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March  2020, 16(2): 887-909. doi: 10.3934/jimo.2018183

Financing strategies for a capital-constrained supplier under yield uncertainty

1. 

College of Economics and Management, Nanjing Forestry University, Nanjing, Jiangsu 210037, China

2. 

Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA

* Corresponding author: Tao Pang. Email: tpang@ncsu.edu

Received  March 2018 Revised  September 2018 Published  March 2020 Early access  December 2018

Fund Project: This work is partially supported by the National Social Science Foundation of China (Grant No. 17BGL236)

We consider a supply chain consisting of a supplier and a distributor, in which the supplier has a capital constraint and faces productivity yield uncertainty. To solve the capital constraint problem, we propose an advance payment with risk compensation (APRC) mechanism, under which the distributor finances the supplier with an advance payment, and the supplier provides a price discount to compensate the distributor for the supplier's bankruptcy risk. The optimal solutions are derived under the APRC mechanism and the results indicate that under the APRC, the whole supply chain performs as well as if there is no capital constraint, in terms of profits and optimal strategies. Therefore, the APRC is an efficient solution for the supplier's capital constraint issue. In addition, when the deficit is big, the APRC provides an alternative financing arrangement and it can bring higher profits for both parties. Another very interesting finding is that, when the capital deficit is small, the supplier can do better with the bank loan financing, despite that a higher interest rate needs to be paid in this case.

Citation: Hongjun Peng, Tao Pang. Financing strategies for a capital-constrained supplier under yield uncertainty. Journal of Industrial and Management Optimization, 2020, 16 (2) : 887-909. doi: 10.3934/jimo.2018183
References:
[1]

K. Annadurai and R. Uthayakumar, Analysis of partial trade credit financing in a supply chain by EOQ-based model for decaying items with shortages, International Journal of Advanced Manufacturing Technology, 61 (2012), 1139-1159. 

[2]

J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. 

[3]

G. S. CaiX. F. Chen and Z. G. Xiao, The roles of bank and trade credits: Theoretical analysis and empirical evidence, Production and Operations Management, 23 (2014), 583-598. 

[4]

F. CaroK. Rajaram and J. Wollenweber, Process location and product distribution with uncertain yields, Operations Research, 60 (2012), 1050-1063.  doi: 10.1287/opre.1120.1087.

[5]

K. B. Chen and T. J. Xiao, Production planning and backup sourcing strategy of a buyer-dominant supply chain with random yield and demand, International Journal of Systems Science, 46 (2015), 2799-2817.  doi: 10.1080/00207721.2013.879234.

[6]

S. C. Chen and J. T. Teng, Retailer's optimal ordering policy for deteriorating items with maximum lifetime under supplier's trade credit financing, Applied Mathematical Modelling, 38 (2015), 4049-4061.  doi: 10.1016/j.apm.2013.11.056.

[7]

X. F. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357. 

[8]

X. F. Chen and A. Y. Wang, Trade credit contract with limited liability in the supply chain with budget constraints, Annals of Operations Research, 196 (2012), 153-165.  doi: 10.1007/s10479-012-1119-0.

[9]

M. S. ChernQ. H. PanJ. T. TengY. L. Chan and S. C. Chen, Stackelberg solution in a vendor-buyer supply chain model with permissible delay in payments, International Journal of Production Economics, 144 (2013), 397-404. 

[10]

M. Dada and Q. H. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.

[11]

A. Federgruen and N. Yang, Competition under generalized attraction models: Applications to quality competition under yield uncertainty, Management Science, 55 (2009), 2028-2043.

[12]

H. Gurnani and Y. Gerchak, Coordination in decentralized assembly systems with uncertain component yield, European Journal of Operational Research, 176 (2007), 1559-1576.  doi: 10.1016/j.ejor.2005.09.036.

[13]

F. HuC. C. Lim and Z. D. Lu, Coordination of supply chains with a flexible ordering policy under yield and demand uncertainty, International Journal of Production Economics, 146 (2013), 686-693. 

[14]

C. K. HuangD. M. TsaiJ. C. Wu and K. J. Chung, An integrated vendor-buyer inventory model with order-processing cost reduction and permissible delay in payments, European Journal of Operational Research, 202 (2010), 473-478. 

[15]

L. Jiang and Z. Hao, Alleviating supplier's capital restriction by two-order arrangement, Operations Research Letters, 42 (2014), 444-449.  doi: 10.1016/j.orl.2014.07.009.

[16]

B. JingX. F. Chen and G. S. Cai, Equilibrium Financing in a Distribution Channel with Capital Constraint, Production and Operations Management, 21 (2012), 1090-1101. 

[17]

B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. 

[18]

B. Keren, The single-period inventory problem: Extension to random yield from the perspective of the supply chain, OMEGA-International Journal of Management Science, 37 (2009), 801-810. 

[19]

P. Kouvelis and W. H. Zhao, Financing the newsvendor: Supplier vs. bank, and the structure of optimal trade credit contracts, Operations Research, 60 (2012), 566-580.  doi: 10.1287/opre.1120.1040.

