Abstract
One of the important problems in system structure's analysis is how to modify strongly connected systems to partial ordering structures that satisfy transitivity. This paper presents an effective method for the above partial order structuring problem. The problem is first formulated into a 0-1 linear programming problem with m constraints and n variables, where m and n are the number of cycles and edges, respectively, in the strongly connected system. To solve the 0-1 linear programming problem, we develop a solution algorithm based on the concept of relaxation strategy. This method has an excellent ability on calculation time. Consequently, this method can be easily applied to the large-scale strongly connected system which has a large number of components and cycles. The effectiveness of the method is demonstrated by applying this to two real problems; a ranking problem based on pairwise comparison and a simulation problem of a sulfuric acid plant.
