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doi: 10.3934/jimo.2021042

Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain

1. 

School of Economics and Management, Hebei University of Technology, Tianjin 300401, China

2. 

The Center for Enterprise Informatization and Management Innovation, Tianjin Humanities and Social Science Key Research Base, Tianjin 300401, China

* Corresponding author: Jing Zhang

Received  April 2020 Revised  December 2020 Published  March 2021

Fund Project: The first author is supported by NSF grant 14BGL055, 18BGL012

By applying Stackelberg game theory, this paper investigates the supply chain with a risk-neutral retailer and a risk-averse supplier, measuring risk-averse behavior by using conditional value-at-risk (CVaR). The equilibrium solutions of the supplier's wholesale price and the retailer's order quantity are obtained under two financing strategies: supplier financing (SF) and supplier investment (SI). It is found that the supplier's risk aversion is a crucial factor affecting both parties' financing decisions, and the supplier should offer different financing strategies to the retailer based on his risk attitude and the profit-sharing coefficient. However, the retailer prefers SF regardless of the supplier's risk aversion. Taking bank credit financing as a basic model, the advantages of SF and SI have been investigated. A Pareto improvement region for the two finance strategies has been identified and some suggestions are provided for the supplier's optimal utility. Then we extend to the situation that both parties are risk-averse and use the financing cost-sharing mechanism to achieve centralized decision-making.

Citation: Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021042
References:
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F. ChenA. Federgruen and Y. Zheng, Coordination mechanisms for a distribution system with one supplier and multiple retailers, Management Science, 47 (2001), 611-733.  doi: 10.1287/mnsc.47.5.693.10484.  Google Scholar

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H. Emmons and S. M. Gilbert, The role of returns policies in pricing and inventory decision for catalogue goods, Management Science, 44 (1998), 276–283. https://www.jstor.org/stable/2634501 Google Scholar

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Y. FanY. Feng and Y. Shou, A risk-averse and buyer-led supply chain under option contract: CVaR minimization and channel coordination, International Journal of Production Economics, 219 (2020), 66-81.  doi: 10.1016/j.ijpe.2019.05.021.  Google Scholar

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X. GanS. P. Sethi and H. Yan, Channel coordination with a risk-neutral supplier and a downside-risk-averse retailer, Production and Operations Management, 14 (2009), 80-89.  doi: 10.1111/j.1937-5956.2005.tb00011.x.  Google Scholar

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M. GiannettiM. Burkart and T. Ellingsen, What you sell is what you lend? Explaining trade credit contracts, The Review of Financial Studies, 24 (2011), 1261-1298.  doi: 10.1093/rfs/hhn096.  Google Scholar

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J. Heydari and Y. Norouzinasab, A two-level discount model for coordinating a decentralized supply chain considering stochastic price-sensitive demand, Journal of Industrial Engineering, International, 11, (2015), 531–542. doi: 10.1007/s40092-015-0119-5.  Google Scholar

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B. HuJ. Qu and C. Meng, Supply chain coordination under option contracts with joint pricing under price-dependent demand, International Journal of Production Economics, 205 (2018), 74-86.  doi: 10.1016/j.ijpe.2018.08.033.  Google Scholar

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J. Huang and W. Yang and Y. Tu, Financing mode decision in a supply chain with financial constraint, International Journal of Production Economics, 220 (2020). doi: 10.1016/j. ijpe. 2019.07.014.  Google Scholar

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L. JinfaS. Boyu and C. Nan, The supply chain coordination of risk preferred retailer under information asymmetry, Procedia Manufacturing, 30 (2019), 658-662.  doi: 10.1016/j.promfg.2019.02.093.  Google Scholar

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K. KangY. ZhaoY. Ma and Z. Li, Green supply chain poverty alleviation through microfinance game model and cooperative analysis, Journal of Cleaner Production, 226 (2019), 1022-1041.  doi: 10.1016/j.jclepro.2019.04.099.  Google Scholar

