# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021178
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## Strategy selection of inventory financing based on overconfident retailer

 1 School of Business Administration, Nanchang Institute of Technology, Nanchang, 330099, Jiangxi, China 2 School of Information Management, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, China 3 Modern Economics & Management College, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, China 4 School of Transportation and Logistics, East China Jiaotong University, Nanchang, 330013, Jiangxi, China

* Corresponding author: Weifan Jiang

Received  April 2021 Revised  August 2021 Early access October 2021

Fund Project: The first author is supported by Science and Technology Project (No.GJJ171003) founded by the Education Department of Jiangxi Province of China, the National Natural Science Foundation of China (No.71761015, No.71862014) and the Natural Science Foundation of Jiangxi Province of China (No.20202BABL201012)

Overconfidence of financing enterprises in market demand will have a significant impact on their business decision-making and banks' decision-making. This paper constructs the demand function based on the retailer's overconfidence and establishes the profit functions of the retailer and the bank respectively. Through Stackelberg game analysis, the influence of the retailer's overconfidence on each decision variable can be analyzed. The study has the following findings. Firstly, overconfidence makes decision-making deviate from rational decision-making. Secondly, the relationship between loan-to-value ratio and overconfidence is affected by different factors when the banks know the market or do not understand the market. Thirdly, the relationship between retailer's default probability and overconfidence is different when the bank doesn't know the market or knows the market. Fourthly, when the bank does not understand the market but listen to the overconfident retailer's market analysis, he should choose fixed loan-to-value ratio for financing. The overconfident retailer can ask the bank to give a higher loan-to-value ratio to reduce the capital pressure. Fifthly, when the bank conducts market research, the bank should choose the variable loan-to-value ratio contract for financing, while the retailer only needs to make decisions according to the bank's lending strategy.

