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There are many scheduling problems in the healthcare arena, from scheduling nurses and OR rooms, to scheduling doctor’s appointments with no-shows, to triaging patients and doling out vaccinations; but one of the most critical scheduling problems involves organ transplants. A husband and wife team of surgeon (Segev) and mathematician (Gentry) have studied both kidney and liver transplant allocation and have made some groundbreaking recommendations.
For kidney transplants, finding an appropriate match is sometimes difficult. Waiting for a kidney from someone who is deceased can take too long. Unfortunately, even though a pers.ni can function with only one kidney, donating the other kidney to a loved one may not be possible if the blood type and oilier antibodies do not match. One solution is to pair two such incompatible couples so that the donors’ kidneys do not help their loved one directly but do allow them to receive a transplant more quickly. This is known as the Kidney Paired Donation (KPD) program, and before Gentry and Segev completed their research, perhaps 60 such exchanges took place each year. After applying a new matching algorithm to a nationwide set of donors/recipients, more than 600 exchange transplants were occurring each year, saving lives and over $750 million annually in healthcare costs.
Livers come from deceased donors and have a short shelf life of less than four hours, eliminating the possibility of lengthy transit times between donor and transplant center. In the United States, a recipient waiting list used to be divided into 11 geographic districts, and available livers were allocated within the same district (perhaps because of the limited transit time). This led to a disparity in service, with some districts having more need and less availability than others. Desperate patients were known to move into a more receptive district to await transplant. Gentry and Sedev sought to redraw the district boundaries to minimize disparity in access to livers.
Redistricting is a class of problems that uses integer programming (similar to linear programming) to design geographic boundaries between units, and is usually applied to school districts or voting districts. The integer programming model proposed by Gentry and Segev is designed specifically for liver transplant redistricting and is more transparent to the user than previous models. As is common with practical models, the liver committee had some design constraints in mind that reduced the size of the problem. The districts should be adjoining, the number of districts should be at least four and no more than eight, the maximum transport time should be three hours, and each district should have a minimum of six transplant centers. Gentry and Segev added the ranking of patients by need, called the MELD index, to the analysis. MELD prioritizes candidates based on the risk of death while awaiting liver transplantation.
A simulation model was built to test out the proposed 4-district, 6-district, and 8-district models over a five year time frame. The recommended 4-district plan would save 554 lives, cost $25,000 less than other plans, and eliminate the disparity between districts in receiving organs. The Liver Committee that manages allocation policies unanimously approved the 4-district plan (even when transplant centers in their own district would see a reduction in allocations).
Saving lives is an incredible payout for implementing a new scheduling or allocation model. What other kinds of major scheduling/allocation problems do you see in society that could be improved with careful analysis?
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