# Multi-Period Multi-Criteria Decision Making under Uncertainty: A Renewable Energy Transition Case from Germany

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## Abstract

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## 1. Introduction

## 2. Literature Review: MP MADM Approaches

## 3. MP MADM Approach under Deep Uncertainty

#### 3.1. Description of PROMETHEE

- The indifference threshold ${q}_{i}$ defines the largest ${d}_{i}\left({a}_{j},{a}_{k}\right)$ that is considered negligible for the decision maker.
- The preference threshold ${p}_{i}$ defines the minimal ${d}_{i}\left({a}_{j},{a}_{k}\right)$ that is required for a strict preference on a criterion.
- The reversal point ${\sigma}_{i}$ represents the inflection point of the preference function (Type VI) and is derived from the normal distribution.

#### 3.2. Extension of PROMETHEE to the MP Case with Scenarios (MP-PROMETHEE-S)

**Step 1:**MP problem formulation with scenarios

**Step 2:**SP evaluations of alternatives in each period and scenario

**Step 3:**MP aggregation of evaluations, sensitivity analysis, and evaluation of scenarios

## 4. Case Study: Planning the Local Energy Transition in Jühnde

**Step 1:**MP problem formulation with scenarios

**Baseline**represents the real-world development of renewable energy expansion in Jühnde, with two investments in a biogas power plant and PV systems. $\mathsf{\Psi}2$

**Biomass and Photovoltaic**represents the original investment in a bioenergy power plant in 2005 and further extension with rooftop PV systems in 2015. $\mathsf{\Psi}3$

**Biomass and Wind**also represents the original investment in a bioenergy power plant, but is complemented with wind energy in 2015. In $\mathsf{\Psi}4$

**Wind and PV,**the bioenergy plant is substituted by wind energy plants and complemented with rooftop PV systems in 2015 and 2020.

_{2}emissions, and the degree of self-sufficiency of the town. For calculating the transition paths’ performance scores in terms of these criteria, the same assumptions and energy system model were used as in the original case study described in [56]. In particular, we used [89,90,91,92] to quantify the levelized costs of electricity, [93] to quantify the land use, [94] to quantify CO

_{2}emissions, and [95,96] to quantify the self-sufficiency of the town.

**Technical progress (power supply):**This key factor represents the technical progress in terms of efficiency gains of already readily available power generation technologies.**Governmental support:**This represents the governmental support of power generation technologies, e.g., in terms of subsidies or R&D, as well as fostering awareness for energy efficiency in the public.**Public contribution:**This represents the behavior of the public in terms of acceptance of energy-efficient electrical appliances.

_{2}emissions occur, because the power production exceeds the demand in Jühnde and power is fed into the grid. Up to $t=2010$, $\mathsf{\Psi}2$ and $\mathsf{\Psi}3$ have the same performance scores for all criteria in all scenarios, because the renewable capacity expansion in these paths is the same up to this point.

**Step 2:**SP evaluations of alternatives in each period and scenario

**Step 3:**MP aggregation of evaluations, sensitivity analysis, and evaluation of scenarios

_{2}emissions does not have an impact on the ranks of the paths. The smallest deviation from equal weights (25%), which would be necessary for a rank reversal, is a 10.16% increase in the criteria weight of land use in S1. For the given decision problem, the scenarios broaden the range in which rank reversals occur, but the next-best path is always the same, regardless of scenario (provided that the optimal path does change at all). For example, if the weight of LCOE is decreased, $\mathsf{\Psi}1$ becomes the optimal path in each scenario.

## 5. Discussion and Future Research Opportunities

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Results of the MP aggregation ${\varphi}^{net}\left(\mathsf{\Psi}\right)$, with variants 1 and 2 (r = 1%, 5%, and 10%).

