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Stochastic Data Envelopment Analysis with R

CRAN version Downloads License: GPL-3

SdeaR is an open-source R package for Stochastic Data Envelopment Analysis (SDEA) based on chance-constrained programming.

Unlike conventional DEA approaches that assume deterministic input/output data, SdeaR explicitly incorporates uncertainty by modelling inputs and outputs as multivariate normally distributed random variables.

The package provides a comprehensive framework for estimating stochastic efficiency under alternative model specifications, including:

  • Radial chance-constrained DEA models
  • Radial super-efficiency chance-constrained models
  • Directional chance-constrained DEA models
  • Additive chance-constrained DEA models (E-model and P-model)
  • Additive super-efficiency chance-constrained models

with support for:

  • Constant Returns to Scale (CRS)
  • Variable Returns to Scale (VRS)
  • Non-increasing Returns to Scale (NIRS)
  • Non-decreasing Returns to Scale (NDRS)
  • Generalized Returns to Scale (GRS)

Motivation

Data Envelopment Analysis (DEA) is a widely used nonparametric methodology for measuring the relative efficiency of homogeneous decision-making units (DMUs).

Classical DEA assumes exact observations. However, many real-world datasets contain measurement uncertainty, noise, or stochastic variability.

SdeaR fills an important gap in the DEA software ecosystem by providing a robust and user-friendly implementation of chance-constrained DEA models for stochastic data.

Installation

Install from CRAN:

install.packages("SdeaR")

Development version from GitHub:

install.packages("remotes")
remotes::install_github("vjbolos/SdeaR")

Load package:

library(SdeaR)
library(deaR)

Workflow

The standard workflow consists of:

  1. Build a deterministic DEA dataset with deaR
  2. Construct stochastic data with make_deadata_stoch()
  3. Select a stochastic DEA model
  4. Estimate efficiency scores
  5. Extract and analyse results

Minimal Example

Using the classical Program Follow Through dataset:

library(SdeaR)
library(deaR)
data("PFT1981")
# Select Program Follow Through sites
PFT <- PFT1981[1:49, ]
# Create deterministic DEA data
PFT <- make_deadata(PFT, ni = 5, no = 3)
# Define stochastic output variances
c <- 0.5
var_output <- matrix(c^2, nrow = 3, ncol = 49)
# Create stochastic dataset
PFT_stoch <- make_deadata_stoch(
  datadea = PFT,
  var_output = var_output
)
# Run radial stochastic DEA model
results <- modelstoch_radial(PFT_stoch)
# Extract efficiencies
efficiencies(results)

Main Functions

Data preparation

  • make_deadata_stoch()

Constructs stochastic DEA datasets from deterministic deaR objects and covariance specifications.

Supports:

  • Full covariance matrix
  • Input-input covariance arrays
  • Output-output covariance arrays
  • Input-output covariance arrays
  • Diagonal variance structures

Radial models

  • modelstoch_radial()
  • modelstoch_radial_supereff()

Implements chance-constrained radial DEA models and super-efficiency extensions.

Directional models

  • modelstoch_dir()
  • modelstoch_dir_dd()

Supports:

  • Stochastic directions
  • Deterministic directions

Additive models

  • modelstoch_additive()
  • modelstoch_additive_p()
  • modelstoch_addsupereff()

Includes:

  • Expected value models (E-models)
  • Probability models (P-models)
  • Super-efficiency additive models

Documentation

Full reference manual:

https://cran.r-project.org/package=SdeaR

Package PDF manual:

https://cran.r-project.org/web/packages/SdeaR/SdeaR.pdf

Mathematical Framework

All models assume:

  • Inputs and outputs follow a multivariate normal distribution
  • Chance constraints are transformed into deterministic equivalents
  • Constraints are satisfied with probability at least 1 − α

This allows explicit efficiency analysis under uncertainty while preserving tractable optimization formulations.

Software Requirements

  • R >= 3.5

  • Depends on:

    • deaR

Platform-independent and tested on:

  • Windows
  • Linux
  • macOS

Citation

If you use SdeaR in academic work, please cite:

Bolós, V.J., Coll-Serrano, V., & Benítez, R. (2026)

SdeaR: Stochastic Data Envelopment Analysis. R package version 1.0.2.

Related Work

The package extends previous work on:

  • Chance-constrained DEA
  • Stochastic efficiency analysis
  • Directional stochastic DEA models
  • Additive stochastic DEA formulations

and complements the deterministic DEA package:

  • deaR

License

GPL-3

Authors

Vicente J. Bolós
Department of Business Mathematics
University of Valencia

Vicente Coll-Serrano
Department of Applied Economics
University of Valencia

Rafael Benítez
Department of Business Mathematics
University of Valencia

Support

Questions and bug reports:

vicente.bolos@uv.es

GitHub issues:

https://github.com/vjbolos/SdeaR/issues

Read the original on github.com ↗