yuchengxia/envelopment-py

Data Envelopment Analysis implementation in Python

Data Envelopment Analysis

This repository implements the DEA (Data Envelopment Analysis) algorithm in Python, based on numpy (scipy stack). The model is built on the specifications and formulas described and derived in Sherman and Zhu (2006, pp. 49-89).

Brief description

The model is estimated by minimizing the theta expression for each unit, where theta is uy/vx, subject to constraints as defined in equation (2.2) in Sherman and Zhu. This dual linear program is optimized using Sequential Least Squares Programming, as implemented in scipy with the scipy.optimize.fmin_slsqp method.

The model is optimized unit-by-unit, with weights being initialized randomly, with a uniform distribution between -0.5 and 0.5. After each unit's weights are optimized and the algorithm converges, theta (efficiency) of that unit is calculated and saved.

After all units are fit, the fit() function prints thetas for each unit.

Sources

Sherman and Zhu (2006) Service Productivity Management, Improving Service Performance using Data Envelopment Analysis (DEA) [Chapter 2] ISBN: 978-0-387-33211-6