Citation: Weifan Jiang, Jian Liu, Hui Zhou, Miyu Wan. Strategy selection of inventory financing based on overconfident retailer. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021178
##### References:
 [1] W. A. Abbasi, Z. Wang, Y. Zhou and S. Hassan, Research on measurement of supply chain finance credit risk based on Internet of Things, International J. Distributed Sensor Networks, 15 (2019). doi: 10.1177/1550147719874002. [2] V. Babich and M. J. Sobel, Pre-IPO operational and financial decision, Management Science, 50 (2004), 935-948. [3] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. [4] X. L. Chao, J. Chen and S. Y. Wang, Dynamic inventory management with cash flow constraints, Naval Res. Logist., 55 (2008), 758-768.  doi: 10.1002/nav.20322. [5] J. Chod, Inventory, risk shifting, and trade credit, Management Science, 63 (2017), 3207-3225. [6] D. C. Croson, R. Croson and Y. Ren, How to Manage an Overconfident Newsvendor, Working Paper, Cox School of Business, Southern Methodist University, 2008. [7] S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Annals of Operations Research, 2021. doi: 10.1007/s10479-020-03809-z. [8] B. Fischhoff, P. Slovic and S. Lichtenstein, Knowing with certainty: The appropriateness of extreme confidence, J. Experimental Psychology: Human Perception and Performance, 3 (1977), 552-564. [9] L. M. Gelsomino, R. de Boer, M. Steeman and A. Perego, An optimisation strategy for concurrent supply chain finance schemes, J. Purchasing And Supply Management, 25 (2019), 185-196. [10] J. He, X. Jiang, J. Wang, D. Zhu and L. Zhen, VaR methods for the dynamic impawn rate of steel in inventory financing under autocorrelative return, European J. Oper. Res., 223 (2012), 106-115.  doi: 10.1016/j.ejor.2012.06.005. [11] J. He, J. Wang, X. Jiang, X. Chen and L. Chen, The long-term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval, Complexity, 20 (2015), 17-34.  doi: 10.1002/cplx.21516. [12] E. Hofmann, Inventory financing in supply chains: A logistics service provider approach, International J. Physical Distribution & Logistics Management, 39 (2009), 716-740. [13] W. F. Jiang and J. Liu, Inventory financing with overconfident supplier based on supply chain contract, Mathe. Probl. Eng., 2018 (2018), 12pp. doi: 10.1155/2018/5054387. [14] E. Jokivuolle and S. Peura, Incorporation collateral value uncertainty in loss given default estimates and loan-to-value ratios, European Financial Management, 9 (2003), 299-314. [15] P. Kouvelis and W. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. [16] P. J. Lederer and V. R. Singhal, The effect of financing decisions on the choice of manufacturing technologies, International J. Flexible Manufacturing Systems, 6 (1994), 333-360. [17] C. H. Lee and B. Rhee, Coordination contracts in the presence of positive inventory financing costs, International J. Production Economics, 124 (2010), 331-339. [18] M. Li, N. C. Petruzzi and J. Zhang, Overconfident competing newsvendors, Management Science, 63 (2017), 2637-2646. [19] X. Li, P. Zhang, K. Zhang and Y. Li, Research on supply chain financing risk assessment of China's commercial banks, ICIC Express Letters, 10 (2016), 1567-1574. [20] X. Lu, J. Shang, S. Wu, G. G. Hegde, L. Vargas and D. Zhao, Impacts of supplier hubris on inventory decisions and green manufacturing endeavors, European J. Oper. Res., 245 (2015), 121-132.  doi: 10.1016/j.ejor.2015.02.051. [21] J. Ma, Q. Li and B. Bao, Study on complex advertising and price competition dual-channel supply chain models considering the overconfidence manufacturer, Math. Probl. Eng., 2016 (2016), Art. ID 2027146, 18 pp. [22] A. Ozmen, E. Kropat and G. W. Weber, Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155. [23] M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: a trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098. [24] E. Savku and G. W. Weber, Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market, A. Oper. Res., (2020). doi: 10.1007/s10479-020-03768-5. [25] Y. Ren, D. C. Croson and R. Croson, The overconfident newsvendor, J. Oper. Res. Society, 68 (2017), 496-506. [26] Y. Ren and R. Croson, Overconfidence in newsvendor orders: An experimental study, Management Science, 59 (2013), 2502-2517. [27] S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, J. Industrial and Management Optimization, 16 (2020), 553-578. [28] Z. Song, H. Huang, W. Ran and S. Liu, A study on the pricing model for 3PL of inventory financing, Discrete Dynamics in Nature and Society, 2016 (2016). doi: 10.1155/2016/6489748. [29] X. Sun, X. Chu and Z. Wu, Incentive regulation of banks on third party logistics enterprises in principal-agent-based inventory financing, Advances in Manufacturing, 2 (2014), 150-157. [30] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects, Management Science, 48 (2002), 992-1007. [31] Y. Wang, J. Zhou, H. Sun and L. Jiang, Robust inventory financing model with partial information, J. Appl. Math., 2014 (2014), 9pp. doi: 10.1155/2014/236083. [32] L. Xu, X. Shi, P. Du, K. Govindan and Z. Zhang, Optimization on pricing and overconfidence problem in a duopolistic supply chain, Comput. Oper. Res., 101 (2019), 162-172.  doi: 10.1016/j.cor.2018.04.003. [33] X. D. Xu and J. R. Birge, Joint production and financing decisions: Modeling and analysis, Working Paper, Northwestern University, (2004), 29pp. doi: 10.2139/ssrn.652562. [34] N. Yan and B. Sun, System dynamics modeling and simulation for capital-constrained supply chain based on inventory financing, Information Technology Journal, 12 (2013), 8384-8390. [35] H. Zhang, W. Meng, X. Wang and J. Zhang, Application of BSDE in standard inventory financing loan, Discrete Dyn. Nat. Soc., 2017 (2017), Article ID 1031247. doi: 10.1155/2017/1031247. [36] Y. Zhu, C. Xie, G. Wang and X. Yan, Comparison of individual, ensemble and integrated ensemble machine learning methods to predict China's SME credit risk in supply chain finance, Neural Computing & Applications, 28 (2017), 41-50.

