A decentralized multi-level leader-follower game for network design of a competitive supply chain

Document Type : Research Paper


Department of Industrial Engineering, Iran University of Science and Technology, Terhan, Iran


This paper develops a decentralized leader-follower game for network design of a competitive supply chain problem in which a new chain as the leader enters a market with one existing supply chain as a follower. Both chains produce an identical product, customer demand is inelastic and customer utility function is based on Huff gravity-based model. The leader wants to shape his network and set assignments where the follower will show reactions by changing her networks in a sequential manner.
Multi-level mixed integer nonlinear programming model is used to model the problem. Each chain can enter the market in centralized, decentralized or cooperative modes. Enumeration method is applied to solve the problem by the help of Stackelberg equilibrium concept. Finally, some numerical examples are used to explore the algorithm and different mode structures affect the equilibrium solution.


Main Subjects

Aboolian R, Berman O, Krass D (2007) Competitive facility location model with concave demand. Eur J Oper Res 181:598–619.
Aboolian R, Berman O, Krass D (2007) Competitive facility location and design problem. Eur J Oper Res 182:40–62.
Altiparmak F, Gen M, Lin L, Paksoy T (2006) A genetic algorithm approach for multi-objective optimization of supply chain networks. Comput Ind Eng 51:196–215.
Anderson E, Bao Y (2000) Price competition with integrated and decentralized supply chains. Eur J Oper Res 200: 227–234.
Aydin R, Kwong C.K, Ji P (2016) Coordination of the closed-loop supply chain for product line design with consideration of remanufactured products. Journal of Cleaner Production 114: 286–298
Ardalan Z, Karimi S, Naderi B, Khamseh A.A, (2016) Supply chain networks design with multi-mode demand satisfaction policy. Comput Ind Eng 96: 108–117
Badri H, Bashiri M, Hejazi TH (2013) Integrated strategic and tactical planning in a supply chain network design with a heuristic solution method. Comput Oper Res 40:1143–1154.
Bai.Q, Xu X, Xu J, Wang D, (2016) Coordinating a supply chain for deteriorating items with multi-factor-dependent demand over a finite planning horizon. Applied Mathematical Modelling  40:9342–9361
Beamon B (1998) Supply chain design and analysis: models and methods. Int J Prod Econ 55:281–294.
Berman O, Krass D (1998) Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities. Location science 6:41–65.
Bernstein F, Federgruen A (2005) Decentralized supply chains with competing retailers under demand uncertainty. Manage Sci 51(1):18–29.
Boyaci T, Gallego G (2004) Supply chain coordination in a market with customer service competition. Prod Oper Manage 13(1):3–22.
Bo L, Li Q (2016), Dual-channel supply chain equilibrium problems regarding  retail services and fairness concerns. Applied Mathematical Modeling 40: 7349–7367
Chaeb J, Rasti-Barzoki M (2016) Cooperative advertising and pricing in a manufacturer-retailer supply chain with a general demand function; A game-theoretic approach. Computer and industrial engineering, 99:112-123
Chen Y.C, Fang S.C, Wen U.P (2013) Pricing policies for substitutable products in a supply chain with Internet and traditional channels, European Journal of Operational Research 224:542–551
Chen J, Liang L, Yang F(2015). Cooperative quality investment in outsourcing. Int. J. Production Economics 162:174–191
Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153(1):235–56.
Chung S.H, Kwon C (2016), Integrated supply chain management for perishable products: dynamics and oligopolistic competition perspectives with application to pharmaceuticals. International Journal of Production Economics 179:117–129
Cruz J (2008), Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making. European Journal of Operational Research 184:1005–1031
Drezner T, Drezner Z (1998) Facility location in anticipation of future competition. Location science 6:155–173.
Drezner T, Drezner Z, Kalczynski P (2015) A leader–follower model for discrete competitive facility location. Computers & Operations Research 64:51–59
Dong J, Zhang D, Nagurney A (2004) A supply chain network equilibrium model with random demands. Eur J Oper Res 156:194–212.
Eiselt HA, Laporte G (1997) Sequential location problems. Eur J Oper Res 96(2):217–31.
Fahimi K, Seyedhosseini S.M, Makui A (2017) Simultaneous competitive supply chain network design with continuous attractiveness variables, Computers & Industrial Engineering 107:235-250
Farahani RZ, Rezapour SH, Drezner T, Fallah S (2014) Competitive supply chain network design: an overview of classifications, models, solution techniques and applications. Omega 45:92–118.
