# Composite Contracts for Dual-Channel Supply Chain Coordination with the Existence of Service Free Riding

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (i)
- Whether the decentralized supply chain with the existence of free riding can reach system-wide optimization state as the centralized supply chain? If not, how does the decisions under the decentralized scenario deviate from that under the centralized scenario?
- (ii)
- What is the difference of the impact among the three mechanisms on supply chain members’ optimal decisions and customer’s free-riding behavior compared with the decentralized scenario?
- (iii)
- Whether the proposed mechanisms can help the decentralized supply chain realize system-wide optimization?

## 2. Literature Review

## 3. Description of the Problem

#### 3.1. The Dual-Channel Supply Chain

#### 3.2. Customer Channel Choice Based on Purchasing Utility

#### 3.3. Demand Functions

## 4. Decentralized and Centralized Decision Model

#### 4.1. The Decentralized Decision Model

#### 4.1.1. The Retailer’s Best Response

**Proposition 1.**

**Proof of Proposition 1.**

#### 4.1.2. The Manufacturer’s Best Response

#### 4.2. The Centralized Decision Model

**Proposition 2.**

**Proof of Proposition 2.**

**Proposition 3.**

- (i)
- ${\mathit{z}}^{D*}<{\mathit{z}}^{C*}$, ${p}_{\mathrm{m}}^{\mathrm{D}*}<{p}_{\mathrm{m}}^{\mathrm{C}*}$;
- (ii)
- $E{\pi}_{\mathrm{r}}^{\mathrm{D}*}({z}^{\mathrm{D}*},{s}^{\mathrm{D}*})+{\pi}_{\mathrm{m}}^{\mathrm{D}*}({p}_{\mathrm{m}}^{\mathrm{D}*})<E{\pi}^{\mathrm{C}}{}^{*}({p}_{\mathrm{m}}^{\mathrm{C}*},{z}^{\mathrm{C}*},{s}^{\mathrm{C}*})$.

**Proof of Proposition 3.**

- (i)
- By comparing Equation (17) with Equation (19), and Equation (14) with Equation (20), respectively, we can easily find that ${p}_{\mathrm{m}}^{\mathrm{D}*}<{p}_{\mathrm{m}}^{\mathrm{C}*}$ and ${z}^{\mathrm{D}*}<{z}^{\mathrm{C}*}$.
- (ii)
- Firstly, ${z}^{\mathrm{C}*}$, ${\mathit{p}}_{m}^{C*}$ and ${s}^{\mathrm{C}*}$ are the unique optimal solutions of $E{\pi}^{\mathrm{C}}$. Secondly, we can see that the functional forms of $E{\pi}^{\mathrm{C}}$ and ${\pi}_{\mathrm{m}}^{\mathrm{D}}+E{\pi}_{\mathrm{r}}^{\mathrm{D}}$ are identical, thus $E{\pi}_{\mathrm{r}}^{\mathrm{D}*}({z}^{\mathrm{D}*},{s}^{\mathrm{D}*})+{\pi}_{\mathrm{m}}^{\mathrm{D}*}({p}_{\mathrm{m}}^{\mathrm{D}*})<E{\pi}^{\mathrm{C}}{}^{*}({p}_{\mathrm{m}}^{\mathrm{C}*},{z}^{\mathrm{C}*},{s}^{\mathrm{C}*})$. □

## 5. Coordinating Mechanisms

#### 5.1. Mechanism 1: Price Hike

**Proposition 4.**

- (i)
- ${s}^{1*}<{s}^{\mathrm{D}}{}^{*}$, ${\mathit{d}}_{m}^{1*}<{\mathit{d}}_{m}^{D*}$, ${Q}^{1*}>{Q}^{\mathrm{D}}{}^{*}$;
- (ii)
- $E{\pi}_{\mathrm{r}}^{1*}>E{\pi}_{\mathrm{r}}^{\mathrm{D}*}$
- (iii)
- Mechanism 1 cannot coordinate the supply chain.

