Centralized Supply Chain Network Ddesign: Monopoly, Duopoly, and Ooligopoly Competitions under Uncertainty

Document Type: Original Manuscript


1 Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

2 Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran



This paper presents a competitive supply chain network design problem in which one, two, or three supply chains are planning to enter the price-dependent markets simultaneously in uncertain environments and decide to set the prices and shape their networks. The chains produce competitive products either identical or highly substitutable. Fuzzy multi-level mixed integer programming is used to model the competition modes, and then the models are converted into an integrated bi-level one to be solved, in which the inner part sets the prices in dynamic competition and the outer part shapes the network cooperatively.Finally, a real-world problem is investigatedto illustrate how the bi-level model works and discuss how price, market share, total income, and supply chain network behave with respect to key marketing activities such as advertising, promotions, and brand loyalty.

Graphical Abstract

Centralized Supply Chain Network Ddesign: Monopoly, Duopoly, and Ooligopoly Competitions under Uncertainty


  • One, two, or three supply chains decide to shape their networks simultaneously in the centralized mode.
  • The problems are converted into a bi-level model.
  • Possibilistic chance-constrained programming is used to cope with the uncertainty.
  • SCs shape their networks in a cooperative competition.


Main Subjects

Aboolian, R., et al. (2007). "Competitive facility location and design problem." European Journal of Operational Research182(1): 40-62.

Aboolian, R., et al. (2007). "Competitive facility location model with concave demand." European Journal of Operational Research181(2): 598-619.

Altiparmak, F., et al. (2006). "A genetic algorithm approach for multi-objective optimization of supply chain networks." Computers & industrial engineering51(1): 196-215.

Anderson, E. J. and Y. Bao (2010). "Price competition with integrated and decentralized supply chains." European Journal of Operational Research200(1): 227-234.

Ardalan, Z., et al. (2016). "Supply chain networks design with multi-mode demand satisfaction policy." Computers & industrial engineering96: 108-117.

Aydin, R., et al. (2016). "Coordination of the closed-loop supply chain for product line design with consideration of remanufactured products." Journal of Cleaner Production114: 286-298.

Badri, H., et al. (2013). "Integrated strategic and tactical planning in a supply chain network design with a heuristic solution method." Computers & Operations Research40(4): 1143-1154.

Bai, Q., et al. (2016). "Coordinating a supply chain for deteriorating items with multi-factor-dependent demand over a finite planning horizon." Applied Mathematical Modelling40(21): 9342-9361.

Beamon, B. M. (1998). "Supply chain design and analysis:: Models and methods." International journal of production economics55(3): 281-294.

Berman, O. and D. Krass (1998). "Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities." Location Science6(1): 41-65.

Bernstein, F. and A. Federgruen (2005). "Decentralized supply chains with competing retailers under demand uncertainty." Management Science51(1): 18-29.

Boyaci, T. and G. Gallego (2004). "Supply chain coordination in a market with customer service competition." Production and Operations Management13(1): 3-22.

Chaab, J. and M. Rasti-Barzoki (2016). "Cooperative advertising and pricing in a manufacturer-retailer supply chain with a general demand function; A game-theoretic approach." Computers & industrial engineering99: 112-123.

Chen, J., et al. (2015). "Cooperative quality investment in outsourcing." International journal of production economics162: 174-191.

Chen, Y. C., et al. (2013). "Pricing policies for substitutable products in a supply chain with Internet and traditional channels." European Journal of Operational Research224(3): 542-551.

Chung, S. H. and C. Kwon (2016). "Integrated supply chain management for perishable products: Dynamics and oligopolistic competition perspectives with application to pharmaceuticals." International journal of production economics179: 117-129.

Colson, B., et al. (2007). "An overview of bilevel optimization." Annals of operations research153(1): 235-256.

Cruz, J. M. (2008). "Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making." European Journal of Operational Research184(3): 1005-1031.

Dong, J., et al. (2004). "A supply chain network equilibrium model with random demands." European Journal of Operational Research156(1): 194-212.

Drezner, T. and Z. Drezner (1998). "Facility location in anticipation of future competition." Location Science6(1): 155-173.

Drezner, T., et al. (2015). "A leader–follower model for discrete competitive facility location." Computers & Operations Research64: 51-59.

Dubois, D. and H. Prade (1987). "The mean value of a fuzzy number." Fuzzy Sets and Systems24(3): 279-300.

Eiselt, H. A. and G. Laporte (1997). "Sequential location problems." European Journal of Operational Research96(2): 217-231.

Fahimi, K., et al. (2017). "Simultaneous competitive supply chain network design with continuous attractiveness variables." Computers & industrial engineering107: 235-250.

