Skip to main content

A Multistage Algorithm for Blood Banking Supply Chain Allocation Problem


This paper proposes an efficient method for allocating a number of blood centers to a set of hospitals to minimize the total distance between the hospitals and the blood centers, based on the concept of graph partitioning (p-median methodology) and metaheuristic optimization algorithms. For this purpose, a weighted graph is first constructed for the network denoted by G 0. A coarsening process is then performed to match the edges in n stages. Then, the enhanced colliding bodies (ECBO) algorithm is applied to the coarsened model to decompose it into p subdomains by using a p-median methodology. In the present problem, p is the number of blood centers to be allocated for the hospitals. The results indicate that the proposed algorithm performs quite satisfactory from both computational time and optimality points of view.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. 1.

    Luenberger DG, Ye Y (2014) Linear and nonlinear programming. Springer International Publishing, Switzerland

    MATH  Google Scholar 

  2. 2.

    Hsieh C-L (2014) An evolutionary-based optimization for a multi-objective blood banking supply chain model, Lecture notes in computer science, vol 8481. Springer International Publishing, Cham, pp 511–520

  3. 3.

    Kaveh A (2004) Structural mechanics: graph and matrix methods, 3rd edn. Wiley, Chechister

    MATH  Google Scholar 

  4. 4.

    Karypis G, Kumar V (1995) Analysis of multilevel graph partitioning, University of Minnesota, ACM

  5. 5.

    Hendrickson B, Leland R (1992) An improved spectral graph partitioning algorithm for mapping parallel computations, Tech. rep., Sandia National Laboratories, Albuquerque, NM, SAND92-1460

  6. 6.

    Miller GL,Teng S-H, Vavasis SA (1991) A unified geometric approach to graph separators. In: Proc. 31st Annual Symposium on Foundations of Computer Science, IEEE, pp 538–547

  7. 7.

    Nour-Omid B, Raefsky A, Lyzenga G (1986) Solving finite element equations on concurrent computers. In: Noor AK (ed) Parallel computation and their impact on mechanics. American Society of Mechanical Engineering, pp 209–227

  8. 8.

    Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs, Technical Report, Department of Computer Science, University of Minnesota, TR 95-035

  9. 9.

    Birn M, Osipov V, Sanders P, Schulz C, Sitchinava N (2013) Efficient parallel and external matching. In: Euro-Par, vol 8097, LNCS. Springer, Berlin, pp 659–670

  10. 10.

    Boussaïd I, Julien L, Patrick S (2013) A survey on optimization meta-heuristics. Inf Sci 237:82–117

    Article  MATH  Google Scholar 

  11. 11.

    Sheikholeslami R, Kaveh A (2013) A survey of chaos embedded meta-heuristic algorithms. Int J Optim Civil Eng 3:617–633

    Google Scholar 

  12. 12.

    Kaveh A, Rahimi Bondarabady HA (2000) A hybrid graph-genetic method for domain decomposition. Civil-Comp Press, Leuvan, pp 127–134

    MATH  Google Scholar 

  13. 13.

    Kaveh A, Shojaee S (2008) Optimal domain decomposition via p-median methodology using ACO and hybrid ACGA. Finite Elem Anal Des 44:505–512

    Article  Google Scholar 

  14. 14.

    Kaveh A, Mahdavi VR (2015) Optimal domain decomposition using colliding bodies optimization and k-median method. Finite Elem Anal Des 98:41–49

    Article  Google Scholar 

  15. 15.

    Birattari M, Paquete L, Stützle T, Varrentrapp K (2001) Classification of meta-heuristics and design of experiments for the analysis of components, Technical Report AIDA-01-05, FG Intellektik, FB Informatik, Technische Universität Darmstadt, Darmstadt, Germany

  16. 16.

    Yaghini M, Karimi M, Rahbar M (2013) A hybrid met heuristic approach for the capacitated p-median problem. Appl Soft Comput 13:3922–3930

    Article  Google Scholar 

  17. 17.

    Tiwari AK, Sharma P, Pandey PK, Rawat GS, Dixit S, Raina V, Bhargava R (2015) A cost effective model for appropriate administration of red cell units and salvaging un-transfused red cell units by using temperature sensitive indicators for blood component transportation in a hospital setting. Asian J Transfus Sci 9:36–40

    Article  Google Scholar 

  18. 18.

    Optimizing your Blood Supply Chain (2014).

  19. 19.

    Hsieh C-L (2014) An evolutionary-based optimization for a multi-objective blood banking supply chain model, Lecture notes in computer science, vol 8481. Springer International Publishing Switzerland. pp 511–520

  20. 20.

    Cedric Chevalier, Ilya Safro (2009) Comparison of coarsening schemes for multilevel graph partitioning. Springer, Berlin, pp 191–205

    Google Scholar 

  21. 21.

    Hagen L, Kahng AB (1992) A new approach to effective circuit clustering. In: Proc. IEEE International Conference on Computer Aided Design, vol 92, pp 422–427

  22. 22.

    Kaveh A, Mahdavai VR (2014) Colliding bodies optimization method for optimum design of truss structures with continuous variables. Adv Eng Softw 70:1–12

    Article  Google Scholar 

  23. 23.

    Kaveh A, Ilchi Ghazaan M (2014) Enhanced colliding bodies optimization for design problems, with continuous and discrete variables. Adv Eng Softw 77:66–75

    Article  Google Scholar 

  24. 24.

    Kaveh A (2014) Advances in metaheuristic algorithms for optimal design of structures. Springer, Switzerland

    Book  MATH  Google Scholar 

  25. 25.

    Kaveh A, Nasr H (2012) Hybrid harmony search for conditional p-median problems. Int J Civil Eng IUST 10:32–36

    Google Scholar 

  26. 26.

    Kaveh A, Safari H (2014) Hybrid-enhanced charged system search for solving travelling salesman problem and one of its applications: the single-row facility layout problem. Int J Civil Eng IUST 12:363–370

  27. 27.

    Kaveh A, Maniat M (2014) Damage detection in skeletal structures based on charged system search optimization using incomplete modal data. Int J Civil Eng IUST 12:291–298

    Google Scholar 

  28. 28.

    Kaveh A, Gaffarian R (2015) Shape optimization of arch dams with frequency constraints by enhanced charged system search algorithm and neural network. Int J Civil Eng 13:102–111

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to A. Kaveh.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kaveh, A., Ghobadi, M. A Multistage Algorithm for Blood Banking Supply Chain Allocation Problem. Int J Civ Eng 15, 103–112 (2017).

Download citation


  • Graph partitioning
  • Coarsening
  • p-median
  • CBO and ECBO metaheuristic algorithms