American Institute of Mathematical Sciences

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January  2021, 17(1): 261-277. doi: 10.3934/jimo.2019110

Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy

Shuai Huang 1, , Zhi-Ping Fan 1,2,, and  Xiaohuan Wang 1,

1. 

Department of Information Management and Decision Sciences, School of Business Administration, Northeastern University, Shenyang 110169, China
2. 

State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China

* Corresponding author: ZHI-PING FAN

Received  November 2018 Revised  March 2019 Published  September 2019

Fund Project: The study is supported in part by the National Natural Science Foundation of China (Project No. 71871049, 71772034) and the 111 Project (B16009)

To stimulate the capital-constrained manufacturer to produce green products, the government often adopts two incentive mechanisms: green credit (i.e., subsidy offered directly to bank) and subsidy (i.e., subsidy offered directly to manufacturer). This paper examines the optimal interest rate of the bank, and the optimal product green degree and sales price of the manufacturer under the two mechanisms, respectively. Furthermore, we investigate the effects of these mechanisms on the optimal decisions, the profits of players, the social welfare and the environmental benefits. Several important results are obtained. First, when the total government subsidy is low, the green credit mechanism can bring the higher green degree, product sales price and demand, as well as higher profits for the bank and manufacturer, rather than the subsidy mechanism. Otherwise, the result is opposite. Second, the government should adopt the green credit mechanism to support the manufacturer to develop green products when the budget is limited and relatively low. If the government budget is sufficient, the subsidy mechanism is the best choice, which can bring higher economic and environmental benefits.

Keywords: Green credit mechanism, subsidy mechanism, capital-constrained manufacturer, green product, green degree.
Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.
Citation: Shuai Huang, Zhi-Ping Fan, Xiaohuan Wang. Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy. Journal of Industrial & Management Optimization, 2021, 17 (1) : 261-277. doi: 10.3934/jimo.2019110
References:
[1]

M. Aizawa and C. F. Yang, Green credit, green stimulus, green revolution? China's mobilization of banks for environmental cleanup, J. Environ. Dev., 19 (2010), 119-144.  doi: 10.1177/1070496510371192.  Google Scholar

[2]

B. Avci, K. Girotra and S. Netessine, Electric vehicles with a battery switching station: Adoption and environmental impact, Manage. Sci., 61 (2014), 772-794.   Google Scholar

[3]

G. B. Bi, M. Y. Jin, L. Y. Ling and F. Yang, Environmental subsidy and the choice of green technology in the presence of green consumers, Ann. Oper. Res., 255 (2017), 547-568.  doi: 10.1007/s10479-016-2106-7.  Google Scholar

[4]

M. Burkart and T. Ellingsen, In-kind finance: A theory of trade credit, Am. Econ. Rev., 94 (2004), 569-590.  doi: 10.1257/0002828041464579.  Google Scholar

[5]

J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Manage. Sci., 50 (2004), 1274-1292.  doi: 10.1287/mnsc.1040.0278.  Google Scholar

[6]

G. P. Cachon, Retail store density and the cost of greenhouse gas emissions, Manage. Sci., 60 (2014), 1907-1925.   Google Scholar

[7]

E. Cao, L. X. Du and J. H. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, Int. J. Prod. Econ., 208 (2019), 383-399.  doi: 10.1016/j.ijpe.2018.08.001.  Google Scholar

[8]

Y.-K. Che and I. Gale, The optimal mechanism for selling to a budget-constrained buyer, J. Econ. Theory, 92 (2000), 198-233.  doi: 10.1006/jeth.1999.2639.  Google Scholar

[9]

M. C. Cohen, R. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidy for green technology adoption, Manage. Sci., 62 (2016), 1235-1258.   Google Scholar

[10]

S. Du, F. Ma, Z. Fu, L. Zhu and J. Zhang, Game-theoretic analysis for an emission-dependent supply chain in a `cap-and-trade' system, Ann. Oper. Res., 228 (2015), 135-149.  doi: 10.1007/s10479-011-0964-6.  Google Scholar

