SdeaR

Stochastic Data Envelopment Analysis with R

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)

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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.

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Installation

Install from CRAN:

install.packages("SdeaR")

Development version from GitHub:

install.packages("remotes")
# remotes::install_github("vjbolos/SdeaR")
install.packages("SdeaR", repos = c('https://vjbolos.r-universe.dev', 'https://cloud.r-project.org'))

Load package:

library(SdeaR)
library(deaR)

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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

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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)

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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

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Radial models

• modelstoch_radial()
• modelstoch_radial_supereff()

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

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Directional models

• modelstoch_dir()
• modelstoch_dir_dd()

Supports:

• Stochastic directions
• Deterministic directions

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Additive models

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

Includes:

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

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Documentation

Full reference manual:

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

Package PDF manual:

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

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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.

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Software Requirements

• R >= 3.5

• Depends on:

  • deaR

Platform-independent and tested on:

• Windows
• Linux
• macOS

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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.

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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

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License

GPL-3

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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

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Support

Questions and bug reports:

vicente.bolos@uv.es

GitHub issues:

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