Theory and Methodology
Determining the relative eciency of MBA programs using DEA
Amy Colbert
a, Reuven R. Levary
a,*, Michael C. Shaner
baDepartment of Decision Sciences and MIS, School of Business and Administration, Saint Louis University, 3674 Lindell Blvd., St. Louis, MO 63108, USA
bDepartment of Management, School of Business and Administration, Saint Louis University, 3674 Lindell Blvd., St. Louis, MO 63108, USA
Received 1 February 1998; accepted 1 April 1999
Abstract
Data envelopment analysis (DEA) is used here to determine the relative eciency of 24 top ranked US MBA programs. Eciency scores were determined using three output sets of the MBA programs: output that measured student satisfaction, output that measured recruiter satisfaction and output that measured both. DEA is also used here to determine the relative eciency of three foreign MBA programs as compared to several top ranking US MBA programs. The publicized ranking of MBA programs by national magazines has a signi®cant impact on corporate recruiters, potential MBA students and on business schools themselves. A new ranking based on DEA will more completely and accurately represent MBA programs. Further, DEA will make it possible to more fairly compare speci®c programs. Ó 2000 Elsevier Science B.V. All rights reserved.
Keywords:MBA programs; Higher education; DEA
1. Introduction
Masters of Business Administration (MBA) programs are charged with satisfying many cus-tomers with limited resources. Students who enroll in the top MBA programs expect to learn skills that will enable them to operate the world's most successful companies or to create such companies of their own. Students demand a curriculum that is varied but applicable to the business world. After
completing the program, students expect to be placed in challenging positions with lucrative starting salaries.
MBA programs must satisfy the needs of cor-porate recruiters as well as the needs of the stu-dents. The recruiters represent companies from around the world. They expect students from the top MBA programs to have analytical skills that will enable them to solve comprehensive business problems. They also expect students to have learned to perform well as part of a team. Addi-tionally, they expect them to have developed a global view of the business world. If an MBA program has satis®ed these needs, corporate
*Corresponding author. Tel.: 977-3878; fax:
+1-314-977-3897.
E-mail address:[email protected] (R.R. Levary).
0377-2217/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
recruiters will hire their graduates and will provide them with lucrative starting salaries and signing bonuses.
The biennial ranking of business schools that is
prepared by Business Week magazine (Byrne,
1997) is based on surveys of business school graduates and corporate recruiters. The individual programs are ®rst given both a corporate ranking and a graduate ranking and then the two rankings are combined into a single overall ranking. This widely reported ranking is monitored by MBA students, corporate recruiters and business schools alike.
In this study, data from the Business Week
survey (Byrne, 1997) are used to determine the relative eciency of the top MBA programs in the United States. This measure of eciency is based on the level of output produced for each unit of input. Because MBA programs must focus on satisfying the needs of both students and corporate recruiters, the relative eciency of the programs is determined here using three output sets: outputs that measure student satisfaction, outputs that measure recruiter satisfaction, and output that combines the two. Eciency scores calculated us-ing multiple output types for the model are com-pared with the eciency scores based on a single type of output for that model.
Data envelopment analysis (DEA) as a tool for determining the relative eciency of operating units is overviewed in Section 2. Other methods of determining eciency are described in Section 3. Section 4 discusses the utility of DEA in evaluating operating units in the higher education sector. The results and analysis of evaluating the relative e-ciency of MBA programs within the United States is provided in Section 5. In Section 6, the relative eciency of three foreign MBA programs is compared with the relative eciency of several top ranking US MBA programs. A summary and conclusions are the subject of the ®nal section.
2. Using DEA to determine relative eciency
Using DEA, the relative eciency of decision making units (DMUs) that use multiple inputs to produce multiple outputs may be calculated. The
relative eciency of a DMU is calculated using a ratio de®nition of eciency (Charnes et al., 1978). This ratio generalizes the single output to single input de®nition to multiple outputs and inputs without the use of pre-assigned weights. The weights used for each DMU are those which maximize the ratio between the weighted output and weighted input. These weights are determined in such a way that no method of aggregating the inputs and outputs, such as value or market price, is necessary.
DEA is an analytical procedure developed by Charnes et al. (1978) for measuring the relative eciency of DMUs that perform the same type of functions and have identical goals and objectives. Decision making units include departments, sec-tions, branches, and divisions of organizations belonging to the same business sector. If the rela-tive eciency of a set of DMUs performing the same type of function is to be evaluated, the DMUs must use the same type of input to produce the same type of output. Each DMU in a given set can then be ranked according to how eciently it utilizes its inputs to produce its outputs.
