A bi-objective robust optimization model for a blood collection and testing problem: an accelerated stochastic Benders decomposition

Blood transfusion services are vital components of healthcare systems all over the world. In this paper, a generalized network optimization model is developed for a complex blood supply chain in accordance with Iranian blood transfusion organization (IBTO) structure. This structure consist of four types facilities. Blood collection centers, blood collection and processing centers, mobile teams and blood transfusion center have various duties in IBTO structure. The major contribution is to develop a novel hybrid approach based on stochastic programming, e-constraint and robust optimization (HSERO) to simultaneously model two types of uncertainties by including stochastic scenarios for total blood donations and polyhedral uncertainty sets for demands. An accelerated stochastic Benders decomposition algorithm is proposed to solve the problem modeled in this paper. To speed up the convergence of the solution algorithm, valid inequalities are introduced to get better quality lower bounds. In addition, a Pareto-optimal cut generation scheme is used to strengthen the Benders optimality cuts. Numerical illustrations are given to verify the mathematical formulation and also to show the benefits of using the HSERO approach. At the end, the performance improvements achieved by the valid inequalities and the Pareto-optimal cuts are demonstrated in a real world application.