# Pricing and Contract Coordination of BOPS Supply Chain Considering Product Return Risk

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Management of Channels

#### 2.2. Product Return Risks

## 3. Problem Statement

## 4. Model Formulation and Analysis

#### 4.1. Centralized Decision

**Proposition**

**1.**

**Corollary**

**1.**

#### 4.2. Decentralized Decision

#### 4.2.1. BOPS Channel Managed by the Manufacturer

**Proposition**

**2.**

**Corollary**

**2.**

**Corollary**

**3.**

#### 4.2.2. BOPS Channel Managed by the Retailer

**Proposition**

**3.**

**Corollary**

**4.**

## 5. The BOPS Omni-Channel Supply Chain Coordination and Optimization Research

#### 5.1. BOPS Channel Managed by the Manufacturer

**Proposition**

**4.**

#### 5.2. BOPS Channel Managed by the Retailer

**Proposition**

**5.**

## 6. Numerical Analysis

#### 6.1. Optimal Decision and Profit Comparative Analysis

#### 6.2. Sensitivity Analysis of Contract Coefficients τ and φ

#### 6.3. Sensitivity Analysis of SA Effort Service Level Cost Coefficient

#### 6.4. Sensitivity Analysis of Offline Consumer Loyalty θ

## 7. Discussion and Conclusions

#### 7.1. Conclusions

#### 7.2. Theoretical Implications

#### 7.3. Practical Implications

#### 7.4. Limitation and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Influence of contract coefficient on optimal profit. (

**a**) Influence of contract coefficient τ on manufacturer profit; (

**b**) Influence of contract coefficient τ on retailer profit; (

**c**) Influence of contract coefficient τ on supply chain profit; (

**d**) Influence of contract coefficient φ on manufacturer profit; (

**e**) Influence of contract coefficient φ on retailer profit; (

**f**) Influence of contract coefficient φ on supply chain profit.

Literature | Channel Type | Decision Variables | Demand Characteristics | Game Process | Coordination |
---|---|---|---|---|---|

[1] | Omni-channel | Pricing & Inventory | consumer utility | N/A | return shipping fee sharing |

[9] | Omni-channel | Inventory | consumer utility | N/A | N/A |

[18] | Dual-channel | Pricing & Ordering | price-dependent stochastic | Nash | N/A |

[19] | Dual-channel | Pricing & Service | linear involving service factor | Bertrand; Stackelberg | N/A |

[21] | Dual-channel | Pricing & Service | consumer utility | Bertrand | N/A |

[25] | Omni-channel | Pricing | consumer utility | N/A | N/A |

[28] | Omni-channel | Pricing | consumer utility | N/A | N/A |

[31] | Omni-channel | Inventory | consumer utility | N/A | N/A |

[45] | Dual-channel | Pricing | linear | Stackelberg; Nash | N/A |

[43] | Dual-channel | online fresh-keeping effort, marketing effort and offline fresh-keeping effort | differentia equation | N/A | N/A |

[46] | Omni-channel | Pricing & Service | linear involving service factor | Stackelberg | N/A |

[42] | Omni-channel | Pricing | linear | N/A | N/A |

This study | Omni-channel | Pricing & Service | linear involving service and the return risk | Stackelberg | wholesale price contract |

Model | ${\mathit{\omega}}^{\mathbf{*}}$ | ${\mathit{s}}^{\mathbf{*}}$ | ${\mathit{p}}^{\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{S}}^{\mathbf{*}}$ |
---|---|---|---|---|---|---|

C | -- | 0.4769 | 24.8363 | -- | -- | 1844.8401 |

DE | 7.3630 | 0.2509 | 33.5071 | 681.6598 | 934.7571 | 1616.4169 |

HE | 3.5368 | 0.4769 | 24.8363 | 737.9361 | 1106.9041 | 1844.8401 |

DS | 19.3275 | 0.3153 | 35.7494 | 536.8751 | 948.3325 | 1485.2075 |

HS | 11.2728 | 0.4769 | 24.8363 | 737.9361 | 1106.9041 | 1844.8401 |

$\mathsf{\tau}$ | ${\mathit{\omega}}^{\mathit{H}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{E}*}\mathbf{-}{\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{E}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{E}\mathbf{*}}$ |
---|---|---|---|---|---|

0.54 | 0.3663 | 996.2137 | 61.4566 | 848.6265 | 166.9666 |

0.56 | 1.4231 | 1033.1105 | 98.3534 | 811.7297 | 130.0698 |

0.58 | 2.4800 | 1070.0073 | 135.2502 | 774.8329 | 93.1730 |

0.60 | 3.5368 | 1106.9041 | 172.1470 | 737.9361 | 56.2762 |

0.62 | 4.5936 | 1143.8009 | 209.0438 | 701.0393 | 19.3794 |

$\mathsf{\phi}$ | ${\mathit{\omega}}^{\mathit{H}\mathit{S}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{S}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{S}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{S}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{S}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{S}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{S}\mathbf{*}}$ |
---|---|---|---|---|---|

