Taher kouchaki tajani; Ali Mohtashami; maghsoud Amiri; Reza Ehtesham Rasi
Abstract
In this paper, we have proposed a model based on Mixed Integer Non-Linear Programming for the blood supply chain under conditions of uncertainty in supply and demand, from the stage of receiving blood from volunteers to the moment of distribution in demand centers. The challenges addressed in this optimization ...
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In this paper, we have proposed a model based on Mixed Integer Non-Linear Programming for the blood supply chain under conditions of uncertainty in supply and demand, from the stage of receiving blood from volunteers to the moment of distribution in demand centers. The challenges addressed in this optimization model are the reduction of blood supply chain costs along with minimizing the shortage and expiration rate of blood products. The Markov chain has been used to address the uncertainty of donor blood supply. To estimate the needs of medical centers, the received demand is considered fuzzy. Then, the proposed model is solved in small dimensions by GAMS software and in large dimensions by Bat and Whale meta-heuristic algorithms, and the results are presented. In addition, a case study is presented to show the applicability of the proposed model. The results show a reduction in the level of costs as well as a reduction in the shortage and expiration of blood products in the supply chain.IntroductionOne of the important topics researched in the global healthcare systems of different countries is the improvement of supply chain performance. The health system has one of the most complex and challenging supply chains due to its direct relationship with human lives. Issues such as uncertainty in blood demand and supply, blood inventory planning, delivery schedule, ordering time, attention to expiration date, and limited human resources are among the challenging issues in the field of health, especially the supply chain of blood and blood products. A unit of blood, from the time it is received from the donor to the time it is injected into the patient as whole blood or blood product, includes many processes and challenges that must be taken into account to ensure the health of the blood and the health of the supply chain. Redesigning an existing blood supply chain is not possible in the short term due to significant costs and time required, so using existing facilities and optimizing conditions is more preferable than reestablishing equipment, blood centers, and other facilities related to the blood supply chain. In this research, by presenting a mathematical model, we try to optimize the tools and facilities in a blood supply chain. The important goal in the blood supply chain is the cost factor. The costs incurred on the blood supply chain include costs such as blood collection from volunteers, product processing and blood inventory costs in hospitals and blood centers, and blood transfer costs to demand centers. On the other hand, the balance in storage and waste reduction is also very important in this chain. High storage increases the amount of inventory (increase in cost) and also increases the rate of perishability (increase in cost) of blood products. It is important to pay attention to the fact that the reduction of costs should be accompanied by the reduction of shortages and waste. In addition to the lack of blood, improper distribution and untimely supply of blood to hospitals can be completely disastrous. Requests to blood centers are made under certain conditions, such that the requested product(s) are separated in terms of blood group or the presence or absence of a specific antigen. Paying attention to blood groups and compatibility indicators is one of the principles of blood transfusion, and not observing them can cause unfortunate events.Due to the disproportionate percentage of distribution of blood groups among volunteers, there has always been a possibility of a shortage in the supply chain. In the medical world, in case of a shortage of a blood product of a certain group, attempts are made to replace that product from groups that can be matched. This will reduce the shortage and save the lives of patients whose blood with the required blood group and RH is not available at the same moment. In order to solve this challenge, in the upcoming research, a solution based on the versatility of unanswered demands will be considered, which will be included in the mathematical model. Another important issue is the age of the demand for the requested product, which creates an age-based demand in the supply chain. (Some special patients need fresh or normal products according to the type of disease.)MethodologyIn this research, a comprehensive mathematical model has been developed in the form of a MINLP model. The research model is based on a comprehensive blood supply chain consisting of three components: collection, processing, and consumption of blood products. There are three types of collection centers in this model: first, vehicles that serve blood donors at predetermined locations and collect blood; second, fixed collection facilities located in some areas of the city that solely perform the task of collecting blood; and third, blood centers (blood transfusion centers) that perform both blood collection work and other tasks related to product processing, testing, and transfer planning to demand centers and hospitals. The next part of the model is related to the processing of the collected blood. In this part, the blood collected by the collectors in the blood center is aggregated, the percentage of each blood group is determined, and according to the need in the blood centers, products such as red blood cells, platelets, and whole blood plasma are sent to hospitals. It is worth noting that as blood is converted into other products, some characteristics of the product, including the age of the products, differ from each other. Therefore, in the continuation of transferring the products and responding to their demand, the age of the blood product will be considered. Additionally, it should be noted that the blood product requested from the demand centers is in two forms. For some special patients and in special surgeries, a series of blood products with a certain age (young blood) are needed. Therefore, the importance of the age of the blood sent to the hospitals is also seen in the model. In the real world, in the face of a shortage in hospitals, a solution is thought out, which is to use the principle of adaptability of blood groups. Through a pre-accepted adaptability matrix, a series of demands for blood groups g, in case of shortage, can be satisfied with the supply of blood groups f turn around. Deterministic supply chain network design models do not take into account the uncertainties and information related