References | MADM Algorithm | MP Aggregation | Uncertainty Consideration | Criteria Weights | Path Dependency | Specific Features |
---|---|---|---|---|---|---|

[47] | Generic | Not specified | No uncertainties | Dynamic | Not considered | Group decision-making |

[48] | Generic | Decision tree | Probabilities of scenarios | Static | Modeled explicitly | |

[49,50,51,52] | Single synthesizing criteria approach | Confidence levels of periods | Probabilities of scenarios | Static | Not considered | |

[53] | Generic | Not specified | Not specified | Static | Modeled explicitly | |

[54] | PROMETHEE II | Confidence levels of periods | No uncertainties | Static | Not considered | Varying thresholds in preference functions |

[55] | PROMETHEE I | Confidence levels of periods | Monte Carlo simulations of performance scores | Static | Not considered | |

[56] | PROMETHEE II | Arithmetic mean, weighted average (confidence levels of periods), mean of discounted net flows | No uncertainties | Static or dynamic | Modeled explicitly | Varying thresholds in preference functions are aggregated |

[57] | PROMETHEE II | Arithmetic mean or weighted average | No uncertainties | Static or dynamic | Not considered | Weighting factor for MP aggregation can include a discount |

This paper | PROMETHEE II | Arithmetic mean, mean of discounted net flows | Scenarios (without probabilities) | Static of dynamic | Modeled explicitly | Sensitivity analysis of discount factors |

**Table 2.**Power supply of renewable energy technologies in different expansion paths in MWh. Added capacity is depicted in italics.

Power Supply | 2005 | 2010 | 2015 | 2020 | |
---|---|---|---|---|---|

$\mathsf{\Psi}1$ | Biogas power plant | 4816.68 (+4816.68) | 6811.31 (+1994.63) | 6811.31 | 6811.31 |

PV systems | 95.83 (+95.83) | 388.70 (+292.87) | 706.31 (+317.61) | 706.31 | |

Wind power plant | - | - | - | - | |

Ψ2 | Biogas power plant | 4816.68 (+4816.68) | 4816.68 | 4816.68 | 4816.68 |

PV systems | - | - | 2700.94 (+2700.94) | 2700.94 | |

Wind power plant | - | - | - | - | |

Ψ3 | Biogas power plant | 4816.68 (+4816.68) | 4816.68 | 4816.68 | 4816.68 |

PV systems | - | - | - | - | |

Wind power plant | - | - | 2700.94 (+2700.94) | 2700.94 | |

$\mathsf{\Psi}4$ | Biogas power plant | - | - | - | - |

PV systems | 95.83 (+95.83) | 95.83 | 1541.66 (+1445.83) | 2700.94 (+1159.28) | |

Wind power plant | 4816.68 (+4816.68) | 4816.68 | 4816.68 | 4816.68 |

**Table 3.**Cross-impact matrix for the case study. A: technical progress; B: political support; C: public contribution; hist: historical development; +: increased; −: decreased.

A1: Hist | A2: + | A3: − | B1: Hist | B2: + | B3: − | C1: Hist | C2: + | C3: − | |
---|---|---|---|---|---|---|---|---|---|

A1: hist | 2 | 1 | 1 | 2 | 1 | 1 | |||

A2: + | −1 | 1 | −1 | 1 | 1 | 1 | |||

A3: − | 1 | 0 | 1 | 1 | 1 | 1 | |||

B1: hist | 3 | 2 | −2 | 3 | 1 | 1 | |||

B2: + | −1 | 3 | −3 | −1 | 3 | −2 | |||

B3: − | 1 | −1 | 3 | −1 | −2 | 3 | |||

C1: hist | 0 | 0 | 0 | 1 | 0 | 0 | |||

C2: + | 0 | 0 | 0 | 0 | −1 | 0 | |||

C3: − | 0 | 0 | 0 | 0 | 0 | −1 |

Scenario | S1: Reference | S2: Best Case | S3: Worst Case | S4: Efficient Power Generation | S5: Lower Energy Demand | |
---|---|---|---|---|---|---|

Key Factor | ||||||

A: Technical progress | Historic | Increased | Decreased | Increased | Historic | |

B: Political support | Historic | Increased | Decreased | Historic | Historic | |

C: Public contribution | Historic | Increased | Decreased | Historic | Increased |

