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doi: 10.3934/jimo.2020106

## Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing

 1 School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China 2 School of Business, University of International Business and Economics, Beijing 100029, China 3 School of Foreign Language, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi Province 333403, China 4 School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China

* Corresponding author: yefangyu@hnu.edu.cn (Fangyu Ye)

Received  August 2019 Revised  March 2020 Published  June 2020

Fund Project: The research was supported by the National Natural Science Foundation of China under Grant Nos. 71571065 and 71521061.

In this study, we consider a two-echelon supply chain, where two capital constrained suppliers compete to sell their products through a common retailer. The retailer may provide advance payment to one or two suppliers. We show that whether the retailer considers merging with only one supplier depends upon the revenue sharing ratio and the additional administrative costs of the revenue sharing contract. Meanwhile, the supplier who drops out of the market may adopt a hybrid financing scheme by combining bank credit with equity financing to return to the market. We find that the deselected supplier can be allowed to participate in the market when the bank loans ratio is below a certain threshold. We further investigate the impact of the bank loans ratio and competition intensity on the players' decisions and profits. In addition, we find that there exists an optimal bank loans ratio for the deselected supplier. Specifically, it is optimal for the deselected supplier to adopt pure bank credit if the production cost is sufficiently low.

Citation: Qiang Yan, Mingqiao Luan, Yu Lin, Fangyu Ye. Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020106
##### References:
 [1] Y. Alan and and V. Gaur, Operational investment and capital structure under asset-based lending, Manufacturing and Service Operations Management, 20 (2018), 637-654.   Google Scholar [2] V. Babich, A. N. Burnetas and P. H. Ritchken, Competition and diversification effects in supply chains with supplier default risk, Manufacturing and Service Operations Management, 9 (2007), 123-146.   Google Scholar [3] O. Baron, O. Berman and D. Wu, Bargaining within the supply chain and its implications in an industry, Decision Sciences, 47 (2016), 193-218.   Google Scholar [4] J. A. Brander and T. R. Lewis, Oligopoly and financial structure: The limited liability effect, The American Economic Review, 76 (1986), 965-970.   Google Scholar [5] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292.  doi: 10.1287/mnsc.1040.0278.  Google Scholar [6] G. P. Cachon and P. T. Harker, Competition and outsourcing with scale economies, Management Science, 48 (2002), 1227-1368.  doi: 10.1287/mnsc.48.10.1314.271.  Google Scholar [7] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science: Supply Chain Management, North-Holland, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar [8] G. P. Cachon and A. Gürhan Kök, Competing manufacturers in a retail supply chain: On contractual form and coordination, Management Science, 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar [9] G. G. Cai, X. Chen and Z. Xiao, The roles of bank and trade credits: theoretical analysis and empirical evidence, Production and Operations Management, 23 (2014), 583-598.  doi: 10.1111/poms.12035.  Google Scholar [10] C. T. Chang, L. Y. Ouyang, J. K. Teng, K. K. Lai and L. E. Cardenas-Barron, Manufacturer's pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis, International Journal of Production Economics, 218 (2019), 83-95.  doi: 10.1016/j.ijpe.2019.04.039.  Google Scholar [11] X. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357.   Google Scholar [12] X. Chen, G. Cai and J. S. Song, The cash flow advantages of 3PLs as supply chain orchestrators, Manufacturing and Service Operations Management, 21 (2018), 251-477.  doi: 10.1287/msom.2017.0667.  