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G. KaraA. Ozmen and G. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.  Google Scholar

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M. N. KatehakisB. Melamed and J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575.  doi: 10.1111/poms.12571.  Google Scholar

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C. H. Lee and B. D. Rhee, Coordination contracts in the presence of positive inventory financing costs, International Journal of Production Economics, 124 (2010), 331-339.  doi: 10.1016/j.ijpe.2009.11.028.  Google Scholar

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show all references

References:
[1]

Ar shinderA. Kanda and S. G. Deshmukh, Supply chain coordination: Perspectives, empirical studies and research directions, International Journal of Production Economics, 115 (2008), 316-335.  doi: 10.1016/j.ijpe.2008.05.011.  Google Scholar

[2]

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

[3]

G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar

[4]

G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44.  doi: 10.1287/mnsc.1040.0215.  Google Scholar

[5]

X. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357.  doi: 10.1016/j.ijpe.2014.05.001.  Google Scholar

[6]

F. ChenA. Federgruen and Y. Zheng, Coordination mechanisms for a distribution system with one supplier and multiple retailers, Management Science, 47 (2001), 611-733.  doi: 10.1287/mnsc.47.5.693.10484.  Google Scholar

[7]

C. Chiu and T. Choi, Optimal pricing and stocking decisions for newsvendor problem with value-at-risk consideration, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 40 (2010), 1116-1119.  doi: 10.1109/TSMCA.2010.2043947.  Google Scholar

[8]

S. K. Das and S. K Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment, Computers & Industrial Engineering, 132 (2019), 311-324.  doi: 10.1016/j.cie.2019.04.037.  Google Scholar

[9]

L. EeckhoudtC. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794.  doi: 10.1287/mnsc.41.5.786.  Google Scholar

[10]

H. Emmons and S. M. Gilbert, The role of returns policies in pricing and inventory decision for catalogue goods, Management Science, 44 (1998), 276–283. https://www.jstor.org/stable/2634501 Google Scholar

[11]

Y. FanY. Feng and Y. Shou, A risk-averse and buyer-led supply chain under option contract: CVaR minimization and channel coordination, International Journal of Production Economics, 219 (2020), 66-81.  doi: 10.1016/j.ijpe.2019.05.021.  Google Scholar

[12]

X. H. GanS. P. Sethi and H. M. Yan, Coordination of supply chains with risk averse agents, Production and Operations Management, 13 (2004), 135-149.  doi: 10.1111/j.1937-5956.2004.tb00150.x.  Google Scholar

[13]

X. GanS. P. Sethi and H. Yan, Channel coordination with a risk-neutral supplier and a downside-risk-averse retailer, Production and Operations Management, 14 (2009), 80-89.  doi: 10.1111/j.1937-5956.2005.tb00011.x.  Google Scholar

[14]

L. M. GelsominoR. De BoerM. Steeman and A. Perego, An optimisation strategy for concurrent supply chain finance schemes, Journal of Purchasing and Supply Management, 25 (2019), 185-196.  doi: 10.1016/j.pursup.2018.07.004.  Google Scholar

[15]

M. GiannettiM. Burkart and T. Ellingsen, What you sell is what you lend? Explaining trade credit contracts, The Review of Financial Studies, 24 (2011), 1261-1298.  doi: 10.1093/rfs/hhn096.  Google Scholar

[16]

B. C. GiriS. Bardhan and T. Maiti, Coordinating a three-layer supply chain with uncertain demand and random yield, International Journal of Production Research, 54 (2016), 2499-2518.  doi: 10.1080/00207543.2015.1119324.  Google Scholar

[17]

J. Heydari and Y. Norouzinasab, A two-level discount model for coordinating a decentralized supply chain considering stochastic price-sensitive demand, Journal of Industrial Engineering, International, 11, (2015), 531–542. doi: 10.1007/s40092-015-0119-5.  Google Scholar

[18]