$\mathbf{Emission}\text{}\mathbf{Factor}\text{}\mathbf{in}\text{}\mathit{C}{\mathit{O}}_{2}\cdot {\left(\mathit{k}\mathit{W}\mathit{h}\right)}^{-1}$ | $\mathbf{Agricultural}\text{}\mathbf{Land}\text{}\mathbf{Use}\text{}\mathbf{in}\text{}\mathbf{J}\xfc\mathbf{hnde}\text{}\mathbf{in}\text{}{\mathit{m}}^{2}\cdot {(\mathit{M}\mathit{W}\mathit{h})}^{-1}{\mathit{y}}^{-1}$ | $\mathbf{Levelized}\text{}\mathbf{Cos}\mathbf{t}\text{}\mathbf{of}\text{}\mathbf{Electricity}\text{}\mathbf{in}\text{}\mathbf{\u20ac}\cdot {\left(\mathit{k}\mathit{W}\mathit{h}\right)}^{-1}$ | $\mathbf{Electricity}\text{}\mathbf{Demand}\text{}\mathbf{in}\text{}\mathit{M}\mathit{W}\mathit{h}\cdot {\mathit{y}}^{-1}$ | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Scenarios | Power from grid | Bioenergy | Ground-mounted PV | Wind energy | Power from grid | Bioenergy | Rooftop/ground-mounted PV | Wind energy | - | |

S1: Reference Scenario | 2005 | 586 | 980 | 30 | 60 | 0.11 | 0.10 | 0.54 | 0.09 | 8021 |

2010 | 567 | 980 | 30 | 60 | 0.14 | 0.11 | 0.35 | 0.08 | 8021 | |

2015 | 511 | 980 | 30 | 60 | 0.13 | 0.11 | 0.21 | 0.08 | 8021 | |

2020 | 471 | 980 | 30 | 60 | 0.14 | 0.10 | 0.14 | 0.07 | 8021 | |

S2: Best case | 2005 | 527.76 | 882.00 | 27.00 | 54.00 | 0.10 | 0.09 | 0.48 | 0.08 | 7860.58 |

2010 | 474.98 | 793.80 | 24.30 | 48.60 | 0.09 | 0.08 | 0.32 | 0.07 | 7703.37 | |

2015 | 427.49 | 741.42 | 21.87 | 43.74 | 0.08 | 0.07 | 0.19 | 0.06 | 7549.30 | |

2020 | 384.74 | 642.98 | 19.68 | 39.37 | 0.07 | 0.07 | 0.12 | 0.06 | 7398.32 | |

S3: Worst case | 2005 | 645.04 | 1078.00 | 33.00 | 66.00 | 0.12 | 0.11 | 0.59 | 0.10 | 8181.42 |

2010 | 709.54 | 1185.80 | 36.30 | 72.60 | 0.14 | 0.12 | 0.39 | 0.11 | 8345.05 | |

2015 | 780.50 | 1304.38 | 39.93 | 79.86 | 0.15 | 0.13 | 0.23 | 0.12 | 8511.95 | |

2020 | 858.55 | 1434.82 | 43.92 | 87.85 | 0.17 | 0.15 | 0.15 | 0.13 | 8682.19 | |

S4: Efficient power generation | 2005 | 547.67 | 960.4 | 29.4 | 58.8 | 0.11 | 0.10 | 0.54 | 0.09 | 8021 |

2010 | 555.46 | 941.19 | 28.81 | 57.62 | 0.14 | 0.11 | 0.35 | 0.08 | 8021 | |

2015 | 500.49 | 922.37 | 28.24 | 56.47 | 0.13 | 0.11 | 0.21 | 0.08 | 8021 | |

2020 | 462.01 | 903.92 | 27.67 | 55.34 | 0.14 | 0.10 | 0.14 | 0.07 | 8021 | |

S5: Low energy demand in 2020 | 2005 | 586 | 980 | 30 | 60 | 0.11 | 0.10 | 0.54 | 0.09 | 8021 |

2010 | 567 | 980 | 30 | 60 | 0.14 | 0.11 | 0.35 | 0.08 | 8021 | |

2015 | 511 | 980 | 30 | 60 | 0.13 | 0.11 | 0.21 | 0.08 | 8021 | |

2020 | 471 | 980 | 30 | 60 | 0.14 | 0.10 | 0.14 | 0.07 | 6416.8 |

**Table 6.**Decision table. LCOE in cent/kWh; land use in ha/a; CO

_{2}: CO

_{2}emissions in t/a; SS: self-sufficiency in %.

