Computational and Mathematical Organization Theory

, Volume 24, Issue 3, pp 351–377 | Cite as

Evolutionary dynamics of two-actor VMI-driven supply chains

  • Fidel Torres
  • César García-DíazEmail author


The strategy of integration known as vendor-managed inventory (VMI), which allows the coordination of inventory policies between producers and buyers in supply chains, has long been considered a strategy for inventory cost reduction. Although the literature acknowledges the importance of understanding the dynamics of VMI implementation through evolutionary games, research in this topic still remains scarce. This paper studies the dynamics of strategic interaction of a producer–buyer supply chain under a newly developed VMI scheme, which makes use of a synchronization mechanism between the buyer and the producer replenishment cycles. By using this alternative VMI representation, we obtain the mathematical conditions that determine the degree of stability of evolutionarily stable strategies. As other evolutionary game theoretical approaches, we also find a lower bound for penalty costs that ensures a VMI contract, but most importantly, we also find how a VMI implementation might depend on the difference between production and demand rates, regardless of any penalty costs.


Dynamical systems stability Evolutionary game theory Supply chain coordination Vendor-managed inventory 



The authors are grateful to Naly Rakoto for his insightful comments to early versions of this paper, and to the reviewers for their suggestions that have significantly improved our work. The second author thanks the Centre for Research in Social Simulation (CRESS) of the University of Surrey for hosting him during the final stages of this work. The usual disclaimer applies.


