Regional Neonatal Associates is a ninephysician group working for the Neonatal Intensive Care Unit (NICU) at the University of Tennessee Medical Center in Knoxville, Tennessee. The group also serves two local hospitals in the Knoxville area for emergency purposes. For many years, one member of the group would schedule physicians manually.
However, as his retirement approached, there was a need for a more automatic system to schedule physicians.
The physicians wanted this system to balance their workload, as the previous schedules did not properly balance workload among them. In addition, the schedule needed to ensure there would be 24-7 NICU coverage by the physicians, and if possible, accommodate individual preferences of physicians for shift types. To address this problem, the physicians contacted the faculty of Management Science at the University of Tennessee.
The problem of scheduling physicians to shifts was characterized by constraints based on workload and lifestyle choices. The first step in solving the scheduling issue was to group shifts according to their types (day and night). The next step was determining constraints for the problem. The model needed to cover a nineweek period with nine physicians, with two physicians working weekdays and one physician overnight and on weekends. In addition, one physician had to be assigned exclusively for 24-7 coverage to the two local hospitals. Other obvious constraints also needed to be considered.
For example, a day shift could not be assigned to a physician just after a night shift.

Methodology/Solution
The problem was formulated by creating a binary, mixedinteger optimization model. The first model divided workload equally among the nine physicians.
But it could not assign an equal number of day and night shifts among them. This created a question of fair distribution. In addition, the physicians had differing opinions of the assigned workload.
Six physicians wanted a schedule in which an equal number of day and night shifts would be assigned to each physician in the nineweek schedule, while the others wanted a schedule based on individual preference of shifts. To satisfy requirements of both groups of physicians, a new model was formed and named the Hybrid Preference Scheduling Model (HPSM). For satisfying the equality requirement of six physicians, the model first calculated one week's workload and divided it for nine weeks for them.
This way, the work was divided equally for all six physicians. The workload for the three remaining physicians was distributed in the nineweek schedule according to their preference. The resulting schedule was reviewed by the physicians and they found the schedule more acceptable.

Results/Benefits
The HPSM method accommodated both the equality and individual preference requirements of the physicians. In addition, the schedules from this model provided better rest times for the physicians compared to the previous manual schedules, and vacation requests could also be accommodated in the schedules. The HPSM model can solve similar scheduling problems demanding relative preferences among shift types.
Techniques such as mixedinteger programming models can build optimal schedules and help in operations. These techniques have been used in large organizations for a long time. Now it is possible to implement such prescriptive analytic models in spreadsheets and other easily available software.

Questions for Discussion
1. What was the issue faced by the Regional Neonatal Associates group?
2. How did the HPSM model solve all of the physician's requirements?