American Institute of Mathematical Sciences

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September  2021, 17(5): 2855-2887. doi: 10.3934/jimo.2020098

Stackelberg pricing policy in dyadic capital-constrained supply chain considering bank's deposit and loan based on delay payment scheme

Bing-Bing Cao 1, , Zai-Jing Gong 1, and  Tian-Hui You 2,,

1. 

School of Management, Guangzhou University, Guangzhou 510006, China
2. 

Department of Information Management and Decision Sciences, School of Business Administration, Northeastern University, Shenyang 110169, China

* Corresponding author: TIAN-HUI YOU

Received  October 2019 Revised  March 2019 Published  September 2021 Early access  May 2020

Fund Project: The authors are supported by the National Natural Science Foundation of China (Project Nos. 71901075 and 71972059), the Science Foundation of Ministry of Education of China (Project No. 19XJCZH278) and the Philosophy and Social Science Foundation of Guangdong Province (Project No. GD19YGL08)

In reality, supply chain member may apply for loan from bank when he$ \backslash $she is capital-constrained, or may deposit idle capital to bank when he$ \backslash $she is well-funded. This study focuses on the Stackelberg pricing policy considering bank's deposit and loan based on delay payment scheme in a dyadic capital-constrained supply chain. First, the market demand is given, and then the profit functions of supply chain members are built. According to Stackelberg game, the four pricing models are constructed for four scenarios. By solving models, optimal pricing policies of supply chain members for each scenario can be determined. Finally, impacts of the interest rate for fixed deposit by installments, deposit rate and loan rate on optimal pricing policies are analyzed. The research results show that, in manufacturer capital-constrained situation, these rates can affect optimal pricing policies and profits; in retailer capital-constrained situation, deposit rate and loan rate have no effect on them, but the interest rate for fixed deposit by installments can still affect them. Our study provides a feasible way for supply chain members in pricing decision considering bank's deposit and loan based on delay payment scheme in a dyadic capital-constrained supply chain, and contributes to the theoretical research on the capital-constrained supply chain management and the management practice for capital-constrained supply chain members with bank' deposit and loan.

Keywords: Supply chain pricing, delay payment scheme, capital constraint, bank's deposit and loan, Stackelberg game.
Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.
Citation: Bing-Bing Cao, Zai-Jing Gong, Tian-Hui You. Stackelberg pricing policy in dyadic capital-constrained supply chain considering bank's deposit and loan based on delay payment scheme. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2855-2887. doi: 10.3934/jimo.2020098
References:
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B.-B. Cao, Z.-P. Fan and T.-H. You, The optimal pricing and ordering policy for temperature sensitive products considering the effects of temperature on demand, J. Ind. Manag. Optim., 15 (2019), 1153-1184.  doi: 10.3934/jimo.2018090.  Google Scholar

[5]

E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Comput. Ind. Eng., 119 (2018), 50-62.  doi: 10.1016/j.cie.2018.03.024.  Google Scholar

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L. Chen, A. G. Kök and J. D. Tong, The effect of payment schemes on inventory decisions: The role of mental accounting, Manag. Sci., 59 (2013), 436-451.  doi: 10.1287/mnsc.1120.1638.  Google Scholar

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W. Jin, J. Luo and Q. Zhang, Optimal ordering and financing decisions under advance selling and delayed payment for a capital-constrained supply chain, J. Oper. Res. Soc., 69 (2018), 1978-1993.  doi: 10.1080/01605682.2017.1415643.  Google Scholar

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B. Li, S.-M. An and D.-P. Song, Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain, Transport. Res. Part E., 118 (2018), 163-183.  doi: 10.1016/j.tre.2018.06.007.  Google Scholar

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[23]

L.-Y. Ouyang, J.-T. Teng, S. K. Goyal and C.-T. Yang, An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity, European J. Oper. Res., 194 (2009), 418-431.  doi: 10.1016/j.ejor.2007.12.018.  Google Scholar

[24]

Y. Peng, Q. Lu and Y. Xiao, A dynamic Stackelberg duopoly model with different strategies, Chaos Solitons Fractals, 85 (2016), 128-134.  doi: 10.1016/j.chaos.2016.01.024.  Google Scholar

[25]

R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manage. Sci., 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[26]

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[27]

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[28]

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[29]

D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, Internat. J. Prod. Econ., 215 (2019), 3-10.  doi: 10.1016/j.ijpe.2018.09.016.  Google Scholar