[20]

P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. 

[21]

G. M. LaiL. G. Debo and K. Sycara, Sharing inventory risk in supply chain: The implication of financial constraint, OMEGA-International Journal of Management Science, 37 (2009), 811-825. 

[22]

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.

[23]

X. Li and Y. J. Li, On lot-sizing problem in a random yield production system under loss aversion, Annals of Operations Research, 240 (2016), 415-434.  doi: 10.1007/s10479-014-1715-2.

[24]

K. R. Lou and L. Wang, Optimal lot-sizing policy for a manufacturer with defective items in a supply chain with up-stream and down-stream trade credits, Industrial Engineering, 66 (2013), 1125-1130. 

[25]

K. R. Lou and W. C. Wang, Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk, The Journal of the Operational Research Society, 64 (2013), 1551-1556. 

[26]

J. R. Luo and X. Chen, Coordination of random yield supply chains with improved revenue sharing contracts, European Journal of Industrial Engineering, 10 (2016), 81-102. 

[27]

S. Mateut and P. Zanchettin, Credit sales and advance payments: Substitutes or complements?, Economics Letters, 118 (2013), 173-176. 

[28]

L. Moussawi-Haidar and M. Y. Jaber, A joint model for cash and inventory management for a retailer under delay in payments, Industrial Engineering, 66 (2013), 758-767. 

[29]

L. Y. OuyangC. H. Ho and C. H. Su, An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit, Industrial Engineering, 57 (2009), 920-930. 

[30]

H. J. PengT. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, Journal of Cleaner Production, 205 (2018), 291-302. 

[31]

H. J. Peng, T. Pang and F. L. Cao, A mutual-aid mechanism for supply chains with capital constraints, 2016, Available at SSRN: https://ssrn.com/abstract=2862629

[32]

H. J. Peng, M. H. Zhou and L. Qian, Supply Chain Coordination with Uncertainty in Two-echelon Yields, Asia-Pacific Journal of Operational Research, 30 (2013), 1250044, 13 pp. doi: 10.1142/S0217595912500443.

[33]

N. R. S. Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. 

[34]

J. T. TengC. T. Chang and M. S. Chern, Vendor-buyer inventory models with trade credit financing under both non-cooperative and integrated environments, International Journal of Systems Science, 43 (2012), 2050-2061.  doi: 10.1080/00207721.2011.564322.

[35]

A. Thangam, Optimal price discounting and lot-sizing polities for perishable items in a supply chain under advance payment scheme and two-echelon trade credits, International Journal of Production Economics, 139 (2012), 459-472. 

[36]

N. N. Yan and B. W. Sun, Comparative analysis of supply chain financing strategies between different financing modes, Journal of Industrial and Management Optimization, 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073.

[37]

N. N. YanB. W. SunH. 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. 

[38]

Q. H. ZhangD. L. ZhangY. C. Tsao and J. W. Luo, Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity, International Journal of Production Economics, 177 (2016), 34-43. 

show all references

References:
[1]

K. Annadurai and R. Uthayakumar, Analysis of partial trade credit financing in a supply chain by EOQ-based model for decaying items with shortages, International Journal of Advanced Manufacturing Technology, 61 (2012), 1139-1159. 

[2]

J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. 

[3]

G. S. CaiX. F. Chen and Z. G. Xiao, The roles of bank and trade credits: Theoretical analysis and empirical evidence, Production and Operations Management, 23 (2014), 583-598. 

[4]

F. CaroK. Rajaram and J. Wollenweber, Process location and product distribution with uncertain yields, Operations Research, 60 (2012), 1050-1063.  doi: 10.1287/opre.1120.1087.

[5]

K. B. Chen and T. J. Xiao, Production planning and backup sourcing strategy of a buyer-dominant supply chain with random yield and demand, International Journal of Systems Science, 46 (2015), 2799-2817.  doi: 10.1080/00207721.2013.879234.

[6]

S. C. Chen and J. T. Teng, Retailer's optimal ordering policy for deteriorating items with maximum lifetime under supplier's trade credit financing, Applied Mathematical Modelling, 38 (2015), 4049-4061.  doi: 10.1016/j.apm.2013.11.056.

[7]

X. F. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357. 

[8]

X. F. Chen and A. Y. Wang, Trade credit contract with limited liability in the supply chain with budget constraints, Annals of Operations Research, 196 (2012), 153-165.  doi: 10.1007/s10479-012-1119-0.

[9]

M. S. ChernQ. H. PanJ. T. TengY. L. Chan and S. C. Chen, Stackelberg solution in a vendor-buyer supply chain model with permissible delay in payments, International Journal of Production Economics, 144 (2013), 397-404. 

[10]

M. Dada and Q. H. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.

[11]

A. Federgruen and N. Yang, Competition under generalized attraction models: Applications to quality competition under yield uncertainty, Management Science, 55 (2009), 2028-2043.

