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The combined monitoring-based and modeling-based priority setting (COMMPS) provides a procedure for the identification of priority hazardous substances outlined in the Working Document (ENV/191000/01 of January 16, 2001). This procedure is based on scoring a set of criteria which individually make substances more or less hazardous. The way scores are weighted and combined has been established by a panel of experts. Different authors outlined how such a procedure might be affected by subjectiveness of judgment, and alternative solutions based on partial order theory (POT) and random linear extensions (RLE) have been suggested. This method consists of generating a set of RLE and of averaging the rank given to each substance, so that a total order could be determined. Any POT/RLE approach must face the issue of covering as much as possible the space of linear extensions that, in the case of the 85 substances considered by COMMPS, becomes extremely large, and an exhaustive generation of linear extension is not feasible. Therefore, having a faster algorithm would help to consider a larger number of linear extensions in a given time frame. In this paper, we discuss this problem, and we outline a possible solution.