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January  2016, 12(1): 337-355. doi: 10.3934/jimo.2016.12.337

A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain

Ali Naimi Sadigh 1, , S. Kamal Chaharsooghi 1, and  Majid Sheikhmohammady 1,

1. 

Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran, Iran, Iran

Received  September 2014 Revised  March 2015 Published  April 2015

Supply chain members coordinate with each other in order to obtain more profit. The major mechanisms for coordination among supply chain echelons are pricing, inventory management, and ordering decisions. Regarding to these mechanisms, supply chain participants have conflicts of interest. This paper concerns coordination of enterprise decisions including pricing, advertising, ordering, and inventory decisions in a multi-echelon supply chain consisting of multiple suppliers, one manufacturer, and multiple retailers. In the current study, a novel inventory model is presented for both the manufacturer, and the retailers who are able to determine the number of orders for each product. Moreover, each supply chain member has equal power and make their decisions simultaneously. The proposed model considers the relationships among three echelon supply chain members based on a non-cooperative Nash game with pricing and inventory decisions. An iterative solution algorithm is proposed to find Nash equilibrium point of the game. Several numerical examples are presented to study the application of the model as well as the effectiveness of the algorithm. Finally, a comprehensive sensitivity analysis is performed and some important managerial insights are highlighted.
Keywords: Competitive supply chain, pricing, inventory management, Nash game., ordering.
Mathematics Subject Classification: Primary: 91A10, 90B60, 90B0.
Citation: Ali Naimi Sadigh, S. Kamal Chaharsooghi, Majid Sheikhmohammady. A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain. Journal of Industrial and Management Optimization, 2016, 12 (1) : 337-355. doi: 10.3934/jimo.2016.12.337
References:
[1]

P. L. Abad, Optimal price and lot size when the supplier offers a temporary price reduction over an interval, Computers and Operations Research, 30 (2003), 63-74. doi: 10.1016/S0305-0548(01)00081-8.

[2]

G. Aust and U. Buscher, Game theoretic analysis of pricing and vertical cooperative advertising of a retailer-duopoly with a common manufacturer reduction over an interval, Central European Journal of Operational Research, (2014). doi: doi 10.1007/s10100-014-0338-7.

[3]

G. Aust and U. Buscher, Cooperative advertising models in supply chain management: A review, European Journal of Operation Research, 234 (2014), 1-14. doi: 10.1016/j.ejor.2013.08.010.

[4]

T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory, Academic Press, SIAM, 1982.

[5]

M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Third edition. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. doi: 10.1002/0471787779.

[6]

G. G. Cai, Z. G. Zhang and M. Zhang, Game theoretical perspectives on dual channel supply chain competition with price discounts and pricing schemes, International Journal of Production Economics, 117 (2009), 80-96. doi: 10.1016/j.ijpe.2008.08.053.

[7]

L. E. Cardenas-Barron, Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note, Transportation Research Part E, 43 (2007), 647-654. doi: 10.1016/j.tre.2005.09.011.

[8]

W. Chung, S. Talluri and R. Narasimhan, Price markdown scheme in a multiechelon supply chain in a high-tech industry, European Journal of Operational Research, 215 (2011), 581-589. doi: 10.1016/j.ejor.2011.07.002.

[9]

A. Dumrongsiri, M. Fan, A. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European Journal of Operational Research, 187 (2008), 691-718. doi: 10.1016/j.ejor.2006.05.044.

[10]

L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitute products, Manufacturing & Service Operations Management, 11 (2008), 317-339. doi: 10.1287/msom.1080.0221.

[11]

M. Esmaeili, M.-B. Aryanezhad and P. Zeephongeskul, A game theory approach in seller-buyer supply chain, European Journal of Operational Research, 195 (2009), 442-448. doi: 10.1016/j.ejor.2008.02.026.

[12]

M. Esmaeili and P. Zeephongeskul, Seller-buyer models of supply chain management with an asymmetric information structure, International Journal of Production Economics, 123 (2010), 146-154. doi: 10.1016/j.ijpe.2009.07.016.