Fallah, H., et al. (2015). "Competitive closed-loop supply chain network design under uncertainty." Journal of Manufacturing Systems37(Part 3, October): 649-661.

Farahani, R. Z., et al. (2014). "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications." Omega45: 92-118.

Friesz, T. L., et al. (2011). "Competition and disruption in a dynamic urban supply chain." Transportation Research Part B: Methodological45(8): 1212-1231.

Genc, T. S. and P. De Giovanni (2017). "Trade-in and save: A two-period closed-loop supply chain game with price and technology dependent returns." International journal of production economics183: 514-527.

Godinho, P. and J. Dias (2010). "A two-player competitive discrete location model with simultaneous decisions." European Journal of Operational Research207(3): 1419-1432.

Godinho, P. and J. Dias (2013). "Two-player simultaneous location game: Preferential rights and overbidding." European Journal of Operational Research229(3): 663-672.

Hjaila, K., et al. (2017). "Integrated game-theory modelling for multi enterprise-wide coordination and collaboration under uncertain competitive environment." Computers & Chemical Engineering98: 209-235.

Hotelling, H. (1990). Stability in competition. The Collected Economics Articles of Harold Hotelling, Springer: 50-63.

Hsueh, C.-F. (2015). "A bilevel programming model for corporate social responsibility collaboration in sustainable supply chain management." Transportation Research Part E: Logistics and Transportation Review73: 84-95.

Huang, H., et al. (2016). "Equilibrium analysis of pricing competition and cooperation in supply chain with one common manufacturer and duopoly retailers." International journal of production economics178: 12-21.

Huff, D. L. (1964). "Defining and estimating a trading area." The Journal of Marketing: 34-38.

Huff, D. L. (1966). "A programmed solution for approximating an optimum retail location." Land Economics42(3): 293-303.

Inuiguchi, M. and J. Ramık (2000). "Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem." Fuzzy Sets and Systems111(1): 3-28.

Jain, V., et al. (2014). "Universal supplier selection via multi-dimensional auction mechanisms for two-way competition in oligopoly market of supply chain." Omega47: 127-137.

Jeihoonian, M., et al. (2017). "Closed-loop supply chain network design under uncertain quality status: Case of durable products." International journal of production economics183: 470-486.

Keyvanshokooh, E., et al. (2016). "Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition." European Journal of Operational Research249(1): 76-92.

Kress, D. and E. Pesch (2012). "Sequential competitive location on networks." European Journal of Operational Research217(3): 483-499.

Küçükaydin, H., et al. (2011). "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution." European Journal of Operational Research208(3): 206-220.

Küçükaydın, H., et al. (2012). "A leader–follower game in competitive facility location." Computers & Operations Research39(2): 437-448.

Li, B.-X., et al. (2013). "Contract choice game of supply chain competition at both manufacturer and retailer levels." International journal of production economics143(1): 188-197.

Li, B., et al. (2016). "Pricing strategy and coordination in a dual channel supply chain with a risk-averse retailer." International journal of production economics178: 154-168.

Li, D. and A. Nagurney (2015). "A general multitiered supply chain network model of quality competition with suppliers." International journal of production economics170: 336-356.

Li, Q.-H. and B. Li (2016). "Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns." Applied Mathematical Modelling40(15): 7349-7367.

Lipan, F., et al. (2017). "Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior." European Journal of Operational Research.

Liu, B. and K. Iwamura (1998). "Chance constrained programming with fuzzy parameters." Fuzzy Sets and Systems94(2): 227-237.

Meixell, M. J. and V. B. Gargeya (2005). "Global supply chain design: A literature review and critique." Transportation Research Part E: Logistics and Transportation Review41(6): 531-550.

Nagurney, A., et al. (2002). "A supply chain network equilibrium model." Transportation Research Part E: Logistics and Transportation Review38(5): 281-303.

Nagurney, A., et al. (2016). "A Generalized Nash Equilibrium network model for post-disaster humanitarian relief." Transportation Research Part E: Logistics and Transportation Review95: 1-18.

Nagurney, A., et al. (2015). "Supply chain network competition in price and quality with multiple manufacturers and freight service providers." Transportation Research Part E: Logistics and Transportation Review77: 248-267.

Özceylan, E., et al. (2016). "A Closed-Loop Supply Chain Network Design for Automotive Industry in Turkey." Computers & industrial engineering.

Özceylan, E., et al. (2014). "Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing." Transportation Research Part E: Logistics and Transportation Review61: 142-164.

Pishvaee, M. S. and M. Rabbani (2011). "A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment." Advances in Engineering Software42(3): 57-63.

Pishvaee, M. S., et al. (2012). "Robust possibilistic programming for socially responsible supply chain network design: A new approach." Fuzzy Sets and Systems206: 1-20.

