A minimum cost and risk mitigation approach for blood collection
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Due to the limited supply and perishable nature of blood products, effective management of blood collection is critical for high quality healthcare delivery. Whole blood is typically collected over a 6 to 8 hour collection window from volunteer donors at sites, e.g., schools, universities, churches, companies, that are a significant distance from the blood products processing facility and then transported from collection site to processing facility by a blood mobile. The length of time between collecting whole blood and processing it into cryoprecipitate ("cryo"), a critical blood product for controlling massive hemorrhaging, cannot take longer than 8 hours (the 8 hour collection to completion constraint), while the collection to completion constraint for other blood products is 24 hours. In order to meet the collection to completion constraint for cryo, it is often necessary to have a "mid-drive collection"; i.e., for a vehicle other than the blood mobile to pickup and transport, at extra cost, whole blood units collected during early in the collection window to the processing facility. In this dissertation, we develop analytical models to: (1) analyze which collection sites should be designated as cryo collection sites to minimize total collection costs while satisfying the collection to completion constraint and meeting the weekly production target (the non-split case), (2) analyze the impact of changing the current process to allow collection windows to be split into two intervals and then determining which intervals should be designated as cryo collection intervals (the split case), (3) insure that the weekly production target is met with high probability. These problems lead to MDP models with large state and action spaces and constraints to guarantee that the weekly production target is met with high probability. These models are computationally intractable for problems having state and action spaces of realistic cardinality. We consider two approaches to guarantee that the weekly production target is met with high probability: (1) a penalty function approach and (2) a chance constraint approach. For the MDP with penalty function approach, we first relax a constraint that significantly reduces the cardinality of the state space and provides a lower bound on the optimal expected weekly cost of collecting whole blood for cryo while satisfying the collection to completion constraint. We then present an action elimination procedure that coupled with the constraint relaxation leads to a computationally tractable lower bound. We then develop several heuristics that generate sub-optimal policies and provide an analytical description of the difference between the upper and lower bounds in order to determine the quality of the heuristics. For the multiple decision epoch MDP model with chance constraint approach, we first note by example that a straightforward application of dynamic programming can lead to a sub-optimal policy. We then restrict the model to a single decision epoch. We then use a computationally tractable rolling horizon procedure for policy determination. We also present a simple greedy heuristic (another rolling horizon decision making procedure) based on ranking the collection intervals by mid-drive pickup cost per unit of expected cryo collected, which results in a competitive sub-optimal solution and leads to the development of a practical decision support tool (DST). Using real data from the American Red Cross (ARC), we estimate that this DST reduces total cost by about 30% for the non-split case and 70% for the split case, compared to the current practice. Initial implementation of the DST at the ARC Southern regional manufacturing and service center supports our estimates and indicates the potential for significant improvement in current practice.