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Data Envelopment Analysis

The DEA problem is an optimization problem, which computes efficiencies
of sites, based on input and output.

The idea is that each site can choose its own weights to estimate
its efficiency. Some sites will still not be efficient, since
no weight helps them.

Please refer to the literature for more information.
>load dea
Data Envelopment Approach.
Try "help dea.e" for more information.

A random Example

>Output=random(8,2);
>Input=random(8,2);
>graphDEA(Output,Input); insimg;

Data Envelopment Analysis

>showDEA(Output,Input);
Site: 1
Efficiency: 0.0463611
Replace with:
16.6199 of 2

Site: 3
Efficiency: 0.127914
Replace with:
101.147 of 8

Site: 4
Efficiency: 0.257783
Replace with:
48.6189 of 2
30.9739 of 8

Site: 5
Efficiency: 0.519924
Replace with:
67.4029 of 2
28.4808 of 8

Site: 6
Efficiency: 0.229767
Replace with:
45.6377 of 2

Site: 7
Efficiency: 0.733806
Replace with:
55.8282 of 2

Another Example

>Output=[150,50;225,75;90,10;160,40;50,50;75,75;200,50; ...
>350,100;400,90;250,300;350,350;350,400;275,375; ...
>220,40;300,10;320,275;375,230;230,50;290,90;360,70];
>Input=[200,600;600,1200;200,200;600,300;500,200; ...
>320,150;375,450;400,320;550,480;900,660;850,720;720,940; ...
>900,850;250,370;115,250;600,590;550,710;200,280;450,410;415,575];
>solveAllDEA(Output,Input)
[ 0.626931330472  0.313465665236  0.386226415094  0.481509433962  0.5  1
0.459302066225  1  0.745676100629  0.929959331225  1  1
0.936237090256  0.593335549675  1  1  0.901226549931  0.853277885822
0.711866047501  0.623979503148 ]
>graphDEA(Output,Input,0); insimg;

Data Envelopment Analysis

>solveAllDEA(Output,Input,1)
[ 0.885256410256  0.359722222222  1  0.625925925926  0.75  1
0.560623428859  1  1  0.933884297521  1  1  0.976470588235
0.718388609134  1  1  1  0.990477882395  0.73707170658  0.925677710843 ]
>w1=solveAllDEA(Output,Input,0);
>w2=solveAllDEA(Output,Input,1);
>format(10,2); Output|Input|w1'|w2', shortformat();
   150.00     50.00    200.00    600.00      0.63      0.89 
   225.00     75.00    600.00   1200.00      0.31      0.36 
    90.00     10.00    200.00    200.00      0.39      1.00 
   160.00     40.00    600.00    300.00      0.48      0.63 
    50.00     50.00    500.00    200.00      0.50      0.75 
    75.00     75.00    320.00    150.00      1.00      1.00 
   200.00     50.00    375.00    450.00      0.46      0.56 
   350.00    100.00    400.00    320.00      1.00      1.00 
   400.00     90.00    550.00    480.00      0.75      1.00 
   250.00    300.00    900.00    660.00      0.93      0.93 
   350.00    350.00    850.00    720.00      1.00      1.00 
   350.00    400.00    720.00    940.00      1.00      1.00 
   275.00    375.00    900.00    850.00      0.94      0.98 
   220.00     40.00    250.00    370.00      0.59      0.72 
   300.00     10.00    115.00    250.00      1.00      1.00 
   320.00    275.00    600.00    590.00      1.00      1.00 
   375.00    230.00    550.00    710.00      0.90      1.00 
   230.00     50.00    200.00    280.00      0.85      0.99 
   290.00     90.00    450.00    410.00      0.71      0.74 
   360.00     70.00    415.00    575.00      0.62      0.93 

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