When the combined number of inputs and outputs approaches the total number of DMUs in a set, however, DEA may be problematic. Under such circumstances, one must be very cautious interpreting eciency scores (Charnes et al., 1985a).
Numerous re®nements of DEA now enhance its analytical eectiveness. The ``window analysis'' concept (Charnes and Cooper, 1985) was incor-porated into DEA to enable it to trace the per-formance of each DMU over time. Tracing performance over time is done by evaluating the DMUs at dierent time periods. As ``window analysis'' requires that a DMU be de®ned for each time period used in the analysis, it substantially increases the volume of calculations. Thanassoulis and Dyson (1992) developed several DEA based models that can be used to estimate alternative input-output target levels and are helpful in ren-dering relatively inecient organizational units ecient.
The DEA model applied in this study was de-veloped by Banker et al. (1984) and has been used in many applications (e.g., Bessent and Bessent,
1980; Seiford, 1996). Chang and Guh (1991) pointed out some problems of using this model. A comprehensive bibliography of DEA is given in Seiford (1996). The eciency measure for each DMU ranges from 0 to 1. A DMU with an e-ciency value of 1 is considered most ecient. An eciency value smaller than 1 indicates the degree of relative eciency. One possible explanation of a DMU's ineciency is that some of its inputs are not utilized fully. Ecient DMUs achieve greater output per unit of input when compared with in-ecient DMUs. By identifying unutilized re-sources, DEA can provide a ®rm's management with some information regarding causes of ine-ciency.
In order to formulate the DEA model let us
assume thatn-MBA programs are to be evaluated
based on m inputs and s outputs. Let yrj be a
known level of the rth output of program
j r1;2;. . .;s; j1;2;. . .;n and xij be a
known level of the ith input to program
j i1;2;. . .;m. Each MBA program is assigned
a weightwj j1;2;. . .;nfor its input and
out-put. A hypothetical composite MBA program can then be de®ned using weighted inputs and outputs
of the programs being evaluated. The weights wj
are the model decision variables. The eciency of
MBA program k relative to the composite MBA
program can be determined by solving the fol-lowing linear programming problem:
min hk 1 subject to: Xn j1 wj1; 2 Xn j1 wjyrjPyrk; r1;2;. . .;s; 3 Xn j1 wjxij6xikhk; i1;2;. . .;m; 4 hk;wj j1;2;. . .;nP0; 5
wherehk is the relative eciency of MBA program
k.
Minimizing the relative eciency of MBA
program k is equivalent to minimizing the inputs
of the composite MBA program. Constraints (2) ensures that the sum of the weights is equal to 1. Constraints (3) ensure that each output level of the composite MBA program is at least as high as the
output level of MBA program k. Constraints (4)
ensure that each input level of the composite MBA program is at most as high as its input capacity.
3. Other methods of determining eciency
DEA is not the only method that can be used to determine eciency. Ratio analysis is another common method. While the DEA is a ratio model (Charnes et al., 1978), we refer here to a ratio analysis method that is not a DEA based method. Using ratio analysis, a ratio comparing outputs to inputs is computed. A simple ratio compares one measure of input to one measure of output. For example, an educational unit might use total cost per student enrolled to measure eciency. This measure treats all students as if they were identical. The dierences in the amount of knowledge gained or starting salaries earned are not considered.
Multiple inputs and outputs may be incorpo-rated into ratio analysis by calculating multiple ratios. However, this makes it dicult to deter-mine overall eciency. A measure of overall e-ciency can be computed by aggregating all inputs and outputs. This requires assigning a weight to each input and output. While such weights may be determined according to the value or market price of each input and output, this information is not always available. When the market value of each input and output is missing, one may consider using the Cook and Kress (1990) approach to termine the set of weights. Cook and Kress de-veloped a methodology for aggregating preference ranking and applied their approach to aggregate votes in a preferential election. Their model
de-termines for each candidate i the best set of
weightswjto apply to thejth place standingmijfor
each candidate.
Multiple regression is another method for de-termining eciency. Using multiple regression, output level is modeled as a function of various input levels. Operating units that are relatively ecient lie above the modeled relationship and
have positive residuals. Operating units that are relatively inecient lie below the modeled rela-tionship and have negative residuals. This method has several drawbacks. First, because single-equation multiple regression can model only one output level, a single output measure must be de-termined or all outputs must be arti®cially com-bined into a single indicator. Multiple-equation regression models can be used when an operating unit has multiple outputs. Like multiple ratios, however, this method does not produce an overall measure of eciency. Multiple residuals provide dierent measures of the operating unit's eciency. Another drawback of regression analysis is that it compares eciency with average performance rather than with the best performance. Addition-ally, ``regression analysis requires the parametric speci®cation of a production function, that is, an equation detailing how inputs are combined to produce outputs'' (Sexton, 1986, p. 9). This is of-ten dicult because such a function may be un-known for the industry in question.
