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doi: 10.3934/jimo.2021062

Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort

1. 

College of Science, Liaoning Technical University, Fuxin 123000, China

2. 

College of Information Science and Engineering, Northeastern University, Shenyang 110004, China

* Corresponding author: Zijiao Sun

Received  November 2020 Revised  January 2021 Published  March 2021

Fund Project: This work is supported by the National Science Foundation of China (Grant No. 51704140)

Promoting the sale of green agriculture products through online platforms has become the main focus of agricultural industries. In a supply chain consisting of an e-tailer and third-party logistics (TPL), both the promotion effort of the e-tailer and the logistics service effort of TPL can affect the demand. Considering that logistics service contracts may be provided by the e-tailer or TPL, this study defines two different timing sequences. Three types of contracts, i.e., fixed-price, revenue-sharing, and cost-sharing contracts, are used to coordinate the supply chain. The game models under different timing sequences and different contract scenarios are established and solved. The promotion effort and logistics service effort under different scenarios are compared theoretically and numerically. The results indicate that both the promotion effort and logistics service effort change with timing sequences and contract types. The timing sequences depending on the contract provider significantly affect the performance of the supply chain. The cost-sharing contract provided by the TPL can motivate the e-tailer to apply the largest effort, and vice versa. The cost-sharing contract provided by the e-tailer can achieve the largest demand that is optimal for both the e-tailer and supply chain. However, the optimal contract for the TPL is conditional.

Citation: Jun Tu, Zijiao Sun, Min Huang. Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021062
References:
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B. Cao and Z. Fan, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, International Journal of Production Research, 56 (2018), 2411-2436.   Google Scholar

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J. Cao and X. Zhang, Coordination strategy of green supply chain under the free market mechanism, Energy Procedia, 36 (2013), 1130-1137.  doi: 10.1016/j.egypro.2013.07.128.  Google Scholar

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M.-B. Jamali and M. Rasti-Barzoki, A game theoretic approach to investigate the effects of third-party logistics in a sustainable supply chain by reducing delivery time and carbon emissions, Journal of Cleaner Production, 235 (2019), 636-652.  doi: 10.1016/j.jclepro.2019.06.348.  Google Scholar

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G. LiL. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E-Logistics And Transportation Review, 126 (2019), 32-48.   Google Scholar

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C. Liu, W. Chen, Q. Zhou and J. Mu, Modelling dynamic freshness-keeping effort over a finite time horizon in a two-echelon online fresh product supply chain, European J. Oper. Res., (2020). Google Scholar

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M. LiuB. DanS. Zhang and S. Ma, Information sharing in an E-tailing supply chain for fresh produce with freshness-keeping effort and value-added service, European J. Oper. Res., 290 (2021), 572-584.  doi: 10.1016/j.ejor.2020.08.026.  Google Scholar

[25]

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[26]

R. LotfiY. Z. MehrjerdiM. S. PishvaeeA. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control and Optimization, 11 (2021), 221-253.   Google Scholar

[27]

Y. Lou, L. Feng, S. He, Z. He and X. Zhao, Logistics service outsourcing choices in a retailer-led supply chain, Transportation Research Part E, 141 (2020), 101944. doi: 10.1016/j.tre.2020.101944.  Google Scholar

[28]

D. Lvanov, Predicting the impacts of epidemic outbreaks on global supply chains: A simulation-based analysis on the coronavirus outbreak (COVID-19/SARS-CoV-2) case, International Journal of Production Economics, 136 (2020), 101922. Google Scholar

[29]

X. MaQ. BaiS. M. IslamS. Wang and X. Liu, Coordinating a three-echelon fresh agricultural products supply chain considering freshness-keeping effort with asymmetric information, Appl. Math. Model., 67 (2019), 337-356.  doi: 10.1016/j.apm.2018.10.028.  Google Scholar

[30]

A. MajumdarM. Shaw and S. K. Sinha, COVID-19 debunks the myth of socially sustainable supply chain: A case of the clothing industry in South Asian countries, Sustainable Production and Consumption, 24 (2020), 150-155.  doi: 10.1016/j.spc.2020.07.001.  Google Scholar

