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]

MultipleResult(score=np.float64(0.888889), id=0, dmu=DMU(input=array([3, 5]), output=array([2.]), id=0), x_weight=[0.333333, 0.0], y_weight=[0.444444], bias=0.0)

[r.score for r in dea.result]

[np.float64(0.888889), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.666667)]

dea.cross_efficiency

[np.float64(0.7166663333333333), np.float64(0.8437494999999999), np.float64(0.937499875), np.float64(0.4444442777777778), np.float64(0.5416665833333334)]

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

See also

Author

John Doyle and Rodney Green.

Title

Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses,

Journal of the Operational Research Society, 1994. https://doi.org/10.1057/jors.1994.84.

See also

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. https://onlinelibrary.wiley.com/doi/abs/10.1002/ev.1441.