[30]

X.-Y. Wu, Z.-P. Fan and B.-B. Cao, Cost-sharing strategy for carbon emission reduction and sales effort: A Nash game with government subsidy, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019040.  Google Scholar

[31]

S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005.  Google Scholar

[32]

X. Xu, X. Cheng and Y. Sun, Coordination contracts for outsourcing supply chain with financial constraint, Internat. J. Prod. Econ., 162 (2015), 134-142.  doi: 10.1016/j.ijpe.2015.01.016.  Google Scholar

[33]

H. Yang, Q. Yan, H. Wan and W. Zhuo, Bargaining equilibrium in a two-echelon supply chain with a capital-constrained retailer, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019077.  Google Scholar

[34]

X. Yang, Y. Peng, Y. Xiao and X. Wu, Nonlinear dynamics of a duopoly Stackelberg game with marginal costs, Chaos Solitons Fractals, 123 (2019), 185-191.  doi: 10.1016/j.chaos.2019.04.007.  Google Scholar

[35]

B. Zhang, D. D. Wu and L. Liang, Optimal option ordering and pricing decisions with capital constraint and default risk, IEEE Systems J., 11 (2017), 1537-1547.  doi: 10.1109/JSYST.2015.2460263.  Google Scholar

[36]

J. Zhang and R. Q. Zhang, Optimal replenishment and pricing decisions under the collect-on-delivery payment scheme, OR Spectrum, 36 (2014), 503-524.  doi: 10.1007/s00291-013-0321-z.  Google Scholar

[37]

W.-G. Zhang, Q. Zhang, K. J. Mizgier and Y. Zhang, Integrating the customers' perceived risks and benefits into the triple-channel retailing, Internat. J. Prod. Res., 55 (2017), 6676-6690.  doi: 10.1080/00207543.2017.1336679.  Google Scholar

[38]

L. Zhao, J. Chang and J. Du, Dynamics analysis on competition between manufacturing and remanufacturing in context of government subsidies, Chaos Solitons Fractals, 121 (2019), 119-128.  doi: 10.1016/j.chaos.2019.01.034.  Google Scholar

[39]

Y.-W. Zhou, B. Cao, Y. Zhong and Y. Wu, Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand, J. Oper. Res. Soc., 68 (2017), 1620-1632.  doi: 10.1057/s41274-016-0161-8.  Google Scholar

[40]

Y.-W. Zhou, Z.-L. Wen and X. Wu, A single-period inventory and payment model with partial trade credit, Comput. Ind. Eng., 90 (2015), 132-145.  doi: 10.1016/j.cie.2015.08.003.  Google Scholar

[41]

W. Zhuo, H. Yang, L. E. Cárdenas-Barrón and H. Wan, Loss-averse supply chain decisions with a capital constrained retailer, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019131.  Google Scholar

show all references

References:
[1]

E. Adida, H. Mamani and S. Nassiri, Bundled payment vs. fee-for-service: Impact of payment scheme on performance, Manage. Sci., 63 (2017), 1606-1624.  doi: 10.1287/mnsc.2016.2445.  Google Scholar

[2]

S. M. Aljazzar, M. Y. Jaber and L. Moussawi-Haidar, Coordination of a three-level supply chain (supplier-manufacturer-retailer) with permissible delay in payments and price discounts, Appl. Math. Model., 48 (2017), 289-302.  doi: 10.1016/j.apm.2017.04.011.  Google Scholar

[3]

B.-B. Cao and Z.-P. Fan, Ordering and sales effort investment for temperature-sensitive products considering retailer's disappointment aversion and elation seeking, Int. J. Prod. Res., 56 (2018), 2411-2436.  doi: 10.1080/00207543.2017.1374577.  Google Scholar

[4]

B.-B. Cao, Z.-P. Fan and T.-H. You, The optimal pricing and ordering policy for temperature sensitive products considering the effects of temperature on demand, J. Ind. Manag. Optim., 15 (2019), 1153-1184.  doi: 10.3934/jimo.2018090.  Google Scholar

[5]

E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Comput. Ind. Eng., 119 (2018), 50-62.  doi: 10.1016/j.cie.2018.03.024.  Google Scholar

[6]

