A stochastic risk-averse framework for blood donation appointment scheduling under uncertain donor arrivals

Blood is a key resource in all health care systems, usually drawn from voluntary donors. We focus on the operations management in blood collection centers, which is a key step to guarantee an adequate blood supply and a good quality of service to donors, by addressing the so-called Blood Donation Appointment Scheduling problem. Its goal is to employ appointment scheduling to balance the production of blood units between days, in order to provide a reasonably constant supply to transfusion centers and hospitals, and reduce non-alignments between physicians' working times and donor arrivals at the collection center. We consider a two-phase solution framework taken from the literature, in which a deterministic linear programming model preallocates time slots to different blood types and a prioritization policy assigns the preallocated slots to the donors when they make a reservation. However, the problem is stochastic in nature and requires consideration of the uncertain arrivals of non-booked donors. In this work, to include the uncertain arrivals, we propose three stochastic counterparts of the preallocation model based on a risk-neutral objective and two risk-averse objectives, respectively, where the Conditional Value-at-Risk is considered as the risk measure in the last two methods. The resulting stochastic frameworks have been tested considering the historical data of one of the largest Italian collection centers, the Milan Department of the "Associazione Volontari Italiani Sangue" (AVIS). Results show the effectiveness of the stochastic models, especially the mean-risk one, and the need to include the uncertainty of arrivals in order to better balance the production of blood units.