Math problems in business are literally everywhere—most often hiding in plain sight. Therefore it is very gratifying when I see math problems covered in the mainstream press. Of course they don’t call them out as math problems, but there is no doubt they are describing one (and its solution!). The latest example comes from the Wall Street Journal on December 26 of this year. The Opinion section published an article from two public healthcare researchers Eugene Litvak and Dr. Robert G. Lahita entitled “A Simple Way to Save Lives and Money”.
Litvak and Lahita describe one of the classic problems any business faces: extreme variability in demand. In their world, the number and types of patients ebbs and flows daily, and even has a strong seasonal component. Clinics have two choices: expensively staff and capacitize well above the mean level of patient demand, or go the opposite way, with overcrowding contributing to medical errors and suboptimal care. Oddly enough, we see this same sort of problem across businesses of all types, attempting to outguess the customer by having the “just right” inventories of product and the just right locations day after day. My observation is that most businesses not only do a terrible job of managing this, they compound the negative effect by assuming “its just the cost of doing business” with fickle customers. Explaining away problems is one of the most corrosive behaviors in a modern business.
The researcher’s novel solution: better scheduling. Sure, most clinics have calendaring software that allows a patient care rep to schedule Mr. Jones for his gallbladder operation next Thursday with Dr. Smith. But that is not what they are talking about here. Rather, true optimization software looks at overall demand for providers, available rooms, support staff, cleaning rotations, and other contextual conditions and seeks to create an idealized smooth patient flow that takes advantage of sometimes hidden pockets of value-added time. The researchers cite a handful of direct examples across the US where this has been tried with great success. They go on to speculate that if most healthcare providers adopted this approach it would have a game-changing (and cascading) effect on the cost and quality of healthcare in the US.
Optimization works as a mathematical model of the system that it wishes to improve. If it is a factory, it considers every possible (feasible) way to make a slate of products that are currently in demand, but made in the most efficient way—perhaps taking advantage of the raw material stock and existing inventory that is on hand, or working around a machine that is down for maintenance. There is no way for a human to think through thousands of plausible schedules and find the one that generates the most profit for the factory. But this is precisely what these models do, often in a matter of seconds.
If you have an operation—be it a bank, a factory, a warehouse, a plant or even a healthcare clinic that has never been formally optimized, you are wasting money every hour of every day. You might be wondering if mathematical optimization is suitable for your company. If you are, we are happy to offer advice on that question. As a famous philosopher once said, merely asking the uncomfortable question is an eye opening experience.