to the future affecting the supply chain parameters and as a result cannot guarantee the future performance of the supply chain because due to the inherent and fluctuating and sometimes severe change in the environment of many operating systems Parameters in optimization problems have random and non-deterministic characteristics. In this research, two different approaches have been used to face the uncertainty in blood supply and demand values. For the demand, a triangular fuzzy approach has been proposed. According to the conditions of uncertainty, the appropriate alpha cut is selected based on the opinion of the decision-makers, and the demand is adapted to the conditions. Regarding the amount of supply, in order to estimate the number of donors in future periods, we have used the Markov chain to predict the number of donors based on the records in the past.FindingsIn order to evaluate the presented model, it is necessary to solve the research in both small and large sizes to determine the reaction of the research target function to changes in the parameters of the problem. For this purpose, the research model was first coded in GAMS 24.1 software. According to the designed sample problems, up to a certain size, it is possible to solve the problem within a certain time frame using GAMS software. However, as the size of the problem increases and the time to reach the answer also increases, meta-heuristic algorithms such as WOA and BAT were employed to solve this problem. The results indicate that the Whale Optimization Algorithm (WOA) performed better. Subsequently, based on a case study, a problem was presented to illustrate the efficiency of the model and its solution method. The results obtained for the objective function and the values obtained for the main variables of the research demonstrate the effectiveness of the model and its solution approach.ConclusionThe purpose of this article is to design a comprehensive supply chain that includes three parts: collection, processing, and distribution of blood products. The supply chain comprises mobile and fixed blood collection units that receive blood from donors and send it to blood centers. At these centers, blood is processed into required products and then distributed to demand centers based on demands categorized as fresh or normal products. In this research, the objective was to minimize costs such as blood collection, blood inventory in blood centers and hospitals, as well as the cost of blood products expiring due to non-use. To address blood deficiency, the blood compatibility system was incorporated into the model. This system ensures that if a certain product of a certain group is not available, a compatible product from another group is sent as a replacement. The model was solved using the exact solution approach of GAMS software for smaller-sized problems. However, for larger-sized problems, meta-heuristic algorithms such as WOA and BAT were employed to achieve reasonable solving times. Additionally, a fuzzy coefficient was proposed for relatively accurate demand prediction, and the Markov chain and the Kolmograph left-hand theorem were utilized to predict the number of blood donors. The results obtained from small-sized problems using accurate solver algorithms, as well as medium and large-sized problems using WOA and BAT meta-heuristic algorithms, demonstrate the efficiency of the designed model. Finally, a sensitivity analysis based on changes in fuzzy coefficients of demand and coefficients, including the alpha cut transformation function, and its effect on the objective function are presented.
Mohsen Jami; Hamidreza Izadbakhsh; Alireza Arshadi Khamseh
Abstract
In the management of the blood supply chain network, the existence of a coherent and accurate program can help increase the efficiency and effectiveness of the network. This research presents an integrated mathematical model to minimize network costs and blood delivery time, especially in crisis conditions. ...
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In the management of the blood supply chain network, the existence of a coherent and accurate program can help increase the efficiency and effectiveness of the network. This research presents an integrated mathematical model to minimize network costs and blood delivery time, especially in crisis conditions. The model incorporates various factors such as the concentration of blood collection, processing, and distribution sites in facilities, emergency transportation, pollution, route traffic (which can cause delivery delays), blood type substitution, and supporter facilities to ensure timely and sufficient blood supply. Additionally, the model considers decisions related to the location of permanent and temporary facilities at three blood collection, processing, and distribution sites, as well as addressing blood shortages. The proposed model was solved for several problems using the Augmented epsilon-constraint method. The results demonstrate that deploying advanced processing equipment in field hospitals, concentrating sites in facilities, and implementing blood type substitution significantly improve network efficiency. Therefore, managers and decision-makers can utilize these proposed approaches to optimize the blood supply chain network, resulting in minimized network costs and blood delivery time.IntroductionOne of the most important aspects of human life is health, which has a significant impact on other aspects of life. In this study, a two-objective mathematical programming model is proposed to integrate the blood supply chain network for both normal and crisis conditions at three levels: blood collection, processing and storage, and blood distribution. The proposed two-objective mathematical model simultaneously minimizes network costs and response time. The model is solved using the augmented epsilon-constraint method. To enhance the responsiveness to patient demand in healthcare facilities and address shortages, the model considers the concentration of levels (collection, processing and storage, and distribution of blood to patients) in facilities, blood type substitution, and supporter facilities. In blood type substitution, not every blood type can be used for every patient. Among several compatible blood groups, there is a prioritization for blood type substitution, allowing for an optimal allocation of blood groups based on the specific needs.Materials and MethodsIn this research, a two-objective mathematical programming model is proposed to design an integrated blood supply chain network at three levels: collection, processing, and distribution of blood in crisis conditions. The proposed model determines decisions related to the number and location of all permanent and temporary facilities at the three levels of blood collection, processing, and distribution, the quantity