Elsevier

Expert Systems with Applications

Volume 137, 15 December 2019, Pages 74-99
Expert Systems with Applications

Mathematical model formulation and hybrid metaheuristic optimization approach for near-optimal blood assignment in a blood bank system

https://doi.org/10.1016/j.eswa.2019.06.059Get rights and content

Highlights

  • Design of a dynamic mathematical model for blood assignment problem.

  • Proposal of a symbiotic optimization search algorithm for the BAP.

  • Implementation of two hybrid SOSGA and SOSSA algorithms to solve the BAP.

  • Suggestions for further development and possible areas of improvement.

Abstract

The shortage and wastage of blood products have been identified as the major contending factors that are frequently encountered in the management of blood supply chain processes. In general, the blood which is considered an essential product for which human existence relies on, has perishability characteristics that allow it to be stored up to a limited number of days. Therefore, this feature constrains the quantity of blood that can be retained in hospitals and blood centers, because keeping excessive number of blood units on inventory may result in blood product wastage. On the other hand, failure to stockpile on inventory can lead to shortage of this resource, and as a result may cause the cancellation of important activities such as treatment of special cases like surgery, accident, disaster circumstance and, in a worst case scenario increases the fatality rates at hospitals. This paper presents a dynamic mathematical model with the goal of improving the efficiency of blood related activities that occur at the blood centers. The model also caters for the assignment of whole blood units of available blood types to various requests. A set of equations that incorporate both the ABO and Rhesus blood groups are derived and presented subsequently. This further extends the initial work where only the ABO blood group was considered. In an effort to implement the developed model, three metaheuristic algorithms namely, symbiotic organisms search, symbiotic organisms search genetic algorithm, and symbiotic organisms search simulated annealing algorithms are proposed to identify the optimal routing for each of the blood types. An extensive numerical study was carried out using datasets from a synthetic blood sample collection process to illustrate the potential of the three metaheuristic algorithms to solve the developed blood assignment model. Furthermore, experimental results show that the hybrid symbiotic organisms search algorithms not only achieve superior accuracy, but also exhibits a higher level of stability, with the hybrid symbiotic organisms search genetic algorithm having the overall best superior performance.

Introduction

Blood is essential for different purposes in the hospitals because it is the essence of life without which human beings cannot survive. Blood and its constituent products namely, white blood cells (WBSs), red blood cells (RBCs), plasma, and platelets are necessary during transfusion processes (Zahiri & Pishvaee, 2017). Human blood is further classified into various grouping of which the ABO and Rhesus (Rh) grouping are very common (Ramezanian and Behboodi, 2017, Zahiri and Pishvaee, 2017, Cheraghi et al., 2017, Adewumi et al., 2012, Elalouf et al., 2015). The demand for blood has however increased due to its limited availability and short lifespan. Furthermore, the scarcity and limited availability of blood has increased the solicitation for donations worldwide (Kaveh and Ghobadi, 2017, Zahiri and Pishvaee, 2017, Ghatreh Samani and Hosseini-Motlagh, 2017). However, despite this effort, shortages of blood are still being reported in most health institutions and blood centres across the world (Kaveh and Ghobadi, 2017, Samani and Hosseini-Motlagh, 2018). Blood groupings or types not only put a natural restriction on blood types issued during transfusion process but also contribute to the scarcity as blood of a particular type might be in dire need when depleted in the blood bank. This sometimes is due to wastage as a result of contamination, infested blood, expiration of blood units in storage and poor management of blood products in general (Adewumi et al., 2012, Akhavan Niaki, 2017, Cheraghi et al., 2017, Elalouf et al., 2015, Ramezanian and Behboodi, 2017). While many have reported various ways of blood management for specific cases and mainly from a management point of view (Beliën and Forcé, 2012, Charpin and Adewumi, 2011, Eskandari-Khanghahi et al., 2018, Khalilpourazari and Khamseh, 2017, Puranam et al., 2017, SANBS 2018, Stanger et al., 2012, Zahiri et al., 2018, Zahiri et al., 2015), there is still a need for more efficient management of available blood products that limit dependency on importation from outside the blood banking system under consideration. This paper only focuses on the RBC component.

