# Research on Timing Sequence Update Strategy Decision of Project Portfolio Based on Coupling Benefits in Strategic Period

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## Abstract

**:**

## 1. Introduction

- (1)
- In this study, we advocate for the adoption of strategic period coupling benefits as the foundational criterion for project portfolio selection. Contrary to solely focusing on enterprise benefits, coupling benefits encompass both the alignment of a project with enterprise strategies and the economic advantages of each project. This approach more effectively realizes enterprise strategic objectives and offers a novel perspective on project portfolio selection.
- (2)
- In recognition of the extended duration over which the selected portfolio will be implemented, we introduce a decision model for the sequential strategic updating of portfolios that is rooted in the concept of coupling benefits over the strategic period. Viewing the entirety of the strategic period, it is segmented into distinct phases. This approach facilitates the strategic selection of projects at any decision-making juncture within the overarching strategic period.
- (3)
- Regarding research methodologies, traditional operation research optimization algorithms encounter challenges in addressing the dynamic project combination problems presented in this study. While multi-agent reinforcement learning (MSA) is an algorithm that was only recently introduced, it remains underexplored in the realm of project portfolio optimization. In this study, we employ the multi-agent reinforcement learning algorithm to investigate project portfolio selection and monitor the implementation of decision-making processes.

## 2. Literature Review

## 3. Construction of Coupling Benefits Model for Project Portfolio Selection in Strategic Period

#### 3.1. Strategic Matching Degree of Project Portfolio Based on Compound Fuzzy Matter–Element Theory

#### 3.2. Project Portfolio Selection Model Based on Coupling Benefits Maximization in Strategic Period

## 4. Portfolio Timing Sequence Strategy Update Decision under Coupling Benefits Maximization in Strategic Period

#### 4.1. Multi-Stage Decision Analysis of Project Portfolio Timing Sequence Strategy Update

#### 4.2. Portfolio Timing Sequence Strategy Update Problem Description

#### 4.3. Construction of Project Portfolio Sequential Strategy Updating Model under Coupling Benefit Maximization in Strategic Period

## 5. Timing Sequence Strategy Update of Project Portfolio Based on Nash Q-Learning Algorithm

#### 5.1. Update Decision Analysis of Project Portfolio Timing Sequence Strategy Based on Multi-Agent Nash Q-Learning Algorithm

#### 5.2. The Principle of Portfolio Sequential Strategy Updating Based on the Nash Q-Learning Algorithm

#### 5.3. Calculation Steps of Project Portfolio Timing Strategy Update Solution Based on Nash Q-Learning Algorithm

## 6. Case Study

#### 6.1. Case Background

#### 6.2. Alternative Project Description

#### 6.3. Evaluation of Project Portfolio Strategy Matching

#### 6.4. Project Portfolio Selection and Sequential Strategy Updating Solution under Coupling Benefit Maximization

#### 6.5. Results Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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$\mathit{Q}-\mathit{T}\mathit{a}\mathit{b}\mathit{l}\mathit{e}$ | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | $\cdot \cdot \cdot $ | ${\mathit{a}}_{\mathit{n}}$ |
---|---|---|---|---|

${s}_{1}$ | $Q({s}_{1},{a}_{1})$ | $Q({s}_{1},{a}_{2})$ | $\cdot \cdot \cdot $ | $Q({s}_{1},{a}_{n})$ |

${s}_{2}$ | $Q({s}_{2},{a}_{1})$ | $Q({s}_{2},{a}_{2})$ | $\cdot \cdot \cdot $ | $Q({s}_{2},{a}_{n})$ |

$\cdot \cdot \cdot $ | $\cdot \cdot \cdot $ | $\cdot \cdot \cdot $ | $\cdot \cdot \cdot $ | $\cdot \cdot \cdot $ |

${s}_{n}$ | $Q({s}_{n},{a}_{1})$ | $Q({s}_{n},{a}_{2})$ | $\cdot \cdot \cdot $ | $Q({s}_{n},{a}_{n})$ |

