E., Gordon M. Fair and Earnest Boyce Distinguished University Professor, Department of Chemical

Engineering, University of Michigan, 4103 ERB, 2200 Bonisteel Blvd., Ann Arbor, Michigan, 48109-2099.

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CE Database subject headings: data envelopment analysis, groundwater sources,

surface water sources, efficiency measurements, infrastructure, decision making,

ownership type.

Introduction

Efficiency measurements are widely used in various industries to benchmark

performance, document operational improvements, and provide other managerial information

(e.g.,, Arogyaswamy and Yasai-Ardekani 1997; Westphal et al. 1997). Conversely, water utilities

exist in relatively non-competitive environments, with few quantifiable operational

measurements being available to compel management efficiency. This paper describes a

procedure by which the efficiency of water utilities can be assessed using data envelopment

analysis (DEA), a procedure widely used to provide objective numerical efficiency rankings for

comparable units.

Background

Data envelopment analysis was first described in a landmark paper by Charnes et al.

(1978), and has since experienced extensive development and growth to become a ubiquitous

efficiency measurement method (Seiford 1996). DEA has been used for efficiency measurements

in such industries as health care (e.g. Banker et al. 1986; Ozcan et al. 1992; Kontodimopoulos

and Niakas 2005); insurance (Brockett et al. 1998); agriculture (Coelli 1995; Wadud and White

2000); food processing (Jayanthi et al. 1999); and many others. DEA has been used to measure

the efficiency of engineered products (Bulla et al. 2000) and has been used to guide the selection

of new technologies (Baker and Talluri 1997).

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Of particular interest to our work in analyzing various operational challenges facing

water utilities is related work analyzing units in sectors which similarly experience extensive

regulatory presence and government control. For example, DEA has been used to examine

changes and policies within public school systems (Bessent and Bessent 1980) and to examine

the efficiency impact of government regulatory changes on units with different ownership

models, such as banks (Bhattacharyya et al. 1997). In other relevant studies, researchers have

used DEA to measure the relative efficiency of government-run publicly-owned forest

management districts and to estimate the potential efficiency gains from different organizational

alternatives (Kao and Yang 1992).

DEA has also been used to measure efficiencies of units within the municipal

infrastructure sector. Bosch et al. (2000) used the procedure to measure the efficiency of

municipal waste collection services, finding that services operating within competitive

environments were more efficient than services operating within monopoly environments.

Worthington and Dollery (2001) used the procedure to study the efficiency of 103 municipal

waste collection units, comparing inefficiency drivers between urban and rural units and between

units covering various geographical scales. These investigators estimated that inputs could be

reduced by 65 percent while maintaining the same level of service if best practices were used by

currently inefficient units.

A few DEA studies have in fact been performed on selected aspects of potable water

supply systems. Akosa et al. (1995) reported on the DEA efficiency analysis of ten water and

sewage infrastructures in Ghana, a low income, West African state. Pursuant to funding agency

interests, the projects had six input variables (technical, financial, economic, institutional, social,

and environmental) representing such things as community input, etc., and three output variables

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(reliability, utilization, and convenience) representing various levels of use. Despite the high

ratio of variables measured to units compared, the analysis indicated that only one unit was fully

efficient when all nine input and output variables were considered. Although a limited number of

compared units were compared, the investigators were able to draw relevant inferences regarding

future funding efforts to optimize benefits.

Variants on DEA-measured efficiencies have been used as input to regulatory pricing

structures relevant to the work described here . The British Office of Water Services (OFWAT)

regulates potable water price structures with the goal of balancing inflationary pressures and

efficiency gains using DEA efficiency results as input to price evaluations. Thanassoulis, for

example, has published a series of papers (2000a; 2000b; 2002) on the use of DEA calculated

efficiency measures to guide the pricing structure of private water and wastewater utilities in

Great Britain. In the first of these paper (2000a) a single input of operating expense was

employed and five outputs were considered; i.e., number of connections, length of the mains

with the distribution system, total water deliveries, measured and estimated water deliveries, and

number of pipe bursts. Ten utilities combining potable water and wastewater units and 22

potable-water-only utilities were included in the study, In an earlier related study performed by

OFWAT only the combined utilities (those providing both water and wastewater services) were

used in defining the efficiency frontier, a fact which Thanassoulis in his paper demonstrates was

a potentially a flawed premise because potable-water-only utilities tended to define the efficiency

frontier. Aida et al. (1998) also performed water utility measurements using DEA to compare

regional water utilities utilities, but did not evaluate the effects of ownership type. Lambert et al.