[12]

H. Gurnani and Y. Gerchak, Coordination in decentralized assembly systems with uncertain component yield, European Journal of Operational Research, 176 (2007), 1559-1576.  doi: 10.1016/j.ejor.2005.09.036.

[13]

F. HuC. C. Lim and Z. D. Lu, Coordination of supply chains with a flexible ordering policy under yield and demand uncertainty, International Journal of Production Economics, 146 (2013), 686-693. 

[14]

C. K. HuangD. M. TsaiJ. C. Wu and K. J. Chung, An integrated vendor-buyer inventory model with order-processing cost reduction and permissible delay in payments, European Journal of Operational Research, 202 (2010), 473-478. 

[15]

L. Jiang and Z. Hao, Alleviating supplier's capital restriction by two-order arrangement, Operations Research Letters, 42 (2014), 444-449.  doi: 10.1016/j.orl.2014.07.009.

[16]

B. JingX. F. Chen and G. S. Cai, Equilibrium Financing in a Distribution Channel with Capital Constraint, Production and Operations Management, 21 (2012), 1090-1101. 

[17]

B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. 

[18]

B. Keren, The single-period inventory problem: Extension to random yield from the perspective of the supply chain, OMEGA-International Journal of Management Science, 37 (2009), 801-810. 

[19]

P. Kouvelis and W. H. Zhao, Financing the newsvendor: Supplier vs. bank, and the structure of optimal trade credit contracts, Operations Research, 60 (2012), 566-580.  doi: 10.1287/opre.1120.1040.

[20]

P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. 

[21]

G. M. LaiL. G. Debo and K. Sycara, Sharing inventory risk in supply chain: The implication of financial constraint, OMEGA-International Journal of Management Science, 37 (2009), 811-825. 

[22]

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.

[23]

X. Li and Y. J. Li, On lot-sizing problem in a random yield production system under loss aversion, Annals of Operations Research, 240 (2016), 415-434.  doi: 10.1007/s10479-014-1715-2.

[24]

K. R. Lou and L. Wang, Optimal lot-sizing policy for a manufacturer with defective items in a supply chain with up-stream and down-stream trade credits, Industrial Engineering, 66 (2013), 1125-1130. 

[25]

K. R. Lou and W. C. Wang, Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk, The Journal of the Operational Research Society, 64 (2013), 1551-1556. 

[26]

J. R. Luo and X. Chen, Coordination of random yield supply chains with improved revenue sharing contracts, European Journal of Industrial Engineering, 10 (2016), 81-102. 

[27]

S. Mateut and P. Zanchettin, Credit sales and advance payments: Substitutes or complements?, Economics Letters, 118 (2013), 173-176. 

[28]

L. Moussawi-Haidar and M. Y. Jaber, A joint model for cash and inventory management for a retailer under delay in payments, Industrial Engineering, 66 (2013), 758-767. 

[29]

L. Y. OuyangC. H. Ho and C. H. Su, An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit, Industrial Engineering, 57 (2009), 920-930. 

[30]

H. J. PengT. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, Journal of Cleaner Production, 205 (2018), 291-302. 

[31]

H. J. Peng, T. Pang and F. L. Cao, A mutual-aid mechanism for supply chains with capital constraints, 2016, Available at SSRN: https://ssrn.com/abstract=2862629

[32]

H. J. Peng, M. H. Zhou and L. Qian, Supply Chain Coordination with Uncertainty in Two-echelon Yields, Asia-Pacific Journal of Operational Research, 30 (2013), 1250044, 13 pp. doi: 10.1142/S0217595912500443.

[33]

N. R. S. Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. 

[34]

J. T. TengC. T. Chang and M. S. Chern, Vendor-buyer inventory models with trade credit financing under both non-cooperative and integrated environments, International Journal of Systems Science, 43 (2012), 2050-2061.  doi: 10.1080/00207721.2011.564322.

[35]

A. Thangam, Optimal price discounting and lot-sizing polities for perishable items in a supply chain under advance payment scheme and two-echelon trade credits, International Journal of Production Economics, 139 (2012), 459-472. 

[36]

N. N. Yan and B. W. Sun, Comparative analysis of supply chain financing strategies between different financing modes, Journal of Industrial and Management Optimization, 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073.

[37]

N. N. YanB. W. SunH. 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. 

[38]

Q. H. ZhangD. L. ZhangY. C. Tsao and J. W. Luo, Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity, International Journal of Production Economics, 177 (2016), 34-43. 

Figure 1.  Optimal $ q_{r} $ and $ q_{s} $ vs. $ r $ $ (\zeta = 50000) $
Figure 2.  Optimal $ q_{r} $ and $ q_{s} $ vs. $ w $
Figure 3.  Optimal $ q_{r} $ and $ q_{s} $ vs. $ c $
Figure 4.  $ r_b $ and $ r_d $ vs. $ \zeta $
Figure 5.  Optimal $ \pi_{s_1} $ and $ \pi_{s_2} $ vs. $ \zeta $
Figure 6.  Bankruptcy risk u vs. $ \zeta $
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