The global shift toward carbon neutrality has intensified the focus on sustainable practices in manufacturing, particularly in the electric vehicle (EV) industry. As consumer demand for personalized products grows, designing efficient supply chain networks (SCNs) that balance sustainability and customization becomes critical. This paper addresses the optimization of a closed-loop SCN for electric vehicle parts, incorporating uncertainties in part supply and demand. We propose a robust optimization model that minimizes transportation, processing, operational, and carbon emission costs while integrating a personalized evaluation mechanism based on hypergeometric distribution. An improved wild dog optimization algorithm (IDOA) is developed to enhance solution accuracy and convergence speed. Numerical experiments and case studies demonstrate the effectiveness of our approach in optimizing China EV supply chains under carbon neutrality goals.
The electric vehicle market, especially in China, has experienced rapid growth due to government policies and environmental awareness. However, the complexity of EV parts SCNs, involving multiple stakeholders like suppliers, manufacturers, customers, and recycling centers, poses challenges in managing costs and emissions. Personalized customization adds another layer of complexity, as customers increasingly seek tailored EV components. This study focuses on designing a sustainable and personalized closed-loop SCN for China EV parts, addressing uncertainties through robust optimization. The model aims to reduce overall costs while promoting carbon reduction, aligning with global sustainability targets.
The SCN structure for electric vehicle parts includes forward and reverse logistics. In the forward flow, parts are categorized into non-personalized (N-p) and personalized (p) components, with the latter further divided into standard and green personalized parts. Suppliers transport N-p parts to non-personalized manufacturers and p parts to personalized manufacturers. The manufacturers then produce non-personalized products for general customers and personalized products (standard and advanced) for respective customer segments. Reverse logistics involve recycling centers collecting and processing reusable products from customers, which are then sent back to suppliers. A key innovation is the personalized evaluation mechanism (EM), which assesses the usage degree of standard personalized parts (BUDP) and green personalized parts (BUDG) to determine product customization levels.
To model this SCN, we define sets, parameters, and decision variables. Let \( C \) represent the set of N-p parts, \( C’ \) the set of p parts, \( T \) the set of non-personalized products, \( T’ \) the set of standard personalized products, and \( K’ \) the set of advanced personalized products. Facilities include suppliers \( E \), non-personalized manufacturers \( F \), personalized manufacturers \( G \), customers \( H, L, M \), and recycling centers \( R \). The objective function minimizes total cost \( Z \), comprising transportation cost \( Z_1 \), processing cost \( Z_2 \), operational cost \( Z_3 \), and carbon emission cost \( Z_4 \):
$$ \min Z = \min Z_1 + \min Z_2 + \min Z_3 + \min Z_4 $$
where:
