The most popular weight restrictions are assurance regions (ARs), which impose ratios between weights to be within certain ranges. ARs can be categorized into two types: ARs type I (ARI) and ARs type II (ARII). ARI specify bounds on ratios between input weights or between output weights, whilst ARII specify bounds on ratios that link input to output weights. DEA models with ARI successfully maximize relative efficiency, but in the presence of ARII the DEA models may underestimate relative efficiency or may become infeasible. In this paper we discuss the problems that can occur in the presence of ARII and propose a new nonlinear model that overcomes the limitations discussed. Also, the dual model is described, which enables the assessment of relative efficiency when trade-offs between inputs and outputs are specified. The application of the model developed is illustrated in the efficiency assessment of Portuguese secondary schools. The efficiency of decision making units (DMUs) in data envelopment analysis (DEA) is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs. The weights are the variables of the DEA model, and DMUs have complete freedom to choose the weights associated with each input and/or output that maximise their relative efficiency. This complete flexibility in the selection of weights is especially important for identifying inefficient DMUs, as when the unit under assessment does not score 100% efficiency, this tells us that its peers are more productive even when the weights of all units are set to maximise the score of the unit assessed. Therefore, no inefficient unit can complain that its score would have been better if a different set of weights was used. However, this complete flexibility may result in some inputs and/or outputs being assigned a zero or negligible weight, meaning that these factors are in fact ignored in the efficiency assessment. One way to limit the range of values that the weights can take is to use weight restrictions. Literature reviews on the use of weight restrictions in DEA can be found in Allen et al. (1997) and Thanassoulis et al. (2004). Several types of weight restrictions (WRs) have been proposed in the DEA literature. In Allen et al. (1997) the direct weight restrictions are categorized into three types: assurance regions type I (first proposed by Thompson et al., 1986), assurance regions type II (first proposed by Thompson et al., 1990 and often called linked cone assurance regions), and absolute weight restrictions (first proposed by Dyson and Thanassoulis, 1988). Assurance regions (AR) are distinct from absolute weight restrictions because instead of imposing the weights to be within a certain range of values, they impose ratios between weights to be within certain ranges. ARI specify these ratios either between input or output weights separately, and ARII specify ratios that link input to output weights. When absolute weight restrictions are imposed directly on DEA models with constant returns to scale (CRS) technology, the models...

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