(1993) used DEA to compare ownership type, but limited their study to public versus private

utilities. Using a single output variable measuring total water production and four input variables

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measuring annual labor use, total energy use, financial value of material inputs, and total value of

capital, Lambert et al. concluded that public utilities were more efficient overall. Anwandter and

Ozuna (2002) concluded that neither decentralization nor the presence of an independent

regulator provided any benefit in the efficiency of Mexican water utilities, and concluded that

competition might have had a greater role in increasing efficiency.

None of the previous studies cited (Lambert et al. 1993; Aida et al. 1998; Thanassoulis

2000a) used non-discretionary type variables for connections, network length, or water delivery,

thus tacitly assuming that the utility had some measure of control over these variables. The

current study builds on these previous studies by using non-discretionary variable types for

variables that are not controllable by the utilities, and by efficiency comparisons of utilities based

on different water sources.

Study focus

Three main objectives underlie the study reported here. The first objective was to

compare the relative efficiencies of different water utility ownership types calculated using

different measurement variables. Three main water utility ownership types were considered;

public utilities owned by local or regional government, private not-for-profit utilities operated by

non-governmental agencies, and private for-profit utilities operated by private enterprise.

Ancillary water utilities, those utilities run as a side operation by a larger concern, were not

evaluated because of their limited financial independence.

The second objective was to compare the efficiencies of groundwater source utilities to

those of surface-water source utilities using various measurement variables. Although there is

clearly a geographic constraint limiting unbounded selection of water source, unbiased efficiency

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data could be important for evaluation of future water resources and policy regarding

development.

The final objective of this paper is to discuss variable selection by presenting a brief

analysis of the measurement discernment of additional variables. In this section, we assessed

differences in efficiency measurements for decision-making units analyzed with increasingly

discrete measurements of output components. A detailed set of variables can discern a finer

resolution of the efficiency measurement than can a sparse set of variables. However, a detailed

set of variables also can artificially inflate the apparent efficiency of the decision-making units

and can result in an incurred cost due to the need to measure each variable.

A series of DEA trials, each with unique input and output variables, were performed to

identify variables significant to the efficiency measurement of each utility type. US EPA

Community Water System Survey Data (EPA, 2002) was used as input into a DEA model to

determine the relative efficiencies of water utilities. Comparisons between utility types were

checked using the Wilcoxon-Mann-Whitney comparison of ranked efficiency measurements.

Two comparisons were performed using the efficiency data obtained from each trial. The first

comparison examined efficiency differences between water utility categories of different

ownership type and water source. Three main utility ownership types are represented by the EPA

Survey Data: public, private not-for-profit, and private for-profit, while water source was either

ground water or surface water. Efficiency measurements varied depending on selection of input

and output variables, but major trends and variables having a significant influence on efficiency

rankings were identified. The second comparison was an inter-ownership evaluation of utility

efficiency within each utility category type using different selections of input and output

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variables. The results of this evaluation were then used to identify significant variables for each

utility category .

Background of data envelopment analysis.

DEA provides a numerical non-arbitrary score of efficiency that can be employed to

improve utility operations. Efficiency rankings can be used to guide utilities to improve

operational efficiencies by providing operational targets and to identify best practices at highly

efficient utilities. The DEA approach can also be used to identify treatment utilities that are

efficient under their particular environmental conditions but which might not be considered

efficient using traditional metrics, e.g. expenditure and treatment volume. The DEA procedure

requires numerical measurement data for all appropriate input and output variables. Each utility

is evaluated with respect to peer utilities using unique sets of measurement variables. The DEA

approach defines an efficiency frontier consisting of all fully efficient utilities, and an efficiency

score is calculated for all non-efficient utilities based on their relative distance from the

efficiency frontier.