Blood Assignment Problem (BAP) was recently proposed in literature as a combinatorial optimization problem to deal with efficient allocation of blood of various types from donors to requesting entities in a way that minimizes wastage (or expiration) and importation from outside the blood bank while stabilizing the system (De Angelis et al., 2001, Olusanya et al., 2015). Though very few related studies on blood management had appeared in the literature (Alfonso et al., 2013, Charpin and Adewumi, 2011, Attari et al., 2018, Govender and Ezugwu, 2018), studies that focused on the mathematical optimization approach to solving the actual BAP as considered in this paper are limited. A similar study by De Angelis et al. (2001) on BAP appeared some years ago with a focus on a case from the Italian Red Cross. The BAP was modeled as a linear programming problem. The author considered the allocation of blood on daily basis with emphasis on the “urgency” of blood request, where urgency was defined at three levels namely, “very urgent”, “urgent” and “not urgent”. Some recent studies by Patil, Ray, and Saha (2018), and Ekici, Özener, and Çoban (2018), reports an initial attempt to model the BAP as a dynamic system with certain assumptions made. However, a number of different supply chain heuristic-based approaches were used to implement each of the proposed models, with varying results obtained (Duan and Liao, 2014, Haijema et al., 2007, Heidari-Fathian and Pasandideh, 2018, Özener and Ekici, 2018). Alfonso et al. (2013) developed a formal Petri net model which was used to describe all relevant donor flows of the various blood collection systems. They also proposed quantitative models that encompassed all components of the blood collection systems, such as the donor arrival process, resource capacities and performance indicators. Elalouf, Tsadikovich, and Hovav (2018) formulated a mix integer programming model for the BAP and subsequently developed two heuristic algorithms, a numeric search and a new improved genetic algorithm to evaluate the proposed BAP model. Abdulwahab and Wahab (2014) introduced a workable model for the establishment of an inventory bank holding perishable blood platelets with a short shelf-life. Their model which was formulated using an approximate dynamic programming concept considered a blood platelet bank with eight blood types, stochastic demand, stochastic supply, and deterministic lead time. Dillon, Oliveira, and Abbasi (2017) proposed a two-stage stochastic programming model for defining optimal periodic review policies for red blood cell inventory management. The focus of their model implementation was on minimizing operational costs, as well as blood shortage and wastage due to expiration, taking into account perishability and demand uncertainty. In another research effort, Samani, Torabi, and Hosseini-Motlagh (2018) proposed a multi-objective mixed integer linear programming model for the design of an integrated blood supply chain network for disaster relief. The model developed by Samani et al., 2018 accounts for special cases of blood supply chains involving uncertain demand of blood products and their irregular supply, perishability of blood products and shortage avoidance. For the current study, a different dynamic modeling and implementation methods are proposed, which includes for the mathematical modeling, the use of a differential equation technique to find a set of equations that incorporates both the ABO and Rh blood grouping, while for the model implementation, the use of a global metaheuristic optimization algorithm to solve the developed model is proposed.

In the last decade, several heuristics-based algorithmic strategies have been proposed in the quest to finding near-optimum or good quality solutions for many complex real-world combinatorial optimization problems among which include the well-known traveling salesman problem, parallel machine scheduling problem, and the blood assignment problem or the BAP as it is referred to in the current paper. Although there are few cases where global optimization metaheuristic algorithms have been employed to solve the BAP, as most of the methods recorded in literature used the traditional heuristic techniques that were developed based on the popular supply chain model (Beliën and Forcé, 2012, Dillon et al., 2017, Lowalekar and Ravichandran, 2010, Samani et al., 2018). Some examples of the few metaheuristic algorithms that have been used to solve the BAP include simulated annealing (SA) (Olusanya and Adewumi, 2014, Yu et al., 2018, April), genetic algorithm (GA) (Adewumi et al., 2012), particle swarm optimization (PSO) (Olusanya et al., 2015), and discrete symbiotic organisms search algorithm (Govender & Ezugwu, 2018). However, all the algorithms from the literature mentioned here draw their inspiration through the observation of physical processes that occur in nature. They are implemented by mimicking different natural systems and processes using mathematical and computational models. The current study is different from other existing studies in the sense that it considers simultaneously the design of a unique dynamic mathematical model and the implementation of two hybrid symbiotic global optimization search algorithms for the BAP. More so, it is also interesting to note that none of these two approaches have previously been considered in the literature to solve the same problem at hand.

