weight construction in DEA analysis

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#1
Hi,

I hava a problem with weight construction in Data envelopment analysis. My goal is to construct weights that reflects the reality of my data. In un-weighted DEA, the results could be that one or more variables (either input- or output) are neglected for any DMU which is not realistic in my data.

I my most simple dataset I have 2 inputs and 1 output with around 100 DMU. It is nursing care data, and one of the inputs are a non-discretionary measure of patient health (I1) (i.e. cannot be changed by the DMU). The other input are cost-data (I2). The inputs are expected to move in same direction. That is, if health is worse (higher value in an index), the cost is expected to be higher.

My output data is an survey-index of the elderlys opinions/gradings of the care they receive.

Inputs: health (I1) and cost (I2)
Output: grading (O1)

The expectation is that if cost goes up, the grading will improve/go up. But if their health is worse than average in the health index, the grading will go down.

So, in short, I want to construct weights that restrict the possibility for any of my inputs (I1 and I2) and output (O1) to be zero. Furthermore, the weight on health
should never be greater than that of the cost (I1<=I2).

The weight of O1 (grading) should be at least equal to that of cost (O1>=I2).

I am using EMS software, and so far my weight construction has looked like this:
Inputs: health (I1) and cost (I2)
Output: grading (O1)


O1; I1; I2
a) 0 -10 1
b) 0 1 -1
a and b to ensure that neither input can be zero if any of them are positive, and ratio: 1<= I2/I1 <=10 so that cost is at least as large as health status
c) 1 -10 0
d)-1 1 0
c and d to ensure that neither O1 and I1 can be zero if any of them are positive, and ratio of grading vs. health is equal that of cost vs. health.


The problem is that something with the weights above are wrong. When I run the model (I try different types of DEA, all same result), the weights are set to 0 for all DMU, resulting in that all DMU are 100% efficient.

Is there anyone who know this type of analysis and could help?

Any comments would be greatly appreciated!

Best regards,

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