Research on impact of dual credit policy on service mode in new energy vehicle supply chain

Di Wu; Yating Song; Peng Li

doi:10.3934/jimo.2025023

Article Contents

2025, Volume 21, Issue 5: 3580-3599. Doi: 10.3934/jimo.2025023

This issue Previous Article Nonconvex regularizer and homotopy-based sparse optimization: Convergent algorithms and applications Next Article A grey wolf optimizer for estimating the stochastic SIRD and optimizing a regime-switching cash flow model

Research on impact of dual credit policy on service mode in new energy vehicle supply chain

School of economics and management, Xi'an University of Technology, Xi'an 710048, China

^*Corresponding author: Peng Li
^*Corresponding author: Peng Li

Received: April 2024

Revised: January 2025

Early access: February 2025

Published: May 2025

The first author is supported by the National Science Basic Research Plan in Shaanxi Province of China under Grant No. 2024JC-YBQN-0759, Project of Shaanxi Social Science Foundation under Grant No.2023D017, Project of Humanities and Social Sciences of the Ministry of Education of China under Grant No. 24YJC630109.

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Abstract

Under the dual credit policy, the new energy vehicle industry is faced with the multi-decision collaborative optimization problem of service level, R&D level and pricing under different service modes. This paper aims at the supply chain structure composed of a new energy vehicle manufacturer and a battery manufacturer, and respectively constructs decision models under three service modes: the new energy vehicle manufacturer providing service, the battery manufacturer providing service, and jointly providing service. On the basis of solving the model by using Stackelberg game theory, numerical analysis is used to put forward management suggestions. The results show that under the joint providing service mode, both enterprises can obtain the highest profit, followed by the mode of the new energy manufacturer providing service, while the profits of both enterprises are the lowest under the mode of the battery manufacturer providing service. The government departments should actively increase the credit price under the policy.

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Mathematics Subject Classification: 91A80.

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Figure 1. Supply chain structure studied in this paper

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Figure 2. Effects of $ p_{0} $ on decisions under M1 mode

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Figure 3. Effects of $ p_{0} $ on decisions under M2 mode

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Figure 4. Effects of $ p_{0} $ on decisions under M3 mode

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Figure 5. Effects of $ p_{0} $ on $ \pi_{1} $

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Figure 6. Effects of $ p_{0} $ on $ \pi_{0} $

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Table 1. Notations used in the models

Notation	Explanation	Notation	Explanation
$ w $	battery price	$ s_1 $	service level of the new energy vehicle manufacturer
$ p_1 $	new energy vehicle price	$ s_2 $	service level of the battery manufacturer
$ p_0 $	credit price	$ \pi_0 $	profit of the battery manufacturer profit of the new energy vehicle manufacturer
$ e $	R&D level	$ \pi_1 $	mensitivity factor of R&D level impacting new energy credits
$ i $	sensitivity factor of new energy vehicle price impacting sales	$ k $	sensitivity factor of service level impacting new energy vehicle sales

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Table 2. Optimal decisions and profits under different service modes

