Optimisation and control of the supply of blood bags in hemotherapic centres via Markov Decision Process with discounted arrival rate

Running a cost-effective human blood transfusion supply chain challenges decision makers in blood services world-wide. In this paper, we develop a Markov decision process with the objective of minimising the overall costs of internal and external collections, storing, producing and disposing of blood bags, whilst explicitly considering the probability that a donated blog bag will perish before demanded. The model finds an optimal policy to collect additional bags based on the number of bags in stock rather than using information about the age of the oldest item. Using data from the literature, we validate our model and carry out a case study based on data from a large blood supplier in South America. The study helped achieve an overall increase of 4.5% in blood donations in one year

Avaliação da política ótima de gerenciamento de estoque de sangue do HEMORIO via processo de decisão de markov

This work develops a Markovian decision model in order to dimension the external collection in HEMORIO, a Brazilian blood institute, focusing on minimizing costs and considering aspects inherent to the problem of blood storage, such as the perishability of the items. In addition to dealing with blood stock management, our mathematical modeling handles waiting queues with variable rates, focusing on controlling the demand one. Although there are several models in the literature dealing with that, the way we apply Markov’s decision-making process to find switchovers to manage the blood stock is a new approach to optimization in this topic. The model is validated based on the literature and we show how the results could be used to improve the institution’s policy and its data. The text concludes the number of external collection teams to be sent according to the number of blood bags in stock, parameterized to guarantee 7 days of self-sufficiency in bloodEste trabalho propõe o estudo de um problema de gerenciamento de estoque de sangue através de técnicas de Processos Estocásticos, em especial focando na abordagem por Processos de decisão de Markov como alternativa às demais encontradas na literatura como por filas com taxas de chegada e/ou serviço variáveis. O estudo de caso que inspira o trabalho é a do principal instituto de sangue do estado do Rio de Janeiro, o HEMORIO, que deseja saber qual a política ótima de envio de equipes de coleta externa que complementam as doações dessa instituição. O texto conclui o número de equipes de coleta externa a serem enviadas em função do número de bolsas de sangue em estoque, parametrizados para garantir 7 dias de autossuficiência em sangue

Ensuring blood is available when it is needed most

The provision of blood to patients in need is an imperative faced by all countries.  Red blood cells (RBCs) are perishable with a life of 42 days.  Inventory managers at hospitals need to know how many RBCs to order so that the probability of experiencing shortages or outdates is minimised.  This is complicated by demand for RBCs being doubly stochastic.  Both the number of patients that need RBCs and quantity of RBCs they will need are random.  For centralised blood banks not only are the orders they receive from hospitals apparently random, the supply of blood is also random. This thesis shows that, in addition to the previously mentioned sources of volatility, the structure of the supply chain induces further volatility.  This occurs due to the presence of delivery delays and negative feedback loops in two locations within the supply chain.  It is shown how this volatility can be addressed with some simple structural changes.  But simply removing system induced volatility does not imply that the supply chain is optimised.  To address optimality the problem is formulated as a Markov decision process (MDP).  A solution to this process uses Stochastic Dynamic Programming (SDP), but this results in a combinatoric explosion making the computation of an exact solution within a reasonable time impossible.  Instead, Stochastic Average Approximation (SAA) is used to derive an approximate solution.  Repeated, sequential application of this is an exercise in Discrete Time Stochastic Control.  A working control solution is provided in python.  This solution can be arranged so as to mimic the two echelon supply chain found in blood inventories.  It is general enough to apply to any discrete perishable inventory system with random demand and/or supply. The approach for blood inventories requires credible estimates of demand for RBCs.  It is shown, using hierarchical Bayesian modelling and Discrete Phase-Type (DPH) distributions, that credible estimates of demand at hospitals of any size can be derived from publicly available information.  In particular a new method for obtaining the parameters of a DPH distribution is formulated and applied to estimating transfusion quantities from publicly available sources. An application of the proposed solution is presented for RBC inventories at both hospitals and at the blood bank.  For the blood bank in particular it is shown how this can be used to determine the quantity of donors needed to meet demand within a desired probability of adequacy

(In Press) On the volatility of blood inventories

Past research underestimates the volatility of blood inventories. Models are calibrated to be correct on average, but average behaviour does not capture the risk of blood inventories to experience outdates or shortages. Volatility in blood inventories does arise from stochastic supply, stochastic demand, perishability and blood issuing policies. However, these are not exhaustive as the logistics or the supply chain can cause dynamic behaviour even without stochastic supply and demand. We use system dynamics to illustrate the response of the blood supply chain to disturbances. This approach captures delays and feedback not previously incorporated into blood supply models. We first show that the structure of the system itself can cause volatility. We then propose a modification to ameliorate volatility. It is hoped that similar changes to real blood inventory systems might improve the robustness of the blood supply chain to shocks, thereby reducing shortages and outdates

System dynamics models to assess shortage and wastage levels in demand-driven blood supply chains

The files 2_proposedDonorModule.mdl, 4_proposedBcModule.mdl, and 6_proposedHospitalModule.mdl contain the independently proposed donor, blood center, and hospital modules.The files 1_Clay-et-al-(2016)_donorModule.mdl, 3_Clay-et-al-(2016)_bcModule.mdl, 5_Clay-et-al-(2016)_hospitalModule.mdl present the donor, blood center, and hospital modules proposed by Clay et al. (2016).File 7_proposedSingleProduct.mdl incudes the proposed model for the single-product system simulations. File 8_proposedMultipleProduct.mdl contains the proposed model for the multi-product system simulations and sensitivity analysis.ReferencesClay, N.M., Abbasi, B., Eberhard, A., Hearne, J., 2016. On the volatility of blood inventories. International Transactions in Operational Research 25, 215–242. doi:10.1111/itor.12326.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV