A Physarum-inspired approach to supply chain network design



A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients’ distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in real-time updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm.



  1. 1.

    基于多头绒泡菌模型在迭代过程中的连续性, 提出了一种新的策略用来解决交通网络中的用户均衡问题;

  2. 2.

    利用用户均衡和系统最优之间的转化关系, 多头绒泡菌模型解决了最优供应链网络设计问题;

  3. 3.

    通过与现有算法相比较, 多头绒泡菌算法不仅找到了最优解, 而且迭代次数更少。

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  1. 1

    Liu Z, Nagurney A. Supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty. Annals Oper Res, 2013, 208: 251–289

    MathSciNet  Article  MATH  Google Scholar 

  2. 2

    Zhang W, Xu D. Integrating the logistics network design with order quantity determination under uncertain customer demands. Expert Syst Appl, 2014, 41: 168–175

    Article  Google Scholar 

  3. 3

    Yu M, Nagurney A. Competitive food supply chain networks with application to fresh produce. Eur J Oper Res, 2013, 224: 273–282

    MathSciNet  Article  MATH  Google Scholar 

  4. 4

    Hu Z, Du X. Lifetime cost optimization with time-dependent reliability. Eng Optim, 2014, 46: 1389–1410

    MathSciNet  Article  Google Scholar 

  5. 5

    Ma H, Suo C. A model for designing multiple products logistics networks. Int J Phys Distrib & Log Manag, 2006, 36: 127–135

    Article  Google Scholar 

  6. 6

    Zhu X, Yao Q. Logistics system design for biomass-to-bioenergy industry with multiple types of feedstocks. Bioresource Tech, 2011, 102: 10936–10945

    Article  Google Scholar 

  7. 7

    Santoso T, Ahmed S, Goetschalckx M, et al. A stochastic programming approach for supply chain network design under uncertainty. Eur J Oper Res, 2005, 167: 96–115

    MathSciNet  Article  MATH  Google Scholar 

  8. 8

    Zhou G, Min H, Gen M. The balanced allocation of customers to multiple distribution centers in the supply chain network: a genetic algorithm approach. Comput Ind Eng, 2002, 43: 251–261

    Article  Google Scholar 

  9. 9

    Trkman P, McCormack K. Supply chain risk in turbulent environments–a conceptual model for managing supply chain network risk. Int J Prod Econ, 2009, 119: 247–258

    Article  Google Scholar 

  10. 10

    Altiparmak F, Gen M, Lin L, et al. A steady-state genetic algorithm for multi-product supply chain network design. Comput Ind Eng, 2009, 56: 521–537

    Article  Google Scholar 

  11. 11

    Ahmadi J A, Azad N. Incorporating location, routing and inventory decisions in supply chain network design. Transport Res Part E: Log Transport Rev, 2010, 46: 582–597

    Article  Google Scholar 

  12. 12

    Nagurney A. Supply chain network design under profit maximization and oligopolistic competition. Transport Res Part E: Log Transport Rev, 2010, 46: 281–294

    Article  Google Scholar 

  13. 13

    Bilgen B. Application of fuzzy mathematical programming approach to the production allocation and distribution supply chain network problem. Expert Syst Appl, 2010, 37: 4488–4495

    Article  Google Scholar 

  14. 14

    Beamon B M. Supply chain design and analysis: models and methods. Int J Prod Econ, 1998, 55: 281–294

    Article  Google Scholar 

  15. 15

    Sabri E H, Beamon B M. A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega, 2000, 28: 581–598

    Article  Google Scholar 

  16. 16

    Handfield R B, Nichols E L. Supply Chain Redesign: Transforming Supply Chains into Integrated Value Systems. Upper Saddle River: FT Press, 2002

    Google Scholar 

  17. 17

    Nagurney A. Optimal supply chain network design and redesign at minimal total cost and with demand satisfaction. Int J Prod Econ, 2010, 128: 200–208

    Article  Google Scholar 

  18. 18

    Jiang W, Yang Y, Luo Y, et al. Determining basic probability assignment based on the improved similarity measures of generalized fuzzy numbers. Int J Comput Commun Control, 2015, 10: 333–347

    Article  Google Scholar 

  19. 19

    Deng Y. Generalized evidence theory. Appl Intell, 2015, 43: 530–543

    Article  Google Scholar 

  20. 20

    Deng Y, Mahadevan S, Zhou D. Vulnerability assessment of physical protection systems: a bio-inspired approach. Int J Unconv Comput, 2015, 3–4: 227–243

    Google Scholar 

  21. 21

    Jiang W, Luo Y, Qin X, et al. An improved method to rank generalized fuzzy numbers with different left heights and right heights. J Intell Fuzzy Syst, 2015, 28: 2343–2355

    MathSciNet  Article  Google Scholar 

  22. 22

    Deng X, Hu Y, Deng Y, et al. Supplier selection using AHP methodology extended by D numbers. Expert Syst Appl, 2014, 41: 156–167

    Article  Google Scholar 

  23. 23

    Deng Y, Chan F T. A new fuzzy dempster MCDM method and its application in supplier selection. Expert Syst Appl, 2011, 38: 9854–9861

    Article  Google Scholar 

  24. 24

    Deng Y, Chan F T, Wu Y, et al. A new linguistic MCDM method based on multiple-criterion data fusion. Expert Syst Appl, 2011, 38: 6985–6993

    Article  Google Scholar 

  25. 25

    Stephenson S L, Stempen H, Hall I. Myxomycetes: a Handbook of Slime Molds. Portland: Timber Press, 1994

    Google Scholar 

  26. 26

    Nakagaki T, Yamada H, Tóth Á. Intelligence: Maze-solving by an amoeboid organism. Nature, 2000, 407:470

    Article  Google Scholar 

  27. 27

    Zhang X, Zhang Z, Zhang Y, et al. Route selection for emergency logistics management: a bio-inspired algorithm. Saf Sci, 2013, 54: 87–91

    Article  Google Scholar 

  28. 28

    Zhang X, Zhang Y, Hu Y, et al. An adaptive amoeba algorithm for constrained shortest paths. Expert Syst Appl, 2013, 40: 7607–7616

    Article  Google Scholar 

  29. 29

    Zhang X, Wang Q, Chan F T S, et al. A Physarum polycephalum optimization algorithm for the bi-objective shortest path problem. Int J Unconv Comput, 2014, 10: 143–162

    Google Scholar 

  30. 30

    Tero A, Kobayashi R, Nakagaki T. Physarum solver: a biologically inspired method of road-network navigation. Phys A, 2006, 363: 115–119

    Article  Google Scholar 

  31. 31

    Zhang X, Huang S, Hu Y, et al. Solving 0-1 knapsack problems based on amoeboid organism algorithm. Appl Math Comput, 2013, 219: 9959–9970

    MathSciNet  MATH  Google Scholar 

  32. 32

    Zhang X, Wang Q, Adamatzky A, et al. A biologically inspired optimization algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths. J Optimiz Theory Appl, in press. doi: 10.1007/s10957-014-0542-6

  33. 33

    Zhang Y, Zhang Z, Deng Y, et al. A biologically inspired solution for fuzzy shortest path problems. Appl Soft Comput, 2013, 13: 2356–2363

    Article  Google Scholar 

  34. 34

    Zhang X, Liu Q, Hu Y, et al. An adaptive amoeba algorithm for shortest path tree computation in dynamic graphs. arXiv: 1311.0460. 2013

    Google Scholar 

  35. 35

    Gunji YP, Shirakawa T, Niizato T, et al. An adaptive and robust biological network based on the vacant-particle transportation model. J Theor Biol, 2011, 272: 187–200

    Article  Google Scholar 

  36. 36

    Shirakawa T, Gunji, Y P. Computation of Voronoi diagram and collision-free path using the plasmodium of physarum polycephalum. Int J Unconv Comput, 2010, 6: 79–88

    Google Scholar 

  37. 37

    Shirakawa T, Gunji Y P. Emergence of morphological order in the network formation of Physarum polycephalum. Biophys Chem, 2007, 128: 253–260

    Article  Google Scholar 

  38. 38

    Gao C, Lan X, Zhang X, et al. A bio-inspired methodology of identifying influential nodes in complex networks. PloS one, 2013, 8: e66732

    Article  Google Scholar 

  39. 39

    Nakagaki T, Iima M, Ueda T, et al. Minimum-risk path finding by an adaptive amoebal network. Phys Rev Lett, 2007, 99: 068104

    Article  Google Scholar 

  40. 40

    Adamatzky A. Route 20, autobahn 7, and slime mold: approximating the longest roads in USA and Germany with slime mold on 3-D terrains. IEEE Trans Cybernetics, 2014, 44: 126–136

    Article  Google Scholar 

  41. 41

    Tero A, Yumiki K, Kobayashi R, et al. Flow-network adaptation in Physarum amoebae. Theory Biosci, 2008, 127: 89–94

    Article  Google Scholar 

  42. 42

    Jones J, Adamatzky A. Computation of the travelling salesman problem by a shrinking blob. Natural Comput, 2014, 13: 1–16

    MathSciNet  Article  Google Scholar 

  43. 43

    Tero A, Takagi S, Saigusa T, et al. Rules for biologically inspired adaptive network design. Science, 2010, 327: 439–442

    MathSciNet  Article  MATH  Google Scholar 

  44. 44

    Adamatzky A, Alonso-Sanz R. Rebuilding Iberian motorways with slime mould. Biosyst, 2011, 105: 89–100

    Article  Google Scholar 

  45. 45

    Adamatzky A. Bioevaluation of World Transport Networks. Singapore: World Scientific, 2012

    Book  Google Scholar 

  46. 46

    Adamatzky A, Martínez G J, Chapa-Vergara S V, et al. Approximating Mexican highways with slime mould. Natural Comput, 2011, 10: 1195–1214

    MathSciNet  Article  Google Scholar 

  47. 47

    Gao C, Yan C, Zhang Z, et al. An amoeboid algorithm for solving linear transportation problem. Phys A, 2014, 398: 179–186

    MathSciNet  Article  Google Scholar 

  48. 48

    Adamatzky A, Martinez G J. Bio-imitation of Mexican migration routes to the USA with slime mould on 3D terrains. J Bionic Eng, 2013, 10: 242–250

    Article  Google Scholar 

  49. 49

    Adamatzky A. Physarum Machines: Computers from Slime Mould. Singapore: World Scientific, 2010

    Google Scholar 

  50. 50

    Adamatzky A, Schubert T. Slime mold microfluidic logic gates. Mater Today, 2014, 17: 86–91

    Article  Google Scholar 

  51. 51

    Nagurney A. A system-optimization perspective for supply chain network integration: the horizontal merger case. Transport Res Part E: Log Transport Rev, 2009, 45: 1–15

    Article  Google Scholar 

  52. 52

    Nagurney A, Woolley T, Qiang Q. Multi-product supply chain horizontal network integration: models, theory, and computational results. Int Trans Oper Res, 2010, 17: 333–349

    Article  MATH  Google Scholar 

  53. 53

    Nagurney A. Supply Chain Network Economics: Dynamics of Prices, Flows and Profits. Cheltenham: Edward Elgar Publishing, 2006

    Google Scholar 

  54. 54

    Nagurney A, Dong J, Zhang D, et al. A supply chain network equilibrium model. Transport Res Part E: Log Transport Rev, 2002, 38: 281–303

    Article  Google Scholar 

  55. 55

    Nagurney A, Woolley T. Environmental and cost synergy in supply chain network integration in mergers and acquisitions. In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems. Berlin: Springer, 2010. 57–78

    Google Scholar 

  56. 56

    Tero A, Kobayashi R, Nakagaki T. A mathematical model for adaptive transport network in path finding by true slime mold. J Theor Biol, 2007, 244: 553–564

    MathSciNet  Article  Google Scholar 

  57. 57

    Bell M G, Lida Y. Transportation Network Analysis. Hoboken: John Wiley & Sons, 1997

    Book  Google Scholar 

  58. 58

    Si BF, Gao ZY. Modeling Network Flow and System Optimization for Traffic and Transportation System (in Chinese). Beijing: China Communications Press, 2013

    Google Scholar 

  59. 59

    Adamatzky A. If BZ medium did spanning trees these would be the same trees as Physarum built. Phys Lett A, 2009, 373: 952–956

    Article  MATH  Google Scholar 

  60. 60

    Gunji Y P, Shirakawa T, Niizato T, et al. Minimal model of a cell connecting amoebic motion and adaptive transport networks. J Theor Biol, 2008, 253: 659–667

    Article  Google Scholar 

  61. 61

    Gunji Y P, Shirakawa T, Niizato T, et al. An adaptive and robust biological network based on the vacant-particle transportation model. J Theor Biol, 2011, 272: 187–200

    Article  Google Scholar 

  62. 62

    Tsompanas M A I, Sirakoulis G C. Modeling and hardware implementation of an amoeba-like cellular automaton. Bioinspir Biomim, 2012, 7: 036013

    Article  Google Scholar 

  63. 63

    Tsompanas M A I, Sirakoulis G C, Adamatzky A. Evolving transport networks with cellular automata models inspired by slime mould. IEEE Trans Cybern, in press. doi: 10.1109/TCYB.2014.2361731

  64. 64

    Kalogeiton V S, Papadopoulos D P, Sirakoulis G C. Hey Physarum! Can you perform SLAM? Int J Unconv Comput, 2014, 10: 271–293

    Google Scholar 

  65. 65

    Adamatzky A, Jones J. Road planning with slime mould: if Physarum built motorways it would route M6/M74 through Newcastle. Int J of Bifurcat Chaos, 2010, 20: 3065–3084

    MathSciNet  Article  Google Scholar 

  66. 66

    Chakravarthy H, Proch P B, Rajan R, et al. Bio inspired approach as a problem solving technique. Netw Complex Syst, 2012, 2: 14–22

    Google Scholar 

  67. 67

    Liu Y, Zhang Z, Gao C, et al. A physarum network evolution model based on IBTM. In: Advances in Swarm Intelligence. Berlin: Springer, 2013. 19–26

    Google Scholar 

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Correspondence to Yong Deng.

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Zhang, X., Adamatzky, A., Yang, XS. et al. A Physarum-inspired approach to supply chain network design. Sci. China Inf. Sci. 59, 052203 (2016). https://doi.org/10.1007/s11432-015-5417-4

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  • supply chain design
  • Physarum
  • capacity investments
  • network optimization
  • adaptivity


  • 供应链网络
  • 多头绒泡菌
  • 网络优化
  • 自适应性