$$ Z_1 = \sum_{e \in E} \sum_{f \in F} \sum_{c \in C} B_{efc} Q_{efc} X_{ec} + \sum_{f \in F} \sum_{h \in H} \sum_{t \in T} B_{fht} Q_{fht} X_{ft} + \sum_{e \in E} \sum_{g \in G} \sum_{c’ \in C’} B_{egc’} Q_{egc’} X_{ec’} + \sum_{g \in G} \sum_{l \in L} \sum_{t’ \in T’} B_{glt’} Q_{glt’} X_{gt’} + \sum_{g \in G} \sum_{m \in M} \sum_{k’ \in K’} B_{gmk’} Q_{gmk’} X_{gk’} + \sum_{h \in H} \sum_{r \in R} \sum_{s \in S} B_{hrs} Q_{hrs} X_{rs} + \sum_{l \in L} \sum_{r \in R} \sum_{s’ \in S’} B_{lrs’} Q_{lrs’} X_{rs’} + \sum_{m \in M} \sum_{r \in R} \sum_{w \in W} B_{mrw} Q_{mrw} X_{rw} + \sum_{r \in R} \sum_{e \in E} \sum_{s \in S} B_{re} Q_{res} X_{rs} + \sum_{r \in R} \sum_{e \in E} \sum_{s’ \in S’} B_{re} Q_{res’} X_{rs’} + \sum_{r \in R} \sum_{e \in E} \sum_{w \in W} B_{re} Q_{rew} X_{rw} $$
$$ Z_2 = \sum_{e \in E} \sum_{c \in C} A_{efc} D_{efc} X_{ec} + \sum_{f \in F} \sum_{h \in H} \sum_{t \in T} A_{fht} D_{fht} X_{ft} + X_{EM} \sum_{e \in E} \sum_{c’ \in C’} A_{egc’} D_{egc’} X_{ec’} + X_{EM} \sum_{g \in G} \sum_{l \in L} \sum_{t’ \in T’} A_{glt’} D_{glt’} X_{gt’} + X_{EM} \sum_{g \in G} \sum_{m \in M} \sum_{k’ \in K’} A_{gmk’} D_{gmk’} X_{gk’} + \sum_{h \in H} \sum_{r \in R} \sum_{s \in S} A_{hrs} D_{hrs} X_{rs} + \sum_{l \in L} \sum_{r \in R} \sum_{s’ \in S’} A_{lrs’} D_{lrs’} X_{rs’} + \sum_{m \in M} \sum_{r \in R} \sum_{w \in W} A_{mrw} D_{mrw} X_{rw} $$
$$ Z_3 = \sum_{e \in E} \sum_{c \in C} H_{efc} X_{ec} + \sum_{e \in E} \sum_{c’ \in C’} H_{egc’} X_{ec’} + \sum_{f \in F} \sum_{t \in T} H_{fht} X_{ft} + \sum_{g \in G} \sum_{t’ \in T’} H_{glt’} X_{gt’} + \sum_{g \in G} \sum_{k’ \in K’} H_{gmk’} X_{gk’} + \sum_{r \in R} \sum_{s \in S} H_{hrs} X_{rs} + \sum_{r \in R} \sum_{s’ \in S’} H_{lrs’} X_{rs’} + \sum_{r \in R} \sum_{w \in W} H_{mrw} X_{rw} $$
$$ Z_4 = \sum_{e \in E} \sum_{f \in F} \sum_{c \in C} O_{efc} Q_{efc} X_{ec} + \sum_{e \in E} \sum_{g \in G} \sum_{c’ \in C’} O_{egc’} Q_{egc’} X_{ec’} + \sum_{f \in F} \sum_{h \in H} \sum_{t \in T} O_{fht} Q_{fht} X_{ft} + X_{EM} \sum_{g \in G} \sum_{l \in L} \sum_{t’ \in T’} O_{glt’} Q_{glt’} X_{gt’} + X_{EM} \sum_{g \in G} \sum_{m \in M} \sum_{k’ \in K’} O_{gmk’} Q_{gmk’} X_{gk’} + \sum_{h \in H} \sum_{r \in R} \sum_{s \in S} O_{hrs} Q_{hrs} X_{rs} + \sum_{l \in L} \sum_{r \in R} \sum_{s’ \in S’} O_{lrs’} Q_{lrs’} X_{rs’} + \sum_{m \in M} \sum_{r \in R} \sum_{w \in W} O_{mrw} Q_{mrw} X_{rw} + \sum_{r \in R} \sum_{e \in E} \sum_{s \in S} O_{res} Q_{res} X_{rs} + \sum_{r \in R} \sum_{e \in E} \sum_{s’ \in S’} O_{res’} Q_{res’} X_{rs’} + \sum_{r \in R} \sum_{e \in E} \sum_{w \in W} O_{rew} Q_{rew} X_{rw} $$
The personalized evaluation mechanism is defined as \( X_{EM} = BUDP + BUDG \), where \( BUDP \) and \( BUDG \) are calculated using hypergeometric distribution. For a product, the probability of a customer selecting personalized parts is given by:
$$ f(x) = h(x, N, n, k) = \frac{ \binom{k}{x} \binom{N – x}{n – x} }{ \binom{N}{n} } $$
where \( N \) is the total number of selectable parts, \( n \) is the number of personalized parts chosen, \( k \) is the maximum number of selectable personalized parts, and \( x \) is the number of selected personalized parts. If \( N \) is large, this approximates a binomial distribution. Constraints ensure that the sum of probabilities is 1 and that the number of personalized parts does not exceed production limits.