Year | $\mathbf{\Psi}1$ | $\mathbf{\Psi}2$ | $\mathbf{\Psi}3$ | $\mathbf{\Psi}4$ | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LCOE | Land Use | CO_{2} | SS | LCOE | Land Use | CO_{2} | SS | LCOE | Land Use | CO_{2} | SS | LCOE | Land Use | CO_{2} | SS | ||

S1 | 2005 | 11.01 | 472.03 | 1823 | 61.25 | 10.51 | 472.03 | 1879 | 60.05 | 10.51 | 472.03 | 1879 | 60.05 | 10.29 | 28.90 | 1823 | 47.63 |

2010 | 12.01 | 667.57 | 465 | 89.77 | 11.61 | 472.03 | 1816 | 60.05 | 11.61 | 472.03 | 1816 | 60.05 | 11.36 | 28.90 | 1762 | 47.63 | |

2015 | 12.24 | 667.57 | 257 | 93.38 | 13.97 | 472.03 | 257 | 83.95 | 9.42 | 488.24 | 257 | 87.83 | 12.47 | 28.90 | 849 | 60.75 | |

2020 | 12.28 | 667.57 | 237 | 93.38 | 14.01 | 472.03 | 237 | 83.95 | 9.47 | 488.24 | 237 | 87.83 | 12.59 | 28.90 | 237 | 65.41 | |

S2 | 2005 | 9.91 | 424.83 | 1556 | 62.50 | 9.44 | 424.83 | 1606 | 61.28 | 9.44 | 424.83 | 1606 | 61.28 | 9.24 | 26.01 | 1556 | 48.20 |

2010 | 10.13 | 583.22 | 239 | 93.47 | 9.05 | 424.83 | 1371 | 62.53 | 9.05 | 424.83 | 1,371 | 62.53 | 8.86 | 26.01 | 1326 | 48.77 | |

2015 | 10.57 | 583.22 | 14 | 95.06 | 12.60 | 424.83 | 14 | 86.08 | 8.07 | 436.64 | 14 | 90.18 | 10.61 | 26.01 | 509 | 62.62 | |

2020 | 10.63 | 583.22 | −46 | 95.54 | 12.71 | 424.83 | −46 | 86.78 | 8.08 | 436.64 | −46 | 90.92 | 11.32 | 26.01 | −46 | 67.60 | |

S3 | 2005 | 12.12 | 519.24 | 2109 | 60.04 | 11.58 | 519.24 | 2170 | 58.87 | 11.58 | 519.24 | 2170 | 58.87 | 11.34 | 31.79 | 2109 | 47.07 |

2010 | 13.16 | 755.84 | 812 | 86.27 | 12.12 | 519.24 | 2504 | 57.72 | 12.12 | 519.24 | 2504 | 57.72 | 11.87 | 31.79 | 2436 | 46.51 | |

2015 | 13.69 | 755.84 | 776 | 88.31 | 15.38 | 519.24 | 776 | 81.80 | 11.69 | 540.81 | 776 | 85.32 | 13.90 | 31.79 | 1681 | 58.87 | |

2020 | 13.91 | 755.84 | 1000 | 86.58 | 15.57 | 519.24 | 1000 | 81.07 | 11.96 | 540.81 | 1000 | 84.45 | 14.13 | 31.79 | 1000 | 63.18 | |

S4 | 2005 | 11.01 | 462.59 | 1786 | 61.25 | 10.51 | 462.59 | 1841 | 60.05 | 10.51 | 462.59 | 1841 | 60.05 | 10.29 | 28.32 | 1786 | 47.63 |

2010 | 12.01 | 650.39 | 456 | 89.77 | 11.61 | 462.59 | 1780 | 60.05 | 11.61 | 462.59 | 1780 | 60.05 | 11.36 | 28.32 | 1727 | 47.63 | |

2015 | 12.24 | 650.39 | 252 | 93.38 | 13.97 | 462.59 | 252 | 83.95 | 9.42 | 477.85 | 252 | 87.83 | 12.47 | 28.32 | 832 | 60.75 | |

2020 | 12.28 | 650.39 | 233 | 93.38 | 14.01 | 462.59 | 233 | 83.95 | 9.47 | 477.85 | 233 | 87.83 | 12.59 | 28.32 | 233 | 65.41 | |