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K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European J. Oper. Res., 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004.  Google Scholar

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X. PuL. Gong and X. Han, Consumer free riding: Coordinating sales effort in a dual-channel supply chain, Electronic Commerce Research and Application, 22 (2017), 1-12.  doi: 10.1016/j.elerap.2016.11.002.  Google Scholar

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X. Qin, Z. Liu and L. Tian, The strategic analysis of logistics service sharing in an e-commerce platform, Omega, 92 (2020), 102153. doi: 10.1016/j.omega.2019.102153.  Google Scholar

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X. QinQ. SuS. H. HuangU. J. Wiersma and M. Liu, Service quality coordination contracts for online shopping service supply chain with competing service providers: integrating fairness and individual rationality, Operational Research, 19 (2019), 269-296.  doi: 10.1007/s12351-016-0288-z.  Google Scholar

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K. Rahmani and M. Yavari, Pricing policies for a dual-channel green supply chain under demand disruptions, Computers & Industrial Engineering, 127 (2019), 493-510.  doi: 10.1016/j.cie.2018.10.039.  Google Scholar

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R. Robina-Ramírez, A. Chamorro-Mera and L. Moreno-Luna, Organic and online attributes for buying and selling agricultural products in the e-marketplace in Spain, Electronic Commerce Research and Applications, 42 (2020), 100992. Google Scholar

[37]

B. ShenX. Xu and S. Guo, The impacts of logistics services on short life cycle products in a global supply chain, Transportation Research Part E, 131 (2019), 153-167.  doi: 10.1016/j.tre.2019.07.013.  Google Scholar

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Q. Wei, J. Zhang and X. Sun, Incentive contract design for supplier switching with considering learning effect, J. Ind. Manag. Optim., (2020). Google Scholar

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D. Wu, J. Chen, P. Li and R. Zhang, Contract coordination of dual channel reverse supply chain considering service level, Journal of Cleaner Production, 260 (2020), 121071.  Google Scholar

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Q. WuY. Mu and Y. Feng, Coordinating contracts for fresh product outsourcing logistics channels with power structures, International Journal of Production Economics, 160 (2015), 94-105.  doi: 10.1016/j.ijpe.2014.10.007.  Google Scholar

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M. Xu, W. Tang and C. Zhou, Procurement strategies of E-retailers under different logistics distributions with quality- and service-dependent demand, Electronic Commerce Research and Applications, 35 (2019), 100853. doi: 10.1016/j.elerap.2019.100853.  Google Scholar

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L. Yang and R. Tang, Comparisons of sales modes for a fresh product supply chain with freshness-keeping effort, Transportation Research Part E-Logistics And Transportation Review, 125 (2019), 425-448.  doi: 10.1016/j.tre.2019.03.020.  Google Scholar

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C. Zhang, Y. Liu and G. Han, Two-stage pricing strategies of a dual-channel supply chain considering consumer's green preference, Computers & Industrial Engineering, 151 (2021), 106988. Google Scholar

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C. ZhangY. WangY. Liu and H. Wang, Coordination contracts for a dual-channel supply chain under capital constraints, J. Ind. Manag. Optim., 17 (2021), 1485-1504.  doi: 10.3934/jimo.2020031.  Google Scholar

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show all references

References:
[1]

N. Alizadeh-Basban and A. A. Taleizadeh, A hybrid circular economy-game theoretical approach in a dual-channel green supply chain considering sale's effort, delivery time, and hybrid remanufacturing, Journal of Cleaner Production, 250 (2020), 119521. doi: 10.1016/j.jclepro.2019.119521.  Google Scholar

[2]

A. Aslani and J. Heydari, Transshipment contract for coordination of a green dual-channel supply chain under channel disruption, Journal of Cleaner Production, 223 (2019), 596-609.  doi: 10.1016/j.jclepro.2019.03.186.  Google Scholar

[3]

B. Bai, N. Chen and X. Li, Application research of nano-storage materials in cold chain logistics of e-tailer fresh agricultural products, Results in Physics, 13 (2019), 102049. Google Scholar

[4]

