# American Institute of Mathematical Sciences

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  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 & Management Optimization, 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. Google Scholar [2] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. Google Scholar [3] G. S. Cai, X. 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. Google Scholar [4] F. Caro, K. Rajaram and J. Wollenweber, Process location and product distribution with uncertain yields, Operations Research, 60 (2012), 1050-1063. doi: 10.1287/opre.1120.1087. Google Scholar [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. Google Scholar [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. Google Scholar [7] X. F. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357. Google Scholar [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. Google Scholar [9] M. S. Chern, Q. H. Pan, J. T. Teng, Y. 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. Google Scholar [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. Google Scholar [11] A. Federgruen and N. Yang, Competition under generalized attraction models: Applications to quality competition under yield uncertainty, Management Science, 55 (2009), 2028-2043.Google Scholar [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. Google Scholar [13] F. Hu, C. 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. Google Scholar [14] C. K. Huang, D. M. Tsai, J. 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. Google Scholar [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. Google Scholar [16] B. Jing, X. F. Chen and G. S. Cai, Equilibrium Financing in a Distribution Channel with Capital Constraint, Production and Operations Management, 21 (2012), 1090-1101. Google Scholar [17] B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. Google Scholar [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. Google Scholar [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. Google Scholar [20] P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. Google Scholar [21] G. M. Lai, L. 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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [27] S. Mateut and P. Zanchettin, Credit sales and advance payments: Substitutes or complements?, Economics Letters, 118 (2013), 173-176. Google Scholar [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. Google Scholar [29] L. Y. Ouyang, C. 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. Google Scholar [30] H. J. Peng, T. 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. Google Scholar [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=2862629Google Scholar [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. Google Scholar [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. Google Scholar [34] J. T. Teng, C. 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. Google Scholar [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. Google Scholar [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. Google Scholar [37] N. N. Yan, B. W. Sun, H. 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. Google Scholar [38] Q. H. Zhang, D. L. Zhang, Y. 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. Google Scholar

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. Google Scholar [2] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. Google Scholar [3] G. S. Cai, X. 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. Google Scholar [4] F. Caro, K. Rajaram and J. Wollenweber, Process location and product distribution with uncertain yields, Operations Research, 60 (2012), 1050-1063. doi: 10.1287/opre.1120.1087. Google Scholar [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. Google Scholar [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. Google Scholar [7] X. F. Chen, A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, 159 (2015), 347-357. Google Scholar [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. Google Scholar [9] M. S. Chern, Q. H. Pan, J. T. Teng, Y. 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. Google Scholar [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. Google Scholar [11] A. Federgruen and N. Yang, Competition under generalized attraction models: Applications to quality competition under yield uncertainty, Management Science, 55 (2009), 2028-2043.Google Scholar [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. Google Scholar [13] F. Hu, C. 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. Google Scholar [14] C. K. Huang, D. M. Tsai, J. 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. Google Scholar [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. Google Scholar [16] B. Jing, X. F. Chen and G. S. Cai, Equilibrium Financing in a Distribution Channel with Capital Constraint, Production and Operations Management, 21 (2012), 1090-1101. Google Scholar [17] B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. Google Scholar [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. Google Scholar [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. Google Scholar [20] P. Kouvelis and W. H. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2016), 2341-2357. Google Scholar [21] G. M. Lai, L. 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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [27] S. Mateut and P. Zanchettin, Credit sales and advance payments: Substitutes or complements?, Economics Letters, 118 (2013), 173-176. Google Scholar [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. Google Scholar [29] L. Y. Ouyang, C. 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. Google Scholar [30] H. J. Peng, T. 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. Google Scholar [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=2862629Google Scholar [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. Google Scholar [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. Google Scholar [34] J. T. Teng, C. 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. Google Scholar [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. Google Scholar [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. Google Scholar [37] N. N. Yan, B. W. Sun, H. 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. Google Scholar [38] Q. H. Zhang, D. L. Zhang, Y. 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. Google Scholar
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