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

Jun Tu; Zijiao Sun; Min Huang

doi:10.3934/jimo.2021062

Article Contents

2022, Volume 18, Issue 3: 2191-2220. Doi: 10.3934/jimo.2021062

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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
^* Corresponding author: Zijiao Sun

Received: November 2020

Revised: January 2021

Early access: March 2021

Published: May 2022

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 91B41, 91B03; Secondary: 90B06.

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Figure 1. Timing sequence when the e-tailer provides the logistics contract

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Figure 2. Timing sequence when the TPL provides the logistics contract

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Figure 3. Effect of logistics marginal effort cost coefficient $ {k_2} $ on promotion effort

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Figure 4. Effect of logistics marginal effort cost coefficient $ {k_2} $ on service effort

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Figure 5. Effect of logistics marginal effort cost coefficient $ {k_2} $ on blue market demand

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Figure 6. Effect of logistics marginal effort cost coefficient $ {k_2} $ on e-tailer's expected utility

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Figure 7. Effect of logistics marginal effort cost coefficient $ {k_2} $ on TPL's expected utility

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Figure 8. Effect of logistics marginal effort cost coefficient $ {k_2} $ on supply chain's expected utility

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Figure 9. Effect of logistics marginal effort cost coefficient $ {k_2} $ on logistics service price

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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	√	√	√	√	√

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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 $
$ i $	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 $
$ j $	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
$ {{e}_{ij}} $	provided by the e-tailer
$ {{e}^{'}_{ij}} $	The effort level of the $ j $th decision-maker in the $ i $th type contract
$ {{e}^{'}_{ij}} $	provided by the TPL
$ {{p}_{i2}} $	The price of the logistics service in the $ i $th type contract provided
$ {{p}_{i2}} $	by the e-tailer
$ {{p}^{'}_{i2}} $	The price of the logistics service in the $ i $th type contract provided
$ {{p}^{'}_{i2}} $	by the TPL

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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]} $
Cost-sharing	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)} $

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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

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