Plastria, F. (2001). "Static competitive facility location: an overview of optimisation approaches." European Journal of Operational Research129(3): 461-470.

Plastria, F. and L. Vanhaverbeke (2008). "Discrete models for competitive location with foresight." Computers & Operations Research35(3): 683-700.

Qiang, Q., et al. (2013). "The closed-loop supply chain network with competition, distribution channel investment, and uncertainties." Omega41(2): 186-194.

Qiang, Q. P. (2015). "The closed-loop supply chain network with competition and design for remanufactureability." Journal of Cleaner Production105: 348-356.

ReVelle, C., et al. (2007). "Location models for ceding market share and shrinking services." Omega35(5): 533-540.

Rezapour, S. and R. Z. Farahani (2010). "Strategic design of competing centralized supply chain networks for markets with deterministic demands." Advances in Engineering Software41(5): 810-822.

Rezapour, S. and R. Z. Farahani (2014). "Supply chain network design under oligopolistic price and service level competition with foresight." Computers & industrial engineering72: 129-142.

Rezapour, S., et al. (2014). "Designing a new supply chain for competition against an existing supply chain." Transportation Research Part E: Logistics and Transportation Review67: 124-140.

Rezapour, S., et al. (2015). "Competitive closed-loop supply chain network design with price-dependent demands." Journal of Cleaner Production93: 251-272.

Rezapour, S., et al. (2011). "Strategic design of competing supply chain networks with foresight." Advances in Engineering Software42(4): 130-141.

Santibanez-Gonzalez, E. D. and A. Diabat (2016). "Modeling logistics service providers in a non-cooperative supply chain." Applied Mathematical Modelling40(13): 6340-6358.

Shankar, B. L., et al. (2013). "Location and allocation decisions for multi-echelon supply chain network–A multi-objective evolutionary approach." Expert Systems with Applications40(2): 551-562.

Shen, Z. (2007). "Integrated supply chain design models: a survey and future research directions." Journal of Industrial and Management Optimization3(1): 1.

Simchi-Levi, D., et al. (1999). Designing and managing the supply chain: Concepts, strategies, and cases, McGraw-Hill New York.

Sinha, S. and S. Sarmah (2010). "Coordination and price competition in a duopoly common retailer supply chain." Computers & industrial engineering59(2): 280-295.

Taylor, D. (2003). Supply chains: a management guides, Pearson Education, Boston.

Torabi, S. A. and E. Hassini (2008). "An interactive possibilistic programming approach for multiple objective supply chain master planning." Fuzzy Sets and Systems159(2): 193-214.

Tsay, A. A. and N. Agrawal (2000). "Channel dynamics under price and service competition." Manufacturing & Service Operations Management2(4): 372-391.

Vahdani, B. and M. Mohammadi (2015). "A bi-objective interval-stochastic robust optimization model for designing closed loop supply chain network with multi-priority queuing system." International journal of production economics170: 67-87.

Varsei, M. and S. Polyakovskiy (2017). "Sustainable supply chain network design: A case of the wine industry in Australia." Omega66: 236-247.

Wang, L., et al. (2017). "Pricing and service decisions of complementary products in a dual-channel supply chain." Computers & industrial engineering.

Wu, D. (2013). "Coordination of competing supply chains with news-vendor and buyback contract." International journal of production economics144(1): 1-13.

Xiao, T. and D. Yang (2008). "Price and service competition of supply chains with risk-averse retailers under demand uncertainty." International journal of production economics114(1): 187-200.

Yang, D., et al. (2015). "Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game." European Journal of Operational Research246(1): 263-280.

Yang, G.-Q., et al. (2015). "Multi-objective biogeography-based optimization for supply chain network design under uncertainty." Computers & industrial engineering85: 145-156.

Yue, D. and F. You (2014). "Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium." Computers & Chemical Engineering71: 347-361.

Zhang, C.-T. and L.-P. Liu (2013). "Research on coordination mechanism in three-level green supply chain under non-cooperative game." Applied Mathematical Modelling37(5): 3369-3379.

Zhang, D. (2006). "A network economic model for supply chain versus supply chain competition." Omega34(3): 283-295.

Zhang, L. and Y. Zhou (2012). "A new approach to supply chain network equilibrium models." Computers & industrial engineering63(1): 82-88.

Zhang, Q., et al. (2016). "Green supply chain performance with cost learning and operational inefficiency effects." Journal of Cleaner Production112: 3267-3284.

Zhao, J. and L. Wang (2015). "Pricing and retail service decisions in fuzzy uncertainty environments." Applied Mathematics and Computation250: 580-592.

Zhu, S. X. (2015). "Integration of capacity, pricing, and lead-time decisions in a decentralized supply chain." International journal of production economics164: 14-23.