$\mathbf{Project}{\mathit{N}}_{\mathit{j}}$ | The Initial Investment ${\mathit{C}}_{\mathit{j}}$ | Annual Revenue ${\mathit{R}}_{\mathit{j}}$ | The Cost of Expanding the Project | Net Cash Flow to Be Increased after Expansion of the Project |
---|---|---|---|---|

Project ${N}_{1}$ | 27,000 | 2396 | 1350 | +405 |

Project ${N}_{2}$ | 21,780 | 1912 | 1089 | +326.7 |

Project ${N}_{3}$ | 16,545 | 1428 | 827.25 | +248.18 |

Project ${N}_{4}$ | 14,783 | 1551 | 739.15 | +221.75 |

Project ${N}_{5}$ | 20,619 | 1896 | 1030.95 | +309.29 |

Project ${N}_{6}$ | 13,520 | 1049 | 676 | +202.8 |

Project ${N}_{7}$ | 9875 | 832 | 493.75 | +148.13 |

Project ${N}_{8}$ | 12,910 | 1143 | 645.5 | +193.65 |

Project ${N}_{9}$ | 10,200 | 985 | 510 | +153 |

Project ${N}_{10}$ | 8090 | 797 | 404.5 | +121.35 |

**Table 3.**Index and description of strategic demand rating of ecological environmental protection project portfolios.

Strategic Dimensions | Objective | Evaluation Index $\mathit{p}$ |
---|---|---|

Economic benefit dimension | The benefits are optimal in the strategic period | Rate of return on investment ${p}_{1}$ |

Ecological benefit dimension | Ecological restoration benefit | Ecological service value completion rate ${p}_{2}$ |

Public service dimensions | Improved public satisfaction | Public satisfaction index ${p}_{3}$ |

Organizational growth dimension | Degree of perfection of enterprise informatization | Level of informatization application ${p}_{4}$ |

Internal process dimension | Project fund management | The effective utilization rate of water conservancy investment ${p}_{5}$ |

${\mathit{T}}_{1}^{\mathit{B}}$ | ${\mathit{T}}_{1}^{\mathit{H}}$ | ${\mathit{T}}_{1}^{\mathit{P}}$ | ${\mathit{T}}_{2}^{\mathit{B}}$ | ${\mathit{T}}_{2}^{\mathit{H}}$ | ${\mathit{T}}_{2}^{\mathit{P}}$ | ${\mathit{T}}_{3}^{\mathit{B}}$ | ${\mathit{T}}_{3}^{\mathit{H}}$ | ${\mathit{T}}_{3}^{\mathit{P}}$ | ${\mathit{T}}_{4}^{\mathit{B}}$ | ${\mathit{T}}_{4}^{\mathit{H}}$ | ${\mathit{T}}_{4}^{\mathit{P}}$ | ${\mathit{T}}_{5}^{\mathit{B}}$ | ${\mathit{T}}_{5}^{\mathit{H}}$ | ${\mathit{T}}_{5}^{\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${T}_{1}^{B}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{1}^{H}$ | -L | -L | -L | −404.5 | 797 | 1078.66 | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{1}^{P}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{2}^{B}$ | -L | -L | -L | -L | -L | -L | −404.5 | 918.35 | 849.45 | -L | -L | -L | -L | -L | -L |

${T}_{2}^{H}$ | -L | -L | -L | -L | -L | -L | −404.5 | 797 | 809 | -L | -L | -L | -L | -L | -L |

${T}_{2}^{P}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{3}^{B}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | −404.5 | 1039.65 | 566.3 | -L | -L | -L |

${T}_{3}^{H}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | −404.5 | 797 | 539.33 | -L | -L | -L |

${T}_{3}^{P}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{4}^{B}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | −404.5 | 1161.15 | 283.14 |

${T}_{4}^{H}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | −404.5 | 797 | 269.66 |

${T}_{4}^{P}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{5}^{B}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{5}^{H}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

