Cross efficiency

Preparing…

Import modules and prepare data.

import matplotlib.pyplot as plt
import pandas as pd

from Pyfrontier.frontier_model import MultipleDEA

df = pd.DataFrame(
    {"price": [3, 2, 4, 6, 4], "rent": [5, 2, 2, 1, 6], "output": [2, 1.5, 3, 2, 2]}
)

dea = MultipleDEA("CRS", "in")
dea.fit(df[["price", "rent"]].to_numpy(), df[["output"]].to_numpy())

dea.result[0]

[r.score for r in dea.result]

dea.cross_efficiency

efficiency_matrix = dea._cross_efficiency_matrix()

plt.figure()
plt.imshow(efficiency_matrix, interpolation="nearest", vmin=0, vmax=1, cmap="Blues")
plt.colorbar()
plt.show()

References

Author John Doyle and Rodney Green. Title Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses, Journal of the Operational Research Society, 1994. :numref:10.1057/jors.1994.84.

Author Sexton, Thomas R. and Silkman, Richard H. and Hogan, Andrew J.. Title Data envelopment analysis: Critique and extensions, New Directions for Program Evaluation, 1986. :numref:https://doi.org/10.1002/ev.1441.