B. HuJ. Qu and C. Meng, Supply chain coordination under option contracts with joint pricing under price-dependent demand, International Journal of Production Economics, 205 (2018), 74-86.  doi: 10.1016/j.ijpe.2018.08.033.  Google Scholar

[19]

B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193.  doi: 10.1016/j.ijpe.2016.11.002.  Google Scholar

[20]

J. Huang and W. Yang and Y. Tu, Financing mode decision in a supply chain with financial constraint, International Journal of Production Economics, 220 (2020). doi: 10.1016/j. ijpe. 2019.07.014.  Google Scholar

[21]

L. JinfaS. Boyu and C. Nan, The supply chain coordination of risk preferred retailer under information asymmetry, Procedia Manufacturing, 30 (2019), 658-662.  doi: 10.1016/j.promfg.2019.02.093.  Google Scholar

[22]

B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20.  doi: 10.1016/j.dss.2013.01.013.  Google Scholar

[23]

K. KangY. ZhaoY. Ma and Z. Li, Green supply chain poverty alleviation through microfinance game model and cooperative analysis, Journal of Cleaner Production, 226 (2019), 1022-1041.  doi: 10.1016/j.jclepro.2019.04.099.  Google Scholar

[24]

G. KaraA. Ozmen and G. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.  Google Scholar

[25]

M. N. KatehakisB. Melamed and J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575.  doi: 10.1111/poms.12571.  Google Scholar

[26]

S. Kolay and G. Shaffer, Contract design with a dominant retailer and a competitive fringe, Management Science, 59 (2013), 2111-2116.  doi: 10.1287/mnsc.1120.1677.  Google Scholar

[27]

P. Kouvelis and W. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357.  doi: 10.1287/mnsc.2015.2248.  Google Scholar

[28]

M. A. Lariviere, Supply chain contracting and coordination with stochastic demand, Quantitative Models for Supply Chain Management, 17 (1999), 233-268.  doi: 10.1007/978-1-4615-4949-9_8.  Google Scholar

[29]

H. Lau and A. H. Lau, Manufacturer's pricing strategy and return policy for a single-period commodity, European Journal of Operational Research, 116 (1999), 291-304.  doi: 10.1016/S0377-2217(98)00123-4.  Google Scholar

[30]

C. H. Lee and B. D. Rhee, Coordination contracts in the presence of positive inventory financing costs, International Journal of Production Economics, 124 (2010), 331-339.  doi: 10.1016/j.ijpe.2009.11.028.  Google Scholar

[31]

C. H. Lee and B. Rhee, Channel coordination using product returns for a supply chain with stochastic salvage capacity, European Journal of Operational Research, 177 (2007), 214-238.  doi: 10.1016/j.ejor.2005.10.044.  Google Scholar

[32]

B. LiS. An and D. Song, Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain, Transportation Research Part E: Logistics and Transportation Review, 118 (2018), 163-183.  doi: 10.1016/j.tre.2018.06.007.  Google Scholar

[33]

B. LiP. HouP. Chen and Q. Li, Pricing strategy and coordination in a dual channel supply chain with a risk-averse retailer, International Journal of Production Economics, 178 (2016), 154-168.  doi: 10.1016/j.ijpe.2016.05.010.  Google Scholar

[34]

D. LiangG. LiL. SunJ. Gao and X. Sun, The effect of risk aversion on manufacturer advertising in a two-stage supply chain, Transportation Journal, 51 (2012), 59-79.  doi: 10.5325/transportationj.51.1.0059.  Google Scholar

[35]

M. PervinS. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[36]

M. PervinS. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price- and stock-sensitive demand, Journal of Industrial and Management Optimization, 16 (2020), 1585-1612.  doi: 10.3934/jimo.2019019.  Google Scholar

[37]

R. QiuJ. Shang and X. Huang, Robust inventory decision under distribution uncertainty: A CVaR-based optimization approach, International Journal of Production Economics, 153 (2014), 13-23.  doi: 10.1016/j.ijpe.2014.03.021.  Google Scholar

