I am studying DEA models and in my textbook there are conflicting definitions on what the sum of the variables in dual model should be.
I am struggling with interpreting the variables as well - I know each variable in the dual model represents a restriction in the primary model and their values are the shadow prices in primary model solution.
CRS
In CRS the sum of the dual variables does not matter. $e^T\lambda - free$. The graphical representation of the effectivity threshold in CRS should look something like this
VRS
In VRS the sum of dual variables should be 1. $e^T\lambda=1$ The graph for VRS should look something like this
NIRS
Here is where the conflicting information start. In one place the sum of lambda is given as $e^T \lambda \leq 1$, in another as $e^T \lambda > 1$. The graph in NIRS should look something like this - I am not 100 % sure on my graph here, I sourced it from here, page 3
NDRS
Again, same conflicting information about the dual variable restriction: $\lambda \geq 1$ and $e^T \lambda < 1$. Graph for NDRS here. Again, if it's incorrect please let me know how to correct it - source, fig 1.
What I would like to know:
- How to interpret $\lambda$ in the dual model
- Which version for the $\lambda$ restrictions for NIRS and NDRS are correct? And how to logically interpret the restriction?