[13]

F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems, 4OR, 5 (2007), 173-210. doi: 10.1007/s10288-007-0054-4.

[14]

B. Fugate, F. Shahin and J. Mentzer, Supply chain management coordination mechanism, Journal of Business Logistics, 27 (2006), 129-161. doi: 10.1002/j.2158-1592.2006.tb00220.x.

[15]

M. Ghoreishi, A. Mirzazadeh, G.-W. Weber and I. Nakhai-Kamalabadi, pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer, Journal of Industrial and Management optimization, 11 (2015), 933-949. doi: 10.3934/jimo.2015.11.933.

[16]

Y. Huang, G. Q. Huang and S. T. Newman, Coordinating pricing and inventory decisions in a multi-level supply chain: A game-theoretic approach, Transportation Research Part E, 47 (2011), 115-129. doi: 10.1016/j.tre.2010.09.011.

[17]

L. Jiang, Y. Wang, X. Yan and W. Dai, Coordinating a three-stage supply chain with competing manufacturers, Central European Journal of Operations Research, 22 (2014), 53-72. doi: 10.1007/s10100-012-0267-2.

[18]

S. Karray, Periodicity of pricing and marketing efforts in a distribution channel, European Journal of Operational Research, 228 (2013), 635-647. doi: 10.1016/j.ejor.2013.02.012.

[19]

M. Kunter, Coordination via cost and revenue sharing in manufacturer-retailer channels, European Journal of Operational Research, 216 (2012), 477-486. doi: 10.1016/j.ejor.2011.07.001.

[20]

H. Li and T. You, Capacity commitment and pricing for substitutable products under competition, Journal of Systems Science and Systems Engineering, 21 (2012), 443-460. doi: 10.1007/s11518-012-5204-3.

[21]

L. Lu, A one-vendor multi-buyer integrated inventory model, European Journal of Operational Research, 81 (1995), 312-323. doi: 10.1016/0377-2217(93)E0253-T.

[22]

G. E. Martin, Note an EOQ model with a temporary sale price, International Journal of Production Economics, 37 (1994), 241-243. doi: 10.1016/0925-5273(94)90174-0.

[23]

M. Khouja, Optimizing inventory decisions in a multi-stage multi-customer supply chain, Transportation Research Part E, 39 (2003), 193-208. doi: 10.1016/S1366-5545(02)00036-4.

[24]

A. Naimi Sadigh, B. Karimi and R. Zanjirani Farahani, A game theoretic approach for two echelon supply chains with continuous depletion, International Journal of Management Science and Engineering Management, 6 (2011), 408-412.

[25]

A. Naimi Sadigh, B. Karimi and M. Mozafari, Manufacturer-retailer supply chain coordination: A bi-level programming approach, Advances in Engineering Software, 45 (2012), 144-152.

[26]

Y. Qin, H. Tang and C. Guo, Channel coordination and volume discounts with price-sensitive demand, International Journal of Production Economics, 105 (2007), 43-53. doi: 10.1016/j.ijpe.2006.02.005.

[27]

K. Ramdas and R. E. Spekman, Chain or shackles: Understanding what drives supply-chain performance, Interfaces, 30 (2000), 3-21. doi: 10.1287/inte.30.4.3.11644.

[28]

S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decision Support Systems, 50 (2011), 539-547. doi: 10.1016/j.dss.2010.11.012.

[29]

S. S. Sana and S. K. Goyal, (Q, r, L) model for stochastic demand with lead-time dependent partial backlogging, Annals of Operations Research, (2014). doi: 10.1007/s10479-014-1731-2.

[30]

S. S. Sana, J. A. Chedid and K. S. Navarro, A three layer supply chain model with multiple suppliers, manufacturers and retailers for multiple items, Applied Mathematics and Computations, 229 (2014), 139-150. doi: 10.1016/j.amc.2013.12.006.