**Proof of Proposition 4.**

- (i)
- From Equation (24), we can acquire the manufacturer’s optimal online price as$${{\mathit{p}}_{\mathrm{m}}^{\prime}}^{1*}=\frac{\alpha [\theta ({p}_{\mathrm{r}}+w-c)+c]}{2}=\alpha {p}_{\mathrm{m}}^{\mathrm{D}*}$$From Equation (25), we can acquire the retailer’s optimal stocking factor and service level as$${z}^{1*}={F}^{-1}(\frac{{p}_{\mathrm{r}}-w-{c}_{\mathrm{r}}}{{p}_{\mathrm{r}}-\phi -{c}_{\mathrm{r}}})$$$${s}^{1*}={[\frac{\lambda D({p}_{\mathrm{r}}-w-{c}_{\mathrm{r}})({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}{\overline{v}\eta (1-\theta )}]}^{\frac{1}{\lambda +2}}$$Since ${{p}_{\mathrm{m}}^{\prime}}^{1*}=\alpha {p}_{\mathrm{m}}^{\mathrm{D}*}>{p}_{\mathrm{m}}^{\mathrm{D}*}$, thus ${s}^{1*}<{s}^{\mathrm{D}}{}^{*}$;The difference between ${d}_{\mathrm{m}}^{1*}$ and ${d}_{\mathrm{m}}^{\mathrm{D}*}$ is$$\begin{array}{ll}\hfill {d}_{\mathrm{m}}^{1*}-{d}_{\mathrm{m}}^{\mathrm{D}*}& =\frac{{B}^{\frac{-\lambda}{\lambda +2}}D}{\overline{v}\theta (1-\theta )}\times \left(\frac{\theta {p}_{\mathrm{r}}-\alpha {p}_{\mathrm{m}}^{\mathrm{D}*}}{{({p}_{r}-\alpha {p}_{\mathrm{m}}^{\mathrm{D}*})}^{\frac{\lambda}{\lambda +2}}}-\frac{\theta {p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*}}{{({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{\frac{\lambda}{\lambda +2}}}\right)\hfill \\ & =\frac{{B}^{\frac{-\lambda}{\lambda +2}}D}{\overline{v}\theta (1-\theta )}\times \left\{{\left(\frac{\theta {p}_{\mathrm{r}}-\alpha {p}_{\mathrm{m}}^{\mathrm{D}*}}{{p}_{\mathrm{r}}-\alpha {p}_{\mathrm{m}}^{\mathrm{D}*}}\right)}^{{}^{\frac{\lambda}{\lambda +2}}}{(\theta {p}_{\mathrm{r}}-\alpha {p}_{\mathrm{m}}^{\mathrm{D}*})}^{{}^{{}^{\frac{2}{\lambda +2}}}}-{\left(\frac{\theta {p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*}}{{p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*}}\right)}^{{}^{\frac{\lambda}{\lambda +2}}}{(\theta {p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{{}^{{}^{\frac{2}{\lambda +2}}}}\right\}\hfill \end{array}$$Since $\frac{\mathsf{\theta}{\mathit{p}}_{r}-{\mathsf{\alpha}}_{m}^{D*}}{{\mathit{p}}_{r}-\mathsf{\alpha}{\mathit{p}}_{m}^{D*}}-\frac{\mathsf{\theta}{\mathit{p}}_{r}-{\mathit{p}}_{m}^{D*}}{{\mathit{p}}_{r}-{\mathit{p}}_{m}^{D*}}=\frac{(1-\alpha )(1-\theta ){\mathit{p}}_{r}{\mathit{p}}_{m}^{D*}}{({\mathit{p}}_{r}-{\mathit{p}}_{m}^{D*})({\mathit{p}}_{r}-\alpha {\mathit{p}}_{m}^{D*})}<0$, thus ${d}_{\mathrm{m}}^{1*}<{d}_{\mathrm{m}}^{\mathrm{D}*}$.The difference between ${d}_{\mathrm{r}}^{1}{}^{*}$ and ${d}_{\mathrm{r}}^{\mathrm{D}}{}^{*}$ is$$\begin{array}{ll}\hfill {d}_{\mathrm{r}}^{1}{}^{*}-{d}_{\mathrm{r}}^{\mathrm{D}}{}^{*}& =(\frac{{p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*}}{\overline{v}{({s}^{\mathrm{D}*})}^{\lambda}(1-\theta )}-\frac{{p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*}}{\overline{v}{({s}^{1*})}^{\lambda}(1-\theta )})\times D\hfill \\ & =\frac{D}{\overline{v}(1-\theta ){({s}^{\mathrm{D}*})}^{\lambda}{({s}^{1*})}^{\lambda}}\times \{{({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{1-\frac{\lambda}{\lambda +2}}{({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{\frac{\lambda}{\lambda +2}}{[\frac{\lambda D({p}_{\mathrm{r}}-{c}_{\mathrm{r}}-w)({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}{\overline{v}\eta (1-\theta )}]}^{\frac{\lambda}{\lambda +2}}\hfill \\ & -{({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}^{1-\frac{\lambda}{\lambda +2}}{({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}^{\frac{\lambda}{\lambda +2}}{[\frac{\lambda D({p}_{\mathrm{r}}-w-{c}_{\mathrm{r}})({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}{\overline{v}\eta (1-\theta )}]}^{\frac{\lambda}{\lambda +2}}\}\hfill \\ & =\frac{D}{\overline{v}(1-\theta ){({s}^{\mathrm{D}*})}^{\lambda}{({s}^{1*})}^{\lambda}}\times {[\frac{\lambda D({p}_{\mathrm{r}}-w-{c}_{\mathrm{r}})({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}{\overline{v}\eta (1-\theta )}]}^{\frac{\lambda}{\lambda +2}}\times [{({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{\frac{2}{\lambda +2}}-{({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}^{\frac{2}{\lambda +2}}]\hfill \end{array}$$It is obvious to see that ${({p}_{\mathrm{r}}-{p}_{\mathrm{m}}^{\mathrm{D}*})}^{\frac{2}{\lambda +2}}-{({p}_{\mathrm{r}}-{{p}_{\mathrm{m}}^{\prime}}^{1*})}^{\frac{2}{\lambda +2}}>0$, thus ${\mathit{d}}_{r}^{l*}>{\mathit{d}}_{r}^{D*}$. From ${Q}^{1*}={d}_{\mathrm{r}}^{1}{}^{*}+{z}^{1*}$, ${Q}^{\mathrm{D}*}={d}_{\mathrm{r}}^{\mathrm{D}}{}^{*}+{z}^{\mathrm{D}*}$ and ${z}^{\mathrm{D}*}={z}^{1*}$, we can obtain ${Q}^{1*}>{Q}^{\mathrm{D}*}$.
- (ii)
- Substituting $z=Q-{d}_{\mathrm{r}}$, ${s}^{1*}$ and ${z}^{1*}$ into Equation (25), ${s}^{\mathrm{D}*}$ and ${z}^{\mathrm{D}*}$ into Equation (6), respectively, we can get the retailer’s optimal expected profits $E{\pi}_{\mathrm{r}}^{1*}$ and $E{\pi}_{\mathrm{r}}^{\mathrm{D}*}$ under Mechanism 1 and under the decentralized scenario, respectively, and the difference between $E{\pi}_{\mathrm{r}}^{1*}$ and $E{\pi}_{\mathrm{r}}^{\mathrm{D}*}$ is$$E{\pi}_{\mathrm{r}}^{1*}-E{\pi}_{\mathrm{r}}^{\mathrm{D}*}=({p}_{\mathrm{r}}-{c}_{\mathrm{r}}-w)({d}_{\mathrm{r}}^{1}{}^{*}-{d}_{\mathrm{r}}^{\mathrm{D}}{}^{*})+\frac{1}{2}\eta {({s}^{\mathrm{D}*})}^{2}-\frac{1}{2}\eta {({s}^{1*})}^{2}$$According to Proposition 4(i), we have ${d}_{\mathrm{r}}^{1}{}^{*}>{d}_{\mathrm{r}}^{\mathrm{D}}{}^{*}$ and $\frac{1}{2}\eta {({s}^{\mathrm{D}*})}^{2}>\frac{1}{2}\eta {({s}^{1*})}^{2}$. Thus, we have $E{\pi}_{\mathrm{r}}^{1*}>E{\pi}_{\mathrm{r}}^{\mathrm{D}*}$.
- (iii)
- Comparing Equation (19) with Equation (26), Equation (20) with Equation (27) and Equation (21) with Equation (28), we can figure out that Mechanism 1 cannot coordinate the supply chain. □