The efficiency score is a non-arbitrary value based on the relative amount of inputs and

outputs respectively used and produced by each utility. The DEA procedure can be either input

or output oriented. An input oriented DEA model assigns the most efficient DMUs an efficiency

score of one, and assigns the less efficient DMUs an efficiency score between one and zero

representing the fraction of their original input they could use to still produce as much output as

their peer DMUs if they were as efficient as the most efficient DMUs. An output oriented DEA

model assigns the most efficient DMUs an efficiency score of one and assigns all of the other

DMUs efficiency scores greater than one representing the fraction increase in output they could

achieve with the same input if they were as efficient as the most efficient DMUs.

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Mathematically, the DEA analysis is performed by optimizing a series of linear programming

equations by varying the relative weights of the measurement variables. Additional background

and methodology can be found in Cooper et al. (2000).

Data source and method of analysis

This efficiency analysis was performed using an input-oriented non-discretionary (non-

controllable) output approach. This approach was dictated by the fundamental environment of

utility service requirements. Water utilities are constrained to fulfill customer requirements. They

do not have the option, for instance, to reduce the number of connections within their distribution

system. Since it is not reasonable to quantify water utility efficiency based on improving output

for a given input, the input-oriented approach was selected.

In some cases it was not clear whether a variable is an input or an output parameter. In

these cases, it was considered an output variable if an increase in its value required more

efficient management ability in order to maintain all other variables constant. For instance, if two

systems were the same in all aspects except total number of connections, the system having

greater connections must be more efficient.

Data acquisition and compilation

The data used in this analysis was obtained from the US EPA Community Water System

Survey Data (EPA, 2002). Due to blanks entries and the presence of illogical data a significant

amount of review was performed to obtain a suitable data set. Water treatment systems were

removed from the set of DMUs when relevant data was missing or nonsensical. For example,

systems which had either zero water delivery reported or which left this field blank were

removed from the analysis.

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In all cases, DMUs with data which were not obviously correctable were deleted from the

analysis, even if other components of the specific DMU contained data which might have been

useful. The result of removing such DMUs is that the DEA analysis might produce a

conservative estimate of the efficiency frontier. All water systems with non-water revenues were

removed from the analysis. Almost uniformly, systems which had non-water revenue present did

not report an average residential bill, indicating that their production of water was an ancillary

activity. Water quality data was not available and thus was not used as an efficiency ranking.

The final set of 714 utilities was comprised of 549 public, 96 private not-for-profit, and

62 private for-profit utilities, with 7 utilities either not reporting ownership information or were

reported as ancillary operations without clear ownership structure. The 714 utilities were

comprised of 389 utilities that used a ground water source and 325 utilities which used a surface

water source.

The DEA analysis was performed using DEA-Solver Pro, an Excel add-in (Saitech, Inc.,

2004) on a Dell Inspiron 5000.

Utility Type Efficiency Comparison: Ownership and Water Source

The water utilities were analyzed for efficiency differences based on ownership type and

water source. The three ownership types, public, private not-for-profit, and private for-profit, and

the two water sources, ground and surface, had their efficiencies calculated with DEA using

several variable sets. The influence of each variable set on the efficiency ranking was then

determined by comparing the relative efficiency of the utilities within each utility type to the

relative efficiency of the utilities within the other utility types. Comparisons between utility types

were checked using the Wilcoxon-Mann-Whitney (WMW) ranked-sum comparison of the

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efficiency measurements. The WMW comparison was used because the underlying distribution

of DEA efficiency measurements is unknown and thus a non-parametric statistic was required.

