improved baseline productivity analysis technique

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Improved Baseline Productivity Analysis TechniqueChien-Liang Lin, Ph.D.1; and Hong-Ming Huang, Ph.D.2

Abstract: Previous studies have aimed to develop effective methods to derive baseline productivity �BP� for labor-intensive activities inconstruction sites. However, there are two different definitions of BPs: one is defined as a performance benchmark of best practice and theother as a standard reflecting a contractor’s normal operating performance. It is necessary to clarify the difference between the twodefinitions and their corresponding BPs. This research introduces data envelopment analysis �DEA� as a new method for deriving BP andcompares DEA with the other four BP deriving methods. DEA is concluded as the best method in terms of objectivity, effectiveness, andconsistency to find BP that represents the best performance a contractor can possibly achieve. With the capability of deriving productivi-ties of multi-input and multi-output activities, the proposed DEA has raised the scale of labor productivity from the level of single factorproductivity to total factor productivity which will help construction researchers and managers to evaluate performances of interests in amuch more effective way.

DOI: 10.1061/�ASCE�CO.1943-7862.0000129

CE Database subject headings: Construction industry; Data analysis; Productivity; Analytical techniques.

Author keywords: Construction industry; Data envelopment analysis; Performance benchmark; Labor productivity; Baseline.

Introduction

Baseline productivity �BP� has been applied in the constructionindustry to assess productivity loss or to serve as a performancebenchmark of best practice. BP can be calculated by variousmethods such as the measured mile analysis �Zink 1986� or Tho-mas’s BP methodology �Thomas and Zavrski 1999�. When BP isused to resolve disputes in productivity loss claims, the terms andconditions specified in the process of mediation or litigation needto be clearly defined. However, there have been different defini-tions and derivations of BP.

Some researchers have defined BP as the best performance acontractor could achieve on a particular project �Thomas et al.1999; Thomas and Zavrski 1999; Thomas and Sanvido 2000;Choi and Minchin 2006�; though others regard BP as a standardreflecting a contractor’s normal operating performance �Gulezianand Samelian 2003�. These two BP definitions are obviously dif-ferent.

As a result, applications of BP could be twofold, one is toapply BP as the performance benchmark for organizations to pur-sue best practices; the other is to use BP as a normal standard forearly detection of abnormal processes or products which deviatefrom the recognized normal conditions. There is a need to furtherexplore the related BP deriving methodologies and applicationsbefore they can be effectively practiced in the construction indus-try.

1Assistant Professor, Dept. of Construction Engineering, NationalKaohsiung First Univ. of Science and Technology, 2 Jhuo-yue Rd. Nan-zih, Kaohsiung 811, Taiwan �corresponding author�. E-mail:[email protected]

2Senior Project Manager, United Steel Engineering and ConstructionCorp., 1 Zhong-gang Rd., Shiao-gang, Kaohsiung 812, Taiwan.

Note. This manuscript was submitted on November 3, 2008; approvedon July 16, 2009; published online on August 10, 2009. Discussion pe-riod open until August 1, 2010; separate discussions must be submittedfor individual papers. This paper is part of the Journal of ConstructionEngineering and Management, Vol. 136, No. 3, March 1, 2010.
©ASCE, ISSN 0733-9364/2010/3-367–376/$25.00.
JOURNAL OF CONSTRUCTION

J. Constr. Eng. Manage. 2

Data envelopment analysis �DEA� has been commonly andsuccessfully used in evaluating the relative efficiencies of produc-ers, but has not been applied in assessing labor productivity onthe construction site. The objectives of this paper are to �1� dem-onstrate the application of DEA to derive BP; and �2� compareDEA with the other methodologies to derive BP so they can bebetter understood and securely applied in the construction indus-try.

Previous Research

Different methodologies for deriving BP have been developed inprevious studies �Zink 1986; Thomas and Zavrski 1999; Gulezianand Samelian 2003; Ibbs and Liu 2005�. In addition to the mea-sured mile analysis �Zink 1986� and Thomas’s BP method �Tho-mas and Zavrski 1999�, Gulezian and Samelian �2003� proposed acontrol chart method to derive BP. Later, Ibbs and Liu �2005�developed a K-means clustering method as an improved mea-sured mile method, and compared the K-means clustering methodwith Zink’s measured mile and Thomas’s BP methodologies. Forthe completeness of this paper, these BP methods will be brieflyintroduced below.

Measured Mile Analysis

The basic approach of the measured mile is to identify an unim-pacted period of construction activity, linearly extrapolate the cu-mulative unimpacted hours to the end of an impacted period, anduses the difference between the projected unimpacted hours andthe actual cumulative hours as the amount of damage hours �Zink1986�. Gulezian and Samelian �2003� argued that the cumulativework hour �wh� process of the measured mile tends to mask varia-tions of daily productivity and cause difficulty in identifyingcausal relationships between productivity shown and correspond-ing managerial problems on site. Ibbs and Liu �2005� also cited
that the unimpacted period and corresponding daily productivity
ENGINEERING AND MANAGEMENT © ASCE / MARCH 2010 / 367

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data cannot be determined objectively, and some projects may noteven have the measured mile period due to the existence of per-vasive disruptions.

Thomas’s BP Method

Thomas and Zavrski �1999� proposed the baseline calculationmethod in the following steps:1. Determine the number of workdays that comprise 10% of the

total workdays;2. Round this number to the next highest odd number; this

number should not be less than 5. This number n defines thesize of �number of days in� the baseline subset;

3. The contents of the baseline subset are selected as the nworkdays that have the highest daily production or output;

4. Note of the daily productivity for these days; and5. The BP is the median of the daily productivity values in the

baseline subset.This method is criticized mostly because the selection of the

10% of the total workday to represent the baseline set is highlysubjective.

