Bridging Mathematical Models and Managerial Decisions

by Auyon Siddiq, Industrial Engineering and Operations Research

Teaching Effectiveness Award Essay, 2015

One of the core focuses of the field of operations research is the development of mathematical models and algorithms to optimize and guide real-world decision making. While the content in a typical operations research course is usually technical, the field itself is actually quite practical; operations research methods have been applied to solving problems in many areas, such as energy, healthcare, finance, and transportation. As the sole GSI for IEOR160, the first of the two-part undergraduate operations research sequence in the IEOR department, I viewed it as part of my job to help convey the idea that the seemingly abstract methods taught in class could in fact have a significant positive impact on how decisions are made in a wide variety of domains.

Challenge. As with many engineering disciplines, closing the gap between theory and practice in operations research is important from an instructional perspective, but not easy to do. In leading discussion sections, I found that focusing on the importance of grasping the essential mathematical tools sometimes obscured the fact that the methods I was teaching had a greater purpose. It was often unclear to me whether the students were developing a genuine appreciation for the course material or simply completing weekly homework in an automated fashion. Simply put, students were gaining technical skills without even realizing how valuable those skills could be.

Idea. Recognizing that the end-of-semester course project was a valuable teaching opportunity, I requested permission from the instructor to design a new course project from scratch. I developed a case study-based project focusing on the optimal allocation of shared operating room time to various departments within a hospital. Students were required to apply knowledge gained from lectures to develop a mathematical model that could produce an operating room schedule that satisfied all the constraints imposed by various hospital departments. Creating a schedule that accommodates multiple (sometimes competing) parties is incredibly difficult to do by hand, and was therefore the perfect problem for showcasing the power of the optimization methods being taught in class. Further, I hoped that the hospital setting would provide a real-world context that the students could easily appreciate.

After developing a baseline model that output a satisfactory schedule, the students were asked to customize their model to evaluate the impact of several hypothetical management policies that I had proposed. For example, “Is it possible to guarantee General Surgery at least eight hours of operation room time every day of the week? How does this policy affect other departments and the overall schedule?” To help close the theory-practice divide, I asked students to imagine themselves as “technical consultants” who had to advise the hospital’s management on the impact of these policies. In addition to ensuring that the students could apply the methods learned in class, I emphasized the value of converting the results of their mathematical models into managerial insights.

Assessment. In general, students were much more enthusiastic when discussing their projects with me in office hours than they were when discussing the weekly homework, with one group expressing interest in carrying over what they learned from the IEOR160 project to their senior-year project in another course. The strongest indicator of success was that many groups went above and beyond the project requirements by using their models to test several new hypothetical policies that they thought of on their own, without my prompts. These groups not only gained the technical know-how to develop the required models, but they demonstrated an advanced understanding of how mathematical models could inform managerial decisions in a practical setting. Seeing the students “connect the dots” on their own in their project reports was very encouraging, and has given me confidence that case study-based projects can be a very effective tool in showing students the practical impacts that their own technical skills can have.