L. Chen, A. G. Kök and J. D. Tong, The effect of payment schemes on inventory decisions: The role of mental accounting, Manag. Sci., 59 (2013), 436-451.  doi: 10.1287/mnsc.1120.1638.  Google Scholar

[7]

L.-H. Chen and F.-S. Kang, Integrated inventory models considering permissible delay in payment and variant pricing strategy, Appl. Math. Model., 34 (2010), 36-46.  doi: 10.1016/j.apm.2009.03.023.  Google Scholar

[8]

Z. Chen, K. Yuan and S. Zhou, Supply chain coordination with trade credit under the CVaR criterion, Int. J. Prod. Res., 57 (2019), 3538-3553.  doi: 10.1080/00207543.2018.1543966.  Google Scholar

[9]

Y. Duan, G. Li and J. Huo, Supply chain coordination for fixed lifetime products with permissible delay in payments, Math. Probl. Eng., 2014 (2014), 11pp. doi: 10.1155/2014/649189.  Google Scholar

[10]

S. Ebrahimi, S.-M. Hosseini-Motlagh and M. Nematollahi, Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand, Internat. J. Mach. Learn. Cyb., 10 (2019), 1037-1050.  doi: 10.1007/s13042-017-0781-6.  Google Scholar

[11]

D. Gao, X. Zhao and W. Geng, A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand, Omega, 49 (2014), 60-68.  doi: 10.1016/j.omega.2014.05.008.  Google Scholar

[12]

B. C. Giri and T. Maiti, Supply chain model with price- and trade credit-sensitive demand under two-level permissible delay in payments, Internat. J. Systems Sci., 44 (2013), 937-948.  doi: 10.1080/00207721.2011.649367.  Google Scholar

[13]

A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadegheih, Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Comput. Intell., 36 (2019), 4-34.  doi: 10.1111/coin.12228.  Google Scholar

[14]

X. Guan, G. Li and Z. Yin, The implication of time-based payment contract in the decentralized assembly system, Ann. Oper. Res., 240 (2016), 641-659.  doi: 10.1007/s10479-014-1579-5.  Google Scholar

[15]

S. Huang, Z.-P. Fan and X. Wang, Optimal operational strategies of supply chain under financing service by a 3PL firm, Internat. J. Prod. Res., 57 (2019), 3405-3420.  doi: 10.1080/00207543.2018.1534017.  Google Scholar

[16]

S. Huang, Z.-P. Fan and X. Wang, The impact of transportation fee on the performance of capital-constrained supply chain under 3PL financing service, Comput. Ind. Eng., 130 (2019), 358-369.  doi: 10.1016/j.cie.2019.02.048.  Google Scholar

[17]

M. Y. Jaber and I. H. Osman, Coordinating a two-level supply chain with delay in payments and profit sharing, Comput. Ind. Eng., 50 (2006), 385-400.  doi: 10.1016/j.cie.2005.08.004.  Google Scholar

[18]

C. K. Jaggi, M. Gupta, A. Kausar and S. Tiwari, Inventory and credit decisions for deteriorating items with displayed stock dependent demand in two-echelon supply chain using Stackelberg and Nash equilibrium solution, Ann. Oper. Res., 274 (2019), 309-329.  doi: 10.1007/s10479-018-2925-9.  Google Scholar

[19]

W. Jin, J. Luo and Q. Zhang, Optimal ordering and financing decisions under advance selling and delayed payment for a capital-constrained supply chain, J. Oper. Res. Soc., 69 (2018), 1978-1993.  doi: 10.1080/01605682.2017.1415643.  Google Scholar

[20]

S. Khalilpourazari and S. H. R. Pasandideh, Multi-item EOQ model with nonlinear unit holding cost and partial backordering: Moth-flame optimization algorithm, J. Industr. Prod. Engrg., 34 (2017), 42-51.  doi: 10.1080/21681015.2016.1192068.  Google Scholar

[21]

B. Li, S.-M. An and D.-P. Song, Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain, Transport. Res. Part E., 118 (2018), 163-183.  doi: 10.1016/j.tre.2018.06.007.  Google Scholar

[22]

R. Li, Y. 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 J. Oper. Res., 278 (2019), 283-295.  doi: 10.1016/j.ejor.2019.04.033.  Google Scholar

[23]

L.-Y. Ouyang, J.-T. Teng, S. K. Goyal and C.-T. Yang, An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity, European J. Oper. Res., 194 (2009), 418-431.  doi: 10.1016/j.ejor.2007.12.018.  Google Scholar