show all references

##### References:
 [1] W. A. Abbasi, Z. Wang, Y. Zhou and S. Hassan, Research on measurement of supply chain finance credit risk based on Internet of Things, International J. Distributed Sensor Networks, 15 (2019). doi: 10.1177/1550147719874002. [2] V. Babich and M. J. Sobel, Pre-IPO operational and financial decision, Management Science, 50 (2004), 935-948. [3] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. [4] X. L. Chao, J. Chen and S. Y. Wang, Dynamic inventory management with cash flow constraints, Naval Res. Logist., 55 (2008), 758-768.  doi: 10.1002/nav.20322. [5] J. Chod, Inventory, risk shifting, and trade credit, Management Science, 63 (2017), 3207-3225. [6] D. C. Croson, R. Croson and Y. Ren, How to Manage an Overconfident Newsvendor, Working Paper, Cox School of Business, Southern Methodist University, 2008. [7] S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Annals of Operations Research, 2021. doi: 10.1007/s10479-020-03809-z. [8] B. Fischhoff, P. Slovic and S. Lichtenstein, Knowing with certainty: The appropriateness of extreme confidence, J. Experimental Psychology: Human Perception and Performance, 3 (1977), 552-564. [9] L. M. Gelsomino, R. de Boer, M. Steeman and A. Perego, An optimisation strategy for concurrent supply chain finance schemes, J. Purchasing And Supply Management, 25 (2019), 185-196. [10] J. He, X. Jiang, J. Wang, D. Zhu and L. Zhen, VaR methods for the dynamic impawn rate of steel in inventory financing under autocorrelative return, European J. Oper. Res., 223 (2012), 106-115.  doi: 10.1016/j.ejor.2012.06.005. [11] J. He, J. Wang, X. Jiang, X. Chen and L. Chen, The long-term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval, Complexity, 20 (2015), 17-34.  doi: 10.1002/cplx.21516. [12] E. Hofmann, Inventory financing in supply chains: A logistics service provider approach, International J. Physical Distribution & Logistics Management, 39 (2009), 716-740. [13] W. F. Jiang and J. Liu, Inventory financing with overconfident supplier based on supply chain contract, Mathe. Probl. Eng., 2018 (2018), 12pp. doi: 10.1155/2018/5054387. [14] E. Jokivuolle and S. Peura, Incorporation collateral value uncertainty in loss given default estimates and loan-to-value ratios, European Financial Management, 9 (2003), 299-314. [15] P. Kouvelis and W. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. [16] P. J. Lederer and V. R. Singhal, The effect of financing decisions on the choice of manufacturing technologies, International J. Flexible Manufacturing Systems, 6 (1994), 333-360. [17] C. H. Lee and B. Rhee, Coordination contracts in the presence of positive inventory financing costs, International J. Production Economics, 124 (2010), 331-339. [18] M. Li, N. C. Petruzzi and J. Zhang, Overconfident competing newsvendors, Management Science, 63 (2017), 2637-2646. [19] X. Li, P. Zhang, K. Zhang and Y. Li, Research on supply chain financing risk assessment of China's commercial banks, ICIC Express Letters, 10 (2016), 1567-1574. [20] X. Lu, J. Shang, S. Wu, G. G. Hegde, L. Vargas and D. Zhao, Impacts of supplier hubris on inventory decisions and green manufacturing endeavors, European J. Oper. Res., 245 (2015), 121-132.  doi: 10.1016/j.ejor.2015.02.051. [21] J. Ma, Q. Li and B. Bao, Study on complex advertising and price competition dual-channel supply chain models considering the overconfidence manufacturer, Math. Probl. Eng., 2016 (2016), Art. ID 2027146, 18 pp. [22] A. Ozmen, E. Kropat and G. W. Weber, Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155. [23] M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: a trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098. [24] E. Savku and G. W. Weber, Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market, A. Oper. Res., (2020). doi: 10.1007/s10479-020-03768-5. [25] Y. Ren, D. C. Croson and R. Croson, The overconfident newsvendor, J. Oper. Res. Society, 68 (2017), 496-506. [26] Y. Ren and R. Croson, Overconfidence in newsvendor orders: An experimental study, Management Science, 59 (2013), 2502-2517. [27] S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, J. Industrial and Management Optimization, 16 (2020), 553-578. [28] Z. Song, H. Huang, W. Ran and S. Liu, A study on the pricing model for 3PL of inventory financing, Discrete Dynamics in Nature and Society, 2016 (2016). doi: 10.1155/2016/6489748. [29] X. Sun, X. Chu and Z. Wu, Incentive regulation of banks on third party logistics enterprises in principal-agent-based inventory financing, Advances in Manufacturing, 2 (2014), 150-157. [30] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects, Management Science, 48 (2002), 992-1007. [31] Y. Wang, J. Zhou, H. Sun and L. Jiang, Robust inventory financing model with partial information, J. Appl. Math., 2014 (2014), 9pp. doi: 10.1155/2014/236083. [32] L. Xu, X. Shi, P. Du, K. Govindan and Z. Zhang, Optimization on pricing and overconfidence problem in a duopolistic supply chain, Comput. Oper. Res., 101 (2019), 162-172.  