Control Chart Method

To distinguish the impacted and unimpacted productivities, Gule-zian and Samelian �2003� applied an individuals control chart forthe daily productivity values to determine a baseline estimate ofcontractor productivity under normal operating conditions. Thismethodology successively recalculates center lines and controllimits to eliminate the unusual or impacted productivity pointsuntil no points fall outside the control limits. The value of thecenter line is the arithmetic mean of the productivity values; andthe control limits are conventionally plotted as three-standard de-viations of the metric from the center line, and calculated as

Center line � 3 standard deviation �1�

However, the control chart is not found through a mathemati-cal syllogism �Neave and Wheeler 1996�, and the choice of themultiplier 3 in Eq. �1� is based simply on empirical evidence thatit works �Shewhart 1931�. In other words, the choice of the three-standard deviation for upper and lower control limits to classifyabnormal products is still subjective.

K-Means Clustering Method

Ibbs and Liu �2005� developed the K-means clustering method toestimate the BP and compared their K-means clustering methodwith Thomas’s BP method and measured mile analysis. The cen-tral idea of the K-means clustering method is to separate theproductivity data into two groups, “unimpacted” or “impacted,”by iteratively evaluating the Euclidean distance among productiv-ity data. This K-means clustering algorithm is objective in termsof the impartial calculation procedure and determination of thesize and choice of the baseline set, which were subjectively pre-defined as 10% of the total workdays by Thomas and Zavrski�1999�.

Comparisons and analysis of the related BP methods weresummarized by Ibbs and Liu �2005�, who concluded K-meansclustering method is the best choice for productivity loss calcula-tion because of its objectivity and neutrality. However problemsof the K-means clustering method have been discovered and will
be shown in the case study of this study.
368 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT


Productivity Calculation Method in PreviousResearch

Construction can be modeled as the process converting input tooutput �Sanvido 1988�. Accordingly, construction labor produc-tivity is generally defined as the ratio between input and output ina given period which could be an hour, a day, or a year anddefined as the forms of either “input/output” �Thomas and Yiak-oumis 1987� or “output/input” �Sonmez and Rowings 1998�.There is no standardized labor productivity definition establishedin the construction industry.

In this paper, labor productivity is defined as the ratio of workhours to the quantity installed in a period of time. The input isusually man hours spent by the crew working on the activity andthe output quantity of work produced. A crew, however, may becomprised of workers with various levels of skill, and usuallythey work on different subtasks together. For example, the dailyproductivity, input of a steel erection activity is the total manhours consumed by a crew consisting of foreman, skilled workers,and helpers, and the output could be numbers of columns andbeams erected. In other words, an activity usually has multipleinputs and multiple outputs. However, the early studies on pro-ductivity generally account the input whs and output quantityaggregately, respectively.

In order to have a common basis of comparison, all produc-tivity data need to be prepared and calculated by a standard pro-cedure such as the one developed by Thomas and Kramer �1988�before all the BP methods can be performed to derive BPs. Theprinciple of the standard procedure will be briefly explained asfollows.

First, productivities of subtasks of an activity have to be de-rived individually. One way to do this is via a multiple regressionmodel without a constant term �Thomas and Sanvido 2000�. Inthe regression model the daily whs serve as the dependent vari-able and the daily quantities of the subtasks serve as the indepen-dent variables. The calculated model coefficients are the unit ratesfor the independent variables.

Then two relative weighing techniques: �1� rules of credit; and�2� conversion factors, are needed to assign the relative weight ofcontribution to different subtasks and units. These two weighingtechniques are based on the principle of earned value, or whsearned, as follows.

The rules of credit technique is used to account for work thatwas part of a final unit of production �Thomas and Kramer 1988�.For example, in a structural steel erection activity, erecting steel�0.8 wh/piece, 60%�, bolting steel �0.42 wh/piece, 32%�, andtightening steel �0.11 wh/piece, 8%� when combined will makeup the installed structural steel �1.33 wh/piece, 100%� �Thomaset al. 1999�.

Conversion factors are used to convert different units of workinto an equivalent quantity of a base or standard unit �Thomas andNapolitan 1995�. For example, in the structural steel erection ac-tivity, erecting one web joist is equivalent to erecting 0.65 piecesof the structural steel, a standard unit �Thomas et al. 1999�. Insummary, fixed parameters such as productivities and correspond-ing relative productivity weights of each subtask need to be cal-culated before the BP can be estimated for any of theaforementioned BP methods.

New Methodology—Data Envelopment Analysis

DEA is a nonparametric method for measuring the relative effi-
ciency of multiple input-multiple output decision making units
© ASCE / MARCH 2010

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�DMUs� based on available observations. A DMU could be aprofit or nonprofit agent or organization and is regarded as theentity responsible for converting inputs into outputs. DEA derivesa line or surface called the frontier that follows the peak perform-ers and envelops the remainder. The frontier connects all the“relatively best” DMUs in the observed population and thus rep-resents the theoretically possible maximum production that aDMU can achieve in any level of inputs.

Charnes, Cooper, and Rhodes �CCR� extended Farrell’s work�Farrell 1957� and developed the original DEA model �Charnes etal. 1978�. This CCR model was applicable to problems of con-stant returns-to-scale, and the derived CCR efficiency of eachDMU combines technical and scale efficiency �SE� �Banker et al.1984�. Technical efficiency �TE� means that producers are doingthe best job to transform resources into products or services with-out waste. SE represents that producers are working at the mostproductive scale size �MPSS� �Banker et al.1984�.