Several studies combined DEA with regression analysis to evaluate operating units which have multiple inputs and outputs. Cooper and Tone (1997) used simulation to study a combined DEA-regression model. Friedman and Sinuany-Stern (1997) developed a methodology using canonical correlation analysis to provide a full rank scaling for all the units. Their methodology closed the gap between the frontier approach of DEA with the average tendencies of statistics.
Compared to the methods mentioned, DEA has several advantages. Multiple inputs and outputs can be used in the DEA model. The weights that will be used to aggregate inputs and outputs are determined using linear programming. No deci-sions need be made regarding the relative impor-tance of each input and output. With DEA, each operating unit's eciency is compared to an ``ideal'' operating unit rather than to average performance.
DEA has some limitations as well, however. As with any other method of determining eciency, all inputs and outputs must be speci®ed and measured. Failure to include a valid input or output or inclusion of an invalid input or output will bias the results. Additionally, DEA can
mea-sure ``relative'' eciency, but not ``absolute'' e-ciency. It compares an operating unit to a subset of peers and not to a theoretical maximum perfor-mance.
4. Using DEA to evaluate higher education operat-ing units
DEA has been used to determine the relative eciency of University departments in several studies (e.g., Ahn, 1987; Ball and Wilkinson, 1992; Beasley, 1995). DEA is particularly useful in evaluating educational units because inputs and outputs are combined using a priori weight. These weights are determined using linear programming and ``are not the values of inputs and outputs in any economic sense'' (Sexton, 1986, p. 10). Because the economic value of many of the inputs and outputs of educational units is dicult to determine, the DEA model is a good choice. With its multiple inputs and outputs, the relative e-ciency of educational units can be calculated. Nonetheless, the speci®cation of inputs and out-puts is often dicult. Many of the outout-puts of ed-ucational units are not measurable. For example, it is dicult to measure a university's contribution to the surrounding community. Other outputs, such as the increase in a student's knowledge may be measured (e.g., using entrance and exit exams) but the accuracy of these measures is questionable. Additionally, this data may not be readily avail-able. Because of the diculties inherent in the speci®cation of inputs and outputs for educational units, some studies have examined the eects of variation in inputs and outputs on eciency scores.
Sinuany-Stern et al. (1994) used DEA to de-termine the relative eciency of 21 departments at Ben-Gurion University. Operational expenditures and faculty salaries were used as inputs. Grant money, number of publications, number of grad-uate students and number of credit hours oered were used as outputs. Fourteen of the departments were found to be inecient. Sinuany-Stern et al. (1994) also tested the eects of variations in inputs and outputs on eciency scores. In one trial, one output was deleted from the original model. The
output was chosen for deletion because no de-partments were relatively inecient in that output. In this trial, two additional departments became inecient. The DEA model was run again with the two inputs combined. Again, two additional de-partments became inecient.
Ahn and Seiford (1993) used DEA to determine the relative eciency of 153 doctoral-degree-granting institutions of higher learning (IHLs). Of these, 104 were public and 49 were private. The purpose of the study was to determine the eect of dierent sets of output variables on the relative eciencies of public and private institutions. Public IHLs are often funded based on an enroll-ment-related output measure. For this reason, Ahn and Seiford predicted that public IHLs would be more ecient when enrollment-related outputs were considered and private IHLs would be more ecient when less closely monitored outputs were considered. This hypothesis was tested using mul-tiple variable sets. In one trial, faculty salaries, physical investment, and overhead expenses were used as input variables. Undergraduate full-time equivalent students (FTEs) and graduate FTEs were used as output variables. Using these enroll-ment-related output variables, public IHLs were found to be more ecient than private IHLs. A second trial used faculty salaries, physical invest-ment, overhead expenses, undergraduate FTEs and graduate FTEs as inputs. Undergraduate de-grees, graduate dede-grees, and grants were used as output variables. Using these less closely moni-tored output variables, private universities were found to be more ecient.
Both studies cited above show that the choice of output variables had an impact on the eciency scores of the operating units in question. Sinuany-Stern et al. (1994) showed that a reduction in the number of input and output variables used, whether by deletion or combination, caused e-ciency scores to decrease or remain the same. Ahn and Seiford (1993) showed that the type of output variables used had an impact on the eciency scores of the operating units in question.
