An aggregate model of project-oriented production

A production system is studied in which thousands of activities are carried out concurrently subject to precedence constraints and limitations on resources such as skilled labor and equipment. Ideally, management proposes a set of milestone dates, obtains an analysis of which milestones cannot be met, and determines which resources are underused or overused. This process continues interactively until milestones, consistent with management’s objectives, are obtained. The authors derive, from elementary principles and basic assumptions (axioms), a continuous-time model of project execution at an aggregate level of detail. The model is approximated via a set of linear inequalities. This data structure can be manipulated easily and quickly by methods of linear programming to perform the required analysis.