Later, based on the CCR model, Banker, Charnes, and Cooper�BCC� developed the BCC method to resolve problems of vari-able returns-to-scale. This BCC method is capable of separatingtechnical and SE from the efficiency derived by the CCR model�Banker et al. 1984�. There are other types of DEA models; butonly the CCR and BCC models will be discussed in this paper.

Recently, there have been a few researches applying DEA inthe management domain of civil engineering. Xue et al. �2008�measured the productivity of China’s construction industry byDEA-based Malmquist productivity indices. Cariaga et al. �2007�presented a hybrid framework that incorporates DEA with valueanalysis and quality function deployment for construction projectsto evaluate design alternatives. El-Mashaleh et al. �2006, 2007�used DEA to evaluate construction firm performance. McCabe etal. �2005� developed an enhanced contractor prequalificationmodel using DEA to determine best contractors. None has appliedDEA to study labor-intensive productivity on the constructionsite.

Construction BP and DEA

A construction project usually consists of many different activitiesand progresses with different work contents performed by differ-ent crews daily. Construction process is recognized and modeledas an input-output process �Sanvido 1988; Thomas et al. 1990;Thomas and Sakarcan 1994�. But it is very difficult to estimatethe production function of an activity performed by a crew notonly because its performance is always influenced by complexfactors, such as variable work contents, weather, locations, inter-ferences from the other activities, and formation of crews; but

Table 1. Case with One Input and Two Outputs

Work day 1 2 3 4

Wh �x� 48 36 48 48

Column �y1� 77 19 0 0

Beam �y2� 0 14 39 26

Table 2. Transformed Case with One Input and Two Outputs

Work day 1 2 3a 4

y1 /x 1.6 0.5 0.0 0.0

y2 /x 0.0 0.4 0.8 0.5a
Indicates work days classified in baseline subset by DEA.


also because the activity will usually produce different daily com-binations of various outputs. Thus output performance will inevi-tably vary for each workday due to the aforementioned inherentcharacteristics of construction work. Under the criteria of speci-fied quality, a contractor will always strive to produce as much aspossible and compete with what it has previously accomplisheddaily. Accordingly if the objective is to estimate the best perfor-mance a contractor could possibly achieve on a particular project,a crew’s performance in each workday can be deemed as theperformance of a unique DMU.

Graphical DEA Example

When DEA is applied, it is suggested that the minimum numberof DMU should be three times the number of variables �Charneset al. 1981�. For simplicity, productivity data of 10 workdaysfrom a steel erection project �Project ID 9701� are excerpted as asimple example in Table 1 to illustrate the DEA-calculated per-formance of a steel erection crew, each with one input and twooutputs. The input �x� is the number of whs in each day. Outputs1 �y1� and 2 �y2� are weights �tons� of columns and beams erectedin each workday, respectively. To obtain a unitized efficient fron-tier and illustrate it graphically, y1 and y2 in Table 1 are dividedby x, respectively, and thus Table 1 is transformed into Table 2.

Data in Table 2 are plotted and shown as Fig. 1, in which theefficient frontier consists of the lines connecting workdays 3, 6, 8,and 5, all of which are the best performers and have efficiency of1. The production possibility set is the region bounded by the axesand the frontier lines. Workdays 1, 2, 4, 7, 9, and 10 are inefficientsince they are not on the frontier and their efficiencies can beevaluated with reference to the frontier lines. For example, in Fig.1, the relative efficiency of workday 10 is evaluated and repre-sented by O-10/O-A, where O-10 and O-A mean “distance fromzero to point 10,” and “distance from zero to point A,” respec-tively.

CCR Model

DEA starts from using fractional programming �FP� to determinethe relative efficiency of each DMU. For a DMU, efficiency isdefined as the ratio of its output divided by its input. The proce-dure of finding the best performers starts from FP. Analyzing therelative efficiencies of n DMUs becomes solving n sets of FPproblems.

5 6 7 8 9 10

32 56 48 56 56 40

67 23 0 46 0 29

0 42 27 34 29 7

a 6a 7 8a 9 10

1 0.4 0.0 0.8 0.0 0.7

0 0.8 0.6 0.6 0.5 0.2

5

2.0.


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For example, for n DMUs, the relative efficiency of a DMU�DMUi� can be evaluated by solving the following set of FP prob-lems shown in

MaxU · Yi

V · Xi

Subject toU · Y j

V · X j� 1�j = 1, . . . ,n�

U � 0

V � 0 �2�

where U=vector of output weights to be obtained= �u1 ,u2 , . . . ,us�; V=vector of input weights to be obtained= �v1 ,v2 , . . . ,vm�; Xi=input vector of DMUi= �x1i ,x2i , . . . ,ymi�;and Yi=output vector of DMUi= �y1i ,y2i , . . . ,ysi�

Two assumptions of the above Eqs. �2� are: �1� for the objec-tive function �max UYi /VXi�, each of the n DMUs attempts tomaximize its efficiency and �2� to derive the relative perfor-mances of all DMUs, the constraints �inequalities� bound the per-formance of each DMU between 0 and 1. The optimizationprocess will derive each DMU’s optimal input and output weights�represented by the two vectors, U and V, respectively� to maxi-mize its performance.

