Study on a Mathematical Basis of Critical Path Method and its Application

Abstract

This paper is concerned with establishing the mathematical basis of the Critical Path Method—a new tool for planning and scheduling projects. The mathematical model upon which the Critical Path Method is based is a parametric linear program that has the objective of computing the utility of a project as a function of its duration. In order to solve the parametric linear program, primal dual algorithm may effectively be used and be solved efficiently by network flow method. This paper contains also the application of this algorithm to the scheduling of quaywall construction at Pier No.8E, Port of Kobe.