Research
Modeling Supply Chains by Critical Paths and Leontief Input-Output Table
We formulate a supply-chain problem by:(1)casting it in the model of critical-path analysis as defined by predecessor/successor relations, and (2)allowing for mutual dependency among the activity nodes and applying Leontief’s input-output structure.
A Note on Simulating Predecessor-Successor Relationships in Critical Path Models
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.
A Note on Identifying Critical Activities in Project Scheduling via Linear Programming on Spreadsheets, with Incidental Pedagogical Remarks
This note presents a speedy resolution of the critical activities for the critical path method (CPM) in project management by first running Excel Solver to obtain the minimized time of the completion of the project in question and next perturbing the required times of all the involved activities concomitantly to reveal the critical activities by observing the difference in the minimized times. We use extensions of decimal places for the classroom demonstration of the above-said perturbation, and consider additions of log(prime numbers) to the required times of all the activities to serve any large-scale professional analyses without using tailored-made software. As a separate incidental pedagogical note, we show a heuristic approach to constructing exactly three constraints to yield positive optimal values for all the three decision variables in linear programming.
A Regression Analysis on the Covid-19 Transmission
This note applies least-squares regression to a cross-section comparison of the total infection numbers of COVID-19 as of a particular date among the fifty states of America to investigate any underlying factors; we also check the Gaussian normality of the time progression of the infection rate.