Since the FP problem tends to have an infinite number ofsolutions, the above Eq. �2� can be replaced as the followingequivalent output-oriented, or maximization, linear programming�LP� problem as shown in

Max U · Yi

Subject to V · Xi = 1

− V · X j + U · Y j � 0 �j = 1, . . . ,n� �3�

Input Oriented CCR Model

It will be more efficient to solve the dual of an original LP prob-

Fig. 1. Performance of a steel erection crew

lem. The above LP can be transformed into a dual which is shown



in Eqs. �4� �Cooper et. al. 2000�. For methods of transforming anoriginal LP to the dual, please refer to Taha �2002�

Min �i

Subject to �i · Xi − X · � � 0

Y · � � Yi

� � 0 �4�

where �i=real variable representing the efficiency of DMUi; Xi

=input vector of DMUi= �x1i ,x2i , . . . ,ymi�; Yi=output vector ofDMUi= �y1i ,y2i , . . . ,ysi�; X=matrix comprising all DMUs’ inputs;Y=matrix comprising all DMUs’ outputs; and �= ��1 ,�2 , . . . ,�n�=nonnegative vector whose elements representthe optimal weights or multipliers for the associated inputs andoutputs of each DMU.

The purpose of the above formulation is now to minimize theinput while retaining the output level. This type of model is calledinput-oriented. As can be seen in Fig. 1, Workday 8 is technicallyefficient because it lies in the frontier and Day 10 is technicallyinefficient. A numerical example of Table 1 will be used to ex-plain the DEA calculation procedure and the meaning of the re-sulting numbers. For example, based on Eq. �4�, the efficiency ofWorkday 8 is evaluated by solving the following dual LP problem

Min �8

Subject to 56�8 − �48�1 + 36�2 + 48�3 + 48�4 + 32�5 + 56�6

+ 48�7 + 56�8 + 56�9 + 40�10� � 0

77�1 + 19�2 + 67�5 + 23�6 + 46�8 + 29�10 � 46

14�2 + 39�3 + 26�4 + 42�6 + 27�7 + 34�8 + 29�9 + 7�10 � 34

�1,�2, . . . ,�10 � 0 �5�

The optimal solution of this problem is �8=1; �8=1; the other�s=0. In the solution, “�8=1” means Workday 8 has a referenceworkday, which is itself, and “�8=1” means the efficiency ofWorkday 8 is 1, which is the largest efficiency value for an input-oriented �min� CCR problem, and it shows Workday 8 has thebest performance.

Similarly, the efficiency of Workday 10 can be evaluated bysolving the following dual problem:

Min �10

Subject to 40�10 − �48�1 + 36�2 + 48�3 + 48�4 + 32�5 + 56�6

+ 48�7 + 56�8 + 56�9 + 40�10� � 0

77�1 + 19�2 + 67�5 + 23�6 + 46�8 + 29�10 � 29

14�2 + 39�3 + 26�4 + 42�6 + 27�7 + 34�8 + 29�9 + 7�10 � 7

�1,�2, . . . ,�10 � 0,�10 free �6�

The optimal solution of this problem is �5=0.291; �8=0.206;�10=0.521; the other �s=0. The above solution means that theoriginal output �29, 7� can possibly be achieved by reducing theinput of Workday 10 from 40 h to its 52.1% �20.84 h�, which isalso equivalent to the combination of 29.1% of Day 5’s and
20.6% of Day 8’s inputs, and can be calculated as follows:

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0.521 � �input of Day 10�

= 0.291 � �input of Day 5� + 0.206 � �input of Day 8�

→ 0.521 � 40 = 20.84 = �0.291 � 32� + �0.206 � 56�

Output Oriented CCR Model

Define �i=1 /�i, and �i=�i /�i for Eqs. �6�, then the minimizationof �i is equivalent to maximization of �i. In terms of the redefinedvariables, the above Min �10 problem now becomes an output-oriented �or max� problem shown as follows:

Max �10

Subject to 48�1 + 36�2 + 48�3 + 48�4 + 32�5 + 56�6 + 48�7

+ 56�8 + 56�9 + 40�10 � 40

77�1 + 19�2 + 67�5 + 23�6 + 46�8 + 29�10 � 29�10

14�2 + 39�3 + 26�4 + 42�6 + 27�7 + 34�8 + 29�9 + 7�10 � 7�10

�1,�2, . . . ,�10 � 0, �10 free �7�

Eqs. �7� can then be generalized as follows:

Max �i

Subject to �X Xi

�Y �iYi

�8�

where �i=real variable representing the efficiency of DMUi; X=matrix comprising all DMU inputs; Y=matrix comprising allDMU outputs; Xi=input vector of DMUi= �x1i ,x2i , . . . ,ymi�; andYi=output vector of DMUi= �y1i ,y2i , . . . ,ysi�; and �= ��1 ,�2 , . . . ,�n�=non-negative vector whose elements representthe optimal weights or multipliers for the associated inputs andoutputs of the corresponding DMUs.

The purpose of Eqs. �7� and �8� is to maximize the outputwhile retaining the input level. This type of model is calledoutput-oriented. The optimal solution of Eqs. �7� are �5=0.559;�8=0.395; �10=1.918; the other �s=0. This solution means thatthe reference set for Workday 10 is Workdays 5 and 8, which arethe best performers; and the performance of a hypothetical refer-ence workday �Point A shown in Fig. 1� can be constructed bycombining 55.9% of the output of Workday 5 with the 39.5% ofthe output of Workday 8. In other words, under the original inputof 40 whs, Workday 10’s output combination is �y1 ,y2�= �29,7�.However, under the same input whs �40 h�, Workday 10’s outputcombination could possibly be augmented by a factor of 1.918, upto �55.6, 13.4�, which is also the sum of 55.9% of Day 5’s outputand 39.5% of Day 8’s output and can be mathematically shown asfollows:

