Financing strategies for a capital-constrained supplier under yield uncertainty

Hongjun Peng; Tao Pang

doi:10.3934/jimo.2018183

Article Contents

2020, Volume 16, Issue 2: 887-909. Doi: 10.3934/jimo.2018183

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$ _1 $

-eigenvalues of generalized Hilbert tensors

Financing strategies for a capital-constrained supplier under yield uncertainty

Hongjun Peng^1, and
Tao Pang^2, ,

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

Received: February 28, 2018

Revised: August 31, 2018

Early access: December 2018

Published: February 2020

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

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 90B50, 91A80; Secondary: 90B30, 91A35, 91B06.

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Figure 1. Optimal $ q_{r} $ and $ q_{s} $ vs. $ r $ $ (\zeta = 50000) $

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Figure 2. Optimal $ q_{r} $ and $ q_{s} $ vs. $ w $

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Figure 3. Optimal $ q_{r} $ and $ q_{s} $ vs. $ c $

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Figure 4. $ r_b $ and $ r_d $ vs. $ \zeta $

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Figure 5. Optimal $ \pi_{s_1} $ and $ \pi_{s_2} $ vs. $ \zeta $

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Figure 6. Bankruptcy risk u vs. $ \zeta $

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