Google Scholar [13] J. Chod, E. Lyandres and S. A. Yang, Trade Credit and Supplier Competition, Journal of Financial Economics, 131 (2019), 484-505.   Google Scholar [14] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.  Google Scholar [15] Y. E. Fang and B. Y. Shou, Managing supply uncertainty under supply chain Cournot competition, European Journal of Operational Research, 243 (2015), 156-176.  doi: 10.1016/j.ejor.2014.11.038.  Google Scholar [16] X. H. Feng, I. Moon and K. Ryu, Supply chain coordination under budget constraints, Computers and Industrial Engineering, 88 (2015), 487-500.  doi: 10.1016/j.cie.2015.08.005.  Google Scholar [17] D. Gupta and L. Wang, A stochastic inventory model with trade credit, Manufacturing and Service Operations Management, 11 (2009), 1-189.  doi: 10.1287/msom.1070.0191.  Google Scholar [18] A. Ha, W. Shang and Y. Wang, Manufacturer rebate competition in a supply chain with a common retailer, Production and Operations Management, 26 (2017), 2122-2136.   Google Scholar [19] L. Jiang and Y. Wang, Supplier competition in decentralized assembly systems with price-sensitive and uncertain demand, Manufacturing and Service Operations Management, 12 (2010), 1-188.  doi: 10.1287/msom.1090.0259.  Google Scholar [20] Y. Jin and J. K. Ryan, Price and service competition in an outsourced supply chain, Production and Operations Management, 21 (2012), 331-344.  doi: 10.1111/j.1937-5956.2011.01247.x.  Google Scholar [21] W. Jin, Q. Zhang and J. Luo, Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints, Omega, 88 (2019), 210-222.  doi: 10.1016/j.omega.2018.04.001.  Google Scholar [22] B. Jing, X. F. Chen and G. Cai, Equilibrium financing in a distribution channel with capital constraint, Production and Operations Management, 21 (2012), 1090-1101.  doi: 10.1111/j.1937-5956.2012.01328.x.  Google Scholar [23] M. N. Katehakis, B. Melamed and J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575.   Google Scholar [24] P. Kouvelis and W. Zhao, Financing the newsvendor: Supplier vs. bank, optimal rates and alternative schemes, Operations Research, 60 (2012), 566-580.  doi: 10.1287/opre.1120.1040.  Google Scholar [25] P. Kouvelis and W. Zhao, Should finance the supply chain? Impact of credit ratings on supply chain decisions, Manufacturing and Service Operations Management, 20 (2018), 1-160.  doi: 10.1287/msom.2017.0669.  Google Scholar [26] Y. F. Lan, H. K. Yan, D. Ren and R. Guo, Merger strategies in a supply chain with asymmetric capital-constrained retailers upon market power dependent trade credit, Omega, 83 (2019), 299-318.  doi: 10.1016/j.omega.2018.08.009.  Google Scholar [27] C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European Journal of Operational Research, 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004.  Google Scholar [28] R. H. Li, Y. L. Chan, C. T. Chang and L. E. Cárdenas-Barrón, Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis, International Journal of Production Economics, 193 (2017), 578-589.  doi: 10.1016/j.ijpe.2017.08.020.  Google Scholar [29] R. H. Li, Y. P. Liu, J. T. Teng and Y. C.Tsao, Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme, European Journal of Operational Research, 278 (2019), 283-295.  doi: 10.1016/j.ejor.2019.04.033.  Google Scholar [30] G. Li, H. M. Wu and S. Xiao, Financing strategies for a capital-constrained manufacturer in a dual-channel supply chain, International Transactions in Operational Research, 27 (2020), 2317-2339.  doi: 10.1111/itor.12653.  Google Scholar [31] Q. Lin, X. Su and Y. Peng, Supply chain coordination in Confirming Warehouse Financing, Computers and Industrial Engineering, 118 (2018), 104-111.  doi: 10.1016/j.cie.2018.02.029.  Google Scholar [32] J. H. Ma, X. Z. Ai, W. Yang and Y. C. Pan, Decentralization versus coordination in competing supply chains under retailers' extended warranties, Annals of Operations Research, 275 (2019), 485-510.  doi: 10.1007/s10479-018-2871-6.  Google Scholar [33] H. Peura, A. Yang and G. M. Lai, Trade credit in competition: A horizontal benefit, Manufacturing and Service Operations Management, 19 (2017), 165-335.  