Low carbon joint strategy and coordination for a dyadic supply chain with Nash bargaining fairness

Jianxin Chen; Lin Sun; Tonghua Zhang; Rui Hou

doi:10.3934/jimo.2021229

Article Contents

2023, Volume 19, Issue 2: 1282-1309. Doi: 10.3934/jimo.2021229

This issue Previous Article Optimal portfolios for the DC pension fund with mispricing under the HARA utility framework Next Article A SMOTE-based quadratic surface support vector machine for imbalanced classification with mislabeled information

Low carbon joint strategy and coordination for a dyadic supply chain with Nash bargaining fairness

1.
School of Management, Guangdong University of Technology, 510520, Guangzhou, China
2.
Faculty of Applied Mathematics, Guangdong University of Technology, 510520, Guangzhou, China
3.
Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

^*Corresponding author: Rui Hou
^*Corresponding author: Rui Hou

Received: November 30, 2020

Revised: September 30, 2021

Early access: January 2022

Published: February 2023

The first author is supported by the Chinese National Funding of Social Science grant 19BGL094

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Abstract

In the paper, fairness concern criterion is utilized to explore the coordination of a dyadic supply chain with a fairness-concerned retailer (acting as a newsvendor), who is committed to low carbon efforts. Two models are developed for stochastic demand disturbances in the forms of multiplicative case and additive case, respectively. Firstly, the optimal joint decision of the retailer and the supply chain are proposed in two scenarios, i.e., decentralized decision and the centralized decision. Secondly, in order to realize channel coordination, the contract of revenue sharing combined with the mechanism of low-carbon cost sharing is designed. Moreover, the influences of the retailer's fairness concern and bargaining power on the joint decision and the contract parameters are also investigated. Finally, numerical examples are given to illustrate the theoretical results and some suggestions to supply chain management are also provided. The results show that the revenue sharing contract can make the supply chain achieved coordination with the cost sharing mechanism of low-carbon efforts. Furthermore, the optimal low-carbon effort level and ordering quantity decrease in terms of fairness-concerned parameter and Nash bargaining power parameter, which increases in unit cost. However, the optimal pricing makes the opposite change.

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Mathematics Subject Classification: Primary: 91B25, 91A12, 91A40; Secondary: 90B60, 90B30, 90B05.

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Figure 1. Relations between the retailer's expected utility and $ \lambda, \gamma, w $ and $ c $ in LCAD model

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Figure 2. Relations between the retailer's expected utility and $ \lambda, \gamma, w $ and $ c $ in LCMD model

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Figure 3. Relationship between objective and key parameters

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Figure 4. Relations between $ U(\pi^{r}_{\phi\varphi}) $, $ \pi^c $ and the retail price $ p $, respectively

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Table 1. Notations

$ d(e, p, \xi) $	Stochastic demand	$ \xi $	Stochastic price-independent component
$ y(p) $	Deterministic demand	$ q_i $	Optimal ordering quantity
$ p_{i} $	Retail price	$ e_i $	Low-carbon effort level
$ w $	Wholesale price	$ c $	Unit cost
$ s $	Salvage value	$ \lambda $	Fairness-concerned parameter of the retailer
$ \gamma $	Retailer's bargaining power	$ \pi_i^r $	Retailer's profit
$ \pi_i^s $	Supplier's profit	$ E(\pi_i^r) $	Expected profit of retailer
$ E(\pi_i^s) $	Supplier's expected profit	$ U(\pi_i^r) $	Utility function of retailer
$ p_i^* $	Optimal ordering	$ i=M,A $	Multiplicative or additive demand

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Table 2. Influence of the important parameter on joint decision ($ \nearrow $ and $ \searrow $ denote the result is increasing and decreasing in corresponding parameters, respectively). * means that the impact needs certain conditions. Specifically, $ p_M^* $ is decreasing in $ s $ whereas $ Q_M^* $ is increasing in $ s $ if $ p_M^*>(2w-s)+2\gamma\lambda(w-c) $

$ i=A, M $	$ \lambda $	$ \gamma $	$ w $	$ c $	$ s $
$ i=A $ $ i=M $
$ p_{i}^* $	$ \nearrow $	$ \nearrow $	$ \nearrow $	$ \searrow $	$ \searrow $ $ \ast $
$ e_{i}^* $	$ \searrow $	$ \searrow $	$ \searrow $	$ \nearrow $	$ \nearrow $ $ \nearrow $
$ Q_{i}^* $	$ \searrow $	$ \searrow $	$ \searrow $	$ \nearrow $	$ \nearrow $ $ \ast $

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Table 3. Influence of $ \lambda $ under LCAD when $ \xi \sim U(-50; 50) $

$ \lambda $	$ w^*_M $	$ p^*_M $	$ e^*_M $	$ Q^*_M $	$ U(\pi_M^r) $	$ \pi_M^s $	$ U(\pi_M^r)+\pi_M^s $
0	3.021	5.6186	0.6179	66.3602	99.9620	67.7538	167.7157
0.5	2.817	5.6185	0.6179	66.3683	119.9643	54.2030	174.1673
1.0	2.681	5.6184	0.6178	66.3716	133.2981	45.1692	178.4673
1.5	2.584	5.6182	0.6177	66.3748	142.8241	38.7164	181.5406

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Table 4. Influence of $ \lambda $ under LCMD when $ \xi\sim U(0.1; 1.9) $

$ \lambda $	$ w^*_M $	$ p^*_M $	$ e^*_M $	$ Q^*_M $	$ U(\pi_M^r) $	$ \pi_M^s $	$ U(\pi_M^r)+\pi_M^s $
0	2.675	5.7809	0.4652	53.5966	68.1482	36.1884	104.3366
0.5	2.540	5.7806	0.4652	53.6026	81.7826	28.9507	110.7334
1.0	2.450	5.7803	0.4652	53.6125	90.8785	24.1256	115.0041
1.5	2.386	5.7802	0.4651	53.6145	97.3717	20.6791	118.0508

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