Appointment scheduling for the blood collection process: a two-stage framework to balance the production of blood units

Blood is fundamental in several care treatments and surgeries, and plays a crucial role in the healthcare system. However, it is a limited resource as it can be produced only by donors and its shelf life is short. The Blood Donation (BD) system aims at providing an adequate supply of blood bags to transfusion centers and hospitals. Its main phases are blood collection, screening, storage, distribution and utilization. An effective collection of blood bags from donors, through suitable scheduling of donations, is fundamental for adequately supplying the entire BD system and optimizing blood usage. Nevertheless, despite its relevance, donor scheduling is only marginally addressed in the literature, while on the contrary a high number of papers deal with blood storage and distribution. In this work, we define the Blood Donation Appointment Scheduling (BDAS) problem, which aims at balancing the production of units among days for the different blood types, in order to provide a near constant supply of blood units to the BD system. We propose a framework for the BDAS that accounts for both booked and non-booked donors. It consists of an offline Mixed Integer Linear Programming model for preallocating time slots to the different blood types, and an online prioritization policy to assign a preallocated slot when a donor calls to make the reservation. Results from the application to one of the main blood collection centers in Italy (i.e., the AVIS Milan) show the applicability of the approach and provides good results in terms of production balancing. Finally, we also discuss two directions of improvement to include the random arrival of donors in the preallocation model: a robust approach (based on the cardinality constrained approach) and a stochastic approach (conditional value at risk).