Stochastic Data Envelopment Analysis

In traditional DEA models, the technologies are developed using the premise that inputs and outputs are precisely measured and are, therefore, deterministic. However, in practical situations, the general production processes are often stochastic. The stochastic production relationship in a DEA setting may arise in different situations, for example, when stochastic variations in inputs and outputs affect the production frontier; when inputs and outputs are faced with stochastic prices while measuring allocative efficiency; when the slacks obtained from the DEA efficiency frontier are analyzed in terms of their statistical distribution; when an economic method is applied to estimate the stochastic production frontier; etc. (Sengupta, 1990). Over the last two decades, many researchers have proposed DEA-based models with stochastic data. Sengupta (2000) applied a stochastic DEA model using mathematical expectations for random inputs and outputs. Banker (1993) added statistical elements to DEA and developed an approach aimed at influencing statistical noise in inference. Many studies (e.g., Cooper et al., 1996, 1998; Land et al., 1993; Olesen & Petersen, 1995, 2016) have introduced chance-constrained programming in DEA to accommodate random changes in data. Banker (1986) proposed a related semi-parametric stochastic frontier analysis (SFA) based on a minimization of the sum of the absolute value of all composed error terms. For parametric and semi-parametric models, see Banker (1989, 1996), Banker and Chang (1995), Banker et al. (1994, 2015), and Banker and Maindiratta (1992). Additional approaches and applications can be found in Charles and Cornillier (2017), Charles and Udhayakumar (2012), Charles et al. (2018), Grosskopf (1996), Horrace and Schmidt (1996), Simar (1996), Simar and Wilson (1998), and Udhayakumar et al. (2011), among others.