To handle uncertainties in part supply \( S_i \) and demand \( D_n \), we employ robust optimization. The uncertain parameters are bounded within intervals: \( S_i \in [S_i – \hat{S}_i, S_i + \hat{S}_i] \) and \( D_n \in [D_n – \hat{D}_n, D_n + \hat{D}_n] \). The robust constraints are formulated as:
$$ \sum_{e \in E} \sum_{f \in F} \sum_{c \in C} Q_{efc} X_{ec} + \sum_{e \in E} \sum_{g \in G} \sum_{c’ \in C’} Q_{efc’} X_{ec’} – (S_i – z_i \Gamma_i – \sum_i \gamma_i) \leq 0 $$
$$ (D_n – z_n \Gamma_n – \sum_n \gamma_n) – \sum_{e \in E} \sum_{f \in F} \sum_{c \in C} Q_{efc} X_{ec} – \sum_{e \in E} \sum_{g \in G} \sum_{c’ \in C’} Q_{efc’} X_{ec’} \leq 0 $$
where \( \Gamma_i \) and \( \Gamma_n \) are robust control coefficients, and \( z_i, z_n, \gamma_i, \gamma_n \) are dual variables. The multi-objective problem is transformed into a single-objective using the LP metric method:
$$ \min Z^* = \omega_1 \frac{Z_1 – Z_1^*}{Z_1^*} + \omega_2 \frac{Z_2 – Z_2^*}{Z_2^*} + \omega_3 \frac{Z_3 – Z_3^*}{Z_3^*} + \omega_4 \frac{Z_4 – Z_4^*}{Z_4^*} $$
where \( Z_1^*, Z_2^*, Z_3^*, Z_4^* \) are ideal values for each objective, and \( \omega_1, \omega_2, \omega_3, \omega_4 \) are weights.
For solution, we propose an Improved Wild Dog Optimization Algorithm (IDOA). The original wild dog algorithm (DOA) simulates hunting strategies—group attack, persecution, and scavenging—but suffers from slow convergence and local optima. IDOA dynamically adjusts strategy probabilities \( P \) and \( Q \) using:
$$ P = \frac{1}{1 + e^{\lambda_1 (t – \lambda_2)}} $$
$$ Q = \lambda_3^t $$
where \( t \) is the iteration count, and \( \lambda_1, \lambda_2, \lambda_3 \) are parameters set to -0.6, 25, and 0.9, respectively. The group attack strategy is enhanced with Lévy flight to improve global search:
$$ \vec{x}_i(m+1) = \beta_1 \frac{ \sum_{k=1}^{n_a} [\vec{\phi_k(m)} – \vec{x}_i(m)] \otimes \text{Lévy} }{ n_a } – \vec{x}^*(m) $$
Initialization uses real-coded matrices representing facility-product relationships. The algorithm iterates to minimize the objective function, with survival rates based on fitness.
We validate IDOA using benchmark functions and compare it with GA, WOA, GWO, SCA, and PSO. Tests on functions like Sphere, Schwefel, and Rosenbrock show IDOA’s superior convergence and accuracy. For instance, on the Sphere function \( F_1(x) = \sum_{i=1}^n x_i^2 \), IDOA achieves an average value of \( 3.57 \times 10^{-262} \), outperforming other algorithms. Friedman tests rank IDOA first with an average rank of 1.67948.
| Function | IDOA | GA | DOA | WOA | GWO | SCA | PSO |
|---|---|---|---|---|---|---|---|
| F1 (Sphere) | 3.57e-262 | 1.47e4 | 3.43e-140 | 1.08e-108 | 1.44e-55 | 3.56e-3 | 6.68e4 |
| F2 (Schwefel) | 3.23e-139 | 4.50e1 | 3.98e-85 | 2.78e-108 | 4.72e-33 | 6.30e-6 | 1.45e12 |
| F3 (Rosenbrock) | 6.19e-257 | 4.99e4 | 2.06e-112 | 2.58e4 | 1.18e-13 | 3.09e3 | 1.43e5 |
| F4 (Step) | 3.71e-132 | 7.23e1 | 1.11e-90 | 3.40e1 | 1.82e-14 | 1.28e1 | 8.66e1 |
For the electric vehicle parts SCN, we define personalized part evaluation scales. Let \( N \) be the total selectable parts, with scales 1 (N=10), 2 (N=20), and 3 (N=30). BUDP and BUDG values are derived from hypergeometric distribution, as shown in Tables 2 and 3.