Breu and Raab (1994) used data from a ranking
of the top 25 national universities byUS News and
World Report to calculate relative eciency. To
determine the ranking of these 25 universities,US
News and World Report used 12 performance in-dicators that measured reputation, student selec-tivity, faculty resources, ®nancial resources and student satisfaction.
Breu and Raab used four of the performance indicators from the student selectivity, faculty resources and ®nancial resources categories as input measures. Input measures included: per-centage of faculty with doctorates, faculty to student ratio, educational and general expendi-tures per student and average or midpoint SAT/ ACT scores. A ®fth input, tuition charge per student, was also included as an input measure. The outputs used by Breu and Raab in their DEA model were graduation rate and freshman retention rate. The two measures were used to
indicate student satisfaction in the US News and
World Reportranking.
TheUS News and World Reportpoll based their ranking on the satisfaction of only one customer group ± students. The operating units used in this study are 24 of the top 25 MBA programs in the
Business Week ranking of MBA programs in
the United States (Byrne, 1997). The data for the study were taken from the surveys and other data
collected by Business Week to rank these MBA
programs. Business Week, however, recognizes
that MBA programs must satisfy numerous cus-tomer groups, the primary ones being students and recruiters. Recognizing the need to satisfy both groups, eciency scores are determined in this study using three dierent output sets. Outputs in the ®rst trial measure both student and recruiter satisfaction. Outputs in the second trial measure only student satisfaction. In the third trial, e-ciency is determined using outputs that measure only recruiter satisfaction.
5. Results and analysis of evaluating the relative eciency of MBA programs
Eciency scores vary based on the type of output used. It is expected that the number of ef-®cient MBA programs will be higher in trial one where both types of output are included in the same model. Sexton (1986, p. 10) explained that ``DMUs will place higher weights on the inputs
that they use least and on the outputs that they produce most''. Because of this, programs that more eciently produce student satisfaction out-puts will place higher weights on these outout-puts while programs that more eciently produced re-cruiter satisfaction outputs will place higher weights on those outputs. As a result, more pro-grams will be relatively ecient when both types of output are included in the same model.
In trial one, two output measures showing student satisfaction were used:
y1± percentage of alumni who donate money to
the program,
y2 ± student satisfaction with teaching,
curricu-lum and placement.
The value of outputy2is based on the survey of
graduates done by Business Week (Byrne, 1997).
Additionally, two output measures were used to represent recruiter satisfaction:
y3 ± average salary of graduates,
y4 ± recruiter satisfaction with analytical skills,
team work, and global view.
The recruiter satisfaction scores were taken
from the Business Week survey of corporate
re-cruiters. Because the resources available to MBA programs must be used to satisfy all customer groups, the same set of inputs was used in each test of relative eciency. These included:
x1± faculty to student ratio,
x2 ± average GMAT score of students in the
program,
x3± number of electives oered.
The relative eciency of 24 programs was de-termined using the three inputs and four outputs described above. The inputs and outputs for each program are given in Tables 1 and 2. Stanford University was excluded from the sample because data on the percentage of alumni who donate money to the program was not available. The DEA model represented by relations (1)±(5) was utilized. Eciency scores are shown in Table 3. The MBA programs listed in Tables 1±3 are ordered identically to the way in which they
are ordered in Business Week (i.e., University of
Pennsylvania's Wharton is ranked at the top). As the above results show, only eight of the 24 programs were found to be inecient. The e-ciency scores ranged from 0.9451 to 1.0.
In trial two, eciency scores were calculated using only outputs that measure student satisfac-tion. These outputs were as follows:
y1± percentage of alumni who donate money to
the program,
y2± student satisfaction with teaching,
y3± student satisfaction with curriculum,
y4± student satisfaction with placement.
In trial three eciency scores were calculated using only the outputs that measure recruiter sat-isfaction. These outputs were as follows:
y1± average salary of graduates,
y2± recruiter satisfaction with analytical skills,
y3± recruiter satisfaction with team work skills,
y4± recruiter satisfaction with graduates' global
view.
Satisfaction scores were included separately rather than as an average so that the number of outputs in trials two and three would be the same as the number of outputs in trial one. Addition-ally, the same inputs were used in these two trials as were used in the ®rst trial. The results from trials two and three are given in Table 3.
The results show that 13 programs were ine-cient in achieving student satisfaction related outputs and nine programs were inecient in achieving recruiter satisfaction related outputs. This supports the hypothesis that more programs will be ecient when a combination of two types of output are used.