[38]

R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of Risk, 2 (2000), 21-41.  doi: 10.21314/JOR.2000.038.  Google Scholar

[39]

S. K. RoyG. Maity and G. W. Weber, Multi-objective two-stage grey transportation problem using utility function with goals, Central European Journal of Operations Research, 25 (2017), 417-439.  doi: 10.1007/s10100-016-0464-5.  Google Scholar

[40]

S. K. RoyM. Pervin and G. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, Journal of Industrial and Management Optimization, 16 (2020), 553-578.  doi: 10.3934/jimo.2018167.  Google Scholar

[41]

S. K. RoyG. MaityG. W. Weber and S. G. A. Gök, Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal, Ann. Oper. Res., 253 (2017), 599-620.  doi: 10.1007/s10479-016-2283-4.  Google Scholar

[42]

A. Sainathan and H. Groenevelt, Vendor managed inventory contracts – coordinating the supply chain while looking from the vendor's perspective, European Journal of Operational Research, 272 (2019), 249-260.  doi: 10.1016/j.ejor.2018.06.028.  Google Scholar

[43]

M. Van BergenM. SteemanM. Reindorp and L. M. Gelsomino, Supply chain finance schemes in the procurement of agricultural products, Journal of Purchasing and Supply Management, 25 (2019), 172-184.  doi: 10.1016/j.pursup.2018.08.003.  Google Scholar

[44]

B. B. Venegas and J. A. Ventura, A two-stage supply chain coordination mechanism considering price sensitive demand and quantity discounts, European Journal of Operational Research, 264 (2018), 524-533.  doi: 10.1016/j.ejor.2017.06.030.  Google Scholar

[45]

X. H. Wang and X. Y. Nan, Coordination of supply chain with bilateral asymmetric information by considering risk aversion of retailer, Chinese Journal of Managemet Science, 23 (2015), 97-107.  doi: 10.16381/j.cnki.issn1003-207x.2015.03.012.  Google Scholar

[46]