Because we used the WMW rank-sum test to compare the efficiencies of the two

populations, the negative t-statistic means that we can claim the first population was generally

more efficient than the second population, while a positive t-statistic means that we can claim the

first population was generally less efficient than the second population. The significance level of

this claim is calculated from the t-statistic using the inverse of the standard normal distribution.

Method of Analysis

The utilities were analyzed with DEA using thirty eight different sets of output variables,

as shown along the right side of Figure 1 – Public Versus Private Not-For-Profit. The three other

comparisons also had figures generated for analysis but were not included due to space

limitations. The output variables were selected from four main categories: age and length of

distribution system and various combinations of connections and treatment volume. The age and

length categories were the average age of the distribution system, and the reported length of the

distribution system, respectively. For connections, the categories were total number of

connections (shown as “total” on the figures), a partial separation into residential and non-

residential connections (shown as “res/non-res” on the figures), and then a complete separation

into residential, industrial/commercial, agriculture, and other connections (shown as “RCAO” on

the figures). For volume, the categories were total flow (shown as “total” on the figures), a

partial separation into residential and non-residential flow (shown as “res/non-res” on the

figures), and then a complete separation into residential, industrial/commercial, agriculture,

unaccounted for water loss, and other flow demands (shown as “RCAOU” on the figures). Each

DEA efficiency analysis was performed using the entire combined set of 714 utilities of all

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ownership categories and used the described selection of variables to calculate an efficiency

score for each utility. For each efficiency analysis, the input variables were annual expenses and

average 5-year capital investments.

After the DEA efficiency analysis was performed for the combined set of ownership

categories, the WMW comparison t-statistic was calculated between the utilities of each of the

three ownership sub-categories: private not-for-profit versus private for-profit; private for-profit

versus public; and public versus private not-for-profit, and the two water source categories,

ground water versus surface water. In order to perform each WMW comparison, the efficiency

data for the combined set of utilities was separated into the relevant sub-categories, and the

efficiency data for the utilities in one of the sub-categories was then compared against the

efficiency data for the utilities in another one of the subcategories. A t-statistic for the

comparison was then calculated.

Efficiency Comparison Results

Figure 1 shows the results of efficiency comparison for the public versus private not-for-

profit ownership categories. Figures for the other comparisons: private not-for-profit versus

private for-profit, private for-profit versus public, and ground water source versus surface water

source are not shown. The WMW t-statistic for each set of variables was plotted from largest to

smallest, with a description of the variables used for each efficiency analysis shown next to each

t-statistic plot. The description of the four categories of variables used in the DEA analysis is

shown as a series of columns along the right side of the plot.

Public Utilities Versus Private Not-for-profit Utilities. The ranked efficiencies of

public utilities versus the private not-for-profit utilities generally showed a moderate yet

statistically significant advantage of the public utilities over the private not-for-profit utilities for

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the majority of cases, as shown in Fig. 1. Twelve of the variable sets used for efficiency analysis

indicated that private not-for-profit utilities were more efficient, while twenty-six of the variable

sets used for efficiency analysis indicated that the public utilities were more efficient.

Only two of the variable sets used for efficiency analysis that showed greater efficiency

from the private not-for-profit utilities had more than 90 percent significance. Similar to the

previous comparison of private for-profit utilities versus public utilities, the variable sets which

showed the least public utility efficiency were either distribution network length and average

pipeline age, or length and age combined with total water volume. Both showed a statistically

significant (greater than 90 percent) efficiency advantage of the private not-for-profit utilities

over the public utilities. It should be noted that the variable set of distribution network length and

average pipeline age used to compare the public utilities against the private not-for-profit utilities

resulted in the most significant t-statistic of any of the variable sets used for any of the utility

comparisons, with essentially 100 percent significance.

In addition, the top eight variable sets showing the greatest efficiency of the private not-

for-profit utilities all used distribution network length and average pipeline age as measurement

variables. In contrast, none of the top eight variable sets which indicated the greatest efficiency

of the public utilities used average network length as a measurement variable and only three of

the eight used average distribution network age as a measurement variable.