Analysis of each program's relative eciency scores provides further insight into the impact of combining two types of output into one model. The number of ecient programs increases when two types of output are used in the same model because programs that more eciently produce one type of output will place a higher weight on that type of output. Based on this, it would seem that a program that eciently produces either student satisfaction outputs or recruiter satisfac-tion outputs can choose weights that will produce an eciency score of one when both types of outputs are considered in the same model. The results above show that 10 programs are ecient in achieving either student satisfaction outputs or recruiter satisfaction outputs, but not both. Of these, seven were able to choose weights in trial one that resulted in an eciency score of one.
Two additional trials were run on the 24 pro-grams tested in trials one through three. Sinuany-Stern et al. (1994) found that eciency scores ei-ther decrease or remain the same when the number of input or output variables included in the DEA model is reduced. In trials four and ®ve, student satisfaction scores and recruiter satisfaction scores were combined into a single indicator as in trial one. This reduced output to two in both trials. The output for trial four was as follows:
y1± percentage of alumni who donate money to
the program,
y2 ± student satisfaction with teaching,
curricu-lum, and placement.
The output for trial ®ve was as follows:
y1 ± average salary of graduates,
y2 ± recruiter satisfaction with analytical skills,
team work, and global view.
The eciency scores from trials four and ®ve are included in Table 3.
Comparing trials two and four, the eciency scores for 12 programs decreased and the eciency scores for the remaining 12 programs remained the same when the number of outputs was reduced. When trials three and ®ve were compared, the ef-®ciency scores for nine programs decreased while the eciency scores for the remaining ®fteen pro-grams remained the same.
Analysis of Table 3 and the solutions to the LP problems formulated by relations (1)±(5) suggests that MBA programs having an eciency score of 1 also had zero slacks and therefore they are Pareto± Koopmans ecient (see Charnes et al., 1985b; Chang and Kao, 1992). Of those having an e-ciency score of one, a single program may have used less of one or two resources but never less of
Table 1
Input data for the top 25 MBA Programs in the United Statesa
MBA program Number
of faculty Number of students Faculty to student ratio Average GMAT score Number of electives
University of Pennsylvania (Wharton) 182 1533 0.119 662 189
University of Michigan 130 1886 0.069 645 125
Northwestern University (Kellogg) 150 2546 0.059 660 100
Harvard University 176 1779 0.099 680 71
University of Virginia (Darden) 54 499 0.108 660 76
Columbia University 110 1380 0.080 660 286
Stanford University 90 725 0.124 690 83
University of Chicago 100 2697 0.037 685 138
Massachusetts Institute of Technology (Sloan) 110 717 0.153 650 110
Dartmouth College (Tuck) 36 377 0.095 669 59
Duke University (Fugua) 92 700 0.131 646 83
University of California at Los Angeles
(Anderson) 92 1160 0.079 651 101
University of California at Berkeley (Haas) 65 740 0.088 652 75
New York University (Stern) 206 3100 0.066 646 135
Indiana University 111 5998 0.019 630 107
Washington University (John M. Olin) 65 545 0.119 606 69
Carnegie Mellon University 83 738 0.112 638 112
Cornell University (Johnson) 47 513 0.092 634 67
University of North Carolina (Kenan-Flagler) 95 427 0.222 630 75
University of Texas 163 824 0.198 631 133
University of Rochester (Simon) 50 686 0.073 630 48
Yale University 41 461 0.089 676 62
Southern Methodist University (Cox) 69 672 0.103 601 50
Vanderbilt University (Owen) 47 427 0.110 615 105
American Graduate School of International
Management (Thunderbird) 100 1420 0.070 572 75
Ta ble 2 Outp ut data for the top 25 MBA progra ms in the United State s a MBA progra m Meas ures of st udent satisfac tion Meas ures of recruiter satisf action Perc entage of alumn i who dona te Stu dent sat isfaction w ith teac hing Stude nt satisfac tion with curriculum Stu dent satisf action with place-me nt Average score Average startin g salar y ($) Rec ruiter satisf action w