The symbiotic organisms search algorithm is a recently proposed global metaheuristic optimization algorithm that was first introduced by Cheng and Prayogo (2014). The algorithmic design was inspired by the symbiotic relationship strategies that exist among organisms for the purpose of survival and propagation of life in the ecosystem. The SOS algorithm was initially used to solve continuous engineering optimization problems. However, several experimental results from literature (Ezugwu et al., 2018, Ezugwu et al., 2017, Zhou et al., 2019, Ezugwu, 2019, Ezugwu and Prayogo, 2018, Ezugwu et al., 2019) show that the SOS algorithm is considerably robust and efficient when used as an optimization tool for finding global optimum solutions to complex mathematical benchmark problems and discrete combinatorial optimization problems. Therefore, the inherent potential of the SOS in finding global solution to the aforementioned optimization problems makes it even more attractive for further investigation in terms of its application to solve a wide range of complex real-world problems, such as the BAP. In addition, since SOS has not gained wide recognition in solving real-world problems, such as, routing and assignment problems, we believe that, this could be the main motivation of this paper to introduce SOS and its variant hybrid algorithms to solve such complex problem like the discrete BAP as proposed in this paper.

This paper presents an extension of the work reported in Charpin and Adewumi (2011) to include all the most common blood groups based on both ABO and Rh grouping. An extended model is therefore presented to manage the dynamics of blood supply chain in the blood bank system. The model is based on a set of derived equations to model the BAP in a more realistic way as obtained in real life. This can thus contribute further into a decision making process regarding blood stocks. Furthermore, the possibility of improving the performance of a recently proposed symbiotic organisms search (SOS) algorithm to solve the blood assignment problem with respect to optimizing the routing of blood allocation is investigated. To achieve this goal, three sets of SOS variant algorithms are developed to identify the optimal routing for each blood type. The three algorithms proposed in this paper for the BAP include the basic SOS algorithm, hybrid Symbiotic Organisms Search Simulated Annealing (SOSSA) algorithm and hybrid Symbiotic Organisms Search Genetic Algorithm (SOSGA). It is also noteworthy to mention here that this paper extends the work presented in Govender and Ezugwu (2018) and Govender and Ezugwu (2019), where the SOS algorithm was first used to solve the BAP. The new improvements carried out on the existing SOS implementation for the BAP covers the design of robust dynamic mathematical model representation of the problem at hand and hybridization of the SOS algorithm with other well-known metaheuristic algorithm namely, GA and SA. The detailed discussion on each of these methods is covered in the later part of the paper. The major contributions of this study are as follows:

  • Proposal of a dynamic mathematical model formulation for the management of blood bank, which considers the complex ABO with Rh factors (positive and negative rhesus) compatibilities among blood groups.

  • Derivation of a set of governing equations for optimizing a decision making process for the blood bank manager

  • Proposal of a hybrid metaheuristic algorithm to determine the near-optimal scheme of the blood assignment problem in a typical dynamic blood bank system.

The rest of the paper is organized as follows: Section 2 presents the modelling of the blood assignment problem as a dynamic system. The improved and hybrid symbiotic organisms search algorithm for solving blood assignment problems is proposed in Section 3. Experimentation and verification of the hybrid algorithms performances with various stochastically generated datasets are discussed in Section 4. Finally, Section 5 concludes the work and suggest future directions.

