IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v264y2018i1d10.1007_s10479-017-2737-3.html
   My bibliography  Save this article

A variational inequality formulation for designing a multi-echelon, multi-product supply chain network in a competitive environment

Author

Listed:
  • Isa Feyzian-Tary

    (University of Tehran)

  • Jafar Razmi

    (University of Tehran)

  • Mohamad Sadegh Sangari

    (University of Tehran)

Abstract

In a competitive environment, supply chains are competing with each other to gain the market share and competition is a critical factor influencing the supply chain network structure. The current paper presents a variational inequality formulation and provides the results for a competitive supply chain network design model. The new-entrant supply chain competes against an existing one in a non-cooperative behavior. The networks include raw material suppliers, manufacturers, retailers, and the same demand markets. The manufacturers produce multiple products with deterministic, price-dependent demand. The goal is to maximize the future revenue of both chains. The problem is modeled by mathematical programming and the governing Nash equilibrium conditions are derived. Then, a finite-dimensional variational inequality formulation is presented to solve the equilibrium problem. Qualitative properties of the equilibrium pattern are provided to establish existence and uniqueness results under reasonable conditions. The modified projection algorithm is used to solve the variational inequality problem. A numerical example is presented in order to show the efficiency of the proposed model and to investigate the behavior of the model under different conditions.