ith analysis
Recru iter satisfac tion with team players Recru iter satisfac tion with w orld view Ave rage sco re Unive rsity of Pen nsylvan ia (Whar ton ) 28.0 67.5 90.0 90.0 82.5 101,7 60 90.0 67.5 90.0 82.5 Unive rsity of M ichigan 24.0 90.0 90.0 90.0 90.0 86,15 5 90.0 90.0 90.0 90.0 Nort hwestern Unive rsity (Ke llogg) 25.0 67.5 67.5 90.0 75.0 98,83 0 67.5 90.0 90.0 82.5 Har vard Uni versity 30.0 90.0 90.0 90.0 90.0 113,5 44 90.0 37.5 90.0 72.5 Unive rsity of V irginia (Dar den) 47.0 90.0 90.0 90.0 90.0 92,89 5 90.0 90.0 67.5 82.5 Colu mbia Unive rsity 27.0 67.5 67.5 67.5 67.5 92,55 0 90.0 67.5 90.0 82.5 Stan ford Unive rsity N/A 37.5 67.5 67.5 57.5 111,2 50 90.0 67.5 90.0 82.5 Unive rsity of C hicago 25.0 37.5 67.5 37.5 47.5 90,09 6 90.0 67.5 90.0 82.5 Massa chuse tts Instit ute of Tech nology (Slo an) 37.0 67.5 67.5 67.5 67.5 100,8 70 90.0 37.5 90.0 72.5 Dar tmouth College (Tu ck) 63.3 90.0 90.0 90.0 90.0 103,6 80 37.5 90.0 67.5 65.0 Duke Unive rsity (Fugu a) 31.0 37.5 67.5 90.0 65.0 84,02 0 67.5 67.5 67.5 67.5 Unive rsity of C alifornia at Los Ang eles (A nderson ) 15.0 67.5 90.0 90.0 82.5 90,78 0 67.5 67.5 37.5 57.5 Unive rsity of C alifornia at Berk eley (Haa s) 10.0 90.0 90.0 67.5 82.5 91,41 0 67.5 37.5 37.5 47.5 New York Unive rsity (Ster n) 20.0 37.5 37.5 67.5 47.5 78,89 5 90.0 90.0 67.5 82.5 Indian a Unive rsity 11.0 67.5 37.5 37.5 47.5 67,77 0 67.5 90.0 67.5 75.0 Wash ington Unive rsity (John M. Olin) 28.0 90.0 90.0 90.0 90.0 61,80 0 37.5 37.5 37.5 37.5 Carn egie M ellon Unive rsity 26.0 90.0 90.0 90.0 90.0 85,69 0 90.0 67.5 67.5 75.0 Corn ell Un iversit y (John son) 20.0 67.5 67.5 67.5 67.5 54,86 5 67.5 90.0 67.5 75.0 Unive rsity of No rth Caro lina (Kenan-Flagler ) 27.0 90.0 67.5 67.5 75.0 80,38 5 37.5 67.5 37.5 47.5 Unive rsity of Te xas 14.0 37.5 67.5 67.5 57.5 69,30 0 37.5 67.5 37.5 47.5
Ta ble 2 (Con tinued ) MBA progra m Meas ures of studen t satisf action M easures of recruiter satisfac tion Percen tage of alumn i who donate Stu dent satisf action w
ith teaching
Stude nt satisfac tion with curriculum Stu dent sat isfaction w
ith placement Average score Ave rage st arting salar y ($) Recru iter satisfac tion with analysis Rec ruiter sat isfaction w ith team play ers Recru iter satisfac tion with w orld view Average score Unive rsity of Roc hester (Sim on) 15.0 67.5 67.5 67.5 67.5 68,440 67.5 37.5 67.5 57.5 Yale Unive rsity 49.0 67.5 67.5 37.5 57.5 87,695 67.5 67.5 67.5 67.5 South ern M ethodist Unive rsity (Co x) 21.0 90.0 67.5 67.5 75.0 62,900 67.5 10.0 10.0 29.2 Vand erbilt Un iversity (Ow en) 25.0 90.0 90.0 67.5 82.5 62,900 37.5 37.5 67.5 47.5 Am erican Gradu ate School of Inte rnati onal Man ageme nt (Thund erbird ) 13.0 37.5 67.5 37.5 47.5 56,585 37.5 37.5 90.0 55.0 a All data was ta ken from By rne (1997 ) and from the comp anion web sit e (www.bu sinesswe ek.com).
all three resources when compared to the other programs.
The results given in Table 3 indicate that Co-lumbia University, Fugua, Kenan-Flagler, Uni-versity of Texas, and Owen are inecient when both student and recruiter measures of satisfaction are considered. Wharton, Harvard University, Darden, Sloan, Stern, Carnegie Mellon and Johnson are found to be inecient with regard only to measures of student satisfaction. The University of California at Los Angeles, Haas and John M. Olin are found to be inecient with re-gard to recruiter satisfaction. Administrators at the ecient MBA programs (University of Mich-igan, Kellogg, University of Chicago, Tuck, Indi-ana University, Simon, Cox, and Thunderbird) can strive to raise to the level of individual input measures to approach the highest existing levels (i.e., faculty to student ratio of 0.222 at
Kenan-Flagler; average GMAT score of 685 at University of Chicago; and number of 286 electives at Co-lumbia University). Administrators of inecient programs can strive to simultaneously improve their level of eciency and raise the level of indi-vidual input measures.
