The examination of redundancy of non-homogeneous weight restrictions for measuring the relative efficiency in BCC model

Data envelopment analysis (DEA) is a mathematical programming technique, which is used to evaluate relative efficiency of decision making units (DMUs) and has been proposed by Charnes et al. (1978). This technique has been extended by Banker et al. (BCC model, 1984). In the CCR model, for each DMU is formed the virtual input and output by weights vi ( i = 1, 2, . . . ,m) and ur (r = 1, 2, . . . , s). These weights are derived from the data instead of being fixed in advance. To each DMU is assigned a best set of weights with values that may vary from one DMU to another.The assigned weights to each DMU may be unrealistic. A few problems may arise if weight restrictions are incorporated in the linear CCR model. First, it may make the CCR model infeasible. Secondly, the fractional linear CCR model and its linear forms are used to measure the maximum relative efficiency of the assessed DMU. Their optimal solutions are regarded as the input and output weights that represent the assessed DMU in the best light in comparison with all the other DMUs in the observed group. This interpretation remains correct if additional homogeneous weight restrictions, including bounds on ratios of weights, very often are incorporated into the CCR model or its linear forms. It has been demonstrated that, in the presence of additional no homogeneous weight restrictions, which includes absolute weight bounds, the CCR model and its linear forms may identify the maximum relative efficiency of the assessed DMU incorrectly. Without additional weight restrictions, this is, of course, equivalent to maximizing the relative efficiency of 1the assessed DMU, but this is generally not so in the presence of additional weight bounds. Furthermore, some papers have been published in this area [1, 2, and 3]. In this paper we incorporate into the BCC model or its linear forms in the presence of additional non homogeneous weight restrictions, which includes absolute weight bounds into the BCC model we may be have above problems and also the optimal value of the resulting models that shows the maximum relative efficiency may be negative or zero. But the efficiencies of other inefficient DMUs are obtained relative to the efficient DMUs, and are assigned efficiency scores between zero and one. This problem happens because a free variable exists in objective function of the BCC model, it makes the value of objective function into (-∞, 1] interval, and it dose not guarantee to obtain correctly evaluate the maximum relative efficiency of the assessed unit