doi: 10.1016/j.cor.2018.04.003. [33] X. D. Xu and J. R. Birge, Joint production and financing decisions: Modeling and analysis, Working Paper, Northwestern University, (2004), 29pp. doi: 10.2139/ssrn.652562. [34] N. Yan and B. Sun, System dynamics modeling and simulation for capital-constrained supply chain based on inventory financing, Information Technology Journal, 12 (2013), 8384-8390. [35] H. Zhang, W. Meng, X. Wang and J. Zhang, Application of BSDE in standard inventory financing loan, Discrete Dyn. Nat. Soc., 2017 (2017), Article ID 1031247. doi: 10.1155/2017/1031247. [36] Y. Zhu, C. Xie, G. Wang and X. Yan, Comparison of individual, ensemble and integrated ensemble machine learning methods to predict China's SME credit risk in supply chain finance, Neural Computing & Applications, 28 (2017), 41-50.
Decision-making process
Sales effort changes with overconfidence
Order quantity changes with overconfidence
Loan-to-value ratio changes with overconfidence
Default probability changes with overconfidence
Expected profits change with overconfidence ($p = 9$)
Expected profits change with overconfidence ($p = 11$)
Sales effort changes with overconfidence
Order quantity changes with overconfidence
Loan-to-value ratio changes with overconfidence
Default probability changes with overconfidence
Expected profits change with overconfidence ($p = 9$)
Expected profits change with overconfidence ($p = 11$)
The real total profits change with overconfidence in the case of BNCO
The real total profits change with overconfidence in the case of BCO
The real profits change with overconfidence in the case of BNCO ($p = 9$)
The real profits change with overconfidence in the case of BCO ($p = 9$)
The real profits change with overconfidence in the case of BNCO ($p = 11$)
The real profits change with overconfidence in the case of BCO ($p = 11$)
Decision variables and model parameters
 Decision variable of the bank $\omega$ the loan-to-value ratio, $\omega_{o}$ is the loan-to-value ratio when the bank is not clear about the overconfidence of the retailer, $\omega_{r}$ is the loan-to-value ratio when the bank is clear about the overconfidence of the retailer Decision variable of the retailer $q_{o}$ the order quantity of the overconfident retailer, $q_{o1}$ is the order quantity when the bank is not clear about the overconfidence of the retailer, $q_{o2}$ is the order quantity when the bank is clear about the overconfidence of the retailer $e_{o}$ the sales effort of the overconfident retailer, $e_{o1}$ is the sales effort when the bank is not clear about the overconfidence of the retailer, $e_{o2}$ is the sales effort when the bank is clear about the overconfidence of the retailer Parameters $r_{1}$ the annual deposit interest rate $r_{2}$ the annual loan interest rate which include all expenses incurred during the pledge period $p$ the sale price of the product $w$ the cost of the product of the retailer $v$ the buyback price of the product $T$ the period of the inventory pledge loan contract, the unit is year, $0  Decision variable of the bank$ \omega $the loan-to-value ratio,$ \omega_{o} $is the loan-to-value ratio when the bank is not clear about the overconfidence of the retailer,$ \omega_{r} $is the loan-to-value ratio when the bank is clear about the overconfidence of the retailer Decision variable of the retailer$ q_{o} $the order quantity of the overconfident retailer,$ q_{o1} $is the order quantity when the bank is not clear about the overconfidence of the retailer,$ q_{o2} $is the order quantity when the bank is clear about the overconfidence of the retailer$ e_{o} $the sales effort of the overconfident retailer,$ e_{o1} $is the sales effort when the bank is not clear about the overconfidence of the retailer,$ e_{o2} $is the sales effort when the bank is clear about the overconfidence of the retailer Parameters$ r_{1} $the annual deposit interest rate$ r_{2} $the annual loan interest rate which include all expenses incurred during the pledge period$ p $the sale price of the product$ w $the cost of the product of the retailer$ v $the buyback price of the product$ T $the period of the inventory pledge loan contract, the unit is year,$ 0
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