X. CaiJ. ChenY. XiaoX. Xu and G. Yu, Fresh-product supply chain management with logistics outsourcing, Omega, 41 (2013), 752-765.  doi: 10.1016/j.omega.2012.09.004.  Google Scholar

[5]

Y. Cang and D. Wang, A comparative study on the online shopping willingness of fresh agricultural products between experienced consumers and potential consumers, Sustainable Computing: Informatics and Systems, 30 (2021), 100493. Google Scholar

[6]

B. Cao and Z. Fan, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, International Journal of Production Research, 56 (2018), 2411-2436.   Google Scholar

[7]

J. Cao and X. Zhang, Coordination strategy of green supply chain under the free market mechanism, Energy Procedia, 36 (2013), 1130-1137.  doi: 10.1016/j.egypro.2013.07.128.  Google Scholar

[8]

S. K. Das and and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-$p$-facility location problem under neutrosophic environment, Computers & Industrial Engineering, 132 (2019), 311-324.  doi: 10.1016/j.cie.2019.04.037.  Google Scholar

[9]

S. K. DasS. K. Roy and G. W. Weber, Heuristic approaches for solid transportation-$p$-facility location problem, CEJOR Cent. Eur. J. Oper. Res., 28 (2020), 939-961.  doi: 10.1007/s10100-019-00610-7.  Google Scholar

[10]

S. K. DasS. K. Roy and G. W. Weber, An exact and a heuristic approach for the transportation-$p$-facility location problem, Comput. Manag. Sci., 17 (2020), 389-407.  doi: 10.1007/s10287-020-00363-8.  Google Scholar

[11]

S. K. DasS. K. Roy and G. Weber, Application of type-2 fuzzy logic to a multi-objective green solid transportation-location problem with dwell time under carbon tax, cap and offset policy: Fuzzy vs. Non-fuzzy techniques, Transactions on Fuzzy Systems, 28 (2020), 2711-2725.   Google Scholar

[12]

N. DemirelaE. ÖzceylanbT. Paksoyb and H. Gökçena, A genetic algorithm approach for optimising a closedloop supply chain network with crisp and fuzzy bjectives, International Journal of Production Research, 52 (2014), 3637-3664.   Google Scholar

[13]

W. FeckeM. Danne and O. Musshoff, E-commerce in agriculture - The case of crop protection product purchases in a discrete choice experiment, Computers and Electronics in Agriculture, 151 (2018), 126-135.  doi: 10.1016/j.compag.2018.05.032.  Google Scholar

[14]

J. Gao, Z. Xiao, H. Wei and G. Zhou, Dual-channel green supply chain management with eco-label policy: A perspective of two types of green products, Energy Procedia, 146 (2020), 106613. Google Scholar

[15]

D. Ghosh and J. Shah, Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164 (2015), 319-329.  doi: 10.1016/j.ijpe.2014.11.005.  Google Scholar

[16]

F. GongD. S. Kung and T. Zeng, The impact of different contract structures on IT investment in logistics outsourcing, International Journal of Production Economics, 195 (2018), 158-167.  doi: 10.1016/j.ijpe.2017.10.009.  Google Scholar

[17]

J. HeydariK. Govindan and A. Aslani, Pricing and greening decisions in a three-tier dual channel supply chain, International Journal of Production Economics, 217 (2019), 185-196.  doi: 10.1016/j.ijpe.2018.11.012.  Google Scholar

[18]

R. HouR. de Koster and Y. Yu, Service investment for online retailers with social media-Does it pay off?, Transportation Research Part E-Logistics And Transportation Review, 118 (2018), 606-628.  doi: 10.1016/j.tre.2018.08.011.  Google Scholar

[19]

M. HuangJ. TuX. Chao and D. Jin, Quality risk in logistics outsourcing: A fourth party logistics perspective, European J. Oper. Res., 276 (2019), 855-879.  doi: 10.1016/j.ejor.2019.01.049.  Google Scholar

[20]

M. B. Jamali and M. Rasti-Barzoki, A game theoretic approach for green and non-green product pricing in chain-to-chain competitive sustainable and regular dual-channel supply chains, Journal of Cleaner Production, 170 (2018), 1029-1043.  doi: 10.1016/j.jclepro.2017.09.181.  Google Scholar