${T}_{5}^{P}$ | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L | -L |

Stage 1–2 | $\mathit{B}3\mathit{B}7\mathit{B}9\mathit{B}10$ | $\mathit{B}3\mathit{B}7\mathit{B}9\mathit{H}10$ | $\mathit{B}3\mathit{B}7\mathit{H}9\mathit{B}10$ | $\mathit{B}3\mathit{B}7\mathit{H}9\mathit{H}10$ | $\mathit{B}3\mathit{H}7\mathit{B}9\mathit{B}10$ | …… |
---|---|---|---|---|---|---|

$B3B7B9B10$ | −406.46 | −165.93 | −178.46 | 133.7 | 121.17 | …… |

$B3B7B9H10$ | −406.46 | −188 | −185.81 | 111.63 | 113.82 | …… |

$B3B7H9B10$ | −406.46 | −165.94 | −178.46 | 105.88 | 93.35 | …… |

$B3B7H9H10$ | −406.46 | −188 | −185.82 | 83.82 | 86 | …… |

$B3H7B9B10$ | −406.46 | −165.94 | −178.46 | 105.88 | 93.35 | …… |

…… | …… | …… | …… | …… | …… | …… |

Project Portfolio | Normalized Strategic Matching Degree | Strategic Period Total Benefits |
---|---|---|

${N}_{3}{N}_{7}{N}_{9}{N}_{10}$ | 0.09 | 263,360 |

${N}_{4}{N}_{7}{N}_{9}{N}_{10}$ | 0.18 | 253,263.4 |

${N}_{6}{N}_{7}{N}_{8}{N}_{10}$ | 0.18 | 261,312 |

${N}_{6}{N}_{7}{N}_{9}{N}_{10}$ | 0.09 | 245,436 |

${N}_{6}{N}_{8}{N}_{9}{N}_{10}$ | 0.18 | 263,350 |

${N}_{7}{N}_{8}{N}_{9}{N}_{10}$ | 0.18 | 241,992 |

Project Portfolio | Normalized Strategic Matching Degree | Strategic Period Coupling Benefits |
---|---|---|

${N}_{3}{N}_{7}{N}_{9}{N}_{10}$ | 0.09 | 6503.273 |

${N}_{4}{N}_{7}{N}_{9}{N}_{10}$ | 0.18 | 6246.982 |

${N}_{6}{N}_{7}{N}_{8}{N}_{10}$ | 0.18 | 3228.727 |

${N}_{6}{N}_{7}{N}_{9}{N}_{10}$ | 0.09 | 6063.273 |

${N}_{6}{N}_{8}{N}_{9}{N}_{10}$ | 0.09 | 6504.727 |

${N}_{7}{N}_{8}{N}_{9}{N}_{10}$ | 0.18 | 5974.545 |

Stage | ${\mathit{T}}_{1}$ | ${\mathit{T}}_{2}$ | ${\mathit{T}}_{3}$ | ${\mathit{T}}_{4}$ | ${\mathit{T}}_{5}$ | |
---|---|---|---|---|---|---|

Project | ||||||

${N}_{6}$ | $\mathrm{M}$ | $\mathrm{E}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{M}$ | |

${N}_{8}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{R}$ | - | |

${N}_{9}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{E}$ | $\mathrm{M}$ | $\mathrm{M}$ | |

${N}_{10}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{M}$ | $\mathrm{M}$ |

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## Share and Cite

**MDPI and ACS Style**

Wu, K.; Feng, J.; Li, S.; Zhang, K.; Hu, D.
Research on Timing Sequence Update Strategy Decision of Project Portfolio Based on Coupling Benefits in Strategic Period. *Water* **2023**, *15*, 3769.
https://doi.org/10.3390/w15213769

**AMA Style**

Wu K, Feng J, Li S, Zhang K, Hu D.
Research on Timing Sequence Update Strategy Decision of Project Portfolio Based on Coupling Benefits in Strategic Period. *Water*. 2023; 15(21):3769.
https://doi.org/10.3390/w15213769

**Chicago/Turabian Style**

Wu, Kaili, Jingchun Feng, Sheng Li, Ke Zhang, and Daisong Hu.
2023. "Research on Timing Sequence Update Strategy Decision of Project Portfolio Based on Coupling Benefits in Strategic Period" *Water* 15, no. 21: 3769.
https://doi.org/10.3390/w15213769