The role of non-Archimedean epsilon in finding the most efficient unit: With an application of professional tennis players

Mehdi Toloo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


The determination of a single efficient decision making unit (DMU) as the most efficient unit has been attracted by decision makers in some situations. Some integrated mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) data envelopment analysis (DEA) models have been proposed to find a single efficient unit by the optimal common set of weights. In conventional DEA models, the non-Archimedean infinitesimal epsilon, which forestalls weights from being zero, is useless if one utilizes the well-known two-phase method. Nevertheless, this approach is inapplicable to integrated DEA models. Unfortunately, in some proposed integrated DEA models, the epsilon is neither considered nor determined. More importantly, based on this lack some approaches have been developed which will raise this drawback. In this paper, first of all some drawbacks of these models are discussed. Indeed, it is shown that, if the non-Archimedean epsilon is ignored, then these models can neither find the most efficient unit nor rank the extreme efficient units. Next, we formulate some new models to capture these drawbacks and hence attain assurance regions. Finally, a real data set of 53 professional tennis players is applied to illustrate the applicability of the suggested models.

Original languageEnglish
Pages (from-to)5334-5346
Number of pages13
JournalApplied Mathematical Modelling
Issue number21-22
Publication statusPublished - Nov 1 2014


  • Data envelopment analysis
  • Integrated model
  • Most efficient unit
  • Non-Archimedean epsilon

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this