The assessment of dynamic efficiency of decision making units using data envelopment analysis

Abstract

The concept of a "production function" as means to measuring efficiency began in 1928 with the seminal paper by Cobb and Douglas (1928). However, until the 1950s, production functions were largely used as a tool for studying the functional distribution of income between capital and labour. Farrell's argument (1957) provides an intellectual basis for redirecting attention from the production function specifically to the deviation from that function as a measure of efficiency. He developed a method so that we can measure efficiency in terms of distance to the "best DMU" on the frontier isoquant. Charnes, Cooper and Rhodes (1978) generalised Farrell's concept to multiple - input multiple - output situations and reformulated it using mathematical programming and thus derived an efficiency measurement known as Data Envelopment Analysis (DEA). Therefore DEA is a linear programming based method for comparing Decision Making Units (DMUs) such as schools, hospitals, etc. In the method originally proposed by Charnes, Cooper and Rhodes (1978) the efficiency of a DMU is defined as a ratio of the weighted sum of outputs to the weighted sum of inputs. Thus in the original DEA approach the notion of time dimension has been ignored. This thesis proposes a IDEA based method for assessing the comparative efficiencies of DMUs operating production processes where input - output levels are inter - temporally dependent. One cause of inter - temporal dependence between input and output levels is stock input which influences output levels over many production periods. Such DMUs cannot be assessed by traditional or 'static' DEA. The method developed in the study overcomes the problem of inter - temporal input - output dependence by using input - output 'paths' mapped out by operating DMUs over time as the basis of assessing them. The aim of this thesis is, therefore, firstly, to address that traditional or "static" IDEA fails to capture the efficiency of DMUs with inter - temporal input - output dependence. Secondly the thesis develops an approach for measuring efficiency under inter - temporal input - output dependence by defining an inter - temporal Production Possibility Set (PPS). The method developed uses path of input - output levels associated with DMUs rather than input - output DMUs observed at one point in time as static IDEA does. Using this PPS, an assessment framework is developed which parallels that of static DEA. The thesis develops mathematical programming models which use input - output paths to measure efficiency, identify peers and target of performance of DMUs. The approach is illustrated using simulated and real data.