on the art of modeling

Operations research is a model-centric discipline. We use many mathematical models such as scheduling, assignment, facility location, inventory, and queueing that are presented in operations research textbooks. Formulating new models is often a major contribution in many of our research papers.

The models in our textbooks came into existence and were once formulated for the first time. As an applied researcher, it is important to train the students in my group in how to formulate models that are elegant and parsimonious and reflect appropriate assumptions in the real application. In a recent lab meeting, we read “On the Art of Modeling” by William T. Morris that was published in Management Science in 1967 that teaches the art of modeling.

Models can play the role of giving structure to experience. Yet we seldom encounter a model which is already available in fully satisfactory form for a given management situation, and the need for creative development or modification is almost universally experienced in management science.

Morris (1967)

Morris describes a looping procedure for creating and modifying models, which acknowledges that models are created iteratively. In each iteration, the model is tested against data or the set of assumptions that characterize it. A new version of the model is produced, which leads to a new test or comparison, which repeats until the modeling process is complete. Modeling takes time, trial and error, and experimentation.

The paper offers three “hypotheses” for creating models that are interesting. The entire paper is worth reading, and I won’t repeat them all here. Here are two parts of the discussion that I found to be useful:

1. Factor the system problem into simpler problems. Identify the right structure for each problem (scheduling, assignment, queueing). This requires setting aside the overarching design objective, which can be difficult for some.
2. Seek analogies. New problems usually have a lot in common with existing models for other applications. Here, we compare our problem at hand with previously developed models and their logical structures. Is the problem a queueing problem or an inventory problem? Is it linear?

I use both of these methods as well as some of the other modeling practices in the paper.

What is your process you use to create models?

Related reading:

• In defense of model simplicity
• In defense of model complexity