[11]

J. Z. Gao, Z. D. Xiao, B. B. Cao and Q. F. Chai, Green supply chain planning considering consumer's transportation process, Transp. Res. Pt. e-Logist. Transp. Rev., 109 (2018), 311-330.  doi: 10.1016/j.tre.2017.12.001.  Google Scholar

[12]

A. Hafezalkotob, Direct and indirect intervention schemas of government in the competition between green and non-green supply chains, J. Clean Prod., 170 (2018), 753-772.  doi: 10.1016/j.jclepro.2017.09.124.  Google Scholar

[13]

J. Hall, Environmental supply chain dynamics, J. Clean Prod., 8 (2000), 455-471.  doi: 10.1016/S0959-6526(00)00013-5.  Google Scholar

[14]

S. Huang, Z.-P. Fan and X. H. 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

[15]

B. Jing, X. F. Chen and G. S. Cai, Equilibrium financing in a distribution channel with capital constraint, Prod. Oper. Manag., 21 (2012), 1090-1101.  doi: 10.1111/j.1937-5956.2012.01328.x.  Google Scholar

[16]

P. R. Kleindorfer, K. Singhal and L. N. Van Wassenhove, Sustainable operations management, Prod. Oper. Manag., 14 (2005), 482-492.  doi: 10.1111/j.1937-5956.2005.tb00235.x.  Google Scholar

[17]

P. Kouvelis and W. H. Zhao, The newsvendor problem and price-only contract when bankruptcy costs exist, Prod. Oper. Manag., 20 (2011), 921-936.  doi: 10.1111/j.1937-5956.2010.01211.x.  Google Scholar

[18]

P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Manage. Sci., 62 (2016), 2149-2455.  doi: 10.1287/mnsc.2015.2248.  Google Scholar

[19]

V. Krishnan and W. Zhu, Designing a family of development-intensive products, Manage. Sci., 52 (2006), 813-825.  doi: 10.1287/mnsc.1050.0492.  Google Scholar

[20]

J.-Y. Liu, Y. Xia, Y. Fan, S.-M. Lin and J. Wu, Assessment of a green credit policy aimed at energy-intensive industries in China based on a financial CGE model, J. Clean Prod., 163 (2017), 293-302.  doi: 10.1016/j.jclepro.2015.10.111.  Google Scholar

[21]

R. Mahmoudi and M. Rasti-Barzoki, Sustainable supply chains under government intervention with a real-world case study: An evolutionary game theoretic approach, Comput. Ind. Eng., 116 (2018), 130-143.  doi: 10.1016/j.cie.2017.12.028.  Google Scholar

[22]

M. Parlar and Z. K. Weng, Balancing desirable but conflicting objectives in the newsvendor problem, IIE Trans., 35 (2003), 131-142.  doi: 10.1080/07408170304380.  Google Scholar

[23]

H. Peura, S. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, M & SOM-Manuf. Serv. Oper. Manag., 19 (2017), 165-335.  doi: 10.1287/msom.2016.0608.  Google Scholar

[24]

G. Raz and A. Ovchinnikov, Coordinating pricing and supply of public interest goods using government rebates and subsidy, IEEE Trans. Eng. Manage., 62 (2015), 65-79.  doi: 10.1109/TEM.2014.2380999.  Google Scholar

[25]

H. H. Song and X. X. Gao, Green supply chain game model and analysis under revenue-sharing contract, J. Clean Prod., 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[26]

C. S. Tang and S. Zhou, Research advances in environmentally and socially sustainable operations, Eur. J. Oper. Res., 223 (2012), 585-594.  doi: 10.1016/j.ejor.2012.07.030.  Google Scholar

[27]

Y.-C. Tsao, P.-L. Lee, C.-H. Chen and Z.-W. Liao, Sustainable newsvendor models under trade credit, J. Clean Prod., 141 (2017), 1478-1491.  doi: 10.1016/j.jclepro.2016.09.228.  Google Scholar