[24]

Y. Peng, Q. Lu and Y. Xiao, A dynamic Stackelberg duopoly model with different strategies, Chaos Solitons Fractals, 85 (2016), 128-134.  doi: 10.1016/j.chaos.2016.01.024.  Google Scholar

[25]

R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manage. Sci., 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[26]

H. N. Soni, Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment, Int. J. Prod. Econ., 146 (2013), 259-268.  doi: 10.1016/j.ijpe.2013.07.006.  Google Scholar

[27]

A. A. Taleizadeh, M. Noori-Daryan and R. Tavakkoli-Moghaddam, Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under buyback of defective items, Int. J. Prod. Res., 53 (2015), 4553-4582.  doi: 10.1080/00207543.2014.997399.  Google Scholar

[28]

A. A. Taleizadeh, N. Rabiei and M. Noori-Daryan, Coordination of a two-echelon supply chain in presence of market segmentation, credit payment, and quantity discount policies, Int. Trans. Oper. Res., 26 (2019), 1576-1605.  doi: 10.1111/itor.12618.  Google Scholar

[29]

D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, Internat. J. Prod. Econ., 215 (2019), 3-10.  doi: 10.1016/j.ijpe.2018.09.016.  Google Scholar

[30]

X.-Y. Wu, Z.-P. Fan and B.-B. Cao, Cost-sharing strategy for carbon emission reduction and sales effort: A Nash game with government subsidy, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019040.  Google Scholar

[31]

S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005.  Google Scholar

[32]

X. Xu, X. Cheng and Y. Sun, Coordination contracts for outsourcing supply chain with financial constraint, Internat. J. Prod. Econ., 162 (2015), 134-142.  doi: 10.1016/j.ijpe.2015.01.016.  Google Scholar

[33]

H. Yang, Q. Yan, H. Wan and W. Zhuo, Bargaining equilibrium in a two-echelon supply chain with a capital-constrained retailer, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019077.  Google Scholar

[34]

X. Yang, Y. Peng, Y. Xiao and X. Wu, Nonlinear dynamics of a duopoly Stackelberg game with marginal costs, Chaos Solitons Fractals, 123 (2019), 185-191.  doi: 10.1016/j.chaos.2019.04.007.  Google Scholar

[35]

B. Zhang, D. D. Wu and L. Liang, Optimal option ordering and pricing decisions with capital constraint and default risk, IEEE Systems J., 11 (2017), 1537-1547.  doi: 10.1109/JSYST.2015.2460263.  Google Scholar

[36]

J. Zhang and R. Q. Zhang, Optimal replenishment and pricing decisions under the collect-on-delivery payment scheme, OR Spectrum, 36 (2014), 503-524.  doi: 10.1007/s00291-013-0321-z.  Google Scholar

[37]

W.-G. Zhang, Q. Zhang, K. J. Mizgier and Y. Zhang, Integrating the customers' perceived risks and benefits into the triple-channel retailing, Internat. J. Prod. Res., 55 (2017), 6676-6690.  doi: 10.1080/00207543.2017.1336679.  Google Scholar

[38]

L. Zhao, J. Chang and J. Du, Dynamics analysis on competition between manufacturing and remanufacturing in context of government subsidies, Chaos Solitons Fractals, 121 (2019), 119-128.  doi: 10.1016/j.chaos.2019.01.034.  Google Scholar

[39]

Y.-W. Zhou, B. Cao, Y. Zhong and Y. Wu, Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand, J. Oper. Res. Soc., 68 (2017), 1620-1632.  doi: 10.1057/s41274-016-0161-8.  Google Scholar

[40]

Y.-W. Zhou, Z.-L. Wen and X. Wu, A single-period inventory and payment model with partial trade credit, Comput. Ind. Eng., 90 (2015), 132-145.  doi: 10.1016/j.cie.2015.08.003.  Google Scholar

[41]

W. Zhuo, H. Yang, L. E. Cárdenas-Barrón and H. Wan, Loss-averse supply chain decisions with a capital constrained retailer, J. Ind. Manag. Optim., preprint. doi: 10.3934/jimo.2019131.  Google Scholar

Figure 1.  Event time line
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Figure 2.  The structure and interaction process of supply chain system in manufacturer capital-constrained situation
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Figure 3.  The structure and interaction process of supply chain system in retailer capital-constrained situation
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