[31]

M. M. SeyedEsfahani, M. Biazaran and M. Gharakhani, A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains, European Journal of Operational Research, 211 (2011), 263-273. doi: 10.1016/j.ejor.2010.11.014.

[32]

J. Shi and T. Xiao, Service investment and consumer returns policy in a vendor-managed inventory supply chain, Journal of Industrial and Management Optimization, 11 (2015), 439-459. doi: 10.3934/jimo.2015.11.439.

[33]

N. Shi, S. Zhou, F. Wang, S. Xu and S. Xiong, Horizontal cooperation and information sharing between suppliers in the manufacturer-supplier triad, International Journal of Production Research, 52 (2014), 4526-4547. doi: 10.1080/00207543.2013.869630.

[34]

Y.-C. Tsao and G.-J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009.

[35]

S. Viswanathan and Q. Wang, Discount pricing decisions in distribution channels with price-sensitive demand, European Journal of Operational Research, 149 (2003), 571-587. doi: 10.1016/S0377-2217(02)00469-1.

[36]

Z. K. Weng, Channel coordination and quantity discounts, Management Science, 41 (1995), 1509-1522. doi: 10.1287/mnsc.41.9.1509.

[37]

J. Yang, J. Xie, X. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European Journal of Operational Research, 227 (2013), 401-407. doi: 10.1016/j.ejor.2012.12.011.

[38]

Y. Yu, L. Liang and G. Q. Huang, Leader-follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices, International Journal of Logistics: Research and Application, 9 (2006), 335-350.

[39]

Y. Yu, F. Chu and H. Chen, A Stackelberg game and its improvement in a VMI system with a manufacturing vendor, European Journal of Operational Research, 192 (2009), 929-948. doi: 10.1016/j.ejor.2007.10.016.

[40]

D. Yue and F. You, Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium, Computers & Chemical Engineering, 71 (2014), 347-361. doi: 10.1016/j.compchemeng.2014.08.010.

[41]

J. Yue, J. Austin, Z. Huang and B. Chen, Pricing and advertisement in a manufacturer-retailer supply chain, European Journal of Operational Research, 231 (2013), 492-502. doi: 10.1016/j.ejor.2013.06.007.

[42]

J. Zhang, J. Xie and B. Chen, Cooperative advertising with bilateral participation, Decision Sciences, 44 (2013), 193-203. doi: 10.1111/j.1540-5915.2012.00382.x.

[43]

J. Zhao, J. Wei and Y. Li, Pricing decisions for substitutable products in a two-echelon supply chain with firms' different channel power, International Journal of Production Economics, 153 (2014), 243-252. doi: 10.1016/j.ijpe.2014.03.005.

[44]

K. Zhu and U. Thonemann, Coordination of pricing and inventory control across products, Naval Research Logistics, 56 (2009), 175-190. doi: 10.1002/nav.20340.

show all references

References:
[1]

P. L. Abad, Optimal price and lot size when the supplier offers a temporary price reduction over an interval, Computers and Operations Research, 30 (2003), 63-74. doi: 10.1016/S0305-0548(01)00081-8.

[2]

G. Aust and U. Buscher, Game theoretic analysis of pricing and vertical cooperative advertising of a retailer-duopoly with a common manufacturer reduction over an interval, Central European Journal of Operational Research, (2014). doi: doi 10.1007/s10100-014-0338-7.

[3]

G. Aust and U. Buscher, Cooperative advertising models in supply chain management: A review, European Journal of Operation Research, 234 (2014), 1-14. doi: 10.1016/j.ejor.2013.08.010.

[4]

T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory, Academic Press, SIAM, 1982.

[5]

M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Third edition. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. doi: 10.1002/0471787779.

[6]

G. G. Cai, Z. G. Zhang and M. Zhang, Game theoretical perspectives on dual channel supply chain competition with price discounts and pricing schemes, International Journal of Production Economics, 117 (2009), 80-96. doi: 10.1016/j.ijpe.2008.08.053.