Fallah H, Eskandari H, Pishvaee MS (2015) Competitive closed-loop supply chain network design under uncertainty. J Manuf Syst 37:649–661.
Friesz T, Lee I, Lin Ch (2011), Competition and disruption in a dynamic urban supply chain. Transportation Research Part B 1212–1231
Genc T, Giovanni P.D (2017). Trade-in and save: A two-period closed-loop supply chain game with price and technology dependent returns. Int. J. Production Economics 183: 514–527
Godinho P, Dias JA (2010) Two competitive discrete location model with simultaneous decisions. Eur J Oper Res 207:1419–1432.
Godinho P, Dias J (2013) Two player simultaneous location game: preferential rights and overbidding. Eur J Oper Res 229:663–672.
Hjaila K, Puigjaner L, Lainez-Aguirre J.M, Espuna A (2016). Scenario-Based Dynamic Negotiation for the Coordination of Multi-Enterprise Supply Chains under Uncertainty. 91: 445–470
Hotelling H (1929) Stability in competition. Econ J 39:41–57.
Huff DL (1964) Defining and estimating a trade area. J Marketing 28:34–8.
Huff DL (1966) A programmed solution for approximating an optimum retail location. Land Econ 42:293–303.
Huang H, Ke H, Wang L, (2016) Equilibrium analysis of pricing competition and cooperation in supply chain with one common manufacturer and duopoly retailers. International Journal of Production Economics 178: 12–21
Huseh C.-F., 2015 A bi-level programming model for corporate social responsibility collaboration in sustainable supply chain management. Transport Res E;73:84–95
Jain V, Panchal G, Kumar S (2014). Universal supplier selection via multi-dimensional auction mechanisms for two-way competition in oligopoly market of supply chain. Omega 47: 127–137
Jeihoonian M, Zanjani M.K, Gendreau (2017) Closed-loop supply chain network design under uncertain quality status: case of durable products International Journal of Production Economics 183: 470–486
Keyvanshokooh E, Ryan S.M, Kabir E (2016), Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition, European Journal of Operational Research 249: 76–92
Krass D, Pesch E (2012) Sequential competitive location on networks. Eur J Oper Res 217:483–499.
Kucukaydın H, Aras N, Altınel IK (2011) Competitive facility location problem with attractiveness adjustment of the follower: a bilevel programming model and its solution. Eur J Oper Res 208(3):206–20.
Kucukaydın H, Aras N, Altınel IK (2012) A leader–follower game in competitive facility location. Comput Oper Res 39:437–448.
Kurata H, Yao DQ, Liu JJ (2007) Pricing policies under direct vs. indirect channel competition and national vs. store brand competition. Eur J Oper Res 180:262–81.
Liu B, Iwamura K (1998) Chance constrained programming with fuzzy parameters. Fuzzy Sets Syst 94:227–237.
Li B, Hou P.W, Chen P, Li Q.H (2016) Pricing strategy and coordination in a dual channel supply chain with a risk-averse retailer. International Journal of Production Economics 178:154–168
Li B.X, Zhou Y.W, Li J.Z, Zhou S.P (2013) Contract choice game of supply chain competition at both manufacturer and retailer levels. International Journal of Production Economics 143:188-197
Li D, Nagurney A 2016, A general multitier supply chain network model of quality competition with supplier. International Journal of Production Economics 170:336–356
Lipan F, Govindan k, Chunfa L (2017) Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior. European Journal of Operational Research 260: 601–612
Meixell M, Gargeya V (2005) Global supply chain design: a literature review and critique. Transport Res E-Log 41:531–550.
Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transport Res E-Log 38:281-303.
Nagurney A, Toyasaki T (2005). Reserve supply chain management and electronic waste recycling: a multi-tiered network equilibrium framework for e-cycling.Transport Res E;41:1–28.
Nagurney A, Saberi S, Shukla Sh, Floden J (2015). Supply chain network competition in price and quality with multiple manufacturers and freight service providers. Transportation Research Part E 77:248-267
Nagurney A, Flores E.A, Soylu C (2016), A Generalized Nash Equilibrium network model for post-disaster humanitarian relief, Transportation Research Part E 95:1-18
Rezapour SH, Farahani RZ (2010) Strategic design of competing centralized supply chain networks for markets with deterministic demands. Adv Eng Softw 41:810–822.
Rezapour SH, Farahani RZ, Ghodsipour SH, Abdollahzadeh S (2011) Strategic design of competing supply chain networks with foresight. Adv Eng Softw 42:130–141.
Rezapour SH, Farahani RZ (2014) Supply chain network design under oligopolistic price and service level competition with foresight. Comput Ind Eng 72:129–142.
Rezapour SH, Farahani RZ, Dullaert W, Borger BD (2014) Designing a new supply chain for competition against an existing supply chain. Transport Res E-Log 67:124–140.
