A zero-one goal programming approach to multi-project scheduling

One of the most complex project scheduling problems revolves around the effort to schedule multiple projects that involve multiple resources--and accomplishing this while achieving multiple managerial objectives. Solving this problem requires not only a typical scheduling model formulation but also a method for leveling resources while considering multiple yet often conflicting objectives. This article examines a zero-one goal programming model that was previously outlined in a single-objective form, a formulation in which one represents scheduling of a particular activity during a particular time period and zero represents the alternative. It extends this formulation--a result of developments in algorithms and computer capabilities--for use on larger projects. In doing so, it outlines the four major problems in project scheduling and discusses these problems in relation to the critical path method (CPM) and Bowman's zero-one linear programming formulation. It then details each of the problems to discuss how the proposed scheduling method either alleviates or is affected by these concerns. It applies this model to resolve the scheduling problems related to simultaneously completing two hypothetical construction projects, an effort through which it explains how project managers can use this model. It defines the model's constraints for time, task completion, sequencing, and resources; it analyzes the results generated from the hypothetical application.