A Note on Simulating Predecessor-Successor Relationships in Critical Path Models

Abstract

For any n entities, we exhaust all possible ordered relationships, from rank (or the highest number of connections in a linear chain, comparable to matrix rank) 0 to (n -1). As an example, we use spreadsheets with the "RAND" function to simulate the case of n = 8 with the order-length = 3, as from a total of 10000 possibilities by the number of combinations of selecting 2 (a pair of predecessor-successor) out of 5 (= card{A, B, C, D} + 1) matchingdestinations followed by an exponentiation of 4 (= 8 -card{A, B, C, D}). Since the essence of this paper is about ordered structures of networks, our findings here may serve multi-disciplinary interests, in particular, that of the critical path method (CPM) in operations with management. In this connection, we have also included, toward the end of this exposition, a linear algebraic treatment that renders a deterministic mathematical programming for optimal predecessorsuccessor network structures.