Dear all. I know it seems idiotic, but I have this problem and my knowledge is not enough to solve it. I am coding a simple DEA model in GAMS for 55 DMUs (Decision Making Units) with 8 input and 2 output in order to compute the score. But the problem is, all score are 1. When I put some restriction on weights, the infeasibility appears. I really appreciate any suggestion to solve my problem. Thank you in advance. Regards 
It's theoretically possible for any number of DMUs to all be "efficient", but it certainly seems unlikely. The first thing to do would be to test the correctness of the model. I'd suggest creating a spreadsheet with the 55x10 table of inputs and outputs, plus 10 cells for the weights assigned to the inputs and outputs and 55 computed efficiencies using those weights. Take a random sample of DMUs (you probably won't want to do this all 55 times), run the DEA model with that DMU as target, plug the resulting weights into the spreadsheet and confirm that the target DMU has efficiency 1 and all others have efficiency <= 1. answered 23 Jan '13, 18:43 Paul Rubin ♦ Dear Paul Rubin I am so thankful for your suggestion. I did what you said for a random dmu. then I calculate the score in Excel using the computed weights from GAMS output for that dmu, using the formula: score = sum(out, weight(out) * Ouput(out)); surprisingly, while the score in GAMS is 1, the compute score in excel is 0.8???!!!! What is wrong with model, it is very simple model that I extracted from Seiford DEA book. what can I do now?
(24 Jan '13, 02:48)
Bob Pay
First question: does a hand calculation using those weights match the Excel result or the GAMS result? Also, do the weights satisfy the normalization constraint (value of inputs for the target DMU = 1)?
(24 Jan '13, 09:56)
Paul Rubin ♦
About first question: Now I am manipulating the lower limit for output weights, for all dmus in separate runs in GAMS to achieve a promising score which is not 1 (unless it is impossible). under this circumstance, hand calculation is like excel. for example the output of gams is z= 0.98 while the actual value is 1.705 ! About second question: yes it is a little weird for me1 I will be so thankful...
(24 Jan '13, 16:03)
Bob Pay
Perhaps you should post your GAMS model (and your data, if it's not proprietary). If you have access to a sharing site where you can make files public (Dropbox, Google Drive, ...), that might be the best route  just post the link(s) here. There's also Pastebin if you don't have a public folder anywhere.
(24 Jan '13, 17:08)
Paul Rubin ♦
Dear Paul I have uploaded the data and gams file in google drive here. data are in Sheet2 of excel file. gams model compute all score in a loop. Thank you so much. I don not know why it is not possible to send a link in comment, so I put it down as answer to this posy "Link text"
(25 Jan '13, 04:28)
Bob Pay

I've looked at the GAMS model (which seems correct to me, although I don't use GAMS). I also replicated the model in AMPL with the shared data and observed that every DMU scored an efficiency rating of 1. Three suggestions:
answered 26 Jan '13, 14:40 Paul Rubin ♦ Dear professor Rubin I am so thankful for your great help and it is really kind of you. I am modifying my data and code according to your suggestions, and I hope get a promising result ( I will report later) To be honest, I ma not very interested in DEA models too, but there was an accident that led me to use this tool. Anyway, I really do not know how thank you. Regards,
(26 Jan '13, 15:12)
Bob Pay
You're welcome. I need to add a few details. First, using market prices for inputs is tricky (whether to merge them into a single cost value or to set lower bounds on weights) if the DMUs acquire their inputs in different markets. You could end up penalizing a DMU just because they reside in an expensive market. Second, the DEA model trick of maximizing output value subject to input value = 1 relies on being able to arbitrarily scale all weights by a given constant. You jeopardize that with arbitrary bounds on the weights. You can find some literature on lower bounds.
(27 Jan '13, 09:06)
Paul Rubin ♦
Regarding the lower bounds, rather than \(w_i\ge \epsilon\) for each weight \(w_i\), with \(\epsilon\) some positive constant, you might try \(w_i\ge\lambda w_j\) for all \(i\neq j\) with \(\lambda\) a positive constant. That preserves first order homogeneity (so the scaling trick that allows the input weight = 1 constraint for the target is unaffected). Even with that and scaling the inputs, though, it seems that in your data every DMU is either efficient or pretty darn close.
(27 Jan '13, 09:15)
Paul Rubin ♦
I have done your primary modification and got so much better result. About the points on lower bound, yes, what I am doing is a not precise, but as I am in hurry, it is a better way. In future, I will do consider your suggestions. But totally, you are right about the condition of DMUs in this data set, they are all near to efficient. I really want to thank you again. I think I need to enhance my knowledge in area of DEA and LP based ranking models.
(28 Jan '13, 16:25)
Bob Pay
You are quite welcome. If you think your problem its resolved, it would help if you accepted one of the solutions (the check mark button) so that the system no longer lists it as unanswered.
(28 Jan '13, 18:57)
Paul Rubin ♦