doi: 10.1287/msom.2016.0608.  Google Scholar [34] L. Qi, J. Shi and X. Xu, Supplier competition and its impact on firm's sourcing strategy, Manufacturing and Service Operations Management, 55 (2015), 91-110.   Google Scholar [35] S. Sinha and S. P. Sarmah, Coordination and price competition in a duopoly common retailer supply chain, Computers and Industrial Engineering, 59 (2010), 280-295.  doi: 10.1016/j.cie.2010.04.010.  Google Scholar [36] A. A. Taleizadeh, D. W. Pentico, M. S. Jabalameli and M. Aryanezhad, An EOQ model with partial delayed payment and partial backordering, Omega, 41 (2013), 354-368.  doi: 10.1016/j.omega.2012.03.008.  Google Scholar [37] S. Tavakoli and A. A. Taleizadeh, An EOQ model for decaying item with full advanced payment and conditional discount, Annals of Operations Research, 259 (2017), 415-436.  doi: 10.1007/s10479-017-2510-7.  Google Scholar [38] A. A. Taleizadeh, Lot-sizing model with advance payment pricing and disruption in supply under planned partial backordering, International Transactions in Operational Research, 24 (2017), 783-800.  doi: 10.1111/itor.12297.  Google Scholar [39] P. Vandenberg, Adapting to the financial landscape: Evidence from small firms in Nairobi, World Development, 31 (2003), 1829-1843.   Google Scholar [40] C. Wang, X. Fan and Z. Yin, Financing online retailers: Bank vs. electronic business platform, equilibrium, and coordinating strategy, European Journal of Operational Research, 276 (2019), 343-356.  doi: 10.1016/j.ejor.2019.01.009.  Google Scholar [41] C. H. Wu, C. W. Chen and C. C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020.  Google Scholar [42] N. N. Yan, B. W. Sun, H. Zhang and C. Q. Liu, A partial credit guarantee contract in a capital-constrained supply chain: Financing equilibrium and coordinating strategy, International Journal of Production Economics, 173 (2016), 122-133.  doi: 10.1016/j.ijpe.2015.12.005.  Google Scholar [43] N. N. Yan, X. L. He and Y. Liu, Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment, Omega, 88 (2019), 162-178.  doi: 10.1016/j.omega.2018.08.003.  Google Scholar [44] H. L. Yang, W. Y. Zhuo and L. S. Shao, Equilibrium evolution in a two- echelon supply chain with financially constrained retailers: The impact of equity financing, International Journal of Production Economics, 185 (2017), 139-149.   Google Scholar [45] S. L. Yang and Y. W. Zhou, Two-echelon supply chain models: considering duopolistic retailers different competitive behaviors, International Journal of Production Economics, 103 (2006), 104-116.  doi: 10.1016/j.ijpe.2005.06.001.  Google Scholar [46] H. Yang, J. Chen, X. Chen and B. Chen, The impact of customer returns in a supply chain with a common retailer, European Journal of Operational Research, 256 (2017), 139-150.  doi: 10.1016/j.ejor.2016.06.011.  Google Scholar [47] H. Yang, F. Sun, J. Chen and B. T. Chen, Financing decisions in a supply chain with a capital-constrained manufacturer as new entrant, International Journal of Production Economics, 216 (2019), 321-332.  doi: 10.1016/j.ijpe.2019.06.014.  Google Scholar [48] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2018), 3667-3689.   Google Scholar [49] Q. Zhang, Y. C. Tsao and T. H. Chen, Economic order quantity under advance payment, Applied Mathematical Modelling, 38 (2014), 5910-5921.  doi: 10.1016/j.apm.2014.04.040.  Google Scholar [50] L. Zhao and A. Huchzermeier, Managing supplier financial distress with advance payment discount and purchase order financing, Managing supplier financial distress with advance payment discount and purchase order financing, Omega, 88 (2019), 77-90.  doi: 10.1016/j.omega.2018.10.019.  Google Scholar [51] Y. W. Zhou, B. Cao, Y. G. Zhong and Y. Z. Wu, Managing supplier financial distress with advance payment discount and purchase order financing, Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand, Omega, 68 (2017), 1620-1632.  doi: 10.1057/s41274-016-0161-8.  Google Scholar

show all references