Eleven of the variable sets used for efficiency analysis which showed greater efficiency

from the public utilities had more than 90 percent significance. All but one of these variable sets

measured some combination of both network connections and water volume delivery. More than

half of these cases used the most discrete measurement possible of both network connections and

water volume delivery in the form of either residential, industrial/commercial, agriculture, and

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other connections, or residential, industrial/commercial, agriculture, unaccounted for water loss,

and other flow demands. By comparison, none of the variable sets which showed greater

efficiency from the private not-for-profit utilities used either connection data or water volume

data at this level of detail. Thus, it appears that public water utilities are more efficient than

private not-for-profit utilities at serving a variety of customer types, and are not as efficient at

serving a single customer type.

Private Not-for-Profit Utilities Versus Private For-Profit Utilities. The ranked

efficiencies of private not-for-profit utilities versus the private for-profit utilities showed a

moderate yet statistically significant advantage of the private not-for-profit utilities over the

private for-profit utilities for almost all cases. Only six sets of output variables showed greater

efficiency of the private for-profit utilities, with the largest difference in efficiency being when

using residential and non-residential connections and residential and nonresidential treatment

volume as output variables. The comparison when using the most pro-private for-profit utility

variable set had a t-statistic of 0.39, indicating only a 30.6 percent chance of true difference

between utilities measured using these variables, which is not a statistically significant

difference. None of the variable sets which indicated that private for-profit utilities were more

efficient used distribution system length as an output variable. This implies that the systems with

the greatest distribution system length were the private not-for-profit systems and that they

would use less input, in the form of capital investment and yearly expenses, to manage a

distribution system of any particular length.

By comparison, 32 variable sets showed that the private not-for-profit utilities are more

efficient than the private for-profit water utilities. The largest t-statistic showing greater private

not-for-profit efficiency was -4.40, and resulted from using distribution network length and

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average pipeline age as output variables. This result is fairly uninteresting since water utilities

are typically valued by the quantity of water they produce, measured by flow volume, and the

number of customers they serve, measured by number of connections. However, the next highest

t-statistic, -2.12, resulted from using distribution network length, average pipeline age, and total

treatment volume as output variables, and was statistically significant with a 96.6 percent

probability of difference. Three more comparisons also demonstrated that the private not-for-

profit utilities are more efficient than the private for-profit water utilities with greater than 90

percent significance.

Private For-Profit Utilities Versus Public Utilities. The ranked efficiencies of private

for-profit utilities versus public utilities showed a strong, statistically significant advantage of the

public utilities over the private for-profit utilities for all but two cases. The only variable sets

used for efficiency analysis which resulted in private for-profit utilities being more efficient than

public utilities were when using distribution network length and average pipeline age, either

alone or combined with total water volume, with 99.6 and 67.6 percent significance respectively.

Every variable set which used some measure of connections within the distribution system to

measure efficiency resulted in the public utilities being evaluated as more efficient than the

private for-profit utilities. There were 25 variable sets used to measure efficiency which

indicated greater efficiency of public utilities over private for-profit utilities with greater then 90

percent significance. None of the top ten variable sets which showed the greatest public utility

efficiency used distribution system length as a measurement variable. However, 13 of the data

sets which used distribution system length still showed greater public utility efficiency with

significance greater than 90 percent. It appears that using distribution system length as a

measurement variable tends to moderately decrease the efficiency of private for-profit water

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utilities compared to public water utilities, but the effect isn’t enough to completely overcome

the efficiency effects of the rest of the variables. The use of completely separated connection or

flow variables tended to push the efficiencies towards the public utilities.

Ground -Water Versus Surface -Water Sources. The ranked efficiencies of ground

water utilities versus surface water utilities generally showed a slight, yet statistically significant

advantage of the ground water utilities over the surface water utilities for the majority of cases,

as shown in Fig. 4. Overall, there were twelve variable sets that demonstrated an efficiency

advantage to surface water utilities while there were twenty-six variables sets that showed

efficiency advantage to ground water utilities. However, eight of the variable sets that showed a

surface water utility advantage and nine of the variable sets that showed a ground water utility

advantage had less than 50 percent significance, indicating that there was a greater than 50-50

chance that these data sets were identical.

