# Developing a Revenue Sharing Method for an Operational Transfer-Operate-Transfer Project

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Common Methods of Revenue Sharing in PPP Projects

#### 2.2. Shapley Value Evolution and Its Application in TOT Project Revenue Sharing

#### 2.3. Main Influencing Factors of Revenue Sharing for TOT Projects

## 3. Methods

#### 3.1. Research Design

#### 3.2. Parameter Calculation of the Effort Level and Input Ratio

#### 3.2.1. Calculation of the Effort Level

_{11}, R

_{12}, R

_{13}. The scores of each indicator are U

_{i1}, U

_{i2}, U

_{i3}, and the weights of each indicator are respectively denoted as w

_{11}, w

_{12}and w

_{13}. Then, the expression of effort level is:

_{11}= 0.45, w

_{12}= 0.24, and w

_{13}= 0.31.

#### 3.2.2. Calculation of the Input Ratio

_{21}, R

_{22}, R

_{23}and R

_{24}, the scores of the secondary index are written as η

_{i1}, η

_{i2}, η

_{i3}, η

_{i4}, and the weights of the secondary index are written as w

_{21}, w

_{22}, w

_{23}and w

_{24}. Then, the correction coefficient of input ratio is expressed as:

#### 3.3. Development of the Operational TOT Project RSM

#### 3.3.1. Relevant Concepts

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

#### 3.3.2. RSM of the Operational TOT Project Based on Fuzzy Payoff Shapley Value

#### 3.3.3. RSM of the Operational TOT Project Based on Double-Fuzzy Shapley Value

#### 3.3.4. RSM of the Operational TOT Project Based on Input Ratio and Double-Fuzzy Shapley Value

## 4. Case Study

#### 4.1. Background of the Case

#### 4.2. Revenue Sharing of the Operational TOT Project Participants

#### 4.2.1. Revenue Sharing of the Operational TOT Project with Method #1

#### 4.2.2. Revenue Sharing of the Operational TOT Project with Method #2

#### 4.2.3. Revenue Sharing of the Operational TOT Project with Method #3

## 5. Results and Analysis

#### 5.1. Comparison 1

#### 5.2. Comparison 2

#### 5.2.1. Changes of Government Revenue Sharing Caused by Effort Level

#### 5.2.2. Changes of Private Partner Revenue Sharing Caused by Effort Level

#### 5.3. Comparison 3

#### 5.4. Potential Application from the Functional Analysis of Method #3

#### 5.5. Comparison of Different Modified Shapley Value Methods

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Comparison of ${\tilde{v}}_{TOT}$ and ${\tilde{\tilde{v}}}_{TOT}$ (${\tilde{\tilde{v}}}_{TOT}^{\eta}$).

**Figure 3.**Comparison of ${\tilde{\beta}}_{g}$, ${\tilde{\tilde{\beta}}}_{g}$ and ${\tilde{\tilde{\beta}}}_{g}^{\eta}$.

**Figure 4.**Comparison of ${\tilde{\gamma}}_{g}$, ${\tilde{\tilde{\gamma}}}_{g}$ and ${\tilde{\tilde{\gamma}}}_{g}^{\eta}$.

**Figure 5.**Comparison of ${\tilde{\beta}}_{c}$, ${\tilde{\tilde{\beta}}}_{c}$ and ${\tilde{\tilde{\beta}}}_{c}^{\eta}$.

**Figure 6.**Comparison of ${\tilde{\gamma}}_{c}$, ${\tilde{\tilde{\gamma}}}_{c}$ and ${\tilde{\tilde{\gamma}}}_{c}^{\eta}$.

Research Study | Modifying Factors | Unconsidered Factors |
---|---|---|

Hu et al. [42] | Investment proportion, risk allocation, contract execution degree, contribution degree. | Contribution of innovation revenue uncertainty, the uncertainty of effort level. |

Li et al. [43] | Risk allocation, investment proportion, contribution of innovation. | Contract execution degree revenue uncertainty, the uncertainty of effort level. |

Yu et al. [44] | Revenue uncertainty, investment proportion, risk allocation, contract execution degree. | Contribution of innovation, contract execution degree the uncertainty of effort level. |

Zhang [45] | Revenue uncertainty, or participation rate less than 1. | Investment proportion, risk allocation, contract execution degree. |

Indicators | 0 | 1 | 2 | 3 | 4 | Number of Experts | Score |
---|---|---|---|---|---|---|---|

Importance of R_{11} relative to R_{12} | 0 | 1 | 4 | 9 | 2 | 16 | 39 |

Importance of R_{11} relative to R_{13} | 0 | 2 | 4 | 8 | 2 | 16 | 37 |

Importance of R_{12} relative to R_{13} | 1 | 6 | 7 | 2 | 0 | 16 | 23 |

Indicators | R_{11} | R_{12} | R_{13} | Score | Corrected Score | Weights |
---|---|---|---|---|---|---|

R_{11} | - | 39 | 37 | 77 | 78 | 0.45 |

R_{12} | 17 | - | 23 | 40 | 41 | 0.24 |

R_{13} | 19 | 33 | - | 42 | 43 | 0.31 |

Total | 169 | 172 | 1 |

Indicators | 0 | 1 | 2 | 3 | 4 | Number of Experts | Score |
---|---|---|---|---|---|---|---|