Section snippets

Dynamic modelling of blood assignment problems

The daily request for blood is not static as the cases of patients also vary, hence there will be a greater request in the case of emergency than the standard daily request (SANBS, 2018). However, as the supply depends largely on whatever is available in the blood bank and perhaps possible donations, most daily requests might not be met and allocation of blood across various blood types might be disproportionate thereby leading to mismanagement. In Fig. 1, the flow of blood whole units in a

Symbiotic organisms search algorithm

In this section, we developed three metaheuristic algorithms to solve the above derived mathematical model for the BAP, starting with the implementation of a modified standard SOS algorithm. Furthermore, because the classical SOS based implementations cannot directly be applied to solve the BAP, which is a discrete combinatorial optimization problem, the algorithm needs to be transformed into its discrete form. Therefore, each of the three SOS variants implementation have been individually

Experiments

The experimental testing platform for the proposed algorithms were conducted on Intel core i5 CPU with 2.5 GHz and 4GB RAM and Windows 10.0 Operating system, while the implementation software for the three algorithmic methods is Java. Due to the SOS algorithm having no form of parameter tuning, the SA and GA parameters have been listed below. However, each algorithm was subjected to 1000 iterations with a population size of 50 individuals or organisms. Furthermore, the SA used an initial

Conclusion

This paper presented an extended dynamic mathematical model of the BAP that considers both the ABO and Rh blood grouping. In a separate effort, the extended model can help in blood management of a blood bank system. As part of the major contribution of this study, three algorithms, namely the SOS, SOSSA, and SOSGA were implemented to test the designed mathematical model. The SOSSA and SOSGA were hybrid implementations of the basic SOS algorithm and implemented techniques from the SA algorithm

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of the paper.

CRediT authorship contribution statement

Absalom E. Ezugwu: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. Micheal O. Olusanya: Conceptualization, Investigation, Methodology, Validation, Visualization, Writing - original draft. Prinolan Govender: Data curation, Software, Validation, Visualization, Writing - original draft, Writing - review & editing.

Acknowledgement

The authors acknowledge the support and mentorship of the late prof. A. O. Adewumi during his lifetime as our supervisor at the School of Mathematics, Statistics and Computer Science. He was also instrumental to the conception of the mathematical modelling aspect of this work based on his previous work.

References (47)

  • A.F. Osorio et al.

    Whole blood or apheresis donations? A multi-objective stochastic optimization approach

    European Journal of Operational Research

    (2018)
  • O.Ö& Özener et al.

    Managing platelet supply through improved routing of blood collection vehicles

    Computers & Operations Research

    (2018)
  • K. Puranam et al.

    Managing blood inventory with multiple independent sources of supply

    European Journal of Operational Research

    (2017)
  • R. Ramezanian et al.

    Blood supply chain network design under uncertainties in supply and demand considering social aspects

    Transportation Research Part E: Logistics and Transportation Review

    (2017)
  • S.H. Stanger et al.

    Blood inventory management: Hospital best practice

    Transfusion Medicine Reviews

    (2012)
  • B. Zahiri et al.

    A multi-stage stochastic programming approach for blood supply chain planning

    Computers & Industrial Engineering

    (2018)
  • B. Zahiri et al.

    Blood collection management: Methodology and application

    Applied Mathematical Modelling

    (2015)
  • Y. Zhou et al.

    Automatic data clustering using nature-inspired symbiotic organism search algorithm

    Knowledge-Based Systems

    (2019)
  • A. Adewumi et al.

    Optimizing the assignment of blood in a blood banking system: Some initial results

  • S.T. Akhavan Niaki

    Presenting a stochastic multi choice goal programming model for reducing wastages and shortages of blood products at hospitals

    Journal of Industrial and Systems Engineering

    (2017)
  • E. Alfonso et al.

    Modelling and simulation of blood collection systems: Improvement of human resources allocation for better cost‐effectiveness and reduction of candidate donor abandonment

    Vox Sanguinis

    (2013)
  • M.Y.N. Attari et al.

    A bi-objective robust optimization model for a blood collection and testing problem: An accelerated stochastic Benders decomposition

    Annals of Operations Research

    (2018)
  • J.P.& Charpin et al.

    Mathematics in Industry Study Group (MISG 2011)

    (2011)
  • Cited by (0)

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