Modelos matemáticos y estocásticos para control del inventario en bancos de sangre: revisión de la literatura

En este artículo se presenta una revisión de la literatura de las diversas metodologías utilizadas en la construcción de algunos de los más importantes modelos matemáticos y estocásticos que permiten el control del inventario en bancos de sangre, producto perecedero de alto impacto en la conservación de la vida de los seres humanos. Esta revisión se realizó utilizando setenta referencias bibliográficas de las investigaciones más destacadas desde la década de los 70 hasta la fecha, en la que se incluye los diversos comportamientos de la demanda y la donación, la sustitución de los diversos tipos de sangre, la condición multiproducto de los ítems, el deterioro y obsolescencia de los productos sanguíneos, las penalidades por faltantes y las diversas políticas de pedidos. Asimismo, se presentan los modelos más destacados para integrar la cadena de suministro, definida como la mejor estrategia para la optimización de tan vital recurso; al final, se destacan las brechas no cubiertas en este campo de conocimiento, que constituyen en desafíos para futuras investigaciones

Blood supply chain network design considering responsiveness and reliability in conditions of uncertainty using the lagrangian relaxation algorithm

The growing need for adequate and safe blood and the high costs of health systems have prompted governments to improve the functioning of health systems. One of the most critical parts of a health system is the blood supply chain, which accounts for a significant share of the health system's costs. In the present study, with an operational approach, the total network costs are minimized along with the minimization of transportation time and lead time of delivery of blood products. Also, determining the optimal routing decisions is improved the level of responsiveness and reliability of the network. In this research, a multi-objective stochastic nonlinear mixed-integer model has been developed for Tehran's blood supply chain network. Robust scenario-based programming is capable of effectively controlling parametric uncertainty and the level of risk aversion of network decisions. Also, the proposed reliability approach controls the adverse effects of disturbances and creates an adequate confidence level in the capacity of the network blood bank. Lastly, the model is solved through the Lagrangian relaxation algorithm. Comparison of the results shows the high convergence rate of the solutions in the Lagrangian relaxation algorithm

Mergers and Acquisitions in Blood Banking Systems: A Supply Chain Network Approach

Blood banking systems in the United States over the past decade have been faced with a volatile demand for blood, specifically, a decrease in demand for red blood cells, for a variety of reasons. This change in the blood supply chain landscape, accompanied by an increasing emphasis on cost efficiency, is a driver of Mergers & Acquisitions between blood banks. In this paper, we first present supply chain network optimization pre- and post-merger models. The models handle perishability of the life-saving product of blood, include both operational and discarding costs of waste, capture the uncertainty associated with the demand points, as well as the expected total blood supply shortage cost and the total discarding cost at demand points. They also incorporate capacities on the links. Their solution yields the optimal path and link flows plus the frequencies of activities associated with blood collection, shipment, testing and processing, storage, and distribution, and incurred total costs. We provide a cost efficiency (synergy) measure associated with a merger or acquisition in the blood banking industry, as well as measures capturing the expected supply shortage and surplus. The methodological framework and its applicability are then illustrated via a large-scale blood supply chain network example inspired by a pending merger in the real-world in both status quo and disaster scenarios

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

Transshipment in supply chain networks with perishable items

Supply chain management is an efficient approach to managing the flow of information, goods, and services in fulfillment of customer demand. The implementation of supply chain management significantly affects the cost, benefit level, and quality. Over the past decades, multiple strategies for effective supply chain management have been developed in both academia and industry. One such strategy is named lateral transshipment which allows movement of stock between locations at the same echelon level or even across different levels. Although transshipment has been considered in the literature for a long time, there has been limited studies of transshipment for perishable items, most likely because of the complex structure of perishable inventories. The analysis of perishable-inventory systems has been considered in numerous articles because of its potential application in sectors such as chemicals, food, photography, pharmaceuticals, and blood bank management. Blood services in Australia rely on voluntary, non-remunerated donors to satisfy the demand for blood. Blood services confront ongoing challenges in providing an adequate supply of blood and blood products. One of the powerful tools that could improve the efficiency of the blood supply chain is lateral transshipment. This thesis presents three models that have application in the transshipment of perishable items such as blood. The first model (presented in Chapter 2) outlines the development of a new transshipment policy for perishable items, to enhance supply chain performance. A Poissondistributed customer demand is assumed and the effect of reactive transshipment on expected costs are evaluated. A heuristic solution is developed, using partial differential equations to compute performance measures and cost function. The performance of this model is evaluated through a numerical study. The results indicate that this transshipment policy is effective under lost-sale and backordering scenarios. In addition, the performance of the suggested transshipment policy is compared with the current transshipment policy that is practiced in some Australian hospitals. The results suggest that by setting the optimal threshold, a significant cost saving could be obtained with the same average issuing age of the current policy. The second model (presented in Chapter 3) considers a finite-horizon multi-period inventory system with one main hospital connected to several smaller hospitals. The hospitals face random demand and small hospitals are allowed to transship to the big hospital to mitigate their wastage. The problem is formulated as an infinite-horizon dynamic programming model. The objective of this model is to determine an optimal ordering and transshipment policy that minimizes the total expected cost. An approximate dynamic programming (ADP) model is used to approximate the value function with a linear combination of basis functions, using column generation to cope with the course of dimensionality. The numerical results suggest that considerable cost saving can be achieved by using an ADP model. The third model (presented in Chapter 4) proposes a proactive transshipment policy for a network of hospitals with uncertain demand. At the beginning of each review period, each hospital makes decisions on the quantity to order from a central blood bank and to transship to other hospitals. The problem is formulated as a two-stage stochastic programming model where the Quasi-Monte Carlo (QMC) sampling approach is used to generate scenarios and the optimal number of scenarios is determined by conducting stability tests. The performance of the developed model is evaluated through numerical experiences. The numerical results indicate significant potential cost savings in comparison with the current policy in use and the no-transshipment policy

Barriers to Blood Availability Within the New Orleans Area

An adequate and reliable supply of blood and blood components is becoming an increasing public health concern. Over the past decade, researchers have indicated a continued decline in the collection of blood products. An insufficient blood supply may present a risk to both patients and reserves for emergencies and disasters. The purpose of this quantitative, cross-sectional study was to determine whether gender, age group, ethnicity, year, serological tests, and discard factors were associated with the availability of the donated blood supply throughout the New Orleans region. The donated blood supply chain model guided this study. Secondary data were retrieved from The Blood Center of New Orleans, Louisiana. A simple random sample technique was used to select the sample, consisting of 286,625 allogeneic blood donors. Bivariate logistic regression and multiple logistic regression were used to analyze data collected between 2008 and 2017. The bivariate logistic regression showed a statistically significant association (p = .000) between gender (OR = .760; 95% CI .753 – .767), age group (OR = 1.554; 95% CI 1.522 – 1.588), ethnicity (OR = .635; 95% CI .627 – .643), year (OR = .713; 95% CI .696 – .731), and available blood. Similarly, the multiple logistic regression also revealed a statistically significant association (p = .000) between gender (OR = .796; 95% CI .789 – .804), age group (OR = 1.426; 95% CI 1.395 – 1.458), ethnicity (OR = .672; 95% CI .664 – .681), year (OR = .726; 95% CI .708 – .744), and available blood. The knowledge presented in this study promotes positive social change by guiding blood center practitioners on ways to improve current work practices to increase the available donated blood supply and maintain a satisfactory blood inventory

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