[7]

L. E. Cardenas-Barron, Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note, Transportation Research Part E, 43 (2007), 647-654. doi: 10.1016/j.tre.2005.09.011.

[8]

W. Chung, S. Talluri and R. Narasimhan, Price markdown scheme in a multiechelon supply chain in a high-tech industry, European Journal of Operational Research, 215 (2011), 581-589. doi: 10.1016/j.ejor.2011.07.002.

[9]

A. Dumrongsiri, M. Fan, A. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European Journal of Operational Research, 187 (2008), 691-718. doi: 10.1016/j.ejor.2006.05.044.

[10]

L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitute products, Manufacturing & Service Operations Management, 11 (2008), 317-339. doi: 10.1287/msom.1080.0221.

[11]

M. Esmaeili, M.-B. Aryanezhad and P. Zeephongeskul, A game theory approach in seller-buyer supply chain, European Journal of Operational Research, 195 (2009), 442-448. doi: 10.1016/j.ejor.2008.02.026.

[12]

M. Esmaeili and P. Zeephongeskul, Seller-buyer models of supply chain management with an asymmetric information structure, International Journal of Production Economics, 123 (2010), 146-154. doi: 10.1016/j.ijpe.2009.07.016.

[13]

F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems, 4OR, 5 (2007), 173-210. doi: 10.1007/s10288-007-0054-4.

[14]

B. Fugate, F. Shahin and J. Mentzer, Supply chain management coordination mechanism, Journal of Business Logistics, 27 (2006), 129-161. doi: 10.1002/j.2158-1592.2006.tb00220.x.

[15]

M. Ghoreishi, A. Mirzazadeh, G.-W. Weber and I. Nakhai-Kamalabadi, pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer, Journal of Industrial and Management optimization, 11 (2015), 933-949. doi: 10.3934/jimo.2015.11.933.

[16]

Y. Huang, G. Q. Huang and S. T. Newman, Coordinating pricing and inventory decisions in a multi-level supply chain: A game-theoretic approach, Transportation Research Part E, 47 (2011), 115-129. doi: 10.1016/j.tre.2010.09.011.

[17]

L. Jiang, Y. Wang, X. Yan and W. Dai, Coordinating a three-stage supply chain with competing manufacturers, Central European Journal of Operations Research, 22 (2014), 53-72. doi: 10.1007/s10100-012-0267-2.

[18]

S. Karray, Periodicity of pricing and marketing efforts in a distribution channel, European Journal of Operational Research, 228 (2013), 635-647. doi: 10.1016/j.ejor.2013.02.012.

[19]

M. Kunter, Coordination via cost and revenue sharing in manufacturer-retailer channels, European Journal of Operational Research, 216 (2012), 477-486. doi: 10.1016/j.ejor.2011.07.001.

[20]

H. Li and T. You, Capacity commitment and pricing for substitutable products under competition, Journal of Systems Science and Systems Engineering, 21 (2012), 443-460. doi: 10.1007/s11518-012-5204-3.

[21]

L. Lu, A one-vendor multi-buyer integrated inventory model, European Journal of Operational Research, 81 (1995), 312-323. doi: 10.1016/0377-2217(93)E0253-T.

[22]

G. E. Martin, Note an EOQ model with a temporary sale price, International Journal of Production Economics, 37 (1994), 241-243. doi: 10.1016/0925-5273(94)90174-0.

[23]

M. Khouja, Optimizing inventory decisions in a multi-stage multi-customer supply chain, Transportation Research Part E, 39 (2003), 193-208. doi: 10.1016/S1366-5545(02)00036-4.

[24]

A. Naimi Sadigh, B. Karimi and R. Zanjirani Farahani, A game theoretic approach for two echelon supply chains with continuous depletion, International Journal of Management Science and Engineering Management, 6 (2011), 408-412.

[25]

A. Naimi Sadigh, B. Karimi and M. Mozafari, Manufacturer-retailer supply chain coordination: A bi-level programming approach, Advances in Engineering Software, 45 (2012), 144-152.

