The Three-Dimensional Gantt Chart

Developing useful models can be thought of as a process that produces more and more precise representations of the problem at hand. In particular, a problem solving project often involves successively developing a problem statement, formal model, model instance, algorithm output, and final presentation. Yet the field of operations research has traditionally concentrated only on developing the models and algorithms. The representations used for the other project phases have usually been ad hoc. When well done, however, e.g., in spreadsheets, representations can both significantly aid the decision maker and expand the use of OR techniques. One of the principal contributions of the research in Decision Support Systems has been its emphasis on tools to support the development of these representations. OR has both a challenge and an opportunity to move from the art of representation to a science of representation. This paper illustrates this point with an example. The example presents a new representation for a widely studied class of problems, machine scheduling problems, which demonstrates the potential of emerging hardware and software to support the kinds of representations that are required in the modeling process. The representation extends the well known Gantt chart for machine scheduling into a three-dimensional representation. The representation unifies several of the representations that have been developed for these problems. Furthermore, the technology that facilitates the three-dimensional representation also facilitates animation of the machine schedule.