[21]

M.-B. Jamali and M. Rasti-Barzoki, A game theoretic approach to investigate the effects of third-party logistics in a sustainable supply chain by reducing delivery time and carbon emissions, Journal of Cleaner Production, 235 (2019), 636-652.  doi: 10.1016/j.jclepro.2019.06.348.  Google Scholar

[22]

G. LiL. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E-Logistics And Transportation Review, 126 (2019), 32-48.   Google Scholar

[23]

C. Liu, W. Chen, Q. Zhou and J. Mu, Modelling dynamic freshness-keeping effort over a finite time horizon in a two-echelon online fresh product supply chain, European J. Oper. Res., (2020). Google Scholar

[24]

M. LiuB. DanS. Zhang and S. Ma, Information sharing in an E-tailing supply chain for fresh produce with freshness-keeping effort and value-added service, European J. Oper. Res., 290 (2021), 572-584.  doi: 10.1016/j.ejor.2020.08.026.  Google Scholar

[25]

Z. Liu, S. Hua and X. Zhai, Supply chain coordination with risk-averse retailer and option contract: Supplier-led vs. retailer-led, International Journal of Production Economics, 223 (2020), 107518. doi: 10.1016/j.ijpe.2019.107518.  Google Scholar

[26]

R. LotfiY. Z. MehrjerdiM. S. PishvaeeA. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control and Optimization, 11 (2021), 221-253.   Google Scholar

[27]

Y. Lou, L. Feng, S. He, Z. He and X. Zhao, Logistics service outsourcing choices in a retailer-led supply chain, Transportation Research Part E, 141 (2020), 101944. doi: 10.1016/j.tre.2020.101944.  Google Scholar

[28]

D. Lvanov, Predicting the impacts of epidemic outbreaks on global supply chains: A simulation-based analysis on the coronavirus outbreak (COVID-19/SARS-CoV-2) case, International Journal of Production Economics, 136 (2020), 101922. Google Scholar

[29]

X. MaQ. BaiS. M. IslamS. Wang and X. Liu, Coordinating a three-echelon fresh agricultural products supply chain considering freshness-keeping effort with asymmetric information, Appl. Math. Model., 67 (2019), 337-356.  doi: 10.1016/j.apm.2018.10.028.  Google Scholar

[30]

A. MajumdarM. Shaw and S. K. Sinha, COVID-19 debunks the myth of socially sustainable supply chain: A case of the clothing industry in South Asian countries, Sustainable Production and Consumption, 24 (2020), 150-155.  doi: 10.1016/j.spc.2020.07.001.  Google Scholar

[31]

K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European J. Oper. Res., 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004.  Google Scholar

[32]

X. PuL. Gong and X. Han, Consumer free riding: Coordinating sales effort in a dual-channel supply chain, Electronic Commerce Research and Application, 22 (2017), 1-12.  doi: 10.1016/j.elerap.2016.11.002.  Google Scholar

[33]

X. Qin, Z. Liu and L. Tian, The strategic analysis of logistics service sharing in an e-commerce platform, Omega, 92 (2020), 102153. doi: 10.1016/j.omega.2019.102153.  Google Scholar

[34]

X. QinQ. SuS. H. HuangU. J. Wiersma and M. Liu, Service quality coordination contracts for online shopping service supply chain with competing service providers: integrating fairness and individual rationality, Operational Research, 19 (2019), 269-296.  doi: 10.1007/s12351-016-0288-z.  Google Scholar

[35]

K. Rahmani and M. Yavari, Pricing policies for a dual-channel green supply chain under demand disruptions, Computers & Industrial Engineering, 127 (2019), 493-510.  doi: 10.1016/j.cie.2018.10.039.  Google Scholar

[36]

R. Robina-Ramírez, A. Chamorro-Mera and L. Moreno-Luna, Organic and online attributes for buying and selling agricultural products in the e-marketplace in Spain, Electronic Commerce Research and Applications, 42 (2020), 100992. Google Scholar

[37]

B. ShenX. Xu and S. Guo, The impacts of logistics services on short life cycle products in a global supply chain, Transportation Research Part E, 131 (2019), 153-167.  doi: 10.1016/j.tre.2019.07.013.  Google Scholar