6. Determining the eciency of MBA programs outside the united states using DEA
As technology draws us into a global commu-nity, it is important to consider not only the rela-tive eciency of MBA programs in the United States, but also the relative eciency of MBA programs throughout the world. Although DEA is an appropriate tool for this task, barriers do exist. First, data for MBA programs outside the United States is not readily available. As was
Table 3
Eciency scores of MBA programs for several combinations of outputs and inputsa
MBA program Eciency
score trial 1 Eciency score trial 2 Eciency score trial 3 Eciency score trial 4 Eciency score trial 5
University of Pennsylvania (Wharton) 1.0 0.9269 1.0 0.9135 1.0
University of Michigan 1.0 1.0 1.0 1.0 1.0
Northwestern University (Kellogg) 1.0 1.0 1.0 0.9969 1.0
Harvard University 1.0 0.9652 1.0 0.9652 1.0
University of Virginia (Darden) 1.0 0.9711 1.0 0.9711 1.0
Columbia University 0.9838 0.9365 0.9887 0.9288 0.9832
University of Chicago 1.0 1.0 1.0 1.0 1.0
Massachusetts Institute of Technology (Sloan) 1.0 0.9523 1.0 0.9512 1.0
Dartmouth College (Tuck) 1.0 1.0 1.0 1.0 1.0
Duke University (Fugua) 0.9715 0.9464 0.9786 0.9398 0.9696
University of California at Los Angeles (Anderson) 0.9911 1.0 0.9848 0.9697 0.9819
University of California at Berkeley (Haas) 0.9910 1.0 0.9796 0.9781 0.9796
New York University (Stern) 0.9766 0.9625 1.0 0.9296 0.9766
Indiana University 1.0 1.0 1.0 1.0 1.0
Washington University (John M. Olin) 1.0 1.0 0.9732 1.0 0.9690
Carnegie Mellon University 1.0 0.9634 1.0 0.9634 0.9889
Cornell University (Johnson) 1.0 0.9569 1.0 0.9472 1.0
University of North Carolina (Kenan-Flagler) 0.9895 0.9608 0.9898 0.9550 0.9795
University of Texas 0.9451 0.9373 0.9672 0.9192 0.9420
University of Rochester (Simon) 1.0 1.0 1.0 1.0 1.0
Yale University 1.0 0.9677 0.9995 0.9677 0.9895
Southern Methodist University (Cox) 1.0 1.0 1.0 1.0 1.0
Vanderbilt University (Owen) 0.9842 0.9972 0.9482 0.9790 0.9482
American Graduate School of International
Management (Thunderbird) 1.0 1.0 1.0 1.0 1.0
mentioned earlier, the data used in this study was
taken form the Business Week ranking of MBA
programs (Byrne, 1997). MBA programs outside the United States, however, are not included in the ranking. The data available for these programs was not as complete as the data provided regard-ing MBA programs within the United States.
Further, MBA programs outside the United States may have dierent objectives than programs within the United States. For this reason, it may be dicult to specify a uniform set of outputs for all programs. It may be dicult to construct a uni-form set of inputs as well. Many MBA programs outside the United States, for example, do not require students to take the GMAT admittance exams.
Despite these barriers, an analysis of relative eciency was completed using seven MBA pro-grams within the United States and three MBA programs outside the United States. The seven programs within the United States are the top
seven programs in the Business Week survey for
which the input and output data was available. The MBA programs outside the United States
were pro®led in the Business Week Guide to the
Best Business Schools (Byrne, 1997) but were not included in the ranking. The data used in the DEA analysis is given in Table 4.
The inputs that were used in this model in-cluded:
x1± faculty to student ratio,
x2 ± average GMAT score of students in the
program,
x3± average number of years of work experience
for students in the program.
The outputs that were used in this model included:
y1± percentage of alumni who donate money to
the program,
y2 ± average starting salary of graduates.