�Output of Day 10�

= 0.559 � �Output of Day 5� + 0.395

� �Output of Day 8�

→ �Output of day 10�

= �0.559 � 67,0� + �0.395 � 46,0.395 � 34� = �55.6,13.4�

= �1.918 � 29,1.918 � 7�



CCR Efficiency

So far, however, the efficiency measure described above does notnecessarily satisfy the so called Pareto-Koopmans Efficiencywhich is defined as “a DMU is fully efficient if and only if it isnot possible to improve any input or output without worseningsome other input or output” �Cooper et al. 2000�. To fulfill thePareto-Koopmans Efficiency, penalties in terms of slacks, outputexcesses and input shortfalls, are added in the formulations �Char-nes at al. 1978�, and the Eqs. �8� are improved as the CCR effi-ciency ��CCR� shown as

�CCR = Max �i + �s+ + �s−

Subject to �X + s− = Xi

�Y − s+ = �iYi

�9�

where s+=output excesses vector; s−=input shortfalls vector; and�=infinitesimally small positive number to be determined by theresearcher.

Thus a DMU will be rated as fully CCR-efficient only whenthe new objective, �CCR �=�+�s++�s−�, equals one and all theslacks are equal to zero at the optimal solution. Otherwise CCRefficiency will be less than unity even when �i equals one.

BCC and SE

Based on the CCR model, BCC assume the convex combinationof the observed DMUs as the production possibility set and de-veloped the BCC model which is capable of resolving problemsof variable returns-to-scale �Banker et al. 1984�. The BCC modeland efficiency score ��BCC� are shown as follows:

�BCC = Max �i + �s+ + �s−

Subject to �X + s− = Xi

�Y − s+ = �iYi

e� = 1

� � 0

�10�

where e=row vector with all elements equal to 1.Inefficiency of a DMU might have two sources, TE related

problems or SE related problems. TE related problems are causedby the inefficient operation of the DMU itself. SE related prob-lems arise from the disadvantageous condition under which theDMU is operating. These two efficiency scores can be separatedby considering CCR and BCC efficiencies simultaneously�Banker et al. 1984�.

The CCR model assumes the constant returns-to-scale produc-tion possibility set, i.e., the linear scaling of all observed DMUsand their nonnegative linear combinations are possible and hencethe CCR efficiency ��CCR� is called the “overall technical andscale efficiency” �Banker et al. 1984�, or simply the “global tech-nical efficiency” �Charnes et al. 1978, 1981�. On the other hand,the BCC model assumes the convex combinations of the observedDMUs as the production possibility set and the BCC efficiency��BCC� is called “pure technical efficiency.” The SE is measuredby the ratio �CCR /�BCC. If a DMU is fully efficient in both theCCR and BCC efficiencies �i.e., �CCR=�BCC=1�, it is operating atthe MPSS �Banker et al.1984�. Accordingly, for construction ac-tivities, when the productivity of a workday is evaluated asMPSS, it can be regarded as a workday with baseline perfor-
mance and belongs to the BP set.

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Case Study

Project Description

To evaluate the five BP methods, a building project used in pre-vious BP related researches �Thomas and Sanvido 2000; Ibbs andLiu 2005� is now used to compare the five methods �Measuredmile, Thomas, Control chart, K-means clustering, and DEA� forderiving BP. The project is a three-story, reinforced, concretebuilding with offices, classrooms, and laboratories. On thisproject, the erection of sheet-metal ducts was monitored for 37workdays by Thomas and Sanvido �2000�. The work was dividedinto three sizes of ducts: �1� branch duct; �2� small feeder duct;and �3� large feeder duct. In addition, four vertical floor penetra-tions and 43 fire dampers were installed during the data collectionperiod. The sheet-metal fabrication shop was part of the contrac-tor’s firm. During the study period, the production rates of thefabrication shop and the erection crew were not balanced. Thecontractor shifted workers from the construction site to the fabri-cation shop on several occasions, depending on where increasedproduction was needed. The result was that deliveries were un-even, material shortages were common, and field installation wasinconsistent during much of the work period. The period of timewhen this impact occurred was Workdays 7–26.

Productivity Calculation

To compare the five different BP methods by this case project, therecognized productivity calculation and conversion technique de-veloped by Thomas and Kramer �1988� is used to derive equiva-lent daily output and productivity data which are shown inColumns �3�–�10� of Table 3.

In Column �8� of Table 3, the output of a workday is calculatedas the sum of the products of each subtask quantity and its asso-ciated conversion factors. For instance, the output of Workday 2is calculated as 0�11.76+1.2�3.65+30.6�0.53+0�1+0�0.66=20.6�ft�=6.3�m�. Accordingly the productivity of Work-day 2 is 40 /6.3=6.36�wh /m�.

To have a more meaningful comparison of the different BPs,the average productivity of the case project is calculated as thetotal input �whs� divided by the total output of the entire 37 days,i.e., 1 ,216 /394=3.08�wh /m� �shown in the end of Column �10��which represents the true labor efficiency of the project and, ifnecessary, can be used to trace the true cost of the project. This isa large difference from the figure, 3.48�wh /m�, which is derivedby averaging the 37 productivity values �see Column �10� ofTable 3� to represent the average productivity of the same projectin developing K-means BP method by Ibbs and Liu �2005�.

By the DEA approach, the project case is formulated as aone-input �wh� and five-output �penetration, fire damper, branchduct, small feeder duct, and large feeder duct� DEA problem �seeColumns �2�–�7� of Table 3�, and it can be solved by Eqs. �9� and�10�. The results are the corresponding scores of CCR, BCC, andSE shown in Columns �11�–�13� of Table 3. Those workdays withCCR=BCC=SE=1 are identified as the MPSS, or the BP daysthat form the BP set. The median of the BP set is chosen as thefinal BP in the DEA method of this paper.

