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By William W. Cooper

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Additional info for Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver software

Example text

For this simple example we can illustrate the situations using a two dimensional graph. The linear programming constraints for each DMU have the following inequalities in common with all variables being constrained to be nonnegative. 3 by taking and as axes. The area denoted by P then shows the feasible region for the above constraints. The boundary of P consists of three line segments and two axes. The three line segments correspond to the efficient DMUs C, D and E. We explain this situation using D as an example and we also explain the relationship between this region and the inefficient DMUs using A as an example.

Another type of inefficiency occurs when only some (but not all) outputs (or inputs) are identified as exhibiting inefficient behavior. 7. We can use and B to illustrate “mix inefficiency” or we can use A, and B to illustrate both technical and mix inefficiency. 4/7=1/5, which is the same as the ratio for A in This augments both of the outputs of A without worsening its input and without altering the output proportions. This improvement in technical efficiency does not remove all of the inefficiencies.

A DMU such as F, with and with an excess in inputs and/or a shortage in outputs, is called ratio efficient but mix inefficient. 2 depicts the efficient frontier. 2 in the weight variables (=multiplier) space. 2 has 2 inputs and 1 output, whose value is unitized to 1. For this simple example we can illustrate the situations using a two dimensional graph. The linear programming constraints for each DMU have the following inequalities in common with all variables being constrained to be nonnegative.