# 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:

show all references

##### References:
Optimal $q_{r}$ and $q_{s}$ vs. $r$ $(\zeta = 50000)$
Optimal $q_{r}$ and $q_{s}$ vs. $w$
Optimal $q_{r}$ and $q_{s}$ vs. $c$
$r_b$ and $r_d$ vs. $\zeta$
Optimal $\pi_{s_1}$ and $\pi_{s_2}$ vs. $\zeta$
Bankruptcy risk u vs. $\zeta$
 [1] Gang Xie, Wuyi Yue, Shouyang Wang. Optimal selection of cleaner products in a green supply chain with risk aversion. Journal of Industrial & Management Optimization, 2015, 11 (2) : 515-528. doi: 10.3934/jimo.2015.11.515 [2] Sanjoy Kumar Paul, Ruhul Sarker, Daryl Essam. Managing risk and disruption in production-inventory and supply chain systems: A review. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1009-1029. doi: 10.3934/jimo.2016.12.1009 [3] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effect of disruption risk on a supply chain with price-dependent demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019095 [4] Qiang Lin, Ying Peng, Ying Hu. Supplier financing service decisions for a capital-constrained supply chain: Trade credit vs. combined credit financing. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2019026 [5] Nina Yan, Tingting Tong, Hongyan Dai. Capital-constrained supply chain with multiple decision attributes: Decision optimization and coordination analysis. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1831-1856. doi: 10.3934/jimo.2018125 [6] Honglin Yang, Qiang Yan, Hong Wan, Wenyan Zhuo. Bargaining equilibrium in a two-echelon supply chain with a capital-constrained retailer. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019077 [7] K. F. Cedric Yiu, S. Y. Wang, K. L. Mak. Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains. Journal of Industrial & Management Optimization, 2008, 4 (1) : 81-94. doi: 10.3934/jimo.2008.4.81 [8] Prasenjit Pramanik, Sarama Malik Das, Manas Kumar Maiti. Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1289-1315. doi: 10.3934/jimo.2018096 [9] Qingguo Bai, Fanwen Meng. Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-23. doi: 10.3934/jimo.2019037 [10] Shiva Moslemi, Abolfazl Mirzazadeh. Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty. Numerical Algebra, Control & Optimization, 2017, 7 (4) : 379-401. doi: 10.3934/naco.2017024 [11] Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074 [12] Linyi Qian, Lyu Chen, Zhuo Jin, Rongming Wang. Optimal liability ratio and dividend payment strategies under catastrophic risk. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1443-1461. doi: 10.3934/jimo.2018015 [13] Srdjan Stojanovic. Interest rates risk-premium and shape of the yield curve. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1603-1615. doi: 10.3934/dcdsb.2016013 [14] Jesús Fabián López Pérez, Tahir Ekin, Jesus A. Jimenez, Francis A. Méndez Mediavilla. Risk-balanced territory design optimization for a Micro finance institution. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2018176 [15] Jingzhen Liu, Lihua Bai, Ka-Fai Cedric Yiu. Optimal investment with a value-at-risk constraint. Journal of Industrial & Management Optimization, 2012, 8 (3) : 531-547. doi: 10.3934/jimo.2012.8.531 [16] Jun Wu, Shouyang Wang, Wuyi Yue. Supply contract model with service level constraint. Journal of Industrial & Management Optimization, 2005, 1 (3) : 275-287. doi: 10.3934/jimo.2005.1.275 [17] Kegui Chen, Xinyu Wang, Min Huang, Wai-Ki Ching. Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1397-1422. doi: 10.3934/jimo.2018013 [18] Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130 [19] Linyi Qian, Wei Wang, Rongming Wang. Risk-minimizing portfolio selection for insurance payment processes under a Markov-modulated model. Journal of Industrial & Management Optimization, 2013, 9 (2) : 411-429. doi: 10.3934/jimo.2013.9.411 [20] Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169

2018 Impact Factor: 1.025

## Tools

Article outline

Figures and Tables