#### 5.2. Mechanism 2: Price Hike with Service Cost Sharing

**Proposition 5.**

- (i)
- ${s}^{2*}>{s}^{1}{}^{*}$,${d}_{\mathrm{m}}^{2*}<{d}_{\mathrm{m}}^{1*}$,${Q}^{2*}>{Q}^{1*}$;
- (ii)
- $E{\pi}_{\mathrm{r}}^{2*}>E{\pi}_{\mathrm{r}}^{1*}$;
- (iii)
- Mechanism 2 cannot coordinate the supply chain.

**Proof of Proposition 5.**

#### 5.3. Mechanism 3: Price Hike with Service Cost Sharing and Surplus Compensation

**Proposition 6.**

**Proof of Proposition 6.**

**Corollary 1.**

**Proof of**

**Corollary 1.**

#### 5.4. Members’ Win-Win Situations

## 6. The Impacts of Changing θ on Supply Chain Efficiencies

- ①
- Only increase $w$ to 10 and keep other parameters fixed.

- ②
- Only decrease ${p}_{\mathrm{r}}$ to 15 and keep other parameters fixed.

- ③
- Increase $w$ to 10 and decrease ${p}_{\mathrm{r}}$ to 15 simultaneously.

## 7. Conclusions

#### 7.1. Summary

#### 7.2. Managerial Insights

- (i)
- How does a dual-channel firm treat price difference between channels and service provision when facing customer free-riding behavior?

- (ii)
- How to employ the proposed mechanisms in practice?

