PUBL6415 Decision Science in Public Affairs
YUASA
Final Take Home Exam
Question 1
Data Envelopment Analysis Project:
In this question, you, as a manager, are interested in determining how efficiently units (DMUs) within
your organization or similar organizations operate. To perform this analysis, you decided to employ the
Data Envelopment Analysis (DEA). “DEA determines how efficiently an operating unit converts inputs to
outputs when compared with other units.” It might be difficult to get the data. So you can convert the
example data consists performance outcome and input variables to perform your data analysis. Make the
data fit with the nature of the evaluation scenario.
I provide the hypothetical example data (FinalSp21_DEA_Hypothetical_Data) in case you cannot come
up with your data. The spreadsheet contains a caseid, an input variable, and four output variables. You are
free to assign the name of the five variables to use for your analysis. Of course, you are free to use your
data if you have one.
Before you perform the empirical analysis, please describe your DEA project. Please start with the
narrative of the contexts (i.e., the organization, DMUs, output variables, and input variables). The project
needs to be as realistic as possible even if your project is hypothetical. Provide the full description of each
output and input variable. Select inputs and outputs that are broadly considered to be of strategic
importance to the units being evaluated. Use at least four output and four input variables for your
analysis.
The scores or values of these variables should vary across DUMs. If you enter the same score,
EXCEL may not be able to find a solution.
Then, as you did before, define the decision variables, the objective, and the constraints. Implement your
DEA analysis using either the Excel solver or a Risk solver platform.
Construct the table that includes each DMU DEA efficiency score and the composite unit weights
generated from each solver analysis (Sensitivity Table – the values under the Shadow price column or
Langlange Multiplier column depends on the version of the software). Calculate a hypothetical
Composite unit for each DMU. Compare the calculated Hypothetical Composite Unit score of input(s)
and output(s) of a certain DMU with the actual input and output score of the respected DMU. Needless to
say, these composite unit scores are the same as the actual scores if the efficiency score of DMU is 100%.
But, for the DUM efficiency score of less than 100%, compare the original output and input scores with
the estimated composite Unit score. The main objective of generating the composite unit weight and
the hypothetical composite unit score is to find out the reference unit(s) (or comparison unit(s)) for
each of the inefficient DUM’s benchmarking unit(s).
Write the comparison for each DMU row score and its hypothetical composite unit score for the DMU
with less than 100% DEA efficiency score. We expect that some of the output values might be the same
between the original output value and the corresponding Hypothetical Composite Unit score. However,
the hypothetical composite unit scores of the input variable are likely to be less than the original input
value.
Read BakerCh5.pdf and DEA from Baker Powell.pdf on the DEA Optimization Model.
Write a report on the DEA analysis results.
In this report, you should identify the reference DMU of each inefficient DMU (i.e., the
efficiency score less than 1.0). For each inefficient DMU, you not only identify the reference DMU(s)
but also the shadow price (i.e., the composite weight) of the reference unit(s).
Some of the inefficient DMUs' original scores of the output and input variables might not vary
much from the respected hypothetical composite unit score. But some of the hypothetical composite
units’ scores could be different from the respected original scores. It is possible that the higher level of
relative inefficiency unit shows a large gap between the hypothetical composite unit scores and the
respected original observed score. Provide a summary report to the next meeting where the executives
discuss the strategy of improving the inefficient DMUs' performance.
Construct the summary table and insert it here.
Submit your Excel file. Please make sure to save all sensitivity report sheets and label them with the
corresponding DMU. Label the sensitivity report
sheets based on the DMU ID number.
Submit:
Excel file with your DMU model.
Make sure to include as follows:
Composite unit weights (generate Sensitivity Analysis table for each DUM and Copy
Shadow price) for the respected DMU.
Calculate Hypothetical Composite Unit for All DMUs using the respected
Composite unit weights.
Data analysis report documents (this document should insert in your exam answer document as
Question 1 answer).
Including the interpretation of:
a. The DEA efficiency score of each DMU.
b. Hypothetical Composite Unit of DMU with an efficiency score of less than 100%.