[38]

Q. Wei, J. Zhang and X. Sun, Incentive contract design for supplier switching with considering learning effect, J. Ind. Manag. Optim., (2020). Google Scholar

[39]

D. Wu, J. Chen, P. Li and R. Zhang, Contract coordination of dual channel reverse supply chain considering service level, Journal of Cleaner Production, 260 (2020), 121071.  Google Scholar

[40]

Q. WuY. Mu and Y. Feng, Coordinating contracts for fresh product outsourcing logistics channels with power structures, International Journal of Production Economics, 160 (2015), 94-105.  doi: 10.1016/j.ijpe.2014.10.007.  Google Scholar

[41]

D. Xing and T. Liu, Sales effort free riding and coordination with price match and channel rebate, European J. Oper. Res., 219 (2012), 264-271.  doi: 10.1016/j.ejor.2011.11.029.  Google Scholar

[42]

M. Xu, W. Tang and C. Zhou, Procurement strategies of E-retailers under different logistics distributions with quality- and service-dependent demand, Electronic Commerce Research and Applications, 35 (2019), 100853. doi: 10.1016/j.elerap.2019.100853.  Google Scholar

[43]

N.-N. Yan and B.-W. Sun, Optimal Stackelberg strategies for closed-loop supply chain with third-party reverse logistics, Asia-Pac. J. Oper. Res., 29 (2012), 1250026, 21 pp. doi: 10.1142/S0217595912500261.  Google Scholar

[44]

L. YangG. Cai and J. Chen, Push, pull, and supply chain risk averse attitude, Production and Operation Management, 27 (2018), 1534-1552.   Google Scholar

[45]

L. Yang and R. Tang, Comparisons of sales modes for a fresh product supply chain with freshness-keeping effort, Transportation Research Part E-Logistics And Transportation Review, 125 (2019), 425-448.  doi: 10.1016/j.tre.2019.03.020.  Google Scholar

[46]

D. YangT. Xiao and J. Huang, Dual-channel structure choice of an environmental responsibility supply chain with green investment, Journal of Cleaner Production, 210 (2019), 134-145.  doi: 10.1016/j.jclepro.2018.11.014.  Google Scholar

[47]

Y. Yu and T. Xiao, Pricing and cold-chain service level decisions in a fresh agri-products supply chain with logistics outsourcing, Computers & Industrial Engineering, 111 (2017), 56-66.  doi: 10.1016/j.cie.2017.07.001.  Google Scholar

[48]

Y. YuT. Xiao and Z. Feng, Price and cold-chain service decisions versus integration in a fresh agri-product supply chain with competing retailers, Ann. Oper. Res., 287 (2020), 465-493.  doi: 10.1007/s10479-019-03368-y.  Google Scholar

[49]

C. Zhang, Y. Liu and G. Han, Two-stage pricing strategies of a dual-channel supply chain considering consumer's green preference, Computers & Industrial Engineering, 151 (2021), 106988. Google Scholar

[50]