[28]

S.-C. Tseng and S.-W. Hung, A strategic decision-making model considering the social costs of carbon dioxide emissions for sustainable supply chain management, J. Environ. Manage., 133 (2014), 315-322.  doi: 10.1016/j.jenvman.2013.11.023.  Google Scholar

[29]

K. Wang, R. Q. Zhao and J. Peng, Trade credit contracting under asymmetric credit default risk: Screening, checking or insurance, Eur. J. Oper. Res., 266 (2018), 554-568.  doi: 10.1016/j.ejor.2017.10.004.  Google Scholar

[30]

D. D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, Int. J. Prod. Econ., article in press. doi: 10.1016/j.ijpe.2018.09.016.  Google Scholar

[31]

N. Yan and B. Sun, Comparative analysis of supply chain financing decisions between different financing modes, J. Ind. Manag. Optim., 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073.  Google Scholar

[32]

D. Yang and T. Xiao, Pricing and green level decisions of a green supply chain with government interventions under fuzzy uncertainties, J. Clean Prod., 149 (2017), 1174-1187.   Google Scholar

[33]

D.-X. Yang, Z.-Y. Chen, Y.-C. Yang and P.-Y. Nie, Green financial policies and capital flows, Physica A, 522 (2019), 135-146.  doi: 10.1016/j.physa.2019.01.126.  Google Scholar

[34]

H. Yang, W. Zhuo and L. Shao, Equilibrium evolution in a two-echelon supply chain with financially constrained retailers: The impact of equity financing, Int. J. Prod. Econ., 185 (2017), 139-149.   Google Scholar

[35]

L. H. Zhang, J. G. Wang and J. X. You, Consumer environmental awareness and channel coordination with two substitutable products, Eur. J. Oper. Res., 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043.  Google Scholar

[36]

W. G. Zhu and Y. J. He, Green product design in supply chains under competition, Eur. J. Oper. Res., 258 (2017), 165-180.  doi: 10.1016/j.ejor.2016.08.053.  Google Scholar

show all references

References:
[1]

M. Aizawa and C. F. Yang, Green credit, green stimulus, green revolution? China's mobilization of banks for environmental cleanup, J. Environ. Dev., 19 (2010), 119-144.  doi: 10.1177/1070496510371192.  Google Scholar

[2]

B. Avci, K. Girotra and S. Netessine, Electric vehicles with a battery switching station: Adoption and environmental impact, Manage. Sci., 61 (2014), 772-794.   Google Scholar

[3]

G. B. Bi, M. Y. Jin, L. Y. Ling and F. Yang, Environmental subsidy and the choice of green technology in the presence of green consumers, Ann. Oper. Res., 255 (2017), 547-568.  doi: 10.1007/s10479-016-2106-7.  Google Scholar

[4]

M. Burkart and T. Ellingsen, In-kind finance: A theory of trade credit, Am. Econ. Rev., 94 (2004), 569-590.  doi: 10.1257/0002828041464579.  Google Scholar

[5]

J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Manage. Sci., 50 (2004), 1274-1292.  doi: 10.1287/mnsc.1040.0278.  Google Scholar

[6]

G. P. Cachon, Retail store density and the cost of greenhouse gas emissions, Manage. Sci., 60 (2014), 1907-1925.   Google Scholar

[7]

E. Cao, L. X. Du and J. H. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, Int. J. Prod. Econ., 208 (2019), 383-399.  doi: 10.1016/j.ijpe.2018.08.001.  Google Scholar

[8]

Y.-K. Che and I. Gale, The optimal mechanism for selling to a budget-constrained buyer, J. Econ. Theory, 92 (2000), 198-233.  doi: 10.1006/jeth.1999.2639.  Google Scholar

[9]

M. C. Cohen, R. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidy for green technology adoption, Manage. Sci., 62 (2016), 1235-1258.   Google Scholar

[10]