It should be noted that output y1 was used as
a measure of student satisfaction in the analysis
above and output y2 was used as a measure of
recruiter satisfaction. Based on the conclusions drawn above, it was expected that programs ef-®cient in satisfying either of these two mentioned customer groups would be ecient according to this model as well. These expectations were
con®rmed in the results. The eciency scores from this analysis are included in Table 4. Only one of the 10 programs was found to be ine-cient. It is possible that more programs would have been shown to be inecient if less types of output had been considered in the model. It is also possible that a greater number of inecient programs would have been identi®ed had a wider range of MBA programs been considered (i.e., not only highly regarded programs). Ana-lyzing the results in Table 4 indicate that the ecient MBA programs are also Pareto±Koop-mans ecient.
7. Summary and conclusions
In this study, the eect of various types of output sets on eciency scores was examined. The relative eciency of 24 MBA programs from
Business Week's top 25 programs in the United States was determined using three output sets. The ®rst trial included two outputs that measured student satisfaction and two outputs that mea-sured recruiter satisfaction. The second and third trials segregated these output types. Trial two used only outputs that measured student satisfaction while trial three used only outputs that measured recruiter satisfaction.
The hypothesis that more programs would have an eciency score of one when two types of output were used in the same model was con®rmed in this analysis. This result was expected given that each operating unit chooses the weights to be placed on inputs and outputs in the model. Units under-standably place higher weights on outputs that are eciently produced in an eort to achieve e-ciency scores of one.
This study replicated the result found by Sinu-any-Stern et al. (1994). They found that a reduc-tion in the number of input or output variables used caused eciency scores to decrease or remain the same. In trials two and three, three measures of student satisfaction and three measures of
re-cruiter satisfaction were taken from the Business
Week surveys and used as output measures.
In trials four and ®ve, these satisfaction survey results were combined into one measure of student
Table 4 Input and out put data and e ciency sco res for som e U S and fore ign M B A progra ms a MBA pro gram Numbe r of facul ty Numb er of stud ents Facu lty to studen t ratio Ave rage GMA T score Average years work exper ience Perc entage of alumn i who dona te mone y to the progra m Ave rge start ing salar y ($) E ciency sco re Universit y of Pennsy lvania (Whar ton) 182 1533 0.119 662 189 28.0 101,760 1.0 Universit y of M ichigan 130 1886 0.069 645 125 24.0 86,155 1.0 Northwestern Unive rsity (Ke llog g) 150 2546 0.059 660 100 25.0 98,830 1.0 Harvard Universit y 176 1779 0.099 680 71 30.0 113,544 1.0 Universit y of Virgin ia (Darde n) 54 499 0.108 660 76 47.0 92,895 1.0 Columbia Un iversity 110 1380 0.080 660 286 27.0 92,550 0.989 3 Universit y of Chicago 100 2697 0.037 685 138 25.0 90,096 1.0 INSEAD (Fra nce) 90 1674 0.054 654 60 12.0 80,000 1.0 Londo n Busin ess School (En gland) 110 648 0.170 630 75 10.0 74,804 1.0 Western Busin ess School (Cana da) 85 450 0.189 630 45 31.0 49,000 1.0 a All data w as taken from the By rne (1997 ) and from the comp anion web site (www.bu sinesswe ek.com).
satisfaction and one measure of recruiter satisfac-tion. This reduced the number of outputs in trials four and ®ve to two. A decrease in eciency scores was noted as a result.
This study's analysis of relative eciency of 24 MBA programs had limitations. Data availability
was limited, for example. While theBusiness Week
ranking (Byrne, 1997) provided a reliable source of data, the data was available only for the top MBA programs. In this study, eciency scores were all above 0.9. A more balanced sample of MBA programs might have resulted in a wider range of eciency scores.
Because of limited data regarding MBA pro-grams outside the United States, only three foreign MBA programs were included as part of this e-ciency analysis. The foreign MBA programs were part of a set of ten programs that included seven of the top US programs. Analysis indicated that all three foreign programs and all but one US pro-gram were ecient. Barriers to calculating the relative eciency of programs outside the United States were noted. Methods for overcoming these barriers and using DEA to determine the relative eciency of MBA programs around the world warrant further research.
The results of this study highlight the impor-tance of the inputs and outputs used in determin-ing relative eciency. Varydetermin-ing the inputs and outputs used will aect the calculated eciency scores. It is advisable to carefully consider the objectives of the MBA programs in question when determining which input and output measures to use in DEA. The publicized ranking of MBA programs by national magazines has a signi®cant impact on corporate recruiters, potential MBA students and the business schools themselves. New rankings based on DEA will result in a more complete, accurate representation of MBA pro-grams. Further, DEA will provide better insight as to how the speci®c programs compare with each other.
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