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Article Contents

# Investigating a green supply chain with product recycling under retailer's fairness behavior

• * Corresponding author: Chirantan Mondal
• Due to the rapid increment of environmental pollution and advancement of society, recently many manufacturing firms have started greening their products and focusing on product remanufacturing. The retailing firms are also taking several efforts for marketing those products and thinking more about the fairness of the business. Keeping this in mind, this study investigates the effect of recycling activity and the retailer's fairness behavior on pricing, green improvement, and marketing effort in a closed-loop green supply chain. In the forward channel, the manufacturer sells the green product through the retailer while in the reverse channel, either the manufacturer or the retailer or an independent third-party collects used products. The centralized model and six decentralized models are developed depending on the retailer's fairness behavior and/or product recycling. The optimal results are derived and compared analytically. The analytical results are verified by exemplifying a numerical example. A restitution-based wholesale price contract is developed to resolve the channel conflicts and coordinate the supply chain. Our results reveal that (ⅰ) the manufacturer never selects the third-party as a collector of used products under fair-neutral retailer, (ⅱ) the fairness behavior of the retailer improves her profitability but it diminishes the manufacturer's profit, and (ⅲ) if the manufacturer does not pay much transfer price, then the collection through the third-party is preferable to the fair-minded retailer.

Mathematics Subject Classification: Primary: 90B06, 90B60; Secondary: 91A35, 91B16.

 Citation:

• Figure 1.  Proposed closed-loop supply chain models

Figure 2.  Availability of remanufactured products in the primary market

Figure 3.  Win-win situation for the manufacturer and the retailer

Figure 4.  Sensitivity of optimal results w.r.t. $B$

Figure 5.  Sensitivity of optimal results w.r.t. $\xi$

Table 1.  A comparison of the present study with related existing literatures

 Author(s) Demand sensitivity Carbon Collector Retailer's Loop type Channel price quality effort emission M R T fairness concern open closed coordination Maiti and Giri [27] √ √ $\times$ $\times$ $\times$ $\times$ √ $\times$ $\times$ √ $\times$ Hong et al. [15] √ $\times$ √ $\times$ √ √ √ $\times$ $\times$ √ √ Nie and Du [34] √ $\times$ $\times$ $\times$ $\times$ $\times$ $\times$ √ √ $\times$ √ Liu et al. [24] √ √ √ √ $\times$ $\times$ $\times$ √ √ $\times$ √ Ma et al. [25] √ $\times$ √ $\times$ √ √ √ √ $\times$ √ $\times$ Chen et al. [5] √ √ √ $\times$ √ √ √ $\times$ $\times$ √ $\times$ Modak et al. [30] √ √ $\times$ $\times$ √ √ √ $\times$ $\times$ √ √ Song et al. [41] √ $\times$ $\times$ $\times$ $\times$ $\times$ $\times$ √ √ $\times$ $\times$ Chen and Akmalul'Ulya [4] √ √ √ $\times$ √ √ √ $\times$ $\times$ √ $\times$ Modak et al. [29] √ $\times$ √ $\times$ √ √ √ $\times$ $\times$ √ √ Zhang et al. [49] √ √ $\times$ $\times$ $\times$ $\times$ $\times$ √ √ $\times$ $\times$ Zheng et al. [57] √ $\times$ $\times$ $\times$ √ $\times$ $\times$ √ $\times$ √ √ Zheng et al. [56] √ $\times$ $\times$ $\times$ $\times$ $\times$ √ √ $\times$ √ √ Mondal and Giri [31] √ √ √ $\times$ √ √ √ $\times$ $\times$ √ √ Zhang et al. [54] √ $\times$ $\times$ √ √ $\times$ $\times$ $\times$ $\times$ √ $\times$ Qian et al. [35] √ √ $\times$ √ $\times$ $\times$ $\times$ √ √ $\times$ √ Jian et al. [18] √ √ √ $\times$ √ $\times$ $\times$ $\times$ $\times$ √ √ Du and Zhao [9] √ $\times$ $\times$ $\times$ $\times$ $\times$ $\times$ √ √ $\times$ $\times$ Mondal et al. [33] √ $\times$ √ $\times$ √ √ √ $\times$ $\times$ √ √ Present study √ √ √ √ √ √ √ √ $\times$ √ √ Note: M - Manufacturer; R - Retailer; T - Third-party. Here, quality includes greening level, sustainability level, emission reduction level, etc. and effort includes sales, marketing, greening, CSR effort, etc.

