Study of Trade Credit Strategies and Conditions in Supply Chain Based on Perfectly Competitive Suppliers

Jinjiang Yan; Hong Cheng; Xianyu Wang

doi:10.1007/978-3-642-55182-6_59

Proceedings of the Eighth International Conference on Management Science and Engineering Management pp 677-686 | Cite as

Study of Trade Credit Strategies and Conditions in Supply Chain Based on Perfectly Competitive Suppliers

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Authors and affiliations

Jinjiang Yan
Hong ChengEmail author
Xianyu Wang

Conference paper

First Online: 07 May 2014

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 280)

Abstract

Considering uncertain market demand, this paper focuses on strategies and conditions of trade credit from the perfectly competitive supplier to the retailer. With game theory and financial, the analysis shows that the retailer’s wholesale price is higher than the unit cost. But the retailer’s order quantity has not been distorted. The analysis also shows that the supplier supplies trade credit as the retailer’s will under some condition. But he will limit retailer’s order quantity under some other condition. This study explains the economic phenomena that the supplier will limit the order quantity for some retailer. Some advices about trade credit in supply chain are given to the management decision maker.

Keywords

Uncertain demand Perfectly competition Trade credit strategy Trade credit condition

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Notes

Acknowledgments

The paper is supported by the China National Natural Science Foundation (Grant No. 70571055), the National Natural Science Foundation China (Grant No.71071103) and the Central Universities Basic Research Funds Special Projects of Sichuan University (Grant No. skq201119). We thank the anonymous reviewer for their helpful comments.

Appendix

Proof

We prove conclusion 2 in this appendix.

We denote:

$$G(w) = E[\min [pq + S(Q - q), wQ-\eta ]]-(cQ-\eta )(1+\theta ).$$

The sufficient is proved at first. Because of $E(pq + S(Q-q)) \ge (cQ-\eta )(1+\theta )$, there is:

$$\begin{aligned} G(w)=&~E[\min [pq+S(Q-q), (+\infty )*Q-\eta ]]-(cQ-\eta )(1+\theta )\\ =&~E(pq+S(Q-q))-(cQ-\eta )(1+\theta )\ge 0, \end{aligned}$$

and

$$\begin{aligned} G(c)=&~E[\min [pq +S(Q-q), cQ-\eta ]]-(cQ-\eta )(1+\theta ) \\ \le&~ \min [E(pq+S(Q-q)), cQ-\eta ]-(cQ-\eta )(1+\theta )< 0. \end{aligned}$$

According to the zero point theorem, $w^*\in [c, +\infty ]$ exists and satisfies Eq. (59.3).

The necessary is proved by proving his inverse negative proposition. Its inverse negative proposition is that when $E(pq + S(Q - q))<(cQ - \eta )(1 + \theta )$ any $w^*(w^*\in [c, +\infty ])$ cannot satisfies Eq. (59.3). If there is $w^*\in [c, + \infty ]$ satisfies Eq. (59.3), there is $w^*Q-\eta =(cQ-\eta )(1+\theta )$. According to $E(pq +S(Q-q)) < (cQ - \eta )(1 + \theta )$, there is

$$w^*Q - \eta =(cQ-\eta )(1+\theta ) > E(pq+S(Q-q)).$$

So, any $w^*(w^*\in [0, +\infty ])$ can satisfies

$$G(w^*) = E(pq + S(Q - q))-(cQ-\eta )(1+\theta )< 0.$$

In a word, there is solution $w^*\in [0, +\infty ]$ satisfying Eq. (59.3) if and only if there is $E(pq + S(Q-q)) \ge (cQ-\eta )(1+\theta )$. It is what we wanted to prove.

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Authors and Affiliations

Jinjiang Yan
- 1
Hong Cheng
- 2
Email author
Xianyu Wang
- 1

1.Business SchoolSichuan UniversityChengduPeople’s Republic of China
2.College of Management ScienceChengdu University of TechnologyChengduPeople’s Republic of China

Study of Trade Credit Strategies and Conditions in Supply Chain Based on Perfectly Competitive Suppliers

Abstract

Keywords

Notes

Acknowledgments

References

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