Handbook of Healthcare System Scheduling

It does not take a great deal of research to reach the conclusion that dealing with the long-term problems of health care is going to require an “all-hands-on-deck” combined effort, both personally and professionally. On the personal side, people are going to have to adopt a healthier lifestyle and accept some limits on the care that they receive. Those with the requisite skills are going to have to apply them in a concerted way in order to find savings and improvements in health care.

This also applies to mathematicians. One of the contributions that they can make in the professional area is to develop more efficient and robust algorithms to schedule the delivery of healthcare. Nearly all of us have spent extended time in a waiting room thinking over and over again, “There has to be a better way.” One of the best aspects of this form of improvement is that it makes things better while lowering the costs. That is what this Handbook is about.

The algorithms and scenarios take into account probabilistic models of the need for care, from the routine visit to a physician to scheduling surgery to the necessity for emergency surgery. For the home delivery of health care, it is a complicated knapsack and restricted traveling salesperson (nurse) problem. For highest efficiency, the vehicle must contain all of the materials that the health professional will need on their rounds and the route must be as efficient as possible. Furthermore, the patients that will be visited also place timeframe constraints on the time of the visit, for example some tests or therapies are best done early in the morning while others are more efficient at other times of the day.

I have done some research on the long-term prospects of health care costs, particularly that related to long-term care for Alzheimer’s and chronic heart conditions and it has made me pessimistic that the problems of rising health care costs can be solved. Reading this book was a cure for some of the pessimism, for it demonstrates some possibilities for improving health care that do not involve some people doing without.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.