# A Markov Chain Approach to Multicriteria Decision Analysis with an Application to Offshore Decommissioning

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Multicriteria Decision Analysis

#### 2.2. Uncertainty Analysis

#### 2.3. Probabilistic MCDA Approaches

## 3. Mathematical Formulation

## 4. Numerical Experiments

#### 4.1. An Example with Uncertain Performance Functions

#### 4.2. Application to Decommissioning of Oil and Gas Fields

#### 4.3. Analysis of the Result

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Area | Label | Unit | Criterion |
---|---|---|---|

Safety | 1 | PLL | Safety risk to offshore project personnel |

2 | PLL | Safety risk to other users of the sea | |

3 | PLL | Safety risk to onshore project personnel | |

Environmental | 4 | Score | Operational environmental impacts |

5 | Score | Legacy environmental impacts | |

6 | GJ | Energy use | |

7 | tons of CO_{2} | Emissions | |

Technical | 8 | Score | Technical feasibility |

Social | 9 | £ | Effects on commercial fisheries |

10 | Employees Year | Employment | |

11 | Score | Communities | |

Economic | 12 | ${10}^{6}$ £ | Cost |

_{2}for carbon dioxide.

Alternatives | Description |
---|---|

${a}_{1}$ | Leave tied-in at platform; remote and trenched |

${a}_{2}$ | Leave tied-in at platform; remote and rock-dumped |

${a}_{3}$ | Disconnect from the installation; trench and backfill whole length |

${a}_{4}$ | Disconnect from the installation; rock-dump whole length |

${a}_{5}$ | Recover whole length by cutting and lifting |

${a}_{6}$ | Recover whole length with a reverse S-lay |

Criterion | Alternatives | |||||
---|---|---|---|---|---|---|

${\mathit{a}}_{\mathbf{1}}$ | ${\mathit{a}}_{\mathbf{2}}$ | ${\mathit{a}}_{\mathbf{3}}$ | ${\mathit{a}}_{\mathbf{4}}$ | ${\mathit{a}}_{\mathbf{5}}$ | ${\mathit{a}}_{\mathbf{6}}$ | |

1 | 625.00 | 625.00 | 416.67 | 500.00 | 357.14 | 232.56 |

2 | 12.50 | 10.66 | 625.00 | 625.00 | 833.33 | 833.33 |

3 | 833.33 | 833.33 | 833.33 | 833.33 | 833.33 | 833.33 |

4 | 0.99 | 0.98 | 0.91 | 0.85 | 0.91 | 0.95 |

5 | 0.95 | 0.95 | 1 | 0.90 | 1 | 1 |

6 | $4.11\times {10}^{-5}$ | $4.79\times {10}^{-5}$ | $4.11\times {10}^{-5}$ | $4.11\times {10}^{-5}$ | $4.11\times {10}^{-5}$ | $3.59\times {10}^{-5}$ |

7 | $5.3\times {10}^{-4}$ | $5.3\times {10}^{-4}$ | $4.5\times {10}^{-4}$ | $5.3\times {10}^{-4}$ | $6.3\times {10}^{-4}$ | $5.3\times {10}^{-4}$ |

8 | 0.92 | 1 | 0.80 | 1 | 0.84 | 0.35 |

9 | 0.00 | 0.00 | 228,344.2 | 183,367.3 | 228,344.2 | 228,344.2 |

10 | 6.35 | 3.17 | 9.53 | 6.35 | 19.05 | 31.76 |

11 | 1 | 1 | 1 | 1 | 0.95 | 0.95 |

12 | 0.75 | 0.93 | 0.47 | 0.53 | 0.20 | 0.13 |

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**MDPI and ACS Style**

Moraes, F.F.; Filho, V.J.M.F.; Infante, C.E.D.d.C.; Santos, L.; Arruda, E.F.
A Markov Chain Approach to Multicriteria Decision Analysis with an Application to Offshore Decommissioning. *Sustainability* **2022**, *14*, 12019.
https://doi.org/10.3390/su141912019

**AMA Style**

Moraes FF, Filho VJMF, Infante CEDdC, Santos L, Arruda EF.
A Markov Chain Approach to Multicriteria Decision Analysis with an Application to Offshore Decommissioning. *Sustainability*. 2022; 14(19):12019.
https://doi.org/10.3390/su141912019

**Chicago/Turabian Style**

Moraes, Fernanda F., Virgílio José M. Ferreira Filho, Carlos Eduardo Durange de C. Infante, Luan Santos, and Edilson F. Arruda.
2022. "A Markov Chain Approach to Multicriteria Decision Analysis with an Application to Offshore Decommissioning" *Sustainability* 14, no. 19: 12019.
https://doi.org/10.3390/su141912019