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Li, M.; Zhang, X. Information acquisition and its Incentives in an e-commerce supply chain under the offline showroom model. J. Theor. Appl. Electron. Commer.
**2021**, 16, 1791–1804. [Google Scholar] [CrossRef] - Chen, T.H. Effects of the pricing and cooperative advertising policies in a two-echelon dual-channel supply chain. Comput. Ind. Eng.
**2015**, 87, 250–259. [Google Scholar] [CrossRef] - Modak, N.M.; Kelle, P. Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand. Eur. J. Oper. Res.
**2019**, 272, 147–161. [Google Scholar] [CrossRef] - Hu, W.; Li, Y.J. Retail service for mixed retail and E-tail channels. Ann. Oper. Res.
**2012**, 192, 151–171. [Google Scholar] [CrossRef] - Bell, D.R.; Gallino, S.; Moreno, A. Offline showrooms in omnichannel retail: Demand and operational benefits. Manag. Sci.
**2018**, 64, 1629–1651. [Google Scholar] [CrossRef] - Takahashi, K.; Aoi, T.; Hirotani, D.; Morikawa, K. Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery. Int. J. Prod. Econ.
**2011**, 133, 403–415. [Google Scholar] [CrossRef] - Chiou, J.S.; Wu, L.Y.; Chou, S.Y. You do the service but they take the order. J. Bus. Res.
**2012**, 65, 883–889. [Google Scholar] [CrossRef] - Ryu, M.H.; Cho, Y.; Lee, D. Should small-scale online retailers diversify distribution channels into offline channels? Focused on the clothing and fashion industry. J. Retail. Consum. Serv.
**2019**, 47, 74–77. [Google Scholar] [CrossRef] - Verhoef, P.C.; Neslin, S.A.; Vroomen, B. Multichannel customer management: Understanding the research-shopper phenomenon. Int. J. Res. Mark.
**2007**, 24, 129–148. [Google Scholar] [CrossRef] - van Baal, S.; Dach, C. Free riding and customer retention across retailers’ channels. J. Interact. Mark.
**2005**, 19, 75–85. [Google Scholar] [CrossRef] - Share of Internet Users in the United States Who Have Utilized Showrooming and Webrooming as of September 2014. Available online: http://www.statista.com/statistics/448677/uswebrooming-showroomingpenetration (accessed on 12 February 2016).
- Chiang, W.K.; Chhajed, D.; Hess, J.D. Direct marketing, indirect profits: A strategic analysis of dual-channel supply chain design. Manag. Sci.
**2003**, 49, 1–20. [Google Scholar] [CrossRef] [Green Version] - Cai, G. Channel selection and coordination in dual-channel supply chains. J. Retail.
**2010**, 86, 22–36. [Google Scholar] [CrossRef] - Bian, Y.; Zhu, S.; Sun, Y.; Yan, S. Whether a manufacturer introduces a direct or an indirect online channel in the presence of consumer showrooming behaviour? Int. J. Logist. Res. Appl. 2022, in press. [CrossRef]
- Yan, R.; Pei, Z. The strategic value of cooperative advertising in the dual-channel competition. Int. J. Electron. Commer.
**2015**, 19, 118–143. [Google Scholar] [CrossRef] - Saha, S. Channel characteristics and coordination in three-echelon dual-channel supply chain. Int. J. Syst. Sci.
**2016**, 47, 740–754. [Google Scholar] [CrossRef] - Zhang, F.; Wang, C. Dynamic pricing strategy and coordination in a dual-channel supply chain considering service value. Appl. Math. Model.
**2018**, 54, 722–742. [Google Scholar] [CrossRef] - Yan, R.; Pei, Z.; Ghose, S. Reward points, profit sharing, and valuable coordination mechanism in the O2O era. Int. J. Prod. Econ.
**2019**, 215, 34–47. [Google Scholar] [CrossRef] - Wang, R.; Wang, S.; Yan, S. Pricing and coordination strategies of dual channels considering consumers’ channel preferences. Sustainability
**2021**, 13, 11191. [Google Scholar] [CrossRef] - Balakrishnan, A.; Sundaresan, S.; Zhang, B. Browse-and-switch: Retail-online competition under value uncertainty. Prod. Oper. Manag.
**2014**, 23, 1129–1145. [Google Scholar] [CrossRef] - Zhang, T.; Ge, L.; Gou, Q.; Chen, L. Consumer showrooming, the sunk cost effect and online-offline competition. J. Electron. Commer. Res.
**2018**, 19, 55–74. [Google Scholar] - Guo, J.; Zhou, Y.; Li, B. The optimal pricing and service strategies of a dual-channel retailer under free riding. J. Ind. Manag. Optim.
**2021**, 18, 2049–2076. [Google Scholar] [CrossRef] - Mehra, A.; Kumar, S.; Raju, J.S. Competitive strategies for brick-and-mortar stores to counter “showrooming”. Manag. Sci.
**2018**, 64, 3076–3090. [Google Scholar] [CrossRef] [Green Version] - Jing, B. Showrooming and webrooming: Information externalities between online and offline sellers. Mark. Sci.
