Critical-Path Planning and Scheduling: Mathematical Basis

This paper is concerned with establishing the mathematical basis of the Critical-Path Method—a new tool for planning, scheduling, and coordinating complex engineering-type projects. The essential ingredient of the technique is a mathematical model that incorporates sequence information, durations, and costs for each component of the project. It is a special parametric linear program that, via the primal-dual algorithm, may be solved efficiently by network flow methods. Analysis of the solutions of the model enables operating personnel to answer questions concerning labor needs, budget requirements, procurement and design limitations, the effects of delays, and communication difficulties.