Dear Parag,

For your question i suggest you to see links and attached files in topic.

- DEA Cross Efficiency - Springer

www.springer.com/cda/content/.../9781489975522-c1.pdf?...0... -Second order cone programming approach to two ... - Semantic Scholar

https://pdfs.semanticscholar.org/.../4902ac4ae39f1a98aa35e69c69...

Best regards

Following.

because of their different in orientation.

are the "maximizing outputs subject to given inputs"

and

"minimizing inputs subject to given outputs" same?!

Agree with this answer, because of their difference in orientation.

It is not sufficient to attribute it just to the difference in the orientation between the CCR and the BCC models since "maximizing the outputs subject to the given inputs" and "minimizing the inputs subject to the given outputs" under CRS assumtpion provide reciprocal efficiency scores. Thus, we firstly have to consider the additional free in sign variable in the multiplier BCC model and the additional constraint about the lambdas (Σλ=1) in its envelopment counterpart. This changes the shape of the frontier (BCC efficient frontier) and allows, besides CRS, for increasing and decreasing returns to scale. The above, in conjuction with the orientation that guides the projections, provides non-reciprocal efficiency scores between input and output orientation under VRS assumption.

For a schematic represenation of the above check the attached image.

CRS provided reciprocal values in both orientations, that because you deal with semilar returen to the scall and lambdas, but in VRS model, experence increasing or decreasing return to the efficient scall that affect lambdas in (each variariable) "to achieve maximum output with given inputs or minimum input at same output" every time you run the analysis with different orientation, so you will find non-reciprocal values from VRS model.