A combined continuous-time Markov chain and queueing-inventory model for a blood transfusion network considering ABO/Rh substitution priority and unreliable screening laboratory

Abstract

The uncertain nature of blood supply and demand in a blood supply chain network (BSCN) makes it impossible completely meet the blood demands on time. That’s why there is a vital need to develop a comprehensive model for optimally managing blood networks considering all challenges they face with. Although many researches have studied blood inventory management (BIM) in BSCNs, there is still a lack of models simultaneously considering blood inventory levels in hospital blood banks (HBBs) and blood centers (BCs) as a stochastic process. Also, most models have not evaluated the impact of false positive (FP) and false negative (FN) errors in the screening laboratories (SLs) of BCs. Moreover, no study has modeled the HBB demands as a queueing-inventory model with multiple blood types according to ABO/Rh substitution priority. To fill these gaps, this paper develops a two-echelon blood bank network considering ABO/Rh factors and substitution priority in which inventory levels of all red blood cell (RBC) types in an HBB and BC are simultaneously modeled as eight dependent continuous-time Markov chains (CTMCs). An unobservable M/M/m queueing-inventory system with infected RBCs and (r,Q) policy in the HBB is proposed. The blood requests arrive at the requests queueing system in the HBB, and after processing and departing from the queue, they leave the HBB with exactly-one RBC unit with the same ABO and Rh (Rhesus) groups or compatible with other types of RBC. Lost sales occur if all possible types of RBC for transfusion are unavailable. HBB continuously checks each RBC type's inventory level and places an order to the BC once the inventory level of each one of them reaches a predetermined reorder point. Due to transfusion-transmissible infections (TTIs), an SL conducts a 100 % quality-assured screening in the BC modeled as an M/M/m queueing system. Due to unreliable inspectors, FP and FN errors are considered in the SL. The stationary distribution of the number of requests at the HBB, the number of RBCs in the SL, and joint stationary distributions of inventory level of all RBC types in the HBB and BC are derived. Afterward, each RBC type's waiting-time distribution in the HBB is obtained. Some performance measures and the long-run total cost are extended, and a mixed integer nonlinear programming model (MINLP) is presented. Then, we propose the grasshopper optimization algorithm (GOA) to solve the complicated model. Also, this model is implemented in a case study in Tehran. Results show RBCs types O+ and A+ have the most lost sales, and the management should absorb more donors with these blood groups. Afterward, an approximation method to deal with multiple HBBs is suggested. Finally, several remarkable managerial and practical implications are presented.