0.52 | 8.5808 | 959.3169 | 10.9844 | 885.5233 | 348.6482 |

0.54 | 9.2538 | 996.2137 | 47.8812 | 848.6265 | 311.7514 |

0.56 | 9.9268 | 1033.1105 | 84.7780 | 811.7297 | 274.8546 |

0.58 | 10.5998 | 1070.0073 | 121.6748 | 774.8329 | 237.9578 |

0.60 | 11.2728 | 1106.9041 | 158.5716 | 737.9361 | 201.0610 |

0.62 | 11.9458 | 1143.8009 | 195.4684 | 701.0393 | 164.1642 |

0.64 | 12.6188 | 1180.6977 | 232.3652 | 664.1425 | 127.2674 |

0.66 | 13.2918 | 1217.5945 | 269.262007 | 627.2457 | 90.3706 |

0.68 | 13.9648 | 1254.4913 | 306.1588 | 590.3488 | 53.4738 |

0.70 | 14.6378 | 1291.3881 | 343.055613 | 553.4520 | 16.5770 |

$\mathit{h}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{E}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{E}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{E}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{H}\mathit{S}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{S}\mathbf{*}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{H}\mathit{S}\mathbf{*}}\mathbf{-}{\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{S}\mathbf{*}}$ |
---|---|---|---|---|

5 | 187.3184 | 58.6598 | 182.2710 | 205.3829 |

10 | 178.7620 | 57.3094 | 168.8554 | 202.8754 |

15 | 175.9814 | 56.8740 | 164.5236 | 202.1000 |

20 | 174.6043 | 56.6589 | 162.3830 | 201.7228 |

25 | 173.7821 | 56.5307 | 161.1066 | 201.4998 |

30 | 173.2357 | 56.4456 | 160.2590 | 201.3525 |

35 | 172.8462 | 56.3850 | 159.6551 | 201.2479 |

40 | 172.5546 | 56.3396 | 159.2031 | 201.1698 |

45 | 172.3281 | 56.3044 | 158.8521 | 201.1093 |

50 | 172.1470 | 56.2762 | 158.5716 | 201.0610 |

$\mathsf{\theta}$ | ${\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{S}}\mathbf{-}{\mathit{\pi}}_{\mathit{M}}^{\mathit{D}\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{S}}\mathbf{-}{\mathit{\pi}}_{\mathit{R}}^{\mathit{D}\mathit{E}}$ | ${\mathit{\pi}}_{\mathit{S}}^{\mathit{D}\mathit{S}}\mathbf{-}{\mathit{\pi}}_{\mathit{S}}^{\mathit{D}\mathit{E}}$ | ${\mathit{s}}^{\mathit{D}\mathit{S}\mathbf{*}}\mathbf{-}{\mathit{s}}^{\mathit{D}\mathit{E}\mathbf{*}}$ |
---|---|---|---|---|

0.2 | −450.3341 | 269.7349 | −180.5992 | 0.1942 |

0.22 | −458.8537 | 270.2433 | −188.6104 | 0.1812 |

0.24 | −455.1710 | 261.4272 | −193.7438 | 0.1682 |

0.26 | −439.2859 | 243.2865 | −195.9993 | 0.1552 |

0.28 | −411.1984 | 215.8214 | −195.3771 | 0.1423 |

0.3 | −370.9087 | 179.0317 | −191.8770 | 0.1293 |

0.32 | −318.4165 | 132.9174 | −185.4991 | 0.1163 |

0.34 | −253.7221 | 77.4787 | −176.2434 | 0.1033 |

0.36 | −176.8253 | 12.7154 | −164.1099 | 0.0903 |

0.38 | −87.7261 | −61.3724 | −149.0985 | 0.0774 |

0.4 | 13.5754 | −144.7848 | −131.2094 | 0.0644 |

0.42 | 127.0792 | −237.5216 | −110.4424 | 0.0514 |

0.44 | 252.7854 | −339.5830 | −86.7976 | 0.0384 |

0.46 | 390.6939 | −450.9689 | −60.2750 | 0.0254 |

0.48 | 540.8048 | −571.6794 | −30.8746 | 0.0124 |

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**MDPI and ACS Style**

Yang, S.; Lai, I.K.W.; Tang, H.
Pricing and Contract Coordination of BOPS Supply Chain Considering Product Return Risk. *Sustainability* **2022**, *14*, 5055.
https://doi.org/10.3390/su14095055

**AMA Style**

Yang S, Lai IKW, Tang H.
Pricing and Contract Coordination of BOPS Supply Chain Considering Product Return Risk. *Sustainability*. 2022; 14(9):5055.
https://doi.org/10.3390/su14095055

**Chicago/Turabian Style**

Yang, Shujun, Ivan Kai Wai Lai, and Huajun Tang.
2022. "Pricing and Contract Coordination of BOPS Supply Chain Considering Product Return Risk" *Sustainability* 14, no. 9: 5055.
https://doi.org/10.3390/su14095055