##### References:
 [1] Y. Alan and and V. Gaur, Operational investment and capital structure under asset-based lending, Manufacturing and Service Operations Management, 20 (2018), 637-654.   Google Scholar [2] V. Babich, A. N. Burnetas and P. H. Ritchken, Competition and diversification effects in supply chains with supplier default risk, Manufacturing and Service Operations Management, 9 (2007), 123-146.   Google Scholar [3] O. Baron, O. Berman and D. Wu, Bargaining within the supply chain and its implications in an industry, Decision Sciences, 47 (2016), 193-218.   Google Scholar [4] J. A. Brander and T. R. Lewis, Oligopoly and financial structure: The limited liability effect, The American Economic Review, 76 (1986), 965-970.   Google Scholar [5] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292.  doi: 10.1287/mnsc.1040.0278.  Google Scholar [6] G. P. Cachon and P. T. Harker, Competition and outsourcing with scale economies, Management Science, 48 (2002), 1227-1368.  doi: 10.1287/mnsc.48.10.1314.271.  Google Scholar [7] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science: Supply Chain Management, North-Holland, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar [8] G. P. Cachon and A. Gürhan Kök, Competing manufacturers in a retail supply chain: On contractual form and coordination, Management Science, 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar [9] G. G. Cai, X. Chen and Z. Xiao, The roles of bank and trade credits: theoretical analysis and empirical evidence, Production and Operations Management, 23 (2014), 583-598.  doi: 10.1111/poms.12035.  Google Scholar [10] C. T. Chang, L. Y. Ouyang, J. K. Teng, K. K. Lai and L. E. Cardenas-Barron, Manufacturer's pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis, International Journal of Production Economics, 218 (2019), 83-95.  doi: 10.1016/j.ijpe.2019.04.039.  Google Scholar [11] X. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357.   Google Scholar [12] X. Chen, G. Cai and J. S. Song, The cash flow advantages of 3PLs as supply chain orchestrators, Manufacturing and Service Operations Management, 21 (2018), 251-477.  doi: 10.1287/msom.2017.0667.  Google Scholar [13] J. Chod, E. Lyandres and S. A. Yang, Trade Credit and Supplier Competition, Journal of Financial Economics, 131 (2019), 484-505.   Google Scholar [14] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.  Google Scholar [15] Y. E. Fang and B. Y. Shou, Managing supply uncertainty under supply chain Cournot competition, European Journal of Operational Research, 243 (2015), 156-176.  doi: 10.1016/j.ejor.2014.11.038.  Google Scholar [16] X. H. Feng, I. Moon and K. Ryu, Supply chain coordination under budget constraints, Computers and Industrial Engineering, 88 (2015), 487-500.  doi: 10.1016/j.cie.2015.08.005.  Google Scholar [17] D. Gupta and L. Wang, A stochastic inventory model with trade credit, Manufacturing and Service Operations Management, 11 (2009), 1-189.  doi: 10.1287/msom.1070.0191.  Google Scholar [18] A. Ha, W. Shang and Y. Wang, Manufacturer rebate competition in a supply chain with a common retailer, Production and Operations Management, 26 (2017), 2122-2136.   Google Scholar [19] L. Jiang and Y. Wang, Supplier competition in decentralized assembly systems with price-sensitive and uncertain demand, Manufacturing and Service Operations Management, 12 (2010), 1-188.  doi: 10.1287/msom.1090.0259.  Google Scholar [20] Y. Jin and J. K. Ryan, Price and service competition in an outsourced supply chain, Production and Operations Management, 21 (2012), 331-344.  doi: 10.1111/j.1937-5956.2011.01247.x.  Google Scholar [21] W. Jin, Q. Zhang and J. Luo, Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints, Omega, 88 (2019), 210-222.  doi: 10.1016/j.omega.2018.04.001.  Google Scholar [22] B. Jing, X. F. Chen and G. Cai, Equilibrium financing in a distribution channel with capital constraint, Production and Operations Management, 21 (2012), 1090-1101.  doi: 10.1111/j.1937-5956.2012.01328.x.  Google Scholar [23] M. N. Katehakis, B. Melamed and J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575.   