Only one variable set used for efficiency measurement that demonstrated an efficiency

advantage to surface water utilities had greater than 90 percent significance, while nine variables

sets that showed efficiency advantage to ground water utilities had greater than 90 percent

significance.

The only statistically significant variable set which indicated surface water utility

efficiency advantage was when total water delivery was used as the sole measurement variable.

Adding additional measurement variables which would account for either distribution system

length, or numbers or types of customers, all caused a reduction in surface water utility

efficiency and an increase in ground water utility efficiency. This implies that surface water

utilities are most efficient when they have a few, high-volume, customers such as irrigation or

large industrial demands.

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However, another data trend indicates potentially contrasting results, and that is when the

water delivery category was fully broken down into the component variables of residential,

commercial/industrial, agricultural, other, and unaccounted for water deliveries. DEA efficiency

measurements which used these variables tended to show a moderate trend towards ground water

utilities compared to surface water utilities, with seven of the measurements indicating the

superior efficiency of surface water utilities, and only three indicting the efficiency of ground

water utilities. This result does not indicate a strong trend, since none of the results were at high

levels of significance, but does indicate a mild trend towards the efficiency of surface water

utilities over ground water utilities when delivering a lot of water to a wide variety of customers.

Variable Selection and Additional Information

Since tracking and maintaining information variables entails a cost, it is reasonable to

discuss variable selection criteria. The essential question is: What variables reasonably add new

information? As part of this study, we briefly investigated the additional information provided as

a result of additional measurement variables by using an informational surrogate which measured

the informational spread in efficiency ranking obtained when using additional variables.

Informational spread γ was defined as

( )∑ =

−− =

iiii

n baba

*γ (1)

where a and b are the utility rankings using two sets of measurement variables A and B. Spread

approximates the difference in informational content measured by two variable sets because it

measures the absolute difference in efficiency ranking due to the change in measurement

variables. Large changes in efficiency ranking between variable sets imply a large informational

difference between the variable sets and would result in a large calculated spread.

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Correspondingly, small or random changes in efficiency ranking between variable sets imply a

small informational difference between the variable sets and would result in a small calculated

spread.

For this investigation, the information spread between different measurement variables

was determined for a series of variable sets that were kept constant for all but one measurement

category. Each variable set used for efficiency measurement consisted of distribution network

length, average pipeline age, and variables from both the connection and volume categories. All

the variables measuring length, age, and one of the two remaining categories were kept constant,

and the base efficiency scores for the utilities were determined by excluding the remaining

measurement category. The remaining variable category then was increased to a single value

representing the total value for that category, then to a partial separation into the residential and

non-residential values for that category, and then to a complete separation for that category. The

informational spread was calculated between the basic case, which did not include the varying

category, and between the more advanced cases, which did include the varying category. The

informational spread was plotted against the number of new variables added for each case, as

shown in Fig. 2. The legend shows the number of variables in the basic case, while the x-axis

shows the number of additional variables added for each analysis. There is clearly a trend

towards marginal returns as the variable categories are broken down into more discrete

measurement. The only outlier is the line representing the increase in volume measurement when

length, age, and RCAO connections were kept constant. This plot reveals the decreasing

marginal return on information gained from using a more discrete measurement of any particular

data category.

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Summary

The work reported here reveals a distinct efficiency advantage of public utilities over

private for-profit utilities. Every analysis that used some measure of number of connections

within a distribution system resulted in public utilities being evaluated as more efficient than

private for-profit utilities. In comparing public utilities to private not-for-profit utilities, a much

more moderate yet statistically significant efficiency advantage was evident for the former in the

majority of cases studied. None of the variable set cases that showed greater efficiency for

private not-for-profit utilities used either connection data or water volume data in full detail. The

results also indicate that while public water utilities are more efficient than private not-for-profit

utilities for serving a variety of customer types, the latter are more efficient for serving a single

customer type. Private not-for-profit utilities were found to have a statistically significant

efficiency advantage over private for-profit utilities for almost all selections of management

variables, particularly for managing larger distribution networks.