S5 | 2005 | 11.01 | 472.03 | 1823 | 61.25 | 10.51 | 472.03 | 1879 | 60.05 | 10.51 | 472.03 | 1879 | 60.05 | 10.29 | 28.90 | 1823 | 47.63 |

2010 | 12.01 | 667.57 | 465 | 89.77 | 11.61 | 472.03 | 1816 | 60.05 | 11.61 | 472.03 | 1816 | 60.05 | 11.36 | 28.90 | 1762 | 47.63 | |

2015 | 12.24 | 667.57 | 257 | 93.38 | 13.97 | 472.03 | 257 | 83.95 | 9.42 | 488.24 | 257 | 87.83 | 12.47 | 28.90 | 849 | 60.75 | |

2020 | 11.89 | 667.57 | −519 | 97.96 | 14.06 | 472.03 | −519 | 91.46 | 8.38 | 488.24 | −519 | 95.25 | 12.28 | 28.90 | −519 | 71.21 |

Criterion | Unit | Type | Weight | ${\mathit{p}}_{\mathit{i},1}$ | ${\mathit{p}}_{\mathit{i},2}$ | ${\mathit{p}}_{\mathit{i},3}$ | ${\mathit{p}}_{\mathit{i},4}$ | ${\mathit{p}}_{\mathit{i},5}$ |
---|---|---|---|---|---|---|---|---|

LCOE | cent/kWh | Min | 0.25 | 0.91 | 2.19 | 4.02 | 0.91 | 1.14 |

Land use | ha/a | Min | 0.25 | 127.73 | 111.44 | 144.81 | 124.41 | 127.73 |

CO_{2} emissions | t/a | Min | 0.25 | 270.20 | 226.40 | 338.20 | 264.80 | 270.20 |

Self-sufficiency | % | Max | 0.25 | 8.43 | 8.94 | 7.95 | 8.43 | 8.43 |

$\mathit{t}=2005$ | $\mathit{t}=2010$ | $\mathit{t}=2015$ | $\mathit{t}=2020$ | ||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{\varphi}}^{\mathit{n}\mathit{e}\mathit{t}}\left({\mathit{a}}_{\mathit{j},2005,\mathit{s}}\right)$ | Rank | $\left({\mathit{a}}_{\mathit{j},2010,\mathit{s}}\right)$ | Rank | $\left({\mathit{a}}_{\mathit{j},2015,\mathit{s}}\right)$ | Rank | $\left({\mathit{a}}_{\mathit{j},2020,\mathit{s}}\right)$ | Rank | ||

