# Comparison of Multi-Criteria Group Decision-Making Methods for Urban Sewer Network Plan Selection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of Selected Multi-Criteria Methods

- Full aggregation methods: each criterion is assigned a weight, which indicates the importance of the criterion, then a numerical score for each alternative is calculated and the one with highest score prevails (e.g., AHP).
- Outranking methods: each pair of alternatives is compared for each criterion to rank the alternatives (e.g., ELECTRE, PROMETHEE).
- Goal, aspiration or reference level methods: these methods identify how far each alternative is from the ideal goal or aspiration (e.g., TOPSIS).

#### 2.1. AHP

#### 2.2. TOPSIS

#### 2.3. ELECTRE

- The degree of outranking is equal to the concordance index if there is no criterion that is discordant or where no veto threshold is used;
- The degree of outranking is equal to the concordance with a reduction as the level of discordance increases above a threshold value.

#### 2.4. PROMETHEE

- A unicriterion positive flow of an alternative is a score between $0$ and $1$, which expresses that an alternative is preferred (based on the decision-maker’s preference) over all other alternatives on that particular criterion. The higher the positive flow, the better the action compared to the others.
- A unicriterion negative flow of an alternative is a score between $0$ and $1$, which expresses that other alternatives are preferred to this one. Note that the unicriterion negative flow needs to be minimized since it represents the weakness of an alternative compared to the other alternatives.
- The unicriterion net flow is based on both positive flow and negative flow. Specifically, an alternative’s net flow is calculated by subtracting the negative flows from the positive flows. These values have to be maximized since they represent the balance between the general strength and the general weakness of an alternative.

- A global positive flow indicates that an alternative is globally preferred to all the other alternatives when considering all the criteria. Since the criteria weights are normalized, the global positive flow is always between $0$ and $1$.
- A global negative flow indicates that other alternatives are preferred over a given alternative. It is between $0$ and $1$ and must be minimized.

## 3. Case Study

#### 3.1. Structuring the Decision Problem

- Dynamic performance is a positive quantitative variable, and it represents qualitatively how much rainfall flow volume can be reduced in the pumping station (Table 4).
- The cost of construction is a negative quantitative variable defining how much it costs to implement a plan. It covers the cost of the duration of work, manpower, materials, and machines, etc. (Table 5).
- The cost of maintenance is a negative qualitative variable defining the cost of possible maintenance. For example, regular inspections or repairing damage due to human faults or extreme weather issues. It is not limited to a monetary valuation, as it also includes societal and environmental considerations.
- Environmental impact is a negative qualitative variable that includes the disruption to current inhabitants and existing industries, for example, noise, traffic, air or water pollution, water supply disruptions, etc.
- Potential future profit is a positive qualitative variable indicating the possible benefit a plan could provide after its implementation. For example, more population, or capacity during extreme weather (heavy rain), etc. It is not limited to a monetary valuation as it also includes societal and environmental considerations.

#### 3.2. Implementation of the MCDM Methods

- “Anonymous response: opinions of members of the group are gathered by the formal questionnaire;
- Iteration and controlled feedback: interaction is effected by a systematic exercise conducted in several iterations, with carefully controlled feedback between rounds;
- Statistical group response: the group opinion is defined as an appropriate aggregate of individual opinions on the final round.”

#### 3.2.1. AHP

#### 3.2.2. TOPSIS

#### 3.2.3. ELECTRE III

**Step 1**. Choose the decision setup tool to enter the goal of the sewer network planning, all the available alternatives, plus five criteria and indicate whether each criterion is qualitative or quantitative and minimizing or maximizing.

**Step 2**. Choose the ELECTRE III analysis tool. Open the structured problem from Step 1. Then make selections using the slider bars to indicate which criterion is more important, i.e., a higher weighting. Here, the project manager decided to use the weighting (in Figure 10) derived from the group discussion during the TOPSIS process to define the criteria weights (see Figure 12). The weights are not exactly the same because they are entered using a slider bar.

**Step 3**: For each quantitative criterion, enter its true quantitative data source (numerical value and unit) as well as the indifference, preference and veto thresholds. In this case, the user does not know the meaning thresholds; the tool has already provided the explanation to make sure the user entered reasonable inputs. For each qualitative criterion, the user indicates his/her preference for each alternative using the slider bar. The slider bar assigns an evaluation of extremely poor, very poor, average, good, very good, excellent. Figure 13 and Figure 14 provide some insight into the above description.

#### 3.2.4. PROMETHEE II

**Step 1**. Enter the performance of alternatives for different criteria (see Figure 12).

**Step 2.**Set up the preference parameters, such as maximize or minimize, to indicate whether the criterion is positive or negative; the preference function: the linear function is selected for all criteria; the indifference and preference threshold (see Figure 13 for the setup of one criterion).

**Step 3**. Set the criterion weight values. In this case, the project manager decided to use the weights (in Figure 10) derived from the group discussion during the TOPSIS process. In Smart Picker Pro, users set the weights using a slider bar (see Figure 15). Note that the weights are not exactly the same values as shown in Figure 10, because the slider bar cannot provide the exact value and causes bias (see Figure 16).

