A Variational Study of Optimal Resource Profiles

The paper describes a method of supplementing network analysis by taking a global view of project planning. The sequencing constraints normally found in a project are condensed into restrictions on the quantity of work performed by any stage in its duration. The objective is to minimise cost, where cost is considered to vary both with project duration and with the instantaneous rate of change of resource. Variational methods are used to produce optimal work-time and resource-time project profiles. The form of some constraints likely to arise in a project is considered, and the best profiles subject to certain constraints are derived and discussed. The techniques have been used to obtain a lower bound to project cost and to estimate ideal project duration.