[26]

Y. Qin, H. Tang and C. Guo, Channel coordination and volume discounts with price-sensitive demand, International Journal of Production Economics, 105 (2007), 43-53. doi: 10.1016/j.ijpe.2006.02.005.

[27]

K. Ramdas and R. E. Spekman, Chain or shackles: Understanding what drives supply-chain performance, Interfaces, 30 (2000), 3-21. doi: 10.1287/inte.30.4.3.11644.

[28]

S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decision Support Systems, 50 (2011), 539-547. doi: 10.1016/j.dss.2010.11.012.

[29]

S. S. Sana and S. K. Goyal, (Q, r, L) model for stochastic demand with lead-time dependent partial backlogging, Annals of Operations Research, (2014). doi: 10.1007/s10479-014-1731-2.

[30]

S. S. Sana, J. A. Chedid and K. S. Navarro, A three layer supply chain model with multiple suppliers, manufacturers and retailers for multiple items, Applied Mathematics and Computations, 229 (2014), 139-150. doi: 10.1016/j.amc.2013.12.006.

[31]

M. M. SeyedEsfahani, M. Biazaran and M. Gharakhani, A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains, European Journal of Operational Research, 211 (2011), 263-273. doi: 10.1016/j.ejor.2010.11.014.

[32]

J. Shi and T. Xiao, Service investment and consumer returns policy in a vendor-managed inventory supply chain, Journal of Industrial and Management Optimization, 11 (2015), 439-459. doi: 10.3934/jimo.2015.11.439.

[33]

N. Shi, S. Zhou, F. Wang, S. Xu and S. Xiong, Horizontal cooperation and information sharing between suppliers in the manufacturer-supplier triad, International Journal of Production Research, 52 (2014), 4526-4547. doi: 10.1080/00207543.2013.869630.

[34]

Y.-C. Tsao and G.-J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009.

[35]

S. Viswanathan and Q. Wang, Discount pricing decisions in distribution channels with price-sensitive demand, European Journal of Operational Research, 149 (2003), 571-587. doi: 10.1016/S0377-2217(02)00469-1.

[36]

Z. K. Weng, Channel coordination and quantity discounts, Management Science, 41 (1995), 1509-1522. doi: 10.1287/mnsc.41.9.1509.

[37]

J. Yang, J. Xie, X. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European Journal of Operational Research, 227 (2013), 401-407. doi: 10.1016/j.ejor.2012.12.011.

[38]

Y. Yu, L. Liang and G. Q. Huang, Leader-follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices, International Journal of Logistics: Research and Application, 9 (2006), 335-350.

[39]

Y. Yu, F. Chu and H. Chen, A Stackelberg game and its improvement in a VMI system with a manufacturing vendor, European Journal of Operational Research, 192 (2009), 929-948. doi: 10.1016/j.ejor.2007.10.016.

[40]

D. Yue and F. You, Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium, Computers & Chemical Engineering, 71 (2014), 347-361. doi: 10.1016/j.compchemeng.2014.08.010.

[41]

J. Yue, J. Austin, Z. Huang and B. Chen, Pricing and advertisement in a manufacturer-retailer supply chain, European Journal of Operational Research, 231 (2013), 492-502. doi: 10.1016/j.ejor.2013.06.007.

[42]

J. Zhang, J. Xie and B. Chen, Cooperative advertising with bilateral participation, Decision Sciences, 44 (2013), 193-203. doi: 10.1111/j.1540-5915.2012.00382.x.

[43]

J. Zhao, J. Wei and Y. Li, Pricing decisions for substitutable products in a two-echelon supply chain with firms' different channel power, International Journal of Production Economics, 153 (2014), 243-252. doi: 10.1016/j.ijpe.2014.03.005.

[44]

K. Zhu and U. Thonemann, Coordination of pricing and inventory control across products, Naval Research Logistics, 56 (2009), 175-190. doi: 10.1002/nav.20340.

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