Optimal credit periods under two-level trade credit

Honglin Yang; Heping Dai; Hong Wan; Lingling Chu

doi:10.3934/jimo.2019027

Article Contents

2020, Volume 16, Issue 4: 1753-1767. Doi: 10.3934/jimo.2019027

This issue Previous Article Supplier financing service decisions for a capital-constrained supply chain: Trade credit vs. combined credit financing Next Article Optimal inventory policy for fast-moving consumer goods under e-commerce environment

Optimal credit periods under two-level trade credit

1.
School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China
2.
School of Business, State University of New York at Oswego, Oswego, NY 13126, USA

^* Corresponding author: ottoyang@126.com(HonglinYang)
^* Corresponding author: ottoyang@126.com(HonglinYang)

Received: December 31, 2017

Revised: August 31, 2018

Early access: May 2019

Published: May 2020

This work was supported by the National Natural Science Foundation of China under Grant Nos. 71571065, 71790593 and 71521061

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Abstract

In a two-echelon single-supplier and single-retailer supply chain with permissible delay in payment, we investigate the two-level trade credit policy in which the supplier offers the retailer with limited capital a credit period and in turn the retailer also provides a credit period to customers. The demand rate is sensitive to both retail price and the customerso credit period. By using the backward induction method, we analytically derive the unique equilibrium of both credit periods in the Stackelberg game to determine the retaileros pricing strategy. We find that the optimal retail price is not always decreasing in the credit period offered by the supplier to the retailer. In addition, we characterize the conditions under which the retailer is willing to voluntarily provide customers a credit period. Numerical examples and sensitivity analysis of key parameters are presented to illustrate the theoretical results and managerial insights.

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

Citation:

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Figure 1. The case of two-level trade credit

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Figure 2. $ T+N\leq M $

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Figure 3. $ M<T+N $

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Figure 4. $ M, N $ and $ p $ in case 1

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Figure 5. $ N, D $ and $ TPR $ in case 1

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Figure 6. $ M, TPR $ and $ TPS $ in case 1

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Figure 7. M, N and p in case 1

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Figure 8. N, D and TPR in case 2

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Figure 9. M, TPR and TPS in case 2

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Figure 10. M, N and p in case 3

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Figure 11. N, D and TPR in case 2

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Figure 12. The case of two-level trade credit

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Table 1. The comparisons of three models with permissible delay in payment

Trade credit policy	Demand	Decision variable	Optimal delay period
one-level	price-and-time	$ M $	obtain the analytic solution of
(Yangos et al., 2017)	dependent		optimal $ M $
two-level	price-and-credit	constant	give a solution algorithm
(Shahos et al., 2015)	dependent		of optimal
two-level	price-and-credit	$ M,N $	obtain the analytic solutions
(our paper)	dependent		of optimal $ M $ and $ N $
Note:M represents the credit period offered by the supplier to the retailer, and N represents the credit period provided by the retailer to customers.

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Table 2. Notations and explanations

Notation	Definition
$ w $	wholesale price per unit.
$ p $	retail price per unit (decision variable).
$ M $	credit period offered by the supplier (decision variable).
$ N $	credit period provided by the retailer (decision variable)
$ T $	ordering cycle.
$ D(p,N) $	customers$ ' $ annual demand rate depending on $ p $ and $ N $.
$ I_c $	retailer$ ' $s interest charged per dollar per year.
$ I_e $	retailer$ ' $s interest earned per dollar per year.
$ c $	supplier$ ' $s procurement cost per unit.
$ h $	retailer$ ' $s holding cost per unit.
$ A $	ordering cost per order.
$ TPS $	supplier$ ' $s annual total profit.
$ TPR $	retailer$ ' $s annual total profit.

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Table 3. Sensitivity analysis with respect to γ

Parameter	Value	$ M^* $	$ N^* $	$ p^* $	$ \pi_r^* $	$ \pi_s^* $
$ \gamma $	4500	0.5938	0.0000	2185.6	2295832	4595664
	5000	0.5938	0.0000	2185.6	2295832	4595664
	5500	0.5938	0.0000	2185.6	2295832	4595664
	6000	0.5938	0.0000	2185.6	2295832	4595664
	6500	0.7252	0.3502	2221.8	2500038	4619147
	7000	0.8333	0.5833	2248.3	2720222	4666667
	7500	0.9229	0.7979	2276.4	2957288	4734861
	8000	0.9974	0.9974	2306.0	3212169	4821253
	8500	1.0613	1.0613	2316.5	3481700	4918165
	9000	1.1181	1.1181	2326.9	3762082	5018776

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Table 4. Sensitivity analysis with respect to I_e and I_c

Parameter	Value	$ M^* $	$ N^* $	$ p^* $	$ \pi_r^* $	$ \pi_s^* $
$ I_e $	0.050	1.2530	1.0863	2289.8	3437846	4914066
	0.055	1.0245	0.8245	2269.0	3035272	4772856
	0.060	0.8333	0.5833	2248.3	2720222	4666667
	0.065	0.6701	0.3368	2224.8	2469392	4589728
	0.070	0.5268	0.0000	2186.9	2269113	4542227
$ I_c $	0.07	0.8244	0.8244	2281.5	2734825	4691700
	0.075	0.8304	0.6637	2259.4	2725086	4675004
	0.080	0.8333	0.5833	2248.3	2720222	4666667
	0.085	0.8351	0.5351	2241.7	2717306	4661668
	0.090	0.8363	0.5030	2237.3	2715363	4658337

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