Suggested Citation

  • Isa Feyzian-Tary & Jafar Razmi & Mohamad Sadegh Sangari, 2018. "A variational inequality formulation for designing a multi-echelon, multi-product supply chain network in a competitive environment," Annals of Operations Research, Springer, vol. 264(1), pages 89-121, May.
    • Handle: RePEc:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2737-3
    DOI: 10.1007/s10479-017-2737-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-017-2737-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-017-2737-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zugang Liu & Anna Nagurney, 2013. "Supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty," Annals of Operations Research, Springer, vol. 208(1), pages 251-289, September.
    2. Komal Nagar, 2009. "Evaluating the Effect of Consumer Sales Promotions on Brand Loyal and Brand Switching Segments," Vision, , vol. 13(4), pages 35-48, October.
    3. Anna Nagurney & Dong Li, 2015. "A supply chain network game theory model with product differentiation, outsourcing of production and distribution, and quality and price competition," Annals of Operations Research, Springer, vol. 226(1), pages 479-503, March.
    4. Andy A. Tsay & Narendra Agrawal, 2000. "Channel Dynamics Under Price and Service Competition," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 372-391, August.
    5. Nagurney, Anna, 2010. "Supply chain network design under profit maximization and oligopolistic competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(3), pages 281-294, May.
    6. Qiang, Qiang & Ke, Ke & Anderson, Trisha & Dong, June, 2013. "The closed-loop supply chain network with competition, distribution channel investment, and uncertainties," Omega, Elsevier, vol. 41(2), pages 186-194.
    7. Anna Nagurney & Patrizia Daniele & Shivani Shukla, 2017. "A supply chain network game theory model of cybersecurity investments with nonlinear budget constraints," Annals of Operations Research, Springer, vol. 248(1), pages 405-427, January.
    8. S Rezapour & R Zanjirani Farahani & T Drezner, 2011. "Strategic design of competing supply chain networks for inelastic demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1784-1795, October.
    9. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location model with concave demand," European Journal of Operational Research, Elsevier, vol. 181(2), pages 598-619, September.
    10. Xiao, Tiaojun & Qi, Xiangtong, 2008. "Price competition, cost and demand disruptions and coordination of a supply chain with one manufacturer and two competing retailers," Omega, Elsevier, vol. 36(5), pages 741-753, October.
    11. Nagurney, Anna & Dong, June & Zhang, Ding, 2002. "A supply chain network equilibrium model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 38(5), pages 281-303, September.
    12. Frank M. Bass & Anand Krishnamoorthy & Ashutosh Prasad & Suresh P. Sethi, 2005. "Generic and Brand Advertising Strategies in a Dynamic Duopoly," Marketing Science, INFORMS, vol. 24(4), pages 556-568, February.
    13. Kurata, Hisashi & Yao, Dong-Qing & Liu, John J., 2007. "Pricing policies under direct vs. indirect channel competition and national vs. store brand competition," European Journal of Operational Research, Elsevier, vol. 180(1), pages 262-281, July.
    14. Baghalian, Atefeh & Rezapour, Shabnam & Farahani, Reza Zanjirani, 2013. "Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case," European Journal of Operational Research, Elsevier, vol. 227(1), pages 199-215.
    15. Zhang, Ding, 2006. "A network economic model for supply chain versus supply chain competition," Omega, Elsevier, vol. 34(3), pages 283-295, June.
    16. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    17. Wang, Xin & Ouyang, Yanfeng, 2013. "A continuum approximation approach to competitive facility location design under facility disruption risks," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 90-103.
    18. Ravi Shankar Kumar & Alok Choudhary & Soudagar A. K. Irfan Babu & Sri Krishna Kumar & A. Goswami & M. K. Tiwari, 2017. "Designing multi-period supply chain network considering risk and emission: a multi-objective approach," Annals of Operations Research, Springer, vol. 250(2), pages 427-461, March.
    19. He, Zhou & Wang, Shouyang & Cheng, T.C.E., 2013. "Competition and evolution in multi-product supply chains: An agent-based retailer model," International Journal of Production Economics, Elsevier, vol. 146(1), pages 325-336.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rezapour, Shabnam & Farahani, Reza Zanjirani & Dullaert, Wout & De Borger, Bruno, 2014. "Designing a new supply chain for competition against an existing supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 124-140.
    2. Rezapour, Shabnam & Hassani, Ashkan & Farahani, Reza Zanjirani, 2015. "Concurrent design of product family and supply chain network considering quality and price," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 81(C), pages 18-35.
    3. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    4. Ghavamifar, Ali & Makui, Ahmad & Taleizadeh, Ata Allah, 2018. "Designing a resilient competitive supply chain network under disruption risks: A real-world application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 87-109.
    5. Ata Allah Taleizadeh & Ali Ghavamifar & Amir Khosrojerdi, 2022. "Resilient network design of two supply chains under price competition: game theoretic and decomposition algorithm approach," Operational Research, Springer, vol. 22(1), pages 825-857, March.
    6. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach," Annals of Operations Research, Springer, vol. 261(1), pages 1-43, February.
    7. Jahani, Hamed & Abbasi, Babak & Sheu, Jiuh-Biing & Klibi, Walid, 2024. "Supply chain network design with financial considerations: A comprehensive review," European Journal of Operational Research, Elsevier, vol. 312(3), pages 799-839.
    8. Jahani, Hamed & Abbasi, Babak & Alavifard, Farzad & Talluri, Srinivas, 2018. "Supply chain network redesign with demand and price uncertainty," International Journal of Production Economics, Elsevier, vol. 205(C), pages 287-312.
    9. Dong Li & Anna Nagurney, 2017. "Supply chain performance assessment and supplier and component importance identification in a general competitive multitiered supply chain network model," Journal of Global Optimization, Springer, vol. 67(1), pages 223-250, January.
    10. S Rezapour & R Zanjirani Farahani & T Drezner, 2011. "Strategic design of competing supply chain networks for inelastic demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1784-1795, October.
    11. Nagurney, Anna & Saberi, Sara & Shukla, Shivani & Floden, Jonas, 2015. "Supply chain network competition in price and quality with multiple manufacturers and freight service providers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 248-267.
    12. Meng, Qingfeng & Li, Zhen & Liu, Huimin & Chen, Jingxian, 2017. "Agent-based simulation of competitive performance for supply chains based on combined contracts," International Journal of Production Economics, Elsevier, vol. 193(C), pages 663-676.
    13. Fakheri, Sajjad & Bahrami-Bidoni, Zeynab & Makui, Ahmad & Pishvaee, Mir Saman & Santibanez Gonzalez, Ernesto DR., 2022. "A sustainable competitive supply chain network design for a green product under uncertainty: A case study of Iranian leather industry," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    14. Hafezalkotob, Ashkan, 2017. "Competition, cooperation, and coopetition of green supply chains under regulations on energy saving levels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 228-250.
    15. Huang, Yongxi & Chen, Yihsu, 2014. "Analysis of an imperfectly competitive cellulosic biofuel supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 1-14.
    16. Rezapour, Shabnam & Farahani, Reza Zanjirani & Pourakbar, Morteza, 2017. "Resilient supply chain network design under competition: A case study," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1017-1035.
    17. Ravi Shankar Kumar & Alok Choudhary & Soudagar A. K. Irfan Babu & Sri Krishna Kumar & A. Goswami & M. K. Tiwari, 2017. "Designing multi-period supply chain network considering risk and emission: a multi-objective approach," Annals of Operations Research, Springer, vol. 250(2), pages 427-461, March.
    18. Zhaobo Chen & Chunxian Teng & Ding Zhang & Jiayi Sun, 2016. "Modelling inter-supply chain competition with resource limitation and demand disruption," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(7), pages 1644-1658, May.
    19. Sung Hoon Chung & Robert D. Weaver & Hyun Woo Jeon, 2020. "Sustainable Management of Remanufacturing in Dynamic Supply Chains," Networks and Spatial Economics, Springer, vol. 20(3), pages 703-731, September.
    20. Wang, Xiaolei & Ouyang, Yanfeng & Yang, Hai & Bai, Yun, 2013. "Optimal biofuel supply chain design under consumption mandates with renewable identification numbers," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 158-171.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2737-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.