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An alternating direction method for solving a class of inverse semi-definite quadratic programming problems
A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain
1. | Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran, Iran, Iran |
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.
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.
doi: 10.1016/j.ejor.2013.08.010. |
[4] |
T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory,, Academic Press, (1982).
|
[5] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms,, Third edition. Wiley-Interscience [John Wiley & Sons], (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.
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.
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.
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.
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.
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.
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.
doi: 10.1016/j.ijpe.2009.07.016. |
[13] |
F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, 4OR, 5 (2007), 173.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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. Google Scholar |
[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. Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1016/S0377-2217(02)00469-1. |
[36] |
Z. K. Weng, Channel coordination and quantity discounts,, Management Science, 41 (1995), 1509.
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.
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. Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1016/j.ejor.2013.08.010. |
[4] |
T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory,, Academic Press, (1982).
|
[5] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms,, Third edition. Wiley-Interscience [John Wiley & Sons], (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.
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.
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.
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.
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.
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.
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.
doi: 10.1016/j.ijpe.2009.07.016. |
[13] |
F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, 4OR, 5 (2007), 173.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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. Google Scholar |
[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. Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1016/S0377-2217(02)00469-1. |
[36] |
Z. K. Weng, Channel coordination and quantity discounts,, Management Science, 41 (1995), 1509.
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.
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. Google Scholar |
[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.
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.
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.
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.
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.
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.
doi: 10.1002/nav.20340. |
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