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.