Table 4 shows the BP sets and the final BPs identified by thefive BP methods, respectively. Readers are referred to the corre-sponding context in this paper or related literature for the detailedcomputation process. Some points to notice are as follows.

Zink’s measured mile approach compares productivity during
an unimpacted period of time with productivity during an im-


pacted period of time. For the case project, 6 days �Day 26–31�were identified as unimpacted days �Column �7� of Table 4� byIbbs and Liu �2005� and they derived the measured mile produc-tivity, 3.22�wh /m�, by averaging the six productivity values.Since it is the average productivity of the unimpacted period thatis significant, the measured mile productivity should be calculatedas the period’s total whs divided by the total output, 232 /74.8=3.10�wh /m�, instead of the number, 3.22�wh /m�, proposed byIbbs and Liu �2005�.

The control chart method identifies all 37 workdays as normalperformance days in the first iteration of calculation with three-standard-deviation control limits shown in Column �9� of Table 4.This result is obviously inconsistent with the project descriptionrecorded by Thomas and Sanvido �2000�. Thus productivities ofthe 37 days were reanalyzed by a stricter criterion, two standarddeviations, to further explore the data. In this case, a new BP setconsisting of 32 days was identified in the fourth iterations ofcalculation and the results are shown in Column �8�. Like Ibbsand Liu �2005�, Gulezian and Samelian �2003� also derived thefinal BP of control charts by averaging the daily productivityvalues in their BP set. This calculation approach results in highBP values for the control chart method. In summary, BP derivedfrom control chart method clearly tends to have mediocre perfor-mance due to the following two reasons: �1� it tends to classifymost of the workdays as the BP set and �2� the way it averages theproductivity values of the BP set.

Discussion

Based on Thomas’ observations, 20 days �from Day 7 to 26� ofthe 37 days were impacted. In other words, less than half �46%�of the observed workdays are unimpacted �Thomas and Sanvido2000�. However, as can be seen in Rows �1� and �2� of Table 5, incontrast to the other three methods, both K-means clustering andcontrol chart methods identify more than 70% of workdays asunimpacted, i.e., BP days. This may suggest that these two meth-ods are fundamentally different from the other three methods.

As shown in Row �4� of Table 5, Zink’s method identifies only17% of its BP days as located in the impacted period �Day 7–26,54% of the 37 days� which is classified by Thomas and Sanvido�2000�. However, all the other methods identify most of their BPdays �50–80%� in that impacted period. This may suggest thatZink’s method is fundamentally different from the other methodstoo.

From the above discussions, it seems that all the five methodsare quite different from each other. However, from the view pointof final BP value �see Rows �5� through �7� of Table 5�, Thomas’BP method is the strictest with the best �lowest� BP �1.80 wh /m,58% of the average productivity�; and the DEA method is rankedthe second �2.10 wh /m, 68% of the average productivity�. As canbe seen from Fig. 2 �the plot of Row �6� of Table 5�, it seems thatall the BP methods can be roughly classified into two categories,one with BPs smaller than 70% �ranging from 58 to 68%�, and theother with BPs larger than 90% �ranging from 89–113%�.

More productivity data from eight structural steel erectionprojects �Huang 2008� are analyzed to further explore the charac-teristics of the five BP methods �see Table 6�. All these projects,which were initiated during from 1997 to 1999 in southern Tai-wan, were performed by a government accredited grade-A con-tractor specializing in steel erection. Data on the projects werecollected and recorded in a way similar to the format shown in
Table 1. BPs derived from different methods and the brief of each

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project are summarized in Table 6, on which the following com-parisons and discussion are made.

In average, Thomas’s and DEA methods derive the smallest�best� BPs, accounting for 52 and 53% of the project averageproductivity, respectively. This result corresponds to the findingthat labor is used at only 40–60% of potential efficiency �Con-struction Task Force 1998�. BPs derived from the two methodsalso show minimum standard deviations, 10 and 9%, respectively.

Table 3. Daily Productivity and DEA Performance—Case Projecta

�1� �2� �3� �4� �5� �

Conversion factor 11.76 3.65 0.53

Fire Branch

Penetrations damper duct Sma

Workday Workhours �each� �each� �ft� �f

1 40 4 0.0 0.02 40 0 1.2 30.6

3 40 0 0.0 55.1

4 40 0 0.0 86.3

5 40 0 3.0 40.0

6 24 0 0.0 67.5

7 24 0 0.0 93.68 24 0 0.0 45.9

9 24 0 1.6 23.3

10 24 0 0.0 0.0 1

11 24 0 0.0 27.2

12 24 0 2.0 28.7

13 40 0 0.0 41.7

14 40 0 0.0 80.2

15 40 0 0.0 54.7

16 24 0 2.0 25.1

17 24 0 0.0 90.918 24 0 1.4 16.3

19 24 0 0.0 26.3

20 24 0 2.0 58.0

21 24 0 0.0 0.0 322 24 0 0.0 60.0

23 40 0 0.0 24.3 2

24 40 0 0.0 65.3 125 40 0 0.0 18.8

26 40 0 0.0 47.0 1

27 40 0 0.0 34.5

28 40 0 0.0 39.6

29 32 0 0.0 0.0 3

30 40 0 0.0 11.9 3

31 40 0 0.0 56.7 1

32 40 0 0.0 33.9

33 40 0 10.0 49.434 40 0 10.0 16.935 40 0 10.0 16.936 24 0 0.0 76.8

37 24 0 0.0 49.5

Total 1,216 4 43.2 1,492 22aBoldface indicates baseline subset identified by DEA.bSE=scale efficiency=CCR /BCC.