Table 2.  Decision variables and parameters

 Notations Description Decision variables $w$ unit wholesale price of the manufacturer. $p$ unit selling price of the retailer. $\theta$ level of green innovation. $e$ marketing effort level of the retailer. $\tau$ collection rate of used products. Parameters $D$ market demand. $D_r$ return quantity. $c_m (c_r)$ unit manufacturing (remanufacturing) cost of the new (returned) product. $D_0$ basic market demand. $E_0$ basic carbon emission during production. $E_u (E_t)$ unit (total) carbon emission during production. $\rho$ fraction of remanufactured products available for selling in the primary market. $w_1$ unit selling price of the remanufactured product in the secondary market. $\lambda$ green investment-related cost coefficient. $\eta$ marketing effort-related cost coefficient. $\mu$ collection cost coefficient. $A$ unit price paid to the customer for used products. $B$ unit transfer price of the used products ($B> A$). $\Pi_i^j$ profit function where superscript $j$ denotes the supply chain models ($j = C, MN, RN, TN, MF, RF, TF, CO$) while the subscript $i$ denotes the supply chain members and the entire supply chain, respectively ($i = m, r, t, w$). $(.)^j$ optimal decisions under model $j$.

Table 3.  Optimal results under retailer's fairness concern

 Model-MF Model-RF Model-TF $w^*$ $\frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta (X - A)^2\big] + \mu c_m \alpha \big[\lambda (1 + 2 \xi) \Psi_1 - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}}$ $\frac{ \begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta \Psi_2\big(\Psi_2 + 2(1 + \xi)(X - B)\big)\big] + c_m \alpha \big[\mu \big(\lambda \Psi_1(1 + 2\xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda \Psi_2\big(\Psi_2 + 2 \xi (B - A)\big)\big]\end{array} }{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}}$ $\frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - 2 \alpha^2 \eta \Psi_3\big] + c_m \alpha \big[\mu \big(\lambda (1 + 2 \xi)\Psi_1 - \eta \beta^2\big) + 2 \alpha^2 \eta \lambda \xi^2 \Psi_3\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}}$ $p^*$ $\frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - \alpha^2 \eta (X - A)^2\big] + \mu c_m \alpha \big[\lambda (1 + \xi)(2 \alpha \eta - \gamma^2) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}}$ $\frac{\begin{array}{c}D_0 \lambda (1 + \xi)\big[\mu (6 \alpha \eta - \gamma^2) + 2 \alpha^2 \eta (X - A)\Psi_2\big] + c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}}$ $\frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - 2 \alpha^2 \eta (1 - \xi^2) \Psi_3\big] + c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}}$ $\theta^*$ $\frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}}$ $\frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}}$ $\frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}}$ $e^*$ $\frac{\alpha \eta \lambda (1 + \xi) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}}$ $\frac{\gamma \lambda \mu (1 + \xi) \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}}$ $\frac{\gamma \lambda \mu (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}}$ $\tau^*$ $\frac{\alpha \eta \lambda (X - A) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}}$ $\frac{\alpha \eta \lambda (1 + \xi)\Psi_2 \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}}$ $\frac{\alpha \lambda \eta (B - A) (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}}$ $\Pi_m^*$ $\frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}}$ $\frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}}$ $\frac{D\eta \lambda \mu (1 + \xi)\Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}}$ $\Pi_r^*$ $\frac{\begin{array}{c}\lambda^2 \eta \mu^2 \Psi_1 \Psi_4^2(1 + \xi) (1 + 3 \xi)\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}}$ $\frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi)\Psi_4^2 \big[\mu \Psi_1(1 + 3\xi) + \alpha^2 \eta \Psi_2\big((B - A)(1 + 3\xi) + (X - B)\xi (1 - \xi)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]^2\end{array}}$ $\frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi) \big(\mu \Psi_1 (1 + 3 \xi) + 4 \alpha^2 \eta \xi^2 \Psi_3\big) \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]^2\end{array}}$ $\Pi_t^*$ — — $\frac{\begin{array}{c}\alpha^2 \lambda^2 \eta^2 \mu (1 + \xi)^2 (B - A)^2 \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]^2\end{array}}$ $\Pi_w^*$ $\frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2\big[\mu \big(3 \lambda (1 + \xi)^2 \Psi_1 - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}}$ $\frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big) - \alpha^2 \eta \lambda (1 + \xi)^2 \Psi_2 \big(\Psi_2 + 2 (X - A)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]^2\end{array}}$ $\frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big) + \alpha^2 \eta \lambda (1 + \xi)^2\big((B - A)^2 - 2 (1 - 2 \xi)\Psi_3\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3 \big]^2\end{array}}$ $E_t^*$ $(E_0 - \delta \theta^{MF})D^{MF}$ $(E_0 - \delta \theta^{RF})D^{RF}$ $(E_0 - \delta \theta^{TF})D^{TF}$