of blood collection, processing, and distribution, inventory levels and allocation, amount of blood substitution, and transportation method considering traffic conditions. Achieving an optimal solution for the developed two-objective model, which minimizes both objective functions simultaneously while considering the trade-off between the objective functions, is not feasible. Therefore, multi-objective solution methods can be used to solve problems considering the trade-off between objectives. In this research, the augmented epsilon-constraint method is employed to solve the proposed two-objective mathematical model. In this method, all objective functions, except one, are transformed into constraints and assigned weights. By defining an upper bound for the transformed objective functions, they are transformed into constraints and solved.Discussion and ResultsAlthough the two-objective mathematical model is transformed into a single-objective model using the augmented epsilon-constraint method, this approach can still yield Pareto optimal points. Therefore, managers and decision-makers can create a balanced blood supply chain network considering the importance of costs and blood delivery time. Sensitivity analysis was conducted to examine the effect of changes in the weights of the objective functions and the blood referral rate (RD parameter) on the values of the objective functions for three numerical examples. With changes in the weights of the objective functions relative to each other, the trend of changes in the values of the first and second objective functions for all three solved problems is similar. Specifically, when reducing the weight of the first objective function from 0.9 to 0.1, the values of the first objective function increase, while the values of the second objective function decrease when the weight of the second objective function increases from 0.1 to 0.9. The total amount of processed blood in field hospitals and main blood centers was compared for equal weights and time periods for the three problems. Additionally, the amount of processed blood in field hospitals is significantly higher than in main blood centers. This indicates that eliminating the cost and time of blood transfer in field hospitals (due to the concentration of blood collection, processing, and distribution levels) results in an increased amount of processed blood compared to main blood centers (single-level facilities), ultimately leading to a reduction in network costs.ConclusionThis study presents a two-objective mathematical model for the blood supply chain network, integrating pre- and post-crisis conditions. Decisions are proposed for the deployment of four types of facilities, including temporary blood collection centers, field hospitals, main blood centers, and treatment centers, at three levels of blood collection, processing, and distribution. Additionally, inventory, allocation, blood group substitution, blood shortage, transportation mode, and route traffic (delivery delays) are considered for four 24-hour periods in the model. For the first time in this field, knowledge of concentration levels in facilities is utilized, with simultaneous existence of the three levels of blood collection, processing, and distribution in field hospitals. This problem is formulated in a mixed-integer linear programming model with two objective functions aiming to minimize system costs and blood delivery time. The proposed model is solved using the augmented epsilon-constraint evolution method. Sensitivity analysis is conducted for the weights of the objective functions, and additional experiments (RD parameter) are performed. The sensitivity analysis on the weights of the objective functions reveals that reducing the weight of the first objective function leads to a decrease in blood delivery time, while increasing the weight of the second objective function results in an increase in network costs. The investigation of the impact of reducing the amount of additional testing (RD parameter) on the values of the objective functions confirms that advanced equipment at the processing sites of field hospitals reduces network costs and blood delivery time.
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Abstract
Reducing the cost of wastage and shortage of hospitals' blood products with regard to the compatibility of blood groupsBlood supply chain management is considered one of the main components of the health system of each country. This chain consists of two-component blood collection and supply of products ...
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Reducing the cost of wastage and shortage of hospitals' blood products with regard to the compatibility of blood groupsBlood supply chain management is considered one of the main components of the health system of each country. This chain consists of two-component blood collection and supply of products for blood donors has been formed. This article focuses on the issue of the supply of blood products; that tries to provide a mathematical model to reduce waste costs and a shortage of blood products to hospitals. In this model, while meeting the needs of different groups of hospitals, blood in hospitals is minimized inventory costs. A mathematical model in five hospitals affiliated Blood Transfusion Center of East Azerbaijan is implemented. With regard to the compatibility of blood groups and red cell products supply costs and inventory decreased 18% o + blood group also declined to be compatible with other blood types.Keywords: blood supply chain, RBC, compatibility, BTC
Saeed Yaghobi; Mehdi Kamvar
Abstract
There are issues such as limitation of blood resources, perishability, special preservation conditions of blood products and high wastage and shortage costs of blood products, make management of blood products consumption as one of the most complex issues in healthcare systems. This paper proposes a ...
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There are issues such as limitation of blood resources, perishability, special preservation conditions of blood products and high wastage and shortage costs of blood products, make management of blood products consumption as one of the most complex issues in healthcare systems. This paper proposes a linear mathematical model to optimize consumption of the blood products in hospitals. In the proposed model, in addition to distribution of blood products between hospitals by blood center, possibility of lateral transshipments between hospitals considered as a strategy to deal with demand uncertainty. Furthermore, factor of blood freshness and the need of some surgeries for fresh blood considered in this model as real conditions. Finally, to validate the proposed model, a case related to one blood center and eight hospitals in Tehran city presented and its results discussed