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Figure 1.  Relationship between each participant and financing mechanism
Figure 2.  The effect of $ \eta $ and $ R $ on $ w^{F*} $
Figure 3.  The effect of $ \eta $ and $ c $ on $ q^{F*} $
Figure 4.  Changes of $ w^{I*} $ with $ c $, $ \eta $, $ \beta $ and $ \alpha $
Figure 5.  Changes of $ q^{I*} $ with $ c $, $ \eta $, $ \beta $ and $ \alpha $
Figure 6.  Pareto improvement region under dominant of SF
Figure 7.  Pareto improvement region under dominant of SI
Figure 8.  Range of the transfer payments that can be assigned to a supplier under SF
Figure 9.  Range of the transfer payments that can be assigned to a supplier under SI
Table 1.  Summary of notations
Parameters and variables Description
$ w $ Supplier's wholesale price for each product
$ q $ Retailer's order quantity of the product
Parameters $ \quad $
$ p $ Unit market price
$ c $ Unit production cost of the product
$ y $ Market demand which is a random variable with F(.) and f(.) as the
$ \quad $ cumulative distribution function and the density function
$ R $ The interest rate under SF
$ \alpha $ Supplier's sharing coefficient of retailer's profit
$ \beta $ Supplier investment as a percentage of retailers capital needs
$ \psi $ Supplier's financing cost-sharing coefficient
$ \eta $ Supplier's degree of risk aversion
$ T $ Transfer payment
$ \delta $ Influence of the retailer
Index $ \quad $
$ r $ Parameter's related to the retailer
$ s $ Parameter's related to the supplier
$ i $ Superscript, retailer's financing scheme, where $ i=\{F,I,B\} $
$ C $ The status related to centralized decision
$ a $ Risk-averse scenario
$ n $ Risk-neutral scenario
Parameters and variables Description
$ w $ Supplier's wholesale price for each product
$ q $ Retailer's order quantity of the product
Parameters $ \quad $
$ p $ Unit market price
$ c $ Unit production cost of the product
$ y $ Market demand which is a random variable with F(.) and f(.) as the
$ \quad $ cumulative distribution function and the density function
$ R $ The interest rate under SF
$ \alpha $ Supplier's sharing coefficient of retailer's profit
$ \beta $ Supplier investment as a percentage of retailers capital needs
$ \psi $ Supplier's financing cost-sharing coefficient
$ \eta $ Supplier's degree of risk aversion
$ T $ Transfer payment
$ \delta $ Influence of the retailer
Index $ \quad $
$ r $ Parameter's related to the retailer
$ s $ Parameter's related to the supplier
$ i $ Superscript, retailer's financing scheme, where $ i=\{F,I,B\} $
$ C $ The status related to centralized decision
$ a $ Risk-averse scenario
$ n $ Risk-neutral scenario
Table 2.  Impact of production cost
$ c $ $ w^{F*} $ $ q^{F*} $ $ \pi_{r}^{F*} $ $ CVaR_{s}^{F*} $ $ w^{I*} $ $ q^{I*} $ $ \pi_{r}^{I*} $ $ CVaR_{s}^{I*} $
0.30 1.1500 6.6400 9.3151 1.7040 1.8398 6.6000 3.6000 3.6899
0.35 1.1812 6.5800 9.0218 1.3735 1.8950 6.5333 3.4500 3.6683
0.40 1.2130 6.5200 8.7248 1.0460 1.9513 6.4666 3.3000 3.6433
0.45 1.2454 6.4600 8.4241 0.7214 2.0089 6.4000 3.1499 3.6150
$ c $ $ w^{F*} $ $ q^{F*} $ $ \pi_{r}^{F*} $ $ CVaR_{s}^{F*} $ $ w^{I*} $ $ q^{I*} $ $ \pi_{r}^{I*} $ $ CVaR_{s}^{I*} $
0.30 1.1500 6.6400 9.3151 1.7040 1.8398 6.6000 3.6000 3.6899
0.35 1.1812 6.5800 9.0218 1.3735 1.8950 6.5333 3.4500 3.6683
0.40 1.2130 6.5200 8.7248 1.0460 1.9513 6.4666 3.3000 3.6433
0.45 1.2454 6.4600 8.4241 0.7214 2.0089 6.4000 3.1499 3.6150
Table 3.  Impact of risk aversion
$ \eta $ $ w^{F*} $ $ q^{F*} $ $ \pi_{r}^{F*} $ $ CVaR_{s}^{F*} $ $ w^{I*} $ $ q^{I*} $ $ \pi_{r}^{I*} $ $ CVaR_{s}^{I*} $
0.25 0.9282 7.1000 11.4450 0.2049 1.4904 7.0555 4.6250 3.0361
0.30 1.2130 6.5200 8.7248 1.0460 1.9513 6.4666 3.3000 3.6433
0.35 1.5534 5.9400 5.6682 1.8870 2.5047 5.8777 1.9750 4.2505
0.40 1.9674 5.3600 2.2752 2.7279 3.1812 5.2888 0.6499 4.8577
$ \eta $ $ w^{F*} $ $ q^{F*} $ $ \pi_{r}^{F*} $ $ CVaR_{s}^{F*} $ $ w^{I*} $ $ q^{I*} $ $ \pi_{r}^{I*} $ $ CVaR_{s}^{I*} $
0.25 0.9282 7.1000 11.4450 0.2049 1.4904 7.0555 4.6250 3.0361
0.30 1.2130 6.5200 8.7248 1.0460 1.9513 6.4666 3.3000 3.6433
0.35 1.5534 5.9400 5.6682 1.8870 2.5047 5.8777 1.9750 4.2505
0.40 1.9674 5.3600 2.2752 2.7279 3.1812 5.2888 0.6499 4.8577
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