**2018**, 37, 469–483. [Google Scholar] [CrossRef] - Liu, Y.; Ding, C.; Fan, C.; Chen, X. Pricing decision under dual-channel structure considering fairness and free-riding behavior. Discret. Dyn. Nat. Soc.
**2014**, 536576. [Google Scholar] [CrossRef] [Green Version] - Li, G.; Li, L.; Sun, J. Pricing and service effort strategy in a dual-channel supply chain with showrooming effect. Transp. Res. Part E Logist. Transp. Rev.
**2019**, 126, 32–48. [Google Scholar] [CrossRef] - Tian, C.; Xiao, T.; Shang, J. Channel differentiation strategy in a dual-channel supply chain considering free riding behavior. Eur. J. Oper. Res.
**2022**, 301, 473–485. [Google Scholar] [CrossRef] - Xing, D.; Liu, T. Sales effort free riding and coordination with price match and channel rebate. Eur. J. Oper. Res.
**2012**, 219, 264–271. [Google Scholar] [CrossRef] - Dan, B.; Liu, C.; Xu, G.; Zhang, X. Pareto improvement strategy for service-based free-riding in a dual-channel supply chain. Asia Pac. J. Oper. Res.
**2014**, 31, 1450050. [Google Scholar] [CrossRef] - Luo, M.; Li, G.; Cheng, T.C.E. Free riding and coordination in a dual-channel supply chain in e-commerce. Int. J. Ship. Transp. Logist.
**2016**, 8, 223–249. [Google Scholar] [CrossRef] - Pu, X.; Gong, L.; Han, X. Consumer free riding: Coordinating sales effort in a dual-channel supply chain. Electron. Commer. Res. Appl.
**2017**, 22, 1–12. [Google Scholar] [CrossRef] - Zhou, Y.W.; Guo, J.; Zhou, W. Pricing/service strategies for a dual-channel supply chain with free riding and service-cost sharing. Int. J. Prod. Econ.
**2018**, 196, 198–210. [Google Scholar] [CrossRef] - Liu, C.; Dan, Y.; Dan, B.; Xu, G. Cooperative strategy for a dual-channel supply chain with the influence of free-riding customers. Electron. Commer. Res. Appl.
**2020**, 43, 101001. [Google Scholar] [CrossRef] - Basak, S.; Basu, P.; Avittathur, B.; Sikdar, S. Manufacturer driven strategic coordination as a response to “showrooming”. Decis. Support Syst.
**2020**, 133, 113305. [Google Scholar] [CrossRef] - Xu, S.; Tang, H.; Lin, Z.; Lu, J. Pricing and sales-effort analysis of dual-channel supply chain with channel preference, cross-channel return and free riding behavior based on revenue-sharing contract. Int. J. Prod. Econ.
**2022**, 249, 108506. [Google Scholar] [CrossRef] - Dan, B.; Zhang, S.; Zhou, M. Strategies for warranty service in a dual-channel supply chain with value-added service competition. Int. J. Prod. Res.
**2018**, 56, 5677–5699. [Google Scholar] [CrossRef] - Tsay, A.A.; Agrawal, N. Channel conflict and coordination in the E-commerce age. Prod. Oper. Manag.
**2004**, 13, 93–110. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.M.; Li, Q.W.; Liu, Z.; Chang, C.T. Optimal pricing and remanufacturing mode in a closed-loop supply chain of WEEE under government fund policy. Comput. Ind. Eng.
**2021**, 151, 106951. [Google Scholar] [CrossRef] - Petruzzi, N.C.; Dada, M. Pricing and the newsvendor problem: A review with extensions. Oper. Res.
**1999**, 47, 183–194. [Google Scholar] [CrossRef] [Green Version] - Bernstein, F.; Federgruen, A. Decentralized supply chains with competing retailers under demand uncertainty. Manag. Sci.
**2005**, 51, 18–29. [Google Scholar] [CrossRef] [Green Version] - Yan, R.; Pei, Z. Information asymmetry, pricing strategy and firm’s performance in the retailer- multi-channel manufacturer supply chain. J. Bus. Res.
**2011**, 64, 377–384. [Google Scholar] [CrossRef] - Dumrongsiri, A.; Fan, M.; Jain, A.; Moinzadeh, K. A supply chain model with direct and retail channels. Eur. J. Oper. Res.
**2008**, 187, 691–718. [Google Scholar] [CrossRef] - Liu, W.; Liu, Y.; Zhu, D.; Wang, Y.; Liang, Z. The influences of demand disruption on logistics service supply chain coordination: A comparison of three coordination modes. Int. J. Prod. Econ.
**2016**, 179, 59–76. [Google Scholar] [CrossRef] - Krishnan, H.; Kapuscinski, R.; Butz, D.A. Coordinating contracts for decentralized supply chains with retailer promotional effort. Manag. Sci.
**2004**, 50, 48–63. [Google Scholar] [CrossRef] - Cachon, G.P.; Lariviere, M.A. Supply chain coordination with revenue-sharing contracts: Strengths and limitations. Manag. Sci.
**2005**, 51, 30–44. [Google Scholar] [CrossRef] [Green Version]

