The appropriate total ranking method using DEA for multiple categorized purposes

When one expects to figure out the total ranking of objects from collected data, it is a familiar method to compare the weighted sum of the selection number of rank vote, after determining the weights in a selected rank. Green et al. (European J. Oper. Res. 90(3) (1996) 461), using data envelopment analysis and cross-evaluation, proposed a procedure to order the objects from the ranking of one categorized data. But, they have not taken care of about making the weight of a certain rank 0, and the value of the difference between ranks becomes 0. In actual applications, making the weight of a certain rank 0 means that we throw away the corresponding part of the obtained rank voting data. Further, giving the same weight to different ranks destroys its original ranking character. And then, in this paper, we show that the total ordinal rank of objects may produce a different result according to the difference of the weights between ranks. Consequently, we explain that their ordering is not appropriate to applications. And, we propose a new ordering to solve the weights of ranks by considering feasible solutions’ region of the constraint set in LP. Also, we would like to propose such a method that, if extended, it can be applied more widely not only when the selected category is for a single purpose but also when it is for multiple purposes, especially with an example taken from the personal development issue at a corporation.