| Scale | N | n | u | k | x (Number of Selected Parts) | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | |||||
| 1 | 10 | 5 | 0.1 | 1 | 0.500 | – | – | – | – | – |
| 1 | 10 | 5 | 0.2 | 2 | 0.550 | 0.220 | – | – | – | – |
| 2 | 20 | 10 | 0.1 | 2 | 0.387 | 0.193 | – | – | – | – |
| 2 | 20 | 10 | 0.2 | 4 | 0.268 | 0.301 | 0.201 | 0.088 | – | – |
| 3 | 30 | 15 | 0.1 | 3 | 0.343 | 0.266 | 0.128 | – | – | – |
| 3 | 30 | 15 | 0.2 | 6 | 0.131 | 0.230 | 0.250 | 0.187 | 0.103 | 0.025 |
| Scale | N | n | u | k | x (Number of Selected Parts) | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | |||||
| 1 | 10 | 5 | 0.2 | 2 | 0.550 | 0.220 | – | – | – | – |
| 2 | 20 | 10 | 0.2 | 4 | 0.268 | 0.301 | 0.201 | 0.088 | – | – |
| 3 | 30 | 15 | 0.2 | 6 | 0.131 | 0.230 | 0.250 | 0.187 | 0.103 | 0.025 |
We analyze two scenarios for China EV parts: Scenario 1 where both BUDP and BUDG are below 50%, and Scenario 2 where BUDP exceeds 50% but BUDG is below 50%. XEM values determine product customization levels, with XEM < 0.5 indicating standard personalized products and XEM ≥ 0.5 indicating advanced personalized products. For example, in Scale 1, if BUDP(1) + BUDG(1) = 1.05, it classifies as advanced. The robust model reduces total costs by 34.37% compared to deterministic models under uncertain demand.
Sensitivity analysis examines the impact of robust control coefficient Γ and disturbance level ω on costs. As Γ increases from 0 to 38, costs rise, reflecting higher robustness at the expense of economic efficiency. Similarly, larger ω values (2%, 5%, 10%, 20%) increase costs. Decision-makers can balance robustness and cost by tuning Γ, especially for large-scale China EV supply chains.
We solve the multi-objective problem using IDOA and compare it with GA, DOA, and WOA. For a small-scale SCN (e.g., 3 suppliers, 5 manufacturers), IDOA achieves a total cost of $16,013.40, outperforming others. As scale increases, IDOA’s advantage grows, with large-scale networks (10 suppliers, 14 manufacturers) showing costs of $16,228.55. Convergence curves demonstrate IDOA’s faster and more accurate optimization.
| Scale | XEM | Z1 ($) | Z2 ($) | Z3 ($) | Z4 ($) | Z ($) |
|---|---|---|---|---|---|---|
| 1 | 1.050 | 4,152.76 | 7,222.36 | 4,252.84 | 524.32 | 16,152.28 |
| 1 | 0.220 | 4,249.23 | 5,448.62 | 3,822.54 | 555.76 | 14,076.15 |
| 2 | 0.655 | 4,113.86 | 6,825.59 | 4,187.06 | 529.78 | 15,656.29 |
| 3 | 0.500 | 4,256.13 | 6,509.76 | 4,212.32 | 543.01 | 15,521.22 |
In conclusion, this study presents a robust optimization model for sustainable and personalized electric vehicle parts supply chains, leveraging an improved wild dog algorithm. The personalized evaluation mechanism effectively classifies products, while robust handling of uncertainties ensures cost-effective and environmentally friendly operations. For the China EV market, our approach supports carbon neutrality goals by minimizing emissions and enhancing customization. Future work could incorporate additional environmental factors and dynamic disruptions to further refine SCN design for electric vehicles.