A Note on Simulating Predecessor-Successor Relationships in Critical Path Models
DOI:
https://doi.org/10.34257/GJSFRFVOL21IS2PG1Keywords:
CPM simulation, directed graphs, ordered networks, circuitry designs, logical flows
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 thisconnection, we have also included, toward the end of this exposition, a linear algebraic treatment that renders a deterministic mathematical programming for optimal predecessor-successor network structures.
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Published
2021-01-15
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