“…Among the different indices for measuring productivity changes of decision making units (DMUs) over time, Malmquist indices have commonly been used by researchers and practitioners in various environments. Examples include the health sector (e.g., see Kirigia et al 2007;Chowdhury et al 2011), the electricity industry (e.g., see Tovar et al 2011;Aghdam 2011), telecommunications (e.g., see Lam and Shiu 2010;Hisali and Yawe 2011), the water industry (e.g., see Corton and Berg 2009;Portela et al 2011), agriculture (e.g., see Kao 2010;Xu 2012), transportation (e.g., see Gitto and Mancuso 2012;Pires and Fernandes 2012), the banking industry (e.g., see Asmild et al 2004; Portela and Thanassoulis 2010) and others. Caves et al (1982) introduced the earliest type of the Malmquist index and showed how the change in productivity experienced by an operating unit can be measured over time.…”