S. Du, F. Ma, Z. Fu, L. Zhu and J. Zhang, Game-theoretic analysis for an emission-dependent supply chain in a `cap-and-trade' system, Ann. Oper. Res., 228 (2015), 135-149.  doi: 10.1007/s10479-011-0964-6.  Google Scholar

[11]

J. Z. Gao, Z. D. Xiao, B. B. Cao and Q. F. Chai, Green supply chain planning considering consumer's transportation process, Transp. Res. Pt. e-Logist. Transp. Rev., 109 (2018), 311-330.  doi: 10.1016/j.tre.2017.12.001.  Google Scholar

[12]

A. Hafezalkotob, Direct and indirect intervention schemas of government in the competition between green and non-green supply chains, J. Clean Prod., 170 (2018), 753-772.  doi: 10.1016/j.jclepro.2017.09.124.  Google Scholar

[13]

J. Hall, Environmental supply chain dynamics, J. Clean Prod., 8 (2000), 455-471.  doi: 10.1016/S0959-6526(00)00013-5.  Google Scholar

[14]

S. Huang, Z.-P. Fan and X. H. 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

[15]

B. Jing, X. F. Chen and G. S. Cai, Equilibrium financing in a distribution channel with capital constraint, Prod. Oper. Manag., 21 (2012), 1090-1101.  doi: 10.1111/j.1937-5956.2012.01328.x.  Google Scholar

[16]

P. R. Kleindorfer, K. Singhal and L. N. Van Wassenhove, Sustainable operations management, Prod. Oper. Manag., 14 (2005), 482-492.  doi: 10.1111/j.1937-5956.2005.tb00235.x.  Google Scholar

[17]

P. Kouvelis and W. H. Zhao, The newsvendor problem and price-only contract when bankruptcy costs exist, Prod. Oper. Manag., 20 (2011), 921-936.  doi: 10.1111/j.1937-5956.2010.01211.x.  Google Scholar

[18]

P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Manage. Sci., 62 (2016), 2149-2455.  doi: 10.1287/mnsc.2015.2248.  Google Scholar

[19]

V. Krishnan and W. Zhu, Designing a family of development-intensive products, Manage. Sci., 52 (2006), 813-825.  doi: 10.1287/mnsc.1050.0492.  Google Scholar

[20]

J.-Y. Liu, Y. Xia, Y. Fan, S.-M. Lin and J. Wu, Assessment of a green credit policy aimed at energy-intensive industries in China based on a financial CGE model, J. Clean Prod., 163 (2017), 293-302.  doi: 10.1016/j.jclepro.2015.10.111.  Google Scholar

[21]

R. Mahmoudi and M. Rasti-Barzoki, Sustainable supply chains under government intervention with a real-world case study: An evolutionary game theoretic approach, Comput. Ind. Eng., 116 (2018), 130-143.  doi: 10.1016/j.cie.2017.12.028.  Google Scholar

[22]

M. Parlar and Z. K. Weng, Balancing desirable but conflicting objectives in the newsvendor problem, IIE Trans., 35 (2003), 131-142.  doi: 10.1080/07408170304380.  Google Scholar

[23]

H. Peura, S. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, M & SOM-Manuf. Serv. Oper. Manag., 19 (2017), 165-335.  doi: 10.1287/msom.2016.0608.  Google Scholar

[24]

G. Raz and A. Ovchinnikov, Coordinating pricing and supply of public interest goods using government rebates and subsidy, IEEE Trans. Eng. Manage., 62 (2015), 65-79.  doi: 10.1109/TEM.2014.2380999.  Google Scholar

[25]

H. H. Song and X. X. Gao, Green supply chain game model and analysis under revenue-sharing contract, J. Clean Prod., 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[26]

C. S. Tang and S. Zhou, Research advances in environmentally and socially sustainable operations, Eur. J. Oper. Res., 223 (2012), 585-594.  doi: 10.1016/j.ejor.2012.07.030.  Google Scholar

[27]

