政府奖惩下考虑回收率动态随机的闭环供应链微分博弈

doi:10.16381/j.cnki.issn1003-207x.2021.1138

Abstract

Abstract:

The dynamic equilibrium strategy of the members in a closed-loop supply chain （CLSC）dominated by retailers and recycled by manufacturers is studied under reward-penalty mechanism （RPM）.The random evolution process of the recovery rate is described by using the ITO process.Based on the dynamics model of recycling， three Stackelberg stochastic differential game models of CLSC are established： the government does not impose RPM， the government imposes RPM on the manufacturer as well as the government imposes RPM on both the manufacturer and the retailer.By using stochastic differential game theory， the partial differential equations which the optimal profit function should be satisfied are given.Furthermore， the optimal profit function and equilibrium strategy value of members of CLSC are obtained and compared. In order to further study the effect of RPM on equilibrium strategy and to reveal the stochastic evolution nature of recovery of Waste Electrical and Electronic Equipment（WEEE）. By numerical example， the steady-state analysis and unsteady-state analysis of closed-loop supply chain system are carried out. The results show that the RPMcan encourage manufacturers to make more recycling efforts and thus increase the recycling rate，but it can not mitigate the double marginal effects. Compared with the retailers sharing the responsibility of recycling， the RPM imposed on the manufacturer is more beneficial to the CLSC， which can bring about both economic and environmental benefits.

Key words: closed-loop supply chain, dynamic recovery rate, reward-penalty mechanism, differential game, Ito process

CLC Number:

F270

Daoping Wang,Ke Zhang,Yu Zhou. Differential Game of Closed-Loop Supply Chain with Dynamic Stochastic Recovery Rate under Reward-penalty Mechanism of Government[J]. Chinese Journal of Management Science, 2024, 32(5): 158-170.

Figures/Tables 9

符号	含义
wⁱ (t)	模式i下制造商在t时刻批发给零售商的批发价格，为制造商的决策变量
pⁱ (t)	模式i下零售商在t时刻售卖给消费者的零售价格，为零售商的决策变量
c_n	制造商制造新品的单位生产成本
Δ	废弃电器电子产品再制造所带来的利润残值
Aⁱ (t)	模式i下制造商t时刻的回收努力投入水平，为制造商的决策变量
τⁱ (t)	模式i下废弃电器电子产品的回收率（0<τ<1）
ρ	回收投入系数（ρ>0）
σ	回收率衰减系数（σ>0）
δ(τⁱ (t))	回收率的波动率
dz(t)	标准维纳过程
k	制造商回收废弃电器电子产品的难度系数（k>0）
τ₀	政府对闭环供应链成员设置的目标回收率
b	政府对闭环供应链成员设置的奖惩力度（b>0）
a	市场的潜在需求（a>0）
β	需求对零售价格的敏感系数（0<β<1）
η	需求对回收率的敏感系数（0<η<1）
μ	零售商承担的回收责任分担比例（0<μ<1）
$π M t$	制造商在t时刻的利润
$π R t$	零售商在t时刻的利润
$V M i$	模式i下制造商最优利润函数
$V R i$	模式i下零售商最优利润函数
r	市场利率（由市场上供求关系决定的信贷实际利率）

模式	b	制造商利润 $V M$	零售商利润 $V R$
N	任意值	$0.05 (τ N) 2 + 0.10 τ N + 0.60$ =0.61	$0.12 (τ N) 2 + 0.22 τ N + 1.50$ =1.53
M	0.0	$0.05 (τ M) 2 + 0.10 τ M + 0.60$ =0.61	$0.12 (τ M) 2 + 0.22 τ M + 1.50$ =1.53
	0.1	$0.05 (τ M) 2 + 0.20 τ M + 0.34 ?$ =0.38	$0.12 (τ M) 2 + 0.25 τ M + 2.13$ =2.19
	0.2	$0.05 (τ M) 2 + 0.31 τ M + 0.30$ =0.41	$0.12 (τ M) 2 + 0.27 τ M + 2.87$ =2.98
	0.3	$0.05 (τ M) 2 + 0.42 τ M + 0.48$ =0.69	$0.12 (τ M) 2 + 0.30 τ M + 3.72 ? = 3.89$
	0.4	$0.05 (τ M) 2 + 0.52 τ M + 0.89$ =1.21	$0.12 (τ M) 2 + 0.33 τ M + 4.68 ?$ =4.92
	0.5	$0.05 (τ M) 2 + 0.63 τ M + 1.53$ =1.79	$0.12 (τ M) 2 + 0.35 τ M + 5.75 ?$ =5.91
C	0.0	$0.05 (τ C) 2 + 0.10 τ C + 0.60$ =0.61	$0.12 (τ C) 2 + 0.22 τ C + 1.50$ =1.53
	0.1	$0.05 (τ C) 2 + 0.16 τ C + 0.12$ =0.15	$0.12 (τ C) 2 + 0.28 τ C + 1.77$ =1.82
	0.2	$0.05 (τ C) 2 + 0.23 τ C + 0.19$ =0.25	$0.12 (τ C) 2 + 0.34 τ C + 2.18$ =2.27
	0.3	$0.05 (τ C) 2 + 0.29 τ C + 0.34$ =0.44	$0.12 (τ C) 2 + 0.40 τ C + 2.74$ =2.88
	0.4	$0.05 (τ C) 2 + 0.35 τ C + 0.57$ =0.72	$0.12 (τ C) 2 + 0.45 τ C + 3.45$ =3.65
	0.5	$0.05 (τ C) 2 + 0.42 τ C + 0.88$ =1.06	$0.12 (τ C) 2 + 0.51 τ C + 4.31$ =4.53

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模式	b	τ_∞	w_∞	p_∞	A_∞	p_∞-w_∞
N	任意值	0.11	0.6277	0.95	0.11	0.32
M	0.0	0.11	0.6277	0.95	0.11	0.32
	0.1	0.23	0.6307	1.03	0.23	0.40
	0.2	0.35	0.6337	1.11	0.35	0.48
	0.3	0.47	0.6366	1.19	0.47	0.55
	0.4	0.59	0.6396	1.27	0.59	0.63
	0.5	0.71	0.6426	1.35	0.71	0.71
C	0.0	0.11	0.6277	0.95	0.11	0.32
	0.1	0.18	0.6277	0.10	0.18	0.37
	0.2	0.25	0.6295	1.05	0.25	0.41
	0.3	0.32	0.6331	1.09	0.32	0.46
	0.4	0.40	0.6349	1.14	0.40	0.51
	0.5	0.47	0.6367	1.19	0.47	0.55

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Differential Game of Closed-Loop Supply Chain with Dynamic Stochastic Recovery Rate under Reward-penalty Mechanism of Government

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