Rezapour SH, Farahani RZ, Fahimnia B, Govindan K, Mansouri Y (2015) Competitive closed-loop supply chain network design with price dependent demand. J Clean Prod 93:251–e272.
Rezapour SH, Farahani RZ, Pourakbar M (2016), Resilient Supply Chain Network Design under Competition: A Case Study, European Journal of Operational Research, 259: 1017–1035
Revelle C, Murray AT, Serra D (2007) Location models for ceding market share and shrinking services. Omega 35:533–540.
Özceylan E, Paksoy T, Bektas T(2014) , Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing, Transportation Research Part E 61:142-164
Özceylan E, Demirel N, Çetinkaya C, Demirel E, (2016) A Closed-Loop Supply Chain Network Design for Automotive Industry in Turkey, Computers & Industrial Engineering,  http://dx.doi.org/10.1016/j.cie.2016.12.022
Plastria F (2001) Static competitive facility location: an overview of optimization approaches. Eur J Oper Res 129(3):461–70.
Plastria F, Vanhaverbeke L (2008) Discrete models for competitive location with foresight. Comput Oper Res 35:683–700.
Pishvaee MS, Rabbani M (2011) A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment. Adv Eng Softw 42:57–63.
Pishvaee MS, Torabi SA (2010) A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets Syst 161(26):68–83.
Pishvaee MS, Ramzi J, Torabi SA (2012) Robust possibilistic programming for socially responsible supply chain network design: a new approach. Fuzzy Sets Syst 206:1–20.
Qiang Q, Ke K, Anderson T, Dong J(2013), The closed-loop supply chain network with competition, distribution channel investment, and uncertainties, Omega 41:186-194
Qiang Q 2015, The Closed-loop Supply Chain Network with Competition and Design for Remanufactureability, Journal of Cleaner Production 105:348-356
Santibanez-Gonzalez D.R.E, Diabat A, 2016. Modeling logistics service providers in a non-cooperative supply chain. Applied Mathematical Modelling13-14(40) 6340–6358
Simchi-Levi D, Kaminsky P, Simchi-Levi E (2003) Designing & managing the supply chain: concepts, strategies & case studies, 2nd ed. McGraw Hill, New York, NY.
Sinha S, Sarmah S.P (2010). Coordination and price competition in a duopoly common retailer supply chain. Computers & Industrial Engineering 280-295
Shankar BL, Basavarajappa S, Chen JCH, Rajeshwar S, Kadadevaramath (2013) Location and allocation decisions for multi-echelon supply chain network – a multi-objective evolutionary approach. Expert Syst Appl 40:551–562.
Shen ZJ (2007) Integrated supply chain design models: a survey and future research directions. J Ind Manag Optim 3(1):1–27.
Taylor, DA (2003) Supply chains: a management guides. Pearson Education, Boston.
Torabi SA, Hassini E (2008) An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst 159:193–214.
Vahdani B, Mohamadi M 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 Economics 170: 67–87
Varsei.M, Polyakovskiy S (2017), Sustainable supply chain network design: A case the wine industry in Australia, Omega 66: 236–247
Xiao T, Yang D (2008) Price and service competition of supply chains with risk-averse retailers under demand uncertainty. Int J Prod Econ 114(1):187–200.
Yang D, Jiao R, Ji Y, Du J, Helo P,  Joint (2015)  Optimization for Coordinated Configuration of Product Families and Supply Chains by a Leader-Follower Stackelberg Game. European Journal of Operational Research 246: 263-280
Yang G.Q, Liu Y.K, Yang K (2015), Multi-objective biogeography-based optimization for supply chain network design under uncertainty, Computers & Industrial Engineering, 85: 145–156
Yue D, You F(2014) Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium. Computer sand Chemical Engineering 71: 347-361
Zhang DA (2006) Network economic model for supply chain versus supply chain competing. Omega 34:283–95.
Zhang Q, Tang W, Zhang J (2015). Green supply chain performance with cost learning and operational inefficiency effects. Journal of Cleaner Production 1:18
Zhang C.T, Liu L.P (2013) Research on coordination mechanism in three-level green supply chain under non-cooperative game, Applied Mathematical Modeling 37:3369-3379
Zhang L, Zhou Y (2012), A new approach to supply chain network equilibrium models, Computers & Industrial Engineering 63:82-88
Zhu S 2015. Integration of capacity, pricing, and lead-time decisions in a decentralized supply chain. . Int J Prod Econ 164: 14–23
Zhao J, Wang L (2015) Pricing and retail service decisions in fuzzy uncertainty environments, Applied Mathematics and Computation 250:580-592
Wang L, Song H, Wang Y (2017). Pricing and service decisions of complementary products in a dual-channel supply chain. Computer and industrial engineering, 205: 223–233
Wu D (2013) Coordination of competing supply chains with news-vendor and buyback contract. Int J Prod Econ 144:1-13