  1. Achabal DD, McIntyre SH, Smith SA, Kalyanam K (2000) A decision support system for vendor managed inventory. J Retail 76(4):430–454CrossRefGoogle Scholar
  2. Babu S, Mohan U (2017) An integrated approach to evaluating sustainability in supply chains using evolutionary game theory. Comput Oper Res. doi: 10.1016/j.cor.2017.01.008
  3. Blatherwick A (1998) Vendor-managed inventory: fashion fad or important supply chain strategy? Supply Chain Manag 3(1):10–11CrossRefGoogle Scholar
  4. Cachon GP, Netessine S (2006) Game theory in supply chain analysis. In models, methods, and applications for innovative decision making. In: Johnson MP, Norman B, Secomandi N, Gray P, Greenberg HJ (eds), Tutorials in operations research: models, methods, and applications for innovative decision making, INFORMS annual meeting, p 200–233Google Scholar
  5. Cachon G, Zipkin P (1999) Competitive and cooperative inventory policies in a two-stage supply chain. Manag Sci 45(7):936–947CrossRefGoogle Scholar
  6. Cai J, Hu X, Han Y, Cheng H, Huang W (2016) Supply chain coordination with an option contract under vendor-managed inventor. Int Trans Oper Res 23(6):1163–1183CrossRefGoogle Scholar
  7. Cai J, Tadikamalla PR, Shang J, Huang G (2017) Optimal inventory decisions under vendor managed inventory: substitution effects and replenishment tactics. Appl Math Model 43:611–629CrossRefGoogle Scholar
  8. Choi K, Dai J, Song J (2004) On measuring supplier performance under vendor-managed inventory programs in capacitated supply chains. Manuf Serv Oper Manag 6(1):53–72CrossRefGoogle Scholar
  9. Choudhary D, Shankar R (2015) The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn, Sn) policy. Omega 5:59–70CrossRefGoogle Scholar
  10. Darwish M, Odah O (2010) Vendor-managed inventory model for single-vendor multi-retailer supply chains. Eur J Oper Res 204(3):473–484CrossRefGoogle Scholar
  11. Daugherty P, Myers M, Autry C (1999) Automatic replenishment programs: an empirical examination. J Bus Logist 20(2):63–82Google Scholar
  12. Disney S, Towill D (2002) A procedure for the optimization of the dynamic response of a Vendor Managed Inventory system. Comput Ind Eng 43(1–2):27–58CrossRefGoogle Scholar
  13. Dong Y, Chu K (2002) A supply chain model of vendor managed inventory. Transp Res E 38:75–95CrossRefGoogle Scholar
  14. Ellison G, Fudenberg D (2000) Learning purified mixed equilibria. J Econ Theory 90(1):84–115CrossRefGoogle Scholar
  15. Emigh J (1999) Vendor-managed inventory. Computerworld 33(34):52Google Scholar
  16. Esmaeili M, Allameh G, Tajvidi T (2016) Using game theory for analysing pricing models in closed-loop supply chain from short- and long-term perspectives. Int J Prod Res 54(7):2152–2169CrossRefGoogle Scholar
  17. Forrester JW (1961) Industrial dynamics. MIT Press, CambridgeGoogle Scholar
  18. Friedman D (1991) Evolutionary games in economics. Econometrica 59(3):637–666CrossRefGoogle Scholar
  19. Garg H (2014) Inventory model involving variable lead time, back-order discounts and lost sales using PSO. In: 18th Online world conference on soft computing in industrial application (WSC18), World Wide Web, 1–12 December 2014Google Scholar
  20. Garg H (2015) Fuzzy inventory models for deteriorating items under different types of lead-time distributions. In: Kahraman C, Onar SC (eds) Intelligent techniques in engineering management. Springer, Heidelberg, pp 247–274Google Scholar
  21. Garg H (2016a) A hybrid PSO–GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305Google Scholar
  22. Garg H (2016b) Bi-criteria optimization for finding the optimal replacement interval for maintaining the performance of the process industries. In: Vasant P, Weber G-H, Dieu V-G (eds) Handbook of research on modern optimization algorithms and application in engineering and economics. IGI Global, Hershey, pp 643–675CrossRefGoogle Scholar
  23. Guan R, Zhao X (2010) On contracts for VMI program with continuous review (r, Q) policy. Eur J Oper Res 207:656–667CrossRefGoogle Scholar
  24. Holmström J (1998) Business process innovation in the supply chain—a case study of implementing vendor managed inventory. Eur J Purch Supply Manag 4(2–3):127–131CrossRefGoogle Scholar
  25. Huang Y, Huang GQ, Newman ST (2011) Coordinating pricing and inventory decisions in a multi-level supply chain: a game-theoretic approach. Transp Res E 47:115–129CrossRefGoogle Scholar
  26. Huynh CH, Pan W (2015) Operational strategies for supplier and retailer with risk preference under VMI contract. Int J Prod Econ 169:413–442CrossRefGoogle Scholar
  27. Ketchen DJ Jr, Crook TH, Combs JG, Patterson JD (2012) Improving supply chain performance through organizational design. J Organ Des 1(3):64–72Google Scholar
  28. Kulp SC, Lee HL, Ofek E (2004) Manufacturer benefits from information integration with retail customers. Manag Sci 50(4):431–444CrossRefGoogle Scholar
  29. Lee HL, Padmanabhan V, Whang S (1997) The bullwhip effect in supply chains. Sloan Manag Rev 38(3):93Google Scholar
  30. Lee H, So K, Tang C (2000) The value of information sharing in a two-level supply chain. Manag Sci 46(5):626–643CrossRefGoogle Scholar
  31. Maynard-Smith J (1974) The theory of games and the evolution of animal conflicts. J Theor Biol 47:209–221CrossRefGoogle Scholar
  32. Maynard-Smith J (1982) Evolution and the theory of games. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  33. Maynard-Smith J, Price G (1973) The logic of animal conflict. Nature 146:15–18CrossRefGoogle Scholar
  34. Mena C, Humphries A, Choi TY (2013) Toward a theory of multi-tier supply chain management. J Supply Chain Manag 49(2):58–77CrossRefGoogle Scholar
  35. Niranjan TT, Wagner SM, Thakur-Weigold B (2011) Are you ready for VMI? Ind Eng 43(2):39–44Google Scholar
  36. Paulraj A, Chen IJ, Flynn J (2006) Levels of strategic purchasing: impact on supply integration and performance. J Purch Supply Manag 12:107–122CrossRefGoogle Scholar
  37. Reddy M, Vrat P (2007) Vendor managed inventory model: a case study. J Adv Manag Res 4(1):83–88CrossRefGoogle Scholar
  38. Sandholm WH, Dokumaci E (2007) Dynamo: phase diagrams for evolutionary dynamics. Software suite.
  39. Schotanus F, Telgen J (2007) Developing a typology of organizational forms of cooperative purchasing. J Purch Supply Manag 13:53–68CrossRefGoogle Scholar
  40. Silver E, Pyke D, Peterson R (1998) Inventory management and production planning and scheduling, 3rd edn. Wiley, New YorkGoogle Scholar
  41. Southard P, Swenseth S (2008) Evaluating vendor-managed inventory (VMI) in non-traditional environments using simulation. Int J Prod Econ 116(2):275–287CrossRefGoogle Scholar
  42. Stock GN, Greis NB, Kasarda JD (2000) Enterprise logistics and supply chain structure: the role of fit. J Oper Manag 18:531–547CrossRefGoogle Scholar
  43. Taylor PJ, Jonker L (1978) Evolutionary stable strategies and game dynamics. Math Biosci 40:145–156CrossRefGoogle Scholar
  44. Torres F, Ballesteros F, Villa M (2014) Modeling a coordinated manufacturer–buyer single-item system under vendor-managed inventory. In: Choi T-M (ed) Handbook of EOQ inventory problems. Springer, New York, pp 247–278CrossRefGoogle Scholar
  45. Verma NK, Chatterjee AK (2017) A multiple-retailer replenishment model under VMI: accounting for the retailer heterogeneity. Comput Ind Eng 104:175–187CrossRefGoogle Scholar
  46. Waller M, Johnson E, Davis T (1999) Vendor-Managed Inventory in the retail supply chain. J Bus Logist 20(1):183–203Google Scholar
  47. Yang K, Ruben R, Webster S (2003) Managing vendor inventory in a dual level distribution system. J Bus Logist 24(2):91–108CrossRefGoogle Scholar
  48. Yao Y, Dresner M (2008) The inventory value of information sharing, continuous replenishment and vendor-managed inventory. Transp Res E 44:361–378CrossRefGoogle Scholar
  49. Yao Y, Evers P, Dresner M (2007) Supply chain integration in vendor-managed inventory. Decis Support Syst 43(2):663–674CrossRefGoogle Scholar
  50. Yu Y, Huang G (2010) Nash game model for optimizing market strategies, configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family. Eur J Oper Res 206(2):361–373CrossRefGoogle Scholar
  51. Yu H, Zeng A, Zhao L (2009a) Analyzing the evolutionary stability of the vendor-managed inventory supply chains. Comput Ind Eng 56(1):274–282CrossRefGoogle Scholar
  52. Yu Y, Huang G, Liang L (2009b) Stackelberg game-theoretic model for optimizing advertising, pricing and inventory policies in vendor managed inventory (VMI) production supply chains. Comput Ind Eng 57(1):368–382CrossRefGoogle Scholar
  53. Yu Y, Wan Z, Liang L (2012) A vendor managed inventory supply chain with deteriorating raw materials and products. Int J Prod Econ 136:266–274CrossRefGoogle Scholar
  54. Yu H, Tang L, Xu Y, Wang Y (2015) How much does VMI better than RMI in a global environment? Int J Prod Econ A 170:268–274CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversidad de los AndesBogotáColombia

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