These minimal dispersions suggest that the methods of Thomas



and DEA are the most consistent among the compared methodsfor deriving BP.

BPs derived from the K-means method show medium standarddeviations, 11.6%, and the same range, 29%, as those of Thomasand DEA. However, compared to the methods of Thomas andDEA, BPs of K-means method are obviously distributed in a dis-tinct higher level since they on average account for 94% of theproject average productivity and two of the eight cases even ex-

�7� �8� �9� �10� �11� �12� �13�

0.66

r duct Converted daily DEA

Large Output Prod. Output oriented

�ft� �ft� �m� �wh/m� CCR BCC SEb

0 47.0 14.3 2.79 1.00 1.00 1.000 20.6 6.3 6.36 0.28 0.38 0.73

0 29.2 8.9 4.49 0.35 0.59 0.60

0 45.7 13.9 2.89 0.55 0.92 0.60

0 32.2 9.8 4.07 0.46 0.57 0.81

0 35.7 10.9 2.20 0.72 0.72 1.00

0 49.6 15.1 1.57 1.00 1.00 1.000 24.3 7.4 3.25 0.49 0.49 1.00

0 18.2 5.5 4.33 0.43 0.80 0.54

2.25 18.7 5.7 4.20 0.66 1.00 0.66

1.5 19.9 6.1 3.97 0.37 0.95 0.39

0 22.5 6.9 3.51 0.54 1.00 0.54

3 24.1 7.3 5.45 0.33 0.48 0.68

0 42.5 13.0 3.08 0.51 0.86 0.60

0 34.1 10.4 3.84 0.38 0.63 0.61

0 20.6 6.3 3.81 0.50 1.00 0.50

0 54.9 16.7 1.44 1.00 1.00 1.001.5 16.3 5.0 4.85 0.39 1.00 0.39

0 14.0 4.3 5.64 0.28 0.28 1.00

0 38.0 11.6 2.07 0.85 1.00 0.85

0 30 9.2 2.62 1.00 1.00 1.000 31.8 9.7 2.46 0.64 0.64 1.00

12 43.2 13.2 3.05 0.70 0.79 0.89

29.88 73.3 22.4 1.80 1.00 1.00 1.0020.25 23.3 7.1 5.64 0.68 0.68 1.00

20.69 49.9 15.2 2.62 0.70 0.71 0.99

2.25 26.9 8.2 4.89 0.34 0.47 0.72

23.63 42.0 12.8 3.12 0.79 0.79 1.00

0.75 38.6 11.8 2.72 0.96 1.00 0.96

0 41.5 12.7 3.15 0.76 1.00 0.76

0 46.2 14.1 2.85 0.61 0.86 0.71

0 18.0 5.5 7.31 0.22 0.36 0.60

0 62.7 19.1 2.10 1.00 1.00 1.000 45.4 13.9 2.89 1.00 1.00 1.000 45.4 13.9 2.89 1.00 1.00 1.000 40.7 12.4 1.94 0.82 0.82 1.00

0 26.2 8.0 2.99 0.53 0.53 1.00

118 1,293 394 3.08

6�

1

Feede

ll

t�

00

0

0

0

0

00

0

7.25

4.5

0

0

0

5.13

0

6.751.5

0

0

00

2.34

90

1.31

7.3

5.44

8.07

5.19

6.16

0

0000

0

0

ceed the 100% limit �see Table 6 and Fig. 3�. Zink’s measured


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mile analysis results in a high standard deviation of 18.9%, whichconfirms the finding of other studies �Gulezian and Samelian2003; Ibbs and Liu 2005� that it is very difficult to consistentlyand objectively choose a continuously unimpacted period.

With upper and lower control limits of three-standard devia-tions, the control chart method always derives very high BPs thaton the average account for 117% of the average project produc-tivity. It is suggested that more tests are required for this methodas well as K-means and measured mile analysis before they canbe practiced in the construction industry.

In summary, Thomas’s method and DEA are capable of deriv-ing consistent performance benchmarks for projects. Thomas’s

Table 4. Baseline Productivity Sets Derived from Different BP Methods

�1� �2� �3� �4� �5�

Workday Work hoursDaily

output �m� Thomas DEA

1 40 14.3 2.79

2 40 6.3

3 40 8.9

4 40 13.9

5 40 9.8

6 24 10.9

7 24 15.1 1.57 1.57

8 24 7.4

9 24 5.5

10 24 5.7

11 24 6.1

12 24 6.9

13 40 7.3

14 40 13.0

15 40 10.4

16 24 6.3

17 24 16.7 1.44 1.44

18 24 5.0

19 24 4.3

20 24 11.6

21 24 9.2 2.62

22 24 9.7

23 40 13.2

24 40 22.4 1.80 1.80

25 40 7.1

26 40 15.2 2.62

27 40 8.2

28 40 12.8

29 32 11.8

30 40 12.7

31 40 14.1

32 40 5.5

33 40 19.1 2.10 2.10

34 40 13.9 2.89

35 40 13.9 2.89

36 24 12.4

37 24 8.0

BP 1.80 2.10

BP method has the advantage of simple calculation and derives



almost the same level of BP as DEA. The BP derived from eitherof these two methods can be considered as the best performance acontractor could achieve on a particular project. However Tho-mas’s BP methodology is still questioned for its subjectivity forwhy the 10% rule and the output quantity, instead of productivity,are considered when choosing the BP set �Ibbs and Liu 2005�.

