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

Chirantan Mondal; Bibhas C. Giri

doi:10.3934/jimo.2021129

Article Contents

2022, Volume 18, Issue 5: 3641-3677. Doi: 10.3934/jimo.2021129

This issue Previous Article Median location problem with two probabilistic line barriers: Extending the Hook and Jeeves algorithm Next Article Optimization of the product service supply chain under the influence of presale services

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

Chirantan Mondal^, and
Bibhas C. Giri

Department of Mathematics, Jadavpur University, Kolkata - 700 032, India

^* Corresponding author: Chirantan Mondal
^* Corresponding author: Chirantan Mondal

Received: October 31, 2020

Revised: March 31, 2021

Early access: August 2021

Published: November 2022

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Abstract

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.

Keywords:

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

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Figure 1. Proposed closed-loop supply chain models

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Figure 2. Availability of remanufactured products in the primary market

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

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

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

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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.

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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 $.

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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]</td> </tr> <tr> <td>+ \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]</td> </tr> <tr> <td>+ 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]</td> </tr> <tr> <td>+ 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]</td> </tr> <tr> <td>+ \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]</td> </tr> <tr> <td>+ 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]</td> </tr> <tr> <td>+ 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)</td> </tr> <tr> <td>+ \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)</td> </tr> <tr> <td>- \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)</td> </tr> <tr> <td>+ \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} $

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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

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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

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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

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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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