Importance of R_{21} relative to R_{22} | 0 | 2 | 7 | 4 | 3 | 16 | 35 |

Importance of R_{21} relative to R_{23} | 1 | 4 | 6 | 3 | 2 | 16 | 29 |

Importance of R_{21} relative to R_{24} | 0 | 2 | 7 | 5 | 2 | 16 | 34 |

Importance of R_{22} relative to R_{23} | 0 | 2 | 8 | 4 | 2 | 16 | 33 |

Importance of R_{22} relative to R_{24} | 0 | 2 | 7 | 5 | 2 | 16 | 34 |

Importance of R_{23} relative to R_{24} | 0 | 4 | 6 | 4 | 2 | 16 | 31 |

Indicators | R_{21} | R_{22} | R_{23} | R_{24} | Score | Corrected Score | Weights |
---|---|---|---|---|---|---|---|

R_{21} | - | 35 | 29 | 34 | 98 | 99 | 0.29 |

R_{22} | 21 | - | 33 | 34 | 88 | 89 | 0.26 |

R_{23} | 27 | 23 | - | 31 | 81 | 82 | 0.24 |

R_{24} | 22 | 22 | 25 | - | 69 | 70 | 0.21 |

Total | 336 | 340 |

Indicators | Government | Private Partner | |
---|---|---|---|

Effort Level | Contract execution degree | 1 | 0.75 |

Undertaking task complexity | 0.7 | 1 | |

Mutual satisfaction | 0.9 | 0.7 | |

Input Ratio | Investment proportion | 0.2 | 0.8 |

Risk-sharing proportion | 0.3 | 0.7 | |

Innovation investment proportion | 0.1 | 0.9 | |

Critical problem investment proportion | 0.25 | 0.75 |

**Table 7.**Comparison of the revenue sharing of the government between Method #1 and Method #2 (E = ±0.2).

Indicators | Effort Level | Project Revenue | Revenue-Sharing Ratio (RSR) | Revenue Sharing | ||||
---|---|---|---|---|---|---|---|---|

E = 0.2 | E = −0.2 | E = 0.2 | E = −0.2 | E = 0.2 | E = −0.2 | E = 0.2 | E = −0.2 | |

Method #1 | 1 | 1 | 46.98 | 45.14 | 33.23% | 31.40% | 15.61 | 14.17 |

Method #2 | 0.91 | 0.89 | 41.528 | 37.88 | 38.65% | 35.55% | 16.05 | 13.47 |

Comparison | −0.09 | −0.11 | −5.46 | −7.26 | 5.42% | 4.15% | 0.44 | −0.70 |

Comparison (%) | −9% | −11% | −11.62% | −16.08% | - | - | 5.80% | −4.98% |

**Table 8.**Comparison of the revenue sharing of the private partner between Method #1 and Method #2 (E = 0.2).

Indicators | Effort Level | Project Revenue | RSR | Revenue Sharing |
---|---|---|---|---|

Method #1 | 1 | 46.98 | 67.64% | 31.78 |

Method #2 | 0.81 | 41.52 | 61.35% | 25.47 |

Comparison | −0.19 | −5.46 | −6.29% | −6.30 |

Comparison (%) | 19% | −11.62% | — | −19.84% |

**Table 9.**Comparison of the revenue sharing of the participants between Method #3 and Method #2 (E = 0.2).

Indicators | Government | Private Partner | ||||
---|---|---|---|---|---|---|

Input Ratio | RSR | Revenue Sharing | Input Ratio | RSR | Revenue Sharing | |

Method #2 | 0.5 | 38.65% | 16.05 | 0.5 | 61.35% | 25.47 |

Method #3 | 0.21 | 14.34% | 5.96 | 0.79 | 85.66% | 35.56 |

Comparison | −0.29 | −24.31% | −10.09 | 0.29 | 24.31% | 10.09 |

Comparison (%) | −58% | - | −62.89% | 58% | - | 39.62% |

Factors | Method 3# | Method 4# | Method 5# | Method 6# | Method 7# |
---|---|---|---|---|---|

Modifying forms | |||||

Fuzzy payoff | √ | √ | √ | ||

Fuzzy alliance | √ | √ | |||

Input ratio | √ | √ | √ | √ | |

Effort level | √ | √ | √ | ||

Features | |||||

Flexibility | √ | √ | √ | √ | √ |

Incentive | √ | √ | √ | √ | |

Applications | |||||

Forecasting | √ | √ | √ | ||

Exact distribution | √ | √ | √ |

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## Share and Cite

**MDPI and ACS Style**

Du, Y.; Fang, J.; Ke, Y.; Philbin, S.P.; Zhang, J. Developing a Revenue Sharing Method for an Operational Transfer-Operate-Transfer Project. *Sustainability* **2019**, *11*, 6436.
https://doi.org/10.3390/su11226436

**AMA Style**

Du Y, Fang J, Ke Y, Philbin SP, Zhang J. Developing a Revenue Sharing Method for an Operational Transfer-Operate-Transfer Project. *Sustainability*. 2019; 11(22):6436.
https://doi.org/10.3390/su11226436

**Chicago/Turabian Style**

Du, Yanhua, Jun Fang, Yongjian Ke, Simon P Philbin, and Jingxiao Zhang. 2019. "Developing a Revenue Sharing Method for an Operational Transfer-Operate-Transfer Project" *Sustainability* 11, no. 22: 6436.
https://doi.org/10.3390/su11226436