Google Scholar [24] P. Kouvelis and W. Zhao, Financing the newsvendor: Supplier vs. bank, optimal rates and alternative schemes, Operations Research, 60 (2012), 566-580.  doi: 10.1287/opre.1120.1040.  Google Scholar [25] P. Kouvelis and W. Zhao, Should finance the supply chain? Impact of credit ratings on supply chain decisions, Manufacturing and Service Operations Management, 20 (2018), 1-160.  doi: 10.1287/msom.2017.0669.  Google Scholar [26] Y. F. Lan, H. K. Yan, D. Ren and R. Guo, Merger strategies in a supply chain with asymmetric capital-constrained retailers upon market power dependent trade credit, Omega, 83 (2019), 299-318.  doi: 10.1016/j.omega.2018.08.009.  Google Scholar [27] C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European Journal of Operational Research, 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004.  Google Scholar [28] R. H. Li, Y. L. Chan, C. T. Chang and L. E. Cárdenas-Barrón, Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis, International Journal of Production Economics, 193 (2017), 578-589.  doi: 10.1016/j.ijpe.2017.08.020.  Google Scholar [29] R. H. Li, Y. P. Liu, J. T. Teng and Y. C.Tsao, Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme, European Journal of Operational Research, 278 (2019), 283-295.  doi: 10.1016/j.ejor.2019.04.033.  Google Scholar [30] G. Li, H. M. Wu and S. Xiao, Financing strategies for a capital-constrained manufacturer in a dual-channel supply chain, International Transactions in Operational Research, 27 (2020), 2317-2339.  doi: 10.1111/itor.12653.  Google Scholar [31] Q. Lin, X. Su and Y. Peng, Supply chain coordination in Confirming Warehouse Financing, Computers and Industrial Engineering, 118 (2018), 104-111.  doi: 10.1016/j.cie.2018.02.029.  Google Scholar [32] J. H. Ma, X. Z. Ai, W. Yang and Y. C. Pan, Decentralization versus coordination in competing supply chains under retailers' extended warranties, Annals of Operations Research, 275 (2019), 485-510.  doi: 10.1007/s10479-018-2871-6.  Google Scholar [33] H. Peura, A. Yang and G. M. Lai, Trade credit in competition: A horizontal benefit, Manufacturing and Service Operations Management, 19 (2017), 165-335.  doi: 10.1287/msom.2016.0608.  Google Scholar [34] L. Qi, J. Shi and X. Xu, Supplier competition and its impact on firm's sourcing strategy, Manufacturing and Service Operations Management, 55 (2015), 91-110.   Google Scholar [35] S. Sinha and S. P. Sarmah, Coordination and price competition in a duopoly common retailer supply chain, Computers and Industrial Engineering, 59 (2010), 280-295.  doi: 10.1016/j.cie.2010.04.010.  Google Scholar [36] A. A. Taleizadeh, D. W. Pentico, M. S. Jabalameli and M. Aryanezhad, An EOQ model with partial delayed payment and partial backordering, Omega, 41 (2013), 354-368.  doi: 10.1016/j.omega.2012.03.008.  Google Scholar [37] S. Tavakoli and A. A. Taleizadeh, An EOQ model for decaying item with full advanced payment and conditional discount, Annals of Operations Research, 259 (2017), 415-436.  doi: 10.1007/s10479-017-2510-7.  Google Scholar [38] A. A. Taleizadeh, Lot-sizing model with advance payment pricing and disruption in supply under planned partial backordering, International Transactions in Operational Research, 24 (2017), 783-800.  doi: 10.1111/itor.12297.  Google Scholar [39] P. Vandenberg, Adapting to the financial landscape: Evidence from small firms in Nairobi, World Development, 31 (2003), 1829-1843.   Google Scholar [40] C. Wang, X. Fan and Z. Yin, Financing online retailers: Bank vs. electronic business platform, equilibrium, and coordinating strategy, European Journal of Operational Research, 276 (2019), 343-356.  doi: 10.1016/j.ejor.2019.01.009.  Google Scholar [41] C. H. Wu, C. W. Chen and C. C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020.  Google Scholar [42] N. N. Yan, B. W. Sun, H. Zhang and C. Q. Liu, A partial credit guarantee contract in a capital-constrained supply chain: Financing equilibrium and coordinating strategy, International Journal of Production Economics, 173 (2016), 122-133.  