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Figure 1.  Timing sequence when the e-tailer provides the logistics contract
Figure 2.  Timing sequence when the TPL provides the logistics contract
Figure 3.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on promotion effort
Figure 4.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on service effort
Figure 5.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on blue market demand
Figure 6.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on e-tailer's expected utility
Figure 7.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on TPL's expected utility
Figure 8.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on supply chain's expected utility
Figure 9.  Effect of logistics marginal effort cost coefficient $ {k_2} $ on logistics service price
Table 1.  Position of the present paper
Paper Green topic TPL effort E-tailer effort Contract issue Timing sequence
Lotfi et al. [26]
Cai et al. [4]
Wu et al. [40]
Shen et al. [37]
Huang et al. [19]
Lou et al. [27]
Gong et al. [16]
Zhou et al. [51]
Yang and Tang [45]
Zhou and Ye [52]
Qin et al. [34]
Liu et al. [25]
Yang et al. [44]
Matsui [31]
Present paper
Paper Green topic TPL effort E-tailer effort Contract issue Timing sequence
Lotfi et al. [26]
Cai et al. [4]
Wu et al. [40]
Shen et al. [37]
Huang et al. [19]
Lou et al. [27]
Gong et al. [16]
Zhou et al. [51]
Yang and Tang [45]
Zhou and Ye [52]
Qin et al. [34]
Liu et al. [25]
Yang et al. [44]
Matsui [31]
Present paper
Table 2.  Notations and descriptions used in the paper
Variables Meanings
$ {c_1} $ The unit cost of the e-tailer
$ {c_2} $ The unit cost of the TPL
$ {D_0} $ The market size of green agriculture products
$ {k_1} $ The effort cost coefficient of the e-tailer
$ {k_2} $ The effort cost coefficient of the TPL
$ {p_1} $ The unit price of green agriculture products
$ \alpha $ The marginal effect coefficient of product price on demand
$ \beta $ The marginal effect coefficient of promotion effort on demand
$ \gamma $ The marginal effect coefficient of logistics effort on demand
$ \varepsilon $ The random factor affecting market demand, $ \varepsilon \sim N(0,\sigma ^2) $
$ \theta $ The proportion of logistics effort costs shared by the e-tailer, $ 0<\theta <1 $
$ \varphi $ The revenue-sharing proportion of the e-tailer, $ 0<\varphi <1 $
Subscript
$ i $ The subscript $ i $ denotes the $ i $th type contract. That is, $ i=1, 2, 3 $
denotes the fixed-price, revenue-sharing and cost-sharing contracts
$ j $ The subscript $ j $ represents the $ j $th decision-maker. That is, $ j=1, 2 $
denotes the e-tailer and TPL
Decision variables
$ {{e}_{ij}} $ The effort level of the $ j $th decision-maker in the $ i $th type contract
provided by the e-tailer
$ {{e}^{'}_{ij}} $ The effort level of the $ j $th decision-maker in the $ i $th type contract
provided by the TPL
$ {{p}_{i2}} $ The price of the logistics service in the $ i $th type contract provided
by the e-tailer
$ {{p}^{'}_{i2}} $ The price of the logistics service in the $ i $th type contract provided
by the TPL
Variables Meanings
$ {c_1} $ The unit cost of the e-tailer
$ {c_2} $ The unit cost of the TPL
$ {D_0} $ The market size of green agriculture products
$ {k_1} $ The effort cost coefficient of the e-tailer
$ {k_2} $ The effort cost coefficient of the TPL
$ {p_1} $ The unit price of green agriculture products
$ \alpha $ The marginal effect coefficient of product price on demand
$ \beta $ The marginal effect coefficient of promotion effort on demand
$ \gamma $ The marginal effect coefficient of logistics effort on demand
