decision analysisSlide
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Examples of service institutions:
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Example 1
A Bank (33 branches) wanted to know which branches are efficient and which are inefficient.
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Example 1
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Only 10 branches were operating efficiently.
23 branches were inefficient (using excess input to produce the output).
The DEA results can be used to review the branch operations.
To check the operating differences & best practice branches.
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reduced its total branch staff by 20% within one year.
new operation resulted annual savings of RM6 million.
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in education system
Consider a town with 4 primary schools: SKA, SKB, SKC & SKD.
The state has implemented a series of standards of learning (SOL) in reading, mathematics and history for standard 5 students.
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Thus, every school has 3 output: SOL for reading (SOLR), SOL for maths (SOLM) and SOL for history (SOLH).
The input considered are:
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Which school are less efficient in converting their inputs to outputs relative to other elementary schools in town? Let’s check SKD.
First, let us build the model.
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Decision Variables:
In DEA, the decision variables are “price per unit output” and “price per unit input”
xi = a price per unit of each output
yi = a price per unit of each input
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Objective function
To maximize the value of SKD outputs, which also equal efficiency.
Maximize:
Model Constraints
To be able to compare between schools, the total value of each school’s input must be scaled to 1.
SKD
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Model Constraints
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The objective of this model is to determine whether SKD is efficient/inefficient. If the value of Z (objective function) is equal to 1, the school is efficient. If Z is less than 1, it is inefficient.
The value of the decision variable have little meaning for us.
TRY SOLVE THE MODEL USING
EXCEL SOLVER!
Food of thought…
Pure mathematics is the world's best game.  It is more absorbing than chess, and lasts longer than Monopoly.  It's free.  It can be played anywhere - Archimedes did it in a bathtub. 
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