Spatio-temporal efficiency measurement under undesirable outputs using multi-objective programming: a GAMS representation

Abstract

Time series data in DEA often represent successive versions of the same unit (DMU). In order to assess efficiency of each DMU, several DEA techniques have been employed. One of the problems that conventional DEA models face is that the reference set, when dealing with time series data, is not constructed correctly. This is attributed to the fact that conventional DEA models examine the DMUs and extract their efficiency scores based only the spatial dimension. However, when dealing with time series data for DMUs in the DEA context, the temporal dimension should be also taken into account. This paper is based on Spatio-Temporal DEA (ST-DEA) model (Petridis et al. in Ann Oper Res 238(1–2):475–496, 2016) and extends the presented S-T DEA model by incorporating undesirable inputs/outputs. A GAMS representation of the model for the solution and explanation of ST-DEA model is shown through an illustrative example. The scope of the paper is to analyze the concept of ST-DEA model and demonstrate its applicability via an application explained in GAMS optimization software.