Comparisons of ground water source utilities versus surface water source utilities

generally showed a slight, yet statistically significant, efficiency advantage for the former in the

majority of cases studied. Utilities employing surface-water sources are most efficient when they

serve a few, high-volume demand consumers, such as irrigation or large industrial systems, while

ground-water source utilities tend to be more efficient when delivering large volumes of water to

a wide variety of different types of consumers..

Finally, informational spread behavior as a function of measurement variables employed

indicates decreasing marginal returns on information gained from using more discrete

measurements of any particular data category.

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Acknowledgements

The authors wish to acknowledge Lawrence M. Seiford, Chairman of the Department of

Industrial and Operations Engineering, Warren Sutton, doctoral candidate in the Department of

Industrial and Operations Engineering, and Jill Ostrowski, undergraduate in the Department of

Civil and Environmental Engineering, for their critical appraisal and evaluation of the

manuscript.

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and sanitation projects in Ghana.” Journal of Infrastructure Engineering. 1(1), 56-65.

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MICUSP Version 1.0 - IOE.G3.01.1 - Industrial & Operations Engineering - Third year Graduate - Male - Native Speaker - Research Paper 22

Figure 1. Public versus private, not-for-profit

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

length age ... ...

length age ... total

length age total total

length age ... res/non-res

length age total ...

length age res/non-res ...

length age res/non-res total

length age total res/non-res

.... ... total total

length ... res/non-res total

length ... res/non-res res/non-res

length age res/non-res res/non-res

length age RCAO ...

length age RCAO total

.... ... ... total

length age total RCAOU

length ... RCAO total

.... age RCAO total

length age res/non-res RCAOU

length age RCAO res/non-res

length ... res/non-res RCAOU

.... age res/non-res total

length ... RCAO res/non-res

.... age total total

length age RCAO RCAOU

.... age res/non-res res/non-res

.... ... res/non-res total

length age ... RCAOU

.... ... res/non-res res/non-res

length ... RCAO RCAOU

.... ... total total

.... ... RCAO total

.... age RCAO res/non-res

.... age res/non-res RCAOU

.... ... RCAO res/non-res

.... age RCAO RCAOU

.... ... res/non-res RCAOU

.... ... RCAO RCAOU

Normalized t-statistic

P riv

at e,

N on

-p ro

fit m

or e

ef fic

ie nt

P ub

lic m

or e

ef fic

ie nt

Length Age Connections Volume

10.59

MICUSP Version 1.0 - IOE.G3.01.1 - Industrial & Operations Engineering - Third year Graduate - Male - Native Speaker - Research Paper 23

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 1 2 3 4 5 6 Number of additional variables

S pr

ea d,

d im

en si

on le

7 6 4 4 3 3

Figure 2. Marginal return of increasing information from additional measurement variables

MICUSP Version 1.0 - IOE.G3.01.1 - Industrial & Operations Engineering - Third year Graduate - Male - Native Speaker - Research Paper 24

Table 1. Classification of Input and Output Variables Types Category Variable selections used

(a) Input

Financial Total expenses, Capital improvements

(b) Output, non-discretionary Pipeline • Length of mains, total

• Average pipe age

Connections • Total connections • Residential, Non-residential • Residential, Commercial/Industrial,

Agricultural, Other

Delivery volume • Total water delivery • Treated water, Untreated water • Residential, Total nonresidential • Residential, Commercial/Industrial,

Agricultural, Other nonresidential, Unaccounted for

MICUSP Version 1.0 - IOE.G3.01.1 - Industrial & Operations Engineering - Third year Graduate - Male - Native Speaker - Research Paper 25