	The new energy vehicle manufacturer providing service	The battery manufacturer providing service	Two enterprises jointly providing service
$ p_{1} $	$ \frac{\left[\begin{array}{l}k^2 u\left(h i w \beta p_0+w i^2 \beta^2 p_0^2-2 v-6 i v w\right)\\+2 u^2 i\left(4 v+h^2 w+4 i v w-w i^2 \beta^2 p_0^2\right)+k^4 v w\end{array}\right]}{v\left(k^2-4 i u\right)^2} $	$ \frac{\left[k^2 v w+u\left(4 v+h^2 w+4 i v w-w i^2 \beta^2 p_0^2\right)\right]}{8 i v u} $	$ \frac{\left[\begin{array}{l}k^2 u\left(h i w \beta p_0+w i^2 \beta^2 p_0^2-2 v-8 i v w\right)+\\2 i u^2\left(4 v+h^2 w+4 i v w-w i^2 \beta^2 p_0^2\right)+2 k^4 v w\end{array}\right]}{v\left(k^2-4 i u\right)^2} $
$ e $	$ -i w u\left(h+i \beta p_{0}\right) / v\left(k^{2}-4 i u\right) $	$ w\left(h+i \beta p_{0}\right) / 4 v $	$ -i w u\left(h+i \beta p_{0}\right) / v\left(k^{2}-4 i u\right) $
$ s_{1} $	$ \frac{\left[\begin{array}{l}k^3 v(i w-1)+i k u(4 v-4 i v w)\\+i k u\left(2 h i w \beta p_0+w i^2 \beta^2 p_0^2+h^2 w\right)\end{array}\right]}{v\left(k^2-4 i u\right)^2} $	/	$ \frac{\left[\begin{array}{l}2 i k u^2\left(4 v+h^2 w-4 i v w\right)-2 k^3 v u\\+2 i k u^2\left(2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)+k^5 v w\end{array}\right]}{2 v u\left(k^2-4 i u\right)^2} $
$ s_{2} $	/	$ k w / 4 u $	$ -k w\left(k^{2}-2 i u\right) / 2 u\left(k^{2}-4 i u\right) $
$ p_{1} $}	$ -\frac{u\left[\begin{array}{l}k^2 v(1-i w)+i u\left(4 v+h^2 w-4 i v w\right)\\+i u\left(2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)\end{array}\right]^2}{v^2\left(k^2-4 i u\right)^3} $	$ \frac{\left[k^2 v w+u\left(4 v+h^2 w-4 i v w+2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)\right]^2}{64 i v^2 u^2} $	$ -\frac{\left[\begin{array}{l}2 i u^2\left(4 v+h^2 w-4 i v w\right)+k^4 v w\\+2 i u^2\left(2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)-2 k^2 v u\end{array}\right]}{4 v^2 u\left(k^2-4 i u\right)^3} $
$ \pi_{0} $	$ \frac{i w u\left[\begin{array}{l}2 k^2 v(i w-1)+i u(8 v-8 i v w)\\+i u\left(2 h i w \beta p_0+w i^2 \beta^2 p_0^2+h^2 w\right)\end{array}\right]^2}{v\left(k^2-4 i u\right)^2} $	$ \frac{w\left[k^2 v w+u\left(8 v+h^2 w-8 i v w+2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)\right]^2}{16 v u} $	$ \frac{w\left[\begin{array}{l}4 i v k^2 u^2(3 i w-2)+k^6 v w-4 i k^4 v w u\\+4 i^2 u^3\left(8 v+h^2 w-8 i v w+2 h i w \beta p_0+w i^2 \beta^2 p_0^2\right)\end{array}\right]^2}{4 v u\left(k^2-4 i u\right)^2} $

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Table 3. Effects of $ {p}_{{0}} $ on decisions and profits under M1 mode

$ p_{0} $	$ p_{1}^{*} $	$ e^{*} $	$ s_{1}^{*} $	$ \pi_{1}^{*} $	$ \pi_{0}^{*} $
0.05	1.1285	0.1006	0.5866	0.3854	0.3249
0.10	1.1647	0.1097	0.6167	0.4259	0.3345
0.15	1.2032	0.1189	0.6493	0.4722	0.3449
0.20	1.2441	0.1280	0.6846	0.5249	0.3562
0.25	1.2874	0.1371	0.7224	0.5846	0.3683
0.30	1.3329	0.1463	0.7629	0.6519	0.3813
0.35	1.3809	0.1554	0.8060	0.7276	0.3951

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Table 4. Effects of $ {p}_{0} $ on decisions and profits under M2 mode

$ p_{0} $	$ p_{1}^{*} $	$ e^{*} $	$ s_{2}^{*} $	$ \pi_{1}^{*} $	$ \pi_{0}^{*} $
0.05	0.4380	0.0220	0.0625	0.1154	0.0780
0.10	0.4377	0.0240	0.0625	0.1176	0.0785
0.15	0.4372	0.0260	0.0625	0.1201	0.0790
0.20	0.4365	0.0280	0.0625	0.1227	0.0795
0.25	0.4356	0.0300	0.0625	0.1256	0.0801
0.30	0.4345	0.0320	0.0625	0.1288	0.0807
0.35	0.4332	0.0340	0.0625	0.1321	0.0814

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Table 5. Effects of $ {p}_{0} $ on decisions and profits under M3 mode

$ p_{0} $	$ p_{1}^{*} $	$ e^{*} $	$ s_{1}^{*} $	$ s_{2}^{*} $	$ \pi_{1}^{*} $	$ \pi_{0}^{*} $
0.05	2.0469	0.1006	1.1606	0.1607	1.5086	0.4282
0.10	2.0831	0.1097	1.1906	0.1607	1.5877	0.4378
0.15	2.1216	0.1189	1.2233	0.1607	1.6760	0.4482
0.20	2.1625	0.1280	1.2586	0.1607	1.7740	0.4595
0.25	2.2057	0.1371	1.2964	0.1607	1.8824	0.4716
0.30	2.2513	0.1463	1.3369	0.1607	2.0018	0.4846
0.35	2.2992	0.1554	1.3800	0.1607	2.1330	0.4984

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