S1 | $\mathsf{\Psi}1$ | −0.099 | 4 | 0.117 | 1 | 0.076 | 2 | 0.000 | 2 |

$\mathsf{\Psi}2$ | −0.021 | 2.5 | −0.086 | 3.5 | −0.194 | 3 | −0.278 | 4 | |

$\mathsf{\Psi}3$ | −0.021 | 2.5 | −0.086 | 3.5 | 0.390 | 1 | 0.306 | 1 | |

$\mathsf{\Psi}4$ | 0.141 | 1 | 0.055 | 2 | −0.271 | 4 | −0.028 | 3 | |

S2 | $\mathsf{\Psi}1$ | −0.085 | 4 | 0.000 | 2 | 0.049 | 2 | 0.020 | 2 |

$\mathsf{\Psi}2$ | −0.024 | 2.5 | −0.034 | 3.5 | −0.196 | 3 | −0.278 | 4 | |

$\mathsf{\Psi}3$ | −0.024 | 2.5 | −0.034 | 3.5 | 0.401 | 1 | 0.320 | 1 | |

$\mathsf{\Psi}4$ | 0.133 | 1 | 0.067 | 1 | −0.254 | 4 | −0.062 | 3 | |

S3 | $\mathsf{\Psi}1$ | −0.151 | 4 | 0.000 | 2 | 0.040 | 2 | −0.062 | 3 |

$\mathsf{\Psi}2$ | −0.008 | 2.5 | −0.045 | 3.5 | −0.176 | 3 | −0.247 | 4 | |

$\mathsf{\Psi}3$ | −0.008 | 2.5 | −0.045 | 3.5 | 0.410 | 1 | 0.334 | 1 | |

$\mathsf{\Psi}4$ | 0.168 | 1 | 0.090 | 1 | −0.274 | 4 | −0.025 | 2 | |

S4 | $\mathsf{\Psi}1$ | −0.099 | 4 | 0.117 | 1 | 0.076 | 2 | 0.000 | 2 |

$\mathsf{\Psi}2$ | −0.021 | 2.5 | −0.086 | 3.5 | −0.195 | 3 | −0.278 | 4 | |

$\mathsf{\Psi}3$ | −0.021 | 2.5 | −0.086 | 3.5 | 0.390 | 1 | 0.307 | 1 | |

$\mathsf{\Psi}4$ | 0.141 | 1 | 0.055 | 2 | −0.271 | 4 | −0.028 | 3 | |

S5 | $\mathsf{\Psi}1$ | −0.068 | 4 | 0.144 | 1 | 0.072 | 2 | −0.047 | 3 |

$\mathsf{\Psi}2$ | −0.026 | 2.5 | −0.089 | 3.5 | −0.194 | 3 | −0.258 | 4 | |

$\mathsf{\Psi}3$ | −0.026 | 2.5 | −0.089 | 3.5 | 0.390 | 1 | 0.333 | 1 | |

$\mathsf{\Psi}4$ | 0.120 | 1 | 0.034 | 2 | −0.267 | 4 | −0.029 | 2 |

**Table 9.**Sensitivity analysis: optimal paths with weight thresholds (in %), based on the MP aggregation with variant 1.

S1 | S2 | S3 | S4 | S5 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{w}}_{\mathit{i}}\uparrow $ | ${\mathit{w}}_{\mathit{i}}\downarrow $ | ${\mathit{w}}_{\mathit{i}}\uparrow $ | ${\mathit{w}}_{\mathit{i}}\downarrow $ | ${\mathit{w}}_{\mathit{i}}\uparrow $ | ${\mathit{w}}_{\mathit{i}}\downarrow $ | ${\mathit{w}}_{\mathit{i}}\uparrow $ | ${\mathit{w}}_{\mathit{i}}\downarrow $ | ${\mathit{w}}_{\mathit{i}}\uparrow $ | ${\mathit{w}}_{\mathit{i}}\downarrow $ | |

LCOE | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}1$ 10.85 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}1$ 8.02 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}1$ 4.25 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}1$ 10.84 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}1$ 8.91 |

Land use | $\mathsf{\Psi}4$ 35.16 | $\mathsf{\Psi}1$ 9.66 | $\mathsf{\Psi}4$ 36.27 | $\mathsf{\Psi}1$ 2.36 | $\mathsf{\Psi}4$ 35.63 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}4$ 35.18 | $\mathsf{\Psi}1$ 9.66 | $\mathsf{\Psi}4$ 35.89 | $\mathsf{\Psi}1$ 9.18 |

CO_{2} emissions | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}3$ - |

Self-sufficiency | $\mathsf{\Psi}1$ 37.92 | $\mathsf{\Psi}4$ 12.42 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}4$ 10.86 | $\mathsf{\Psi}3$ - | $\mathsf{\Psi}4$ 12.22 | $\mathsf{\Psi}1$ 37.93 | $\mathsf{\Psi}4$ 12.41 | $\mathsf{\Psi}1$ 39.7 | $\mathsf{\Psi}4$ 11.54 |

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**MDPI and ACS Style**

Witt, T.; Klumpp, M. Multi-Period Multi-Criteria Decision Making under Uncertainty: A Renewable Energy Transition Case from Germany. *Sustainability* **2021**, *13*, 6300.
https://doi.org/10.3390/su13116300

**AMA Style**

Witt T, Klumpp M. Multi-Period Multi-Criteria Decision Making under Uncertainty: A Renewable Energy Transition Case from Germany. *Sustainability*. 2021; 13(11):6300.
https://doi.org/10.3390/su13116300

**Chicago/Turabian Style**

Witt, Tobias, and Matthias Klumpp. 2021. "Multi-Period Multi-Criteria Decision Making under Uncertainty: A Renewable Energy Transition Case from Germany" *Sustainability* 13, no. 11: 6300.
https://doi.org/10.3390/su13116300