Table 4.  Optimal results of the proposed models

 Optimal Without fairness With fairness results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO $w$ 525.499 529.530 529.530 484.279 488.405 488.222 - 372.201 $p$ 720.948 719.742 722.926 720.817 719.514 722.601 522.136 522.136 $\theta$ 0.83066 0.83599 0.82193 0.73948 0.74459 0.73247 1.70843 1.70843 $e$ 0.32575 0.32784 0.32233 0.32479 0.32704 0.32171 0.66997 0.66997 $\tau$ 0.32249 0.21637 0.21274 0.28709 0.20289 0.21233 0.66327 0.66327 $\Pi_m$ 8160.02 8212.36 8074.27 7264.27 7314.53 7195.46 - 9973.38 $\Pi_r$ 4192.51 4176.24 4104.85 5060.96 5048.37 4967.26 - 6809.43 $\Pi_t$ - - 67.8844 - - 67.6264 - - $\Pi_w$ 12352.5 12388.6 12247.0 12325.2 12362.9 12230.3 16782.8 16782.8 $E_u$ 0.83387 0.83280 0.83561 0.85211 0.85108 0.85351 0.65831 0.65831 $E_t$ 17.9277 18.0196 17.7764 18.2658 18.3701 18.1225 29.1094 29.1094

Table 5.  Optimal results of the proposed models when $\rho = 0$

 Optimal Without fairness With fairness results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO $w$ 532.607 537.992 537.853 491.302 497.210 496.564 - 385.372 $p$ 724.435 723.963 727.008 723.929 723.400 726.202 536.602 536.602 $\theta$ 0.81527 0.81735 0.80391 0.72725 0.72933 0.71833 1.64456 1.64456 $e$ 0.31971 0.32053 0.31525 0.31942 0.32033 0.31550 0.64493 0.64493 $\tau$ 0.03517 0.21155 0.20807 0.03137 0.23256 0.20823 0.07094 0.07094 $\Pi_m$ 8008.80 8029.26 7897.21 7144.19 7164.59 7056.50 - 9672.70 $\Pi_r$ 4038.56 3992.09 3926.80 4895.02 4839.26 4772.80 - 6482.72 $\Pi_t$ - - 64.9398 - - 65.0397 - - $\Pi_w$ 12047.4 12021.4 11889.0 12039.2 12003.9 11894.3 16155.4 16155.4 $E_u$ 0.83695 0.83653 0.83922 0.85455 0.85413 0.85634 0.67109 0.67109 $E_t$ 17.6604 17.6967 17.4616 18.0154 18.0581 17.8315 28.5650 28.5650

Table 6.  Optimal results of the proposed models when $\rho = 1$

 Optimal Without fairness With fairness results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO $w$ 521.843 527.354 527.391 480.679 486.583 486.085 - 360.962 $p$ 719.155 718.656 721.876 719.221 718.735 721.678 514.474 514.474 $\theta$ 0.83858 0.84078 0.82656 0.74574 0.74766 0.73610 1.74226 1.74226 $e$ 0.32885 0.32972 0.32414 0.32754 0.32838 0.32331 0.68324 0.68324 $\tau$ 0.39791 0.21761 0.21393 0.35386 0.19506 0.21338 0.82672 0.82672 $\Pi_m$ 8237.79 8259.44 8119.78 7325.84 7344.61 7231.05 - 10141.5 $\Pi_r$ 4272.81 4224.26 4151.26 5147.11 5091.53 5017.71 - 6973.61 $\Pi_t$ - - 68.6518 - - 68.2972 - - $\Pi_w$ 12510.6 12483.7 12339.7 12473.0 12436.1 12317.1 17115.1 17115.1 $E_u$ 0.83228 0.83184 0.83469 0.85085 0.85047 0.85278 0.65155 0.65155 $E_t$ 18.0642 18.1021 17.8568 18.3935 18.4324 18.1967 29.3808 29.3808

Table 7.  Optimal results of the proposed models when $w_1 = 0$

 Optimal Without fairness With fairness results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO $w$ 530.503 533.809 533.738 489.220 492.515 492.433 - 384.801 $p$ 723.403 721.876 724.989 723.006 721.308 724.419 532.377 532.377 $\theta$ 0.81982 0.82656 0.81282 0.73088 0.73755 0.72533 1.66322 1.66322 $e$ 0.32150 0.32414 0.31875 0.32101 0.32394 0.31858 0.65224 0.65224 $\tau$ 0.17682 0.21393 0.21038 0.15764 0.21808 0.21026 0.35873 0.35873 $\Pi_m$ 8053.58 8119.78 7984.76 7179.79 7245.31 7125.30 - 9753.86 $\Pi_r$ 4083.84 4082.61 4014.35 4943.93 4950.75 4868.60 - 6584.80 $\Pi_t$ - - 66.3876 - - 66.3141 - - $\Pi_w$ 12137.4 12202.4 12065.5 12123.7 12196.1 12060.2 16338.7 16338.7 $E_u$ 0.83604 0.83469 0.83744 0.85382 0.85249 0.85493 0.66736 0.66736 $E_t$ 17.7398 17.8568 17.6177 18.0898 18.2264 17.9759 28.7283 28.7283

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