negative data on the centralized resource allocation model

data envelopment analysis (dea) is a technique based on mathematical programming for evaluating the efficiency of homogeneous decision making units (dmus). in this technique, inefficient dmus are projected onto the frontier, which was constructed by the best performers. centralized resource allocation (cra) is a method in which all dmus are projected onto the efficient frontier through solving just one dea model. moreover, cra model is an appropriate method for evaluating the efficiency score of systems, which contain numbers of dmus such as banks, chain restaurants, and university departments. this paper focuses on developing the cra model along with the negative data through using the ideal point for the system as the cra model is formulated based on semi positive inputs and outputs. the concept, which has been discussed throughout this paper, is illustrated by using two numerical examples.