#### 3.3. Results Summary and Post-Analysis Interview

#### 3.4. Comparative Analysis and Discussion

#### 3.4.1. Comparison of Criteria Weights

#### 3.4.2. Comparison of Alternative Scores

## 4. Conclusions and Future Work

- Five criteria require ten pairwise comparisons to determine the criteria weights in AHP, which is more time consuming. The other three methods only need ten inputs. By increasing the number of criteria and alternatives, AHP is not a practical method to implement.
- The criteria weights and scores of the four methods are inconsistent, with AHP showing the greatest variation (Figure 19 and Figure 20). This is most likely because of inaccuracies with AHP’s 1–9 fundamental scale, decision fatigue and decision-makers’ perception that qualitative criteria with low weights have minor impact on the decision results.
- There are visible differences in the results of the four methods (Table 10). It needs to be pointed out that ELECTRE III was unable to provide a conclusive result, identifying both P1 and P2 as the best alternatives. PROMETHEE II and TOPSIS prefer P1, while AHP selects P2 as the best option. In general, P2 receives extremely high scores on three criteria and extremely low scores on the other two criteria, while P1 has a more or less average evaluation on different criteria. When considering this, decision-makers all prefer P1 over P2.
- TOPSIS requires all the performances for different criteria to be expressed in the same measurement unit. This makes decision-makers feel that TOPSIS is limited when the true numerical experimental values cannot be used as input directly.
- PROMETHEE is the favored method for decision-makers in terms of the decisive result identifying P1 as the best option and decision-makers’ satisfaction with the implementation process.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Degree of Importance | Definition | Explanation |
---|---|---|

1 | Equal importance | Two candidates contribute equally to the objective. |

3 | Moderate importance | Experience and judgment slightly favor one candidate over another. |

5 | Strong importance | Experience and judgment strongly favor one candidate over another. |

7 | Very strong importance | One candidate is favored very strongly over another. |

9 | Extreme importance | The evidence favoring one candidate over another is of the highest possible order of affirmation. |

Degrees of 2, 4, 6 and 8 can be used to express intermediate values. Degrees of 1.1, 1.2, 1.3, etc. can be used for alternatives that are very close in importance. |

Number of Rows in the Matrix | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|

$RI$ | 0.525 | 0.880 | 1.109 | 1.248 | 1.342 | 1.406 | 1.450 | 1.485 |

Source | Status | Aim | ||
---|---|---|---|---|

C1 | Dynamic performance | Quantitative | Positive | Maximize |

C2 | Cost of construction | Quantitative | Negative | Minimize |

C3 | Cost of maintenance | Qualitative | Negative | Minimize |

C4 | Environmental impact | Qualitative | Negative | Minimize |

C5 | Potential future profit | Qualitative | Positive | Maximize |

Alternatives | Dynamic Performance (L/s) |
---|---|

P1 | 196.41 |

P2 | 75.64 |

P3 | 214.34 |

P4 | 105.87 |

Plan | Total Cost (CAD) |
---|---|

P1 | 1,884,753 |

P2 | 437,606 |

P3 | 4,127,967 |

P4 | 2,680,820 |

P1 | Project Manager | Civil Engineer 1 | Civil Engineer 2 | Road Operator 1 | Road Operator 2 | Wea&Env Expert | Sanitary Engineer 1 | Sanitary Engineer 2 | Average |
---|---|---|---|---|---|---|---|---|---|

Dynamic performance | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 7 | 7.375 |

Cost of construction | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6.125 |

Cost of maintenance | 7 | 7 | 6 | 6 | 6 | 6 | 6 | 6 | 6.25 |

Environmental impact | 7 | 7 | 7 | 7 | 7 | 6 | 7 | 7 | 6.875 |

Potential future profit | 7 | 7 | 8 | 8 | 8 | 7 | 7 | 7 | 7.375 |

Alternatives Criteria | P1 | P2 | P3 | P4 |
---|---|---|---|---|

Dynamic performance | 7.375 | 4.875 | 8.375 | 5 |

Cost of construction | 6.125 | 8.5 | 3 | 4.5 |

Cost of maintenance | 6.25 | 7.75 | 5.125 | 5.125 |

Environmental impact | 6.875 | 7.375 | 3.25 | 3.875 |

Potential future profit | 7.375 | 2.875 | 8.375 | 5.125 |

TOPSIS Results | P1 | P2 | P3 | P4 |
---|---|---|---|---|

Rank
| 1st | 2nd | 3rd | 4th |

Relative closeness
| 0.6663 | 0.5538 | 0.4462 | 0.2672 |

Descending Order | Ascending Order | Final Order | |
---|---|---|---|

First | P1 | P2 | P1 P2 |

Second | P2 | P1 | P3 |

Third | P3 P4 | P3 | P4 |

Fourth | P4 |

1st | 2nd | 3rd | 4th | |
---|---|---|---|---|

AHP | P2 | P1 | P3 | P4 |

TOPSIS | P1 | P2 | P3 | P4 |

ELECTRE III | P1 P2 | P3 | P4 | |

PROMETHEE II | P1 | P2 | P3 | P4 |

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**MDPI and ACS Style**

Wu, Z.; Abdul-Nour, G.
Comparison of Multi-Criteria Group Decision-Making Methods for Urban Sewer Network Plan Selection. *CivilEng* **2020**, *1*, 26-48.
https://doi.org/10.3390/civileng1010003

**AMA Style**

Wu Z, Abdul-Nour G.
Comparison of Multi-Criteria Group Decision-Making Methods for Urban Sewer Network Plan Selection. *CivilEng*. 2020; 1(1):26-48.
https://doi.org/10.3390/civileng1010003

**Chicago/Turabian Style**

Wu, Zhen, and Georges Abdul-Nour.
2020. "Comparison of Multi-Criteria Group Decision-Making Methods for Urban Sewer Network Plan Selection" *CivilEng* 1, no. 1: 26-48.
https://doi.org/10.3390/civileng1010003