Key Related Studies | Service Decision | The Role of Service in Valuation for Product | Dual-Channel Supply Chain | Contract Strategy | Control the Number of Free-Riding | Win-Win | System-Wide Optimization |
---|---|---|---|---|---|---|---|

[28] | ✓ | ✗ | ✓ | Price match | ✗ | ✓ | ✗ |

[29] | ✓ | ✗ | ✓ | Two-way cost sharing | ✗ | ✓ | ✓ |

[30] | ✓ | ✗ | ✓ | Three-part tariff transfer payment | ✗ | ✓ | ✓ |

[31] | ✓ | ✗ | ✓ | Cost sharing | ✗ | ✓ | ✗ |

[32] | ✓ | ✗ | ✓ | Cost sharing | ✗ | ✗ | ✗ |

[33] | ✗ | ✗ | ✓ | Agency selling | ✓ | ✓ | ✗ |

[34] | ✓ | ✗ | ✓ | Three-part tariff with cost sharing | ✗ | ✗ | ✗ |

[22] | ✓ | ✗ | ✗ | Revenue sharing | ✗ | ✓ | ✗ |

[35] | ✓ | ✗ | ✓ | Revenue sharing | ✗ | ✓ | ✓ |

This research | ✓ | ✓ | ✓ | Price hike with cost-sharing and surplus compensation | ✓ | ✓ | ✓ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, C.; Dan, B.; Zhang, X.; Zhang, H.
Composite Contracts for Dual-Channel Supply Chain Coordination with the Existence of Service Free Riding. *J. Theor. Appl. Electron. Commer. Res.* **2022**, *17*, 789-808.
https://doi.org/10.3390/jtaer17020041

**AMA Style**

Liu C, Dan B, Zhang X, Zhang H.
Composite Contracts for Dual-Channel Supply Chain Coordination with the Existence of Service Free Riding. *Journal of Theoretical and Applied Electronic Commerce Research*. 2022; 17(2):789-808.
https://doi.org/10.3390/jtaer17020041

**Chicago/Turabian Style**

Liu, Can, Bin Dan, Xumei Zhang, and Haiyue Zhang.
2022. "Composite Contracts for Dual-Channel Supply Chain Coordination with the Existence of Service Free Riding" *Journal of Theoretical and Applied Electronic Commerce Research* 17, no. 2: 789-808.
https://doi.org/10.3390/jtaer17020041