[Help-glpk] [Fwd: Using GLPK for DEA]

[Andrew Makhorin]

-------- Forwarded Message --------
From: Amogh Tolay <address@hidden>
To: address@hidden
Subject: Using GLPK for DEA
Date: Sun, 8 Jan 2012 20:35:18 +0530

Dear Sir/Madam


I have been trying to use GLPK to solve a Data Envelopment Problem using
the CCR model. I am a novice and I was unable to find the way to
implement such problems with GLPK. It would be great if you could help
me out! The problem is to find the CCR efficiency of a two-input and
two-output problem which is something as follows:
Labels:    A     B     C     D
Input1:    20,   19,   25,   27
Input2:    151, 131, 160, 168


Output1: 100, 150, 160, 180
Output2:  90,  50,   55,   72


I need to maximize the efficiency and find the corresponding weights.
That is, I need to apply the CCR model with variable weights to optimize
this problem. Thus, for Label A, the set of equations are: 
(where u1, u2 are the weights for inputs of A and v1, v2 are the weights
for outputs of A.)


maximize 100v1+90v2;


subject to:
20u1+151u2=1;
100v1+90v2<=20u1+151u2;
150v1+50v2<=19u1+131u2;
160v1+55v2<=25u1+160u2;
180v1+72v2<=27u1+168u2;


where u1, u2, v1 and v2 are all greater than 0.


I haven't been able to figure out as to how to implement this problem
using GLPK without converting it to Standard Form. Is it necessary to
convert such equations to Standard Form before using GLPK? If so, can
you please guide me to convert such problems into a format that GLPK can
handle? 
I tried searching for documentation for such problems, but unfortunately
I couldnt find anything. If I am missing some online
resources/documentations which specifically deal with such problems, I
would be glad if you could point them out to me.
It would be really kind of you if you could help a novice like me. :)

Thank You
--------
Amogh