# A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

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## Abstract

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA (S-T DEA) approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

## Keywords

Data Envelopment Analysis Efficiency OR in software Multiobjective programming Linear Programming## Notes

### Acknowledgments

Konstantinos Petridis would like to acknowledge that part of this work was co-funded within the framework of the Action “State Scholarships Foundation’s (IKY) mobility grants programme for the short term training in recognized scientific/research centers abroad for candidate doctoral or postdoctoral researchers in Greek universities or research” from the European Social Fund (ESF) programme “Lifelong Learning Programme 2007–2013”.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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