An exact criterion space search algorithm for a bi-objective blood collection problem

Blood shortages are one of the main challenges in blood supply chains. To supply required blood, blood center managers face conflicting collection objectives involving costs and patients’ lives. Moreover, some challenging decisions must be made, such as routing, blood collection, location of blood stations, transshipment policy and holding inventory. In this study, a bi-objective mixed integer mathematical model is developed to address all the above-mentioned issues in the network. The model focuses on precisely determining the location of collection stations (permanent and temporary), transshipment and inventory of the blood center, routes and the quantity of collected blood to optimize the two objectives of decreasing total blood shortages and costs. Next, a subtour cut generation (SCG) method is introduced to enhance the solution approach of the problem. It leads to solving large instances more efficiently. The problem is critical and complex since missing even a non-dominated solution may lead to both negative financial impact and noncompensable outcomes. To extract all non-dominated solutions, an exact criterion space search method, called the triangle splitting method (TSM), is adopted. Several experiments are investigated for some instances from the literature. In addition, a real case study is considered. Results indicate that designing the network using the proposed mathematical model can significantly reduce total blood costs and shortages. Consequently, by utilizing the proposed methodology, blood center decision makers will have the opportunity to choose the most preferred point among extracted non-dominated solutions. Furthermore, the performance of the adopted TSM was compared with an improved non-dominated sorting genetic algorithm (NSGA-II) and lexmin epsilon constraint (LEPS). The results confirm that the adopted TSM algorithm performs much better than the improved NSGA-II and LEPS, considering bi-objective performance measures.