Mathematical model formulation and hybrid metaheuristic optimization approach for near-optimal blood assignment in a blood bank system.

• Design of a dynamic mathematical model for blood assignment problem. • Proposal of a symbiotic optimization search algorithm for the BAP. • Implementation of two hybrid SOSGA and SOSSA algorithms to solve the BAP. • Suggestions for further development and possible areas of improvement. The shortage and wastage of blood products have been identified as the major contending factors that are frequently encountered in the management of blood supply chain processes. In general, the blood which is considered an essential product for which human existence relies on, has perishability characteristics that allow it to be stored up to a limited number of days. Therefore, this feature constrains the quantity of blood that can be retained in hospitals and blood centers, because keeping excessive number of blood units on inventory may result in blood product wastage. On the other hand, failure to stockpile on inventory can lead to shortage of this resource, and as a result may cause the cancellation of important activities such as treatment of special cases like surgery, accident, disaster circumstance and, in a worst case scenario increases the fatality rates at hospitals. This paper presents a dynamic mathematical model with the goal of improving the efficiency of blood related activities that occur at the blood centers. The model also caters for the assignment of whole blood units of available blood types to various requests. A set of equations that incorporate both the ABO and Rhesus blood groups are derived and presented subsequently. This further extends the initial work where only the ABO blood group was considered. In an effort to implement the developed model, three metaheuristic algorithms namely, symbiotic organisms search, symbiotic organisms search genetic algorithm, and symbiotic organisms search simulated annealing algorithms are proposed to identify the optimal routing for each of the blood types. An extensive numerical study was carried out using datasets from a synthetic blood sample collection process to illustrate the potential of the three metaheuristic algorithms to solve the developed blood assignment model. Furthermore, experimental results show that the hybrid symbiotic organisms search algorithms not only achieve superior accuracy, but also exhibits a higher level of stability, with the hybrid symbiotic organisms search genetic algorithm having the overall best superior performance. [ABSTRACT FROM AUTHOR]