Monday, May 30, 2016

Data Envelopment Analysis (DEA) - ppt and practice problems..


Data Envelopment Analysis is an Operations Research Tool that uses Linear Programming formulation to find the relative efficiency between different Decision Making Units (DMU) in a service or manufacturing setup. (though it is very popular in the service world)

Even though it is used as an effective setup to find the relative efficiency of various decision making units in the service sector with multiple inputs and multiple output, it can be equally applied in a manufacturing setup, trying to compare the efficiencies of different manufacturing departments or plants of a manufacturing company. 

Good explanation of cells in the spreadsheet to be embedded with formula
Originally it is the idea from Charnes, Cooper and Rhodes in their paper in EJOR, '78), who together did a brilliant job using Linear Programming Problem formulation for a non-linear efficiency problem.

You will find some of the links here of some interest. Depending on the number of DMUs, you have to formulate as much LPPs. Hence manual solution may be difficult considering that one has multiple inputs and multiple outputs,

A spreadsheet solver (LP solver in Excel) or the solver in Google spreadsheet can be used.

Entering cell details in LP solver as parameters
The basic principle on which DEA formulation works is to model the efficiency expression of the different decision making units (DMUs). A non-linear efficiency expression, the objective function, is reduced to a linear expression by equating the input expression for that DMU to unity and including it as a constraint in the constraint set.

I make it a point to see that students desiring to understand DEA should know previously how to solve an Linear programming problem using any spreadsheet, Excel or Google sheet, helpful links are given below ...

Some links are given here .

Excellent self explaining ppt oreoared by me : 

another LP solver tutorial youtube video (how to formulate)

Explains the computer solution of LPP by using LP solver , youtube video ..


points to ponder :

1. why is the initial efficiency obj function considered non-linear ?
2. How is the non-linear function converted to a linear function ?

george..
at

2 comments:

  1. Venkatesh Ganapathy9:29 PM

    Sir, found the following additional, you may add in the blog if found relevant

    https://www.researchgate.net/publication/226038831_Data_Envelopment_Analysis_History_Models_and_Interpretations

    www.springer.com/cda/content/document/cda.../9780387332116-c2.pdf?SGWID..

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  2. Venkatesh Ganapathy9:58 PM

    Linear function is an equation whose graph can be expressed as a straight line; example y= a + bx is a linear function; y= dependent variable and x=independent variable;
    Initial objective function is non linear because ???
    a. relative weights assigned to each inputs and outputs
    b. Conservative view of DEA that gives benefit of doubt to each unit being evaluated; this means that inefficiency calculated is less than actual inefficiency.
    Perhaps this is why initial function is considered non linear (not sure though ..:)

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