$ \varepsilon $ The random factor affecting market demand, $ \varepsilon \sim N(0,\sigma ^2) $
$ \theta $ The proportion of logistics effort costs shared by the e-tailer, $ 0<\theta <1 $
$ \varphi $ The revenue-sharing proportion of the e-tailer, $ 0<\varphi <1 $
Subscript
$ i $ The subscript $ i $ denotes the $ i $th type contract. That is, $ i=1, 2, 3 $
denotes the fixed-price, revenue-sharing and cost-sharing contracts
$ j $ The subscript $ j $ represents the $ j $th decision-maker. That is, $ j=1, 2 $
denotes the e-tailer and TPL
Decision variables
$ {{e}_{ij}} $ The effort level of the $ j $th decision-maker in the $ i $th type contract
provided by the e-tailer
$ {{e}^{'}_{ij}} $ The effort level of the $ j $th decision-maker in the $ i $th type contract
provided by the TPL
$ {{p}_{i2}} $ The price of the logistics service in the $ i $th type contract provided
by the e-tailer
$ {{p}^{'}_{i2}} $ The price of the logistics service in the $ i $th type contract provided
by the TPL
Table 3.  The optimal results
Contract Provided by Promotion effort Logistics effort Market demand
Fixed-price (Revenue-sharing) E-tailer $ \frac{-\beta \left( {{k}_{2}}A+{{\gamma }^{2}}B \right)}{{{k}_{2}}(C-2G)} $ $ \frac{\gamma \left[K+\left( C-G \right)B \right]}{{{k}_{2}}\left( C-2G \right)} $ $ \frac{-G\left({k_2} A+\gamma^2 B \right)}{{k_2}\left(C-2G\right)} $
TPL $ \frac{\beta [(N+C-G)B-K]}{{k_1}\left(C+N-G\right)} $ $ \frac{\gamma\left(\beta^2B+{k_1}A\right)}{2C+N-G} $ $ \frac{(N+C)\left({k_1}A+\beta^2B\right)}{{k_1}\left(2C+N-G\right)} $
Cost-sharing E-tailer $ \frac{-\beta {\left( {{m}^{2}}{{k}_{2}}A+{{\gamma }^{2}}B \right)}}{{{m}^{2}}C+\left( \theta -2 \right)G } $ $ \frac{\gamma \left[ m\left( K+BC \right)-BG \right]}{{{k}_{2}}\left[ {{m}^{2}}C+\left( \theta -2 \right)G \right]} $ $ \frac{-{{\gamma }^{2}}\left(K+BC\theta+G\right)}{{k_2}\left[m^2C+\left(\theta-2\right)G\right]} $
TPL $ \frac{\beta[m(N+C)-G]B-mK ]}{m{k_1}\left(2C+N-G\right)} $ $ \frac{\gamma\left({{k}_{1}} A+{{\beta }^{2}}B\right)}{m\left(2C+N\right)-G} $ $ \frac{m(N+C)\left({k_1}A+\beta^2B\right)}{m{k_1}\left(2C+N-G\right)} $
Contract Provided by Promotion effort Logistics effort Market demand
Fixed-price (Revenue-sharing) E-tailer $ \frac{-\beta \left( {{k}_{2}}A+{{\gamma }^{2}}B \right)}{{{k}_{2}}(C-2G)} $ $ \frac{\gamma \left[K+\left( C-G \right)B \right]}{{{k}_{2}}\left( C-2G \right)} $ $ \frac{-G\left({k_2} A+\gamma^2 B \right)}{{k_2}\left(C-2G\right)} $
TPL $ \frac{\beta [(N+C-G)B-K]}{{k_1}\left(C+N-G\right)} $ $ \frac{\gamma\left(\beta^2B+{k_1}A\right)}{2C+N-G} $ $ \frac{(N+C)\left({k_1}A+\beta^2B\right)}{{k_1}\left(2C+N-G\right)} $
Cost-sharing E-tailer $ \frac{-\beta {\left( {{m}^{2}}{{k}_{2}}A+{{\gamma }^{2}}B \right)}}{{{m}^{2}}C+\left( \theta -2 \right)G } $ $ \frac{\gamma \left[ m\left( K+BC \right)-BG \right]}{{{k}_{2}}\left[ {{m}^{2}}C+\left( \theta -2 \right)G \right]} $ $ \frac{-{{\gamma }^{2}}\left(K+BC\theta+G\right)}{{k_2}\left[m^2C+\left(\theta-2\right)G\right]} $
TPL $ \frac{\beta[m(N+C)-G]B-mK ]}{m{k_1}\left(2C+N-G\right)} $ $ \frac{\gamma\left({{k}_{1}} A+{{\beta }^{2}}B\right)}{m\left(2C+N\right)-G} $ $ \frac{m(N+C)\left({k_1}A+\beta^2B\right)}{m{k_1}\left(2C+N-G\right)} $
Table 4.  Parameter setting
Parameters $ {c_1} $ $ {c_2} $ $ {D_0} $ $ {k_1} $ $ l $ $ {p_1} $ $ \alpha $ $ \beta $ $ \gamma $ $ \theta $ $ \sigma $ $ \varphi $
Value 2 4 70 10 2 20 2 9 12 0.5 3 0.4
Parameters $ {c_1} $ $ {c_2} $ $ {D_0} $ $ {k_1} $ $ l $ $ {p_1} $ $ \alpha $ $ \beta $ $ \gamma $ $ \theta $ $ \sigma $ $ \varphi $
Value 2 4 70 10 2 20 2 9 12 0.5 3 0.4
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