DEA is the best method for deriving BP due to the followingadvantages: �1� performance benchmark and relative efficiencyscores can be derived just by recording the number of predefinedinputs and outputs in each workday and this multi-inputs andmulti-outputs capability of DEA has raise the scale of traditionallabor productivity from the level of single factor productivity to

�7� �8� �9�

Baseline productivity set

ns Zink

Control chart

Two standard deviation Three standard deviation

Iteration 4 Iteration 1

2.79 2.79

6.36

4.49 4.49

2.89 2.89

4.07 4.07

2.2 2.2

1.57 1.57

3.25 3.25

4.33 4.33

4.2 4.2

3.97 3.97

3.51 3.51

5.45

3.08 3.08

3.84 3.84

3.81 3.81

1.44 1.44

4.85 4.85

5.64

2.07 2.07

2.62 2.62

2.46 2.46

3.05 3.05

1.80 1.80

5.64

2.62 2.62 2.62

4.89 4.89 4.89

3.12 3.12 3.12

2.72 2.72 2.72

3.15 3.15 3.15

2.85 2.85 2.85

7.31

2.10 2.10

2.89 2.89

2.89 2.89

1.94 1.94

2.99 2.99

3.10 3.08 3.48

�6�

K-mea

2.79

2.89

2.2

1.57

3.25

3.97

3.51

3.08

3.84

3.81

1.44

2.07

2.62

2.46

3.05

1.80

2.62

3.12

2.72

3.15

2.85

2.10

2.89

2.89

1.94

2.99

2.75

total factor productivity �TFP�; �2� calculations for rules of credit


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and conversion factors to derive the final productivity are notnecessarily required; �3� DEA is very objective; �4� rigorousmathematical theory based on economic principles has been wellestablished for DEA; and �5� references for DEA research andapplications have been extensively developed.

Table 5. Summary of Different BP Methods

�1�

Thomas

�1� Number of BP days 5

�2� =�1� /37 �%� 14

�3� Number of BP Days between day 7 and 26 4

�4� =�3� / �1� �%� 80

�5� BP �wh /m� 1.80

�6� =�5� /AP a �%� 58

�7� Rank 1aAP=Average producivity=1,216 /394.4=3.08 �wh /m�.

Table 6. BPs of Different Projects Calculated by Different Methods

ProjectID

Workdays

Average production�wh/ton� Thoma

9701 25 1.20 68

9801 54 1.99 48

9802 43 1.76 55

9901 97 2.37 40

9902 36 1.83 56

9903 61 2.31 39

9904 32 1.78 52

9905 61 1.45 60

Average �%� 52

Standard deviation �%� 10.0

Max �%� 68

Min �%� 39

Range �%� 29

Fig. 2. BPs of five methods

CC=Control chart method.JOURNAL OF CONSTRUCTION


Conclusions

BP is an important concept and has been critically applied in theconstruction industry. This paper introduces DEA as a bettermethod to derive BP which is defined as the best performance acontractor could achieve on a particular project herein. Theoryand examples of DEA are carefully demonstrated. Five differentBP deriving methods including DEA are compared. It is foundthat both Thomas’s method and DEA are capable of deriving con-sistent BP; however, objectivity of Thomas’s BP method re-mained in question. As for the other methods, it is suggested thatmore research is required before they can be further practiced inthe construction industry.

It is concluded that DEA is the best method to derive contrac-tors’ relative performances and benchmarks for best practice onsite due to its objectivity, effectiveness, and completeness of sup-porting economic theory. In addition to the advantage of excep-tional objectivity, the proposed DEA is capable of derivingproductivities of activities with multi-inputs and multi-outputs,and thus has raised the scale of traditional labor productivity fromthe level of single factor productivity to TFP, which will makeconstruction researchers and managers able to evaluate perfor-mances of interests in a much more complete, effective, and ac-curate way.

�3� �4� �5� �6�

K-means Zink

Control chart

2 Std 3 Std

26 6 32 37

70 16 86 100

14 1 17 20

54 17 53 54

0 2.75 3.10 3.08 3.48

89 101 100 113

3 5 4 6

BP in terms of project average productivity�%�

DEA K-means Zink CCa �3 Std�

68 87 87 109

60 84 60 107

48 84 73 119

47 91 121 117

52 89 86 106

54 111 73 134

39 113 70 113

59 95 69 135

53 94 80 117

9.0 11.6 18.9 11.6

68 113 121 135

39 84 60 106

29 29 61 29

�2�

DEA

8

22

4

50

2.1

68

2

s

a


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Notation

The following symbols are used in this paper:m � number of inputs for each DMU;n � number of DMUs;s � number of outputs for each DMU;

s+ � output excesses vector;s− � input shortfalls vector;U � vector of output weights= �u1 ,u2 , . . . ,us�;V � vector of input weights= �v1 ,v2 , . . . ,vm�;X � matrix comprising all DMUs’ inputs;Y � matrix comprising all DMUs’ outputs;Xi � input vector of DMUi= �x1i ,x2i , . . . ,ymi�;Yi � output vector of DMUi= �y1i ,y2i , . . . ,ysi�;� � infinitesimally small positive number to be

determined by the researcher;�i � real variable representing the efficiency of

DMUi;� � non-negative vector whose elements represent

the optimal weights or multipliers for theassociated inputs and outputs of each DMU= ��1 ,�2 , . . . ,�n�;

� � ��1 ,�2 , . . . ,�n�=nonnegative vector whoseelements represent the optimal weights ormultipliers for the associated inputs and outputsof the corresponding DMUs;

�i � �i /�i; and�i � 1 /�i.

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improved baseline productivity analysis technique

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