doi: 10.1016/j.ijpe.2015.12.005.  Google Scholar [43] N. N. Yan, X. L. He and Y. Liu, Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment, Omega, 88 (2019), 162-178.  doi: 10.1016/j.omega.2018.08.003.  Google Scholar [44] H. L. Yang, W. Y. Zhuo and L. S. Shao, Equilibrium evolution in a two- echelon supply chain with financially constrained retailers: The impact of equity financing, International Journal of Production Economics, 185 (2017), 139-149.   Google Scholar [45] S. L. Yang and Y. W. Zhou, Two-echelon supply chain models: considering duopolistic retailers different competitive behaviors, International Journal of Production Economics, 103 (2006), 104-116.  doi: 10.1016/j.ijpe.2005.06.001.  Google Scholar [46] H. Yang, J. Chen, X. Chen and B. Chen, The impact of customer returns in a supply chain with a common retailer, European Journal of Operational Research, 256 (2017), 139-150.  doi: 10.1016/j.ejor.2016.06.011.  Google Scholar [47] H. Yang, F. Sun, J. Chen and B. T. Chen, Financing decisions in a supply chain with a capital-constrained manufacturer as new entrant, International Journal of Production Economics, 216 (2019), 321-332.  doi: 10.1016/j.ijpe.2019.06.014.  Google Scholar [48] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2018), 3667-3689.   Google Scholar [49] Q. Zhang, Y. C. Tsao and T. H. Chen, Economic order quantity under advance payment, Applied Mathematical Modelling, 38 (2014), 5910-5921.  doi: 10.1016/j.apm.2014.04.040.  Google Scholar [50] L. Zhao and A. Huchzermeier, Managing supplier financial distress with advance payment discount and purchase order financing, Managing supplier financial distress with advance payment discount and purchase order financing, Omega, 88 (2019), 77-90.  doi: 10.1016/j.omega.2018.10.019.  Google Scholar [51] Y. W. Zhou, B. Cao, Y. G. Zhong and Y. Z. Wu, Managing supplier financial distress with advance payment discount and purchase order financing, Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand, Omega, 68 (2017), 1620-1632.  doi: 10.1057/s41274-016-0161-8.  Google Scholar
The evolution process of the three different strategies
The Pareto Zone
Wholesale price changes with $\theta$
Retailer's profit changes with $\theta$
Supplier's profit changes with $\theta$
Wholesale price changes with $b$
Retailer's profit changes with $b$
Order quantity changes with b
Retailer’s profit changes with b
Supplier’s profit changes with b
Notations and explanations
 Notation Explanation $b$ Competitive intensity of the products, where $0\leq b\leq 1$. $c$ Unit production cost. $\theta$ Bank loans ratio, where $0<\theta<1$. $r_f$ Interest rate of bank loans. $\lambda$ Revenue sharing ratio. $p_i^j$ Retailer's retail price for product $i$ in Strategy $j$, where $i=1$ and $2$, and $j=AA,A$ and $AE$. $w_i^j$ Wholesale price charged by $S_i$ in Strategy $j$. $q_i^j$ Retailer's order quantity from $S_i$ in Strategy $j$. $k_1$ Retailer's additional administrative costs associated with the revenue sharing contract in Strategy $A$. $k_2$ Supplier $S_1$'s additional administrative costs associated with the revenue sharing contract in Strategy $A$. $\pi_R^j$ Retailer's profit in Strategy $j$. $\pi_{S_i}^j$ Supplier $S_i$'s profit in Strategy $j$.
 Notation Explanation $b$ Competitive intensity of the products, where $0\leq b\leq 1$. $c$ Unit production cost. $\theta$ Bank loans ratio, where $0<\theta<1$. $r_f$ Interest rate of bank loans. $\lambda$ Revenue sharing ratio. $p_i^j$ Retailer's retail price for product $i$ in Strategy $j$, where $i=1$ and $2$, and $j=AA,A$ and $AE$. $w_i^j$ Wholesale price charged by $S_i$ in Strategy $j$. $q_i^j$ Retailer's order quantity from $S_i$ in Strategy $j$. $k_1$ Retailer's additional administrative costs associated with the revenue sharing contract in Strategy $A$. $k_2$ Supplier $S_1$'s additional administrative costs associated with the revenue sharing contract in Strategy $A$. $\pi_R^j$ Retailer's profit in Strategy $j$. $\pi_{S_i}^j$ Supplier $S_i$'s profit in Strategy $j$.
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