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<p>This study uses data envelopment analysis (DEA) to create a stochastic Malmquist productivity index (MPI). DEA is a popular tool for assessing the relative effectiveness of decision-making units (DMUs). Examples of DMUs include universities, hospitals, manufacturers, sub-sections, supply chains, sports teams and countries. MPI is a robust comparative statistical analysis used to evaluate the DMU's productivity changes between two periods. The integration of DEA and MPI can generate powerful quantitative means of obtaining useful details regarding the relative comparative performance of DMUs, which is beneficial for continuous improvement. Typically, the DMUs examined have vectors of many inputs and outputs that may be deterministic or stochastic in certain cases. This study developed an algorithm using MPI-DEA that assists DMUs in evaluating their relative performance when certain inputs and outputs are stochastic. The developed algorithm is used for stochastic MPI (SMPI) based on chance-constrained programming (CCP), in which the stochastic variables are normally distributed, whereas the remaining variables are deterministic. Accordingly, this study provides future extensions to any programming language used in performance analyses and decision science applications.</p>

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Developing a stochastic Malmquist productivity index for efficiency analysis of decision-making units: a data envelopment analysis approach

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Nahia Mourad,
  • Ahmed Mohamed Habib,
  • Assem Tharwat

摘要

This study uses data envelopment analysis (DEA) to create a stochastic Malmquist productivity index (MPI). DEA is a popular tool for assessing the relative effectiveness of decision-making units (DMUs). Examples of DMUs include universities, hospitals, manufacturers, sub-sections, supply chains, sports teams and countries. MPI is a robust comparative statistical analysis used to evaluate the DMU's productivity changes between two periods. The integration of DEA and MPI can generate powerful quantitative means of obtaining useful details regarding the relative comparative performance of DMUs, which is beneficial for continuous improvement. Typically, the DMUs examined have vectors of many inputs and outputs that may be deterministic or stochastic in certain cases. This study developed an algorithm using MPI-DEA that assists DMUs in evaluating their relative performance when certain inputs and outputs are stochastic. The developed algorithm is used for stochastic MPI (SMPI) based on chance-constrained programming (CCP), in which the stochastic variables are normally distributed, whereas the remaining variables are deterministic. Accordingly, this study provides future extensions to any programming language used in performance analyses and decision science applications.