Y.-C. Tsao, P.-L. Lee, C.-H. Chen and Z.-W. Liao, Sustainable newsvendor models under trade credit, J. Clean Prod., 141 (2017), 1478-1491.  doi: 10.1016/j.jclepro.2016.09.228.  Google Scholar

[28]

S.-C. Tseng and S.-W. Hung, A strategic decision-making model considering the social costs of carbon dioxide emissions for sustainable supply chain management, J. Environ. Manage., 133 (2014), 315-322.  doi: 10.1016/j.jenvman.2013.11.023.  Google Scholar

[29]

K. Wang, R. Q. Zhao and J. Peng, Trade credit contracting under asymmetric credit default risk: Screening, checking or insurance, Eur. J. Oper. Res., 266 (2018), 554-568.  doi: 10.1016/j.ejor.2017.10.004.  Google Scholar

[30]

D. D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, Int. J. Prod. Econ., article in press. doi: 10.1016/j.ijpe.2018.09.016.  Google Scholar

[31]

N. Yan and B. Sun, Comparative analysis of supply chain financing decisions between different financing modes, J. Ind. Manag. Optim., 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073.  Google Scholar

[32]

D. Yang and T. Xiao, Pricing and green level decisions of a green supply chain with government interventions under fuzzy uncertainties, J. Clean Prod., 149 (2017), 1174-1187.   Google Scholar

[33]

D.-X. Yang, Z.-Y. Chen, Y.-C. Yang and P.-Y. Nie, Green financial policies and capital flows, Physica A, 522 (2019), 135-146.  doi: 10.1016/j.physa.2019.01.126.  Google Scholar

[34]

H. Yang, W. Zhuo and L. Shao, Equilibrium evolution in a two-echelon supply chain with financially constrained retailers: The impact of equity financing, Int. J. Prod. Econ., 185 (2017), 139-149.   Google Scholar

[35]

L. H. Zhang, J. G. Wang and J. X. You, Consumer environmental awareness and channel coordination with two substitutable products, Eur. J. Oper. Res., 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043.  Google Scholar

[36]

W. G. Zhu and Y. J. He, Green product design in supply chains under competition, Eur. J. Oper. Res., 258 (2017), 165-180.  doi: 10.1016/j.ejor.2016.08.053.  Google Scholar

Figure 1.  The green credit mechanism
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Figure 2.  The subsidy mechanism
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Figure 3.  The interest rate, product's green degree, sales price and market demand
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Figure 4.  The profits of the bank and the manufacturer
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Figure 5.  The social welfare and the environmental benefits
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Table 1.  The profits of the bank and manufacturer under three scenarios
$ {\Pi ^B} $ $ {\Pi ^M} $
Non-subsidy $ \Pi _0^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2}} \right)}} $ $ \Pi _0^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2}} \right)}}{{8\left( {2k - {\theta ^2}} \right)}} $
Green credit $ \Pi _1^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}} $ $ \Pi _1^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2} - 4k{\tau _1}} \right)}}{{8\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}} $
Subsidy $ \Pi _2^{B*} = \frac{{{a^2}{\theta ^2}{{\left( {1 + {\tau _2}} \right)}^2}}}{{16\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}} $ $ \Pi _2^{M*} = \frac{{{a^2}\left[ {4k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]\left( {1 + {\tau _2}} \right)}}{{8\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}} $
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$ {\Pi ^B} $ $ {\Pi ^M} $
Non-subsidy $ \Pi _0^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2}} \right)}} $ $ \Pi _0^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2}} \right)}}{{8\left( {2k - {\theta ^2}} \right)}} $
Green credit $ \Pi _1^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}} $ $ \Pi _1^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2} - 4k{\tau _1}} \right)}}{{8\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}} $
Subsidy $ \Pi _2^{B*} = \frac{{{a^2}{\theta ^2}{{\left( {1 + {\tau _2}} \right)}^2}}}{{16\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}} $ $ \Pi _2^{M*} = \frac{{{a^2}\left[ {4k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]\left( {1 + {\tau _2}} \right)}}{{8\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}} $
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