A mathematical modeling approach for managing regional blood bank operations

Abstract

Blood bank operations are complex affairs since they involve supply chain management of highly perishable goods such as whole blood and blood products. The Turkish Red Crescent (TRC), who is the main responsible organization in Turkey for collection, testing, separation and distribution of whole blood and blood products, is in constant need of optimizing its operational decisions. We propose a mathematical modeling approach for managing the blood bank operations in the TRC that include the decisions of donation collection, production and distribution to demand points (hospitals). The model minimizes system cost while ensuring maximum level of demand satisfaction. For this purpose, a lexicographic approach is used that first determines the maximum amount of demand that can be satisfied and then solves a cost minimization model, which is a linear mixed-integer programming model. Observing that it may not be possible to find the optimal solution of this model in reasonable time for some real-life problem sizes, we develop a customized heuristic approach for the problem. We demonstrate that the heuristic algorithm provides good quality solutions in negligible time through computational experiments. We finally examine a bi-objective extension of the cost minimization problem, where the quality of the separated blood product is considered alongside system cost. We solve the resulting bi-objective programming problems using the Ɛ- Constraint Method. This extension allows the decision maker to observe the trade-off between cost and quality and implement her most preferred solution among the non-dominated solutions.