General Hospital

Elena Katok, Professor of Supply Chain Management, Penn State University

Case Study

General Hospital (not the real name) is a medium-sized hospital located in an upstate New York town. General, along with several other health care organizations is owned and managed by a large health-care management consortium, called American Health Care Management, Inc. (AHCM) (not its real name either). In mid 1990's, as the health care industry came under increasing pressure to contain costs, AHCM started putting corresponding cost containing pressures on its business units.

Al Markus is a marketing manager for AHCM, assigned to General. His job is to bring in the business to General's operating room unit (OR). A few words should be said at this point about how operating room unit works. Surgeons typically have privileges at more than one hospital. When a surgeon has a patient in need of a surgery, she may have a choice of which hospital to send the patient to. The type of insurance the patient has may play a role in this decision, but often the surgeon has discretion. A patient typically receives several bills for a surgery: from the surgeon, anesthesiologist, the hospital, and so fourth. Hospitals make money by having surgeries performed in their OR's, and are interested in encouraging surgeons to send patient there.

Hospitals provide surgical nursing staff (nurses and technicians), as well as equipment. While surgeons get paid for every surgery they perform, nurses are on a salary. Hospital has to pay nurses regardless of whether they are actually in surgery or not. These salary costs are very significant, and there was a feeling at AHCM that at General these costs were out of hand.

Additionally, surgeons complain that all too often surgeries get postponed because of lack of proper nursing staff. Surgeons do not like to wait for nurses, but surgeries cannot go on unless the right number of nurses is available. Due to this unhappiness, some surgeons actually started leaving General for other hospitals in the community

To make matters worse, there is plenty of unhappiness among the nursing staff. The biggest problem is excessive overtime. Surgical nursing is a very stressful job, and after weeks of working 12 to 16 hour shifts nurses get burned out.

It was Al's job to try to reverse these disturbing trends. From an MBA class Al took several years ago he recalled something about linear programming being applied to staffing problems. He called up one of his old professors and explained the problem to him. The professor indeed thought that LP may be the answer to Al's problems, but to be sure he asked Al to gather data for the next two weeks, keeping track of all surgical procedures that were performed at General, and the nursing requirements for these procedures.

Two weeks later Al visited his old professor and brought the data with him. Together, they assembled the data in such a way as to determine staffing requirement history for the two weeks. This data is presented in Figure 1, and in the electronic supplement to this case study. Al thought that the two-weeks of data were quite representative of what generally happens.

At this point the professor received an urgent phone call for a very large consulting job, and he had to leave town immediately. Al was not really sure how to proceed, and he needs you help. Help him by answering the following questions, and then submitting to him a formal proposal.

Questions

It's always best, when approaching a real problem to start small, and add complications gradually. Assume that the only shifts nurses are allowed to work are 8-hour shifts with a one-hour lunch break after four hours. Lunch breaks are unpaid. If a nurse makes $20 per hour, formulate and solve an LP that minimizes labor costs and also addresses Al's other problems. Write a GAMS program and solve. It is very important to justify all your assumptions, especially data-related ones. Remember that although a nurse costs $20/hr, which is a lot, if a surgeon takes her business elsewhere due to unavailability of nurses, losses to the hospital are significantly higher than $20/hr.
Actually, shifts can be different than in question 1. A full time nurse has to work at least 8 hours, but can work more than that. Any hours after the first eight are considered overtime, and are paid at time and a half. Hospital regulations prohibit nurses from working more than 16 hours at a time. Also, there are several part-time nurses, who are willing to work less than an 8-hour shift. Their hourly rate is the same as full time nurses. Hospital policy is that there should never be more than 2 part-time nurses working simultaneously. The lunch-break requirement is the same as in question 2. A part time nurse has to have a lunch break after 4 hours of work. Modify your GAMS model and solve.
How much is the requirement that no more than two part-timers can work simultaneously is costing General? What about the requirement that a shift cannot exceed 16 hours? Do these answers make intuitive sense to you? Explain.
Actually, lunch-break requirements are more flexible. A nurse can have a lunch break after 3 hours of work, and after at most 5 hours. Include this requirement into your GAMS model and solve.
You presented your model to Al, and he showed it to the head nurse, who almost had a heart attack. "You cannot have a shift start at 10 am, or at 2 PM," she exclaimed. "Nurses will never be willing to do this. Morning shift starts at 6 AM, swing shift at 3 PM, and night shift at 11 PM, everybody knows that!" She then proceeded to tell Al exactly what she thought about the OR consultant who came up with this ludicrous shift schedule. Of course the head nurse did not ask the other nurses what they thought, and you suspect she may be wrong. You need to get your recommendation implemented so you can graduate. How do you proceed?