Dear Gamze,

It seems that you can draw some conclusion about the alternative use of the cost input data. The scores might show that the inputs are more efficiently employed in one alternative output than another. At the risk of being simplistic, you can use your capital, labor, raw materials to make several products. Now, in your different scenarios, you must make the same underlying assumptions, for instance the output must be produced with the same assumption regarding scale, such a constant, variable, decreasing or increasing returns.

Dear Gamze,

If the production process can be described as coint-production (in which same inputs are used to produce multiple outputs, i.e. a DMU, lets say hospital can produce both inpatient and outpatient care with the same inputs, simultaneously), the efficiency literature offers to use all outputs and inputs in a single efficiency model. It is also possible to conduct different single output models, but you should keep in mind that the efficiency scores could be biased due to (if there is) coint-production. On the other hand, as Lall B. Ramrattan pointed out above, assumption regarding scale is also an other important issue.

Dear Prof. Ramrattan and Prof. Atilgan,

Thank you for the answers, I really appreciate them. I think that it is better to be a little bit more specific to describe my case. I am working on water utility data and the only product is the water distributed to the customers. I will use variable return to scale assumption and input orientation for both scenarios. The inputs I am planning to use in both scenarios are energy cost and operating costs other than energy. As the output I am thinking to use operating revenue in the first scenario and volume of distributed water in the second. What I am wondering is that if the utility X is more efficient in the first scenario (revenue as the output) compared to the second one (water volume as the output), can this show that this utility sells water overpriced and needs to lower the water rate? Or the other way round, if the utility Y is less efficient on revenue based scenario compared to water volume based scenario, can I say this utility sells water cheap and can increase the water rate? 

As a side note, since the number of DMUs is small (22) in my study I prefer to keep the number of input and output variables as low as possible to obtain a DEA model with a good discriminating power.

Thanks.