# An Optimisation Model to Consider the NIMBY Syndrome within the Landfill Siting Problem

## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Methodology

#### 3.1. Optimisation Model

**x**= Arg

^{opt}**min (Σ**

_{x}_{i}yc

_{i}(w

_{i}(

**x**)) x

_{i}+ Σ

_{j}d

_{j,min}(

**x**) wp

_{j}c

_{tr}+ Σ

_{i}res

_{i}w

_{i}(

**x**) c

_{comp})

_{i}∈ {0, 1} ∀ i

_{i}x

_{i}≤ l

_{max}

- i indicates an eligible site;
- j indicates a waste source;
**x**is the vector of decision variables x_{i};**x**is the optimal solution;^{opt}- x
_{i}is a binary variable that is equal to 1 if a landfill is located in site i, 0 otherwise; - w
_{i}(**x**) is the annual waste quantity allocated to site i; - yc
_{i}(.) is a function used for calculating the annual cost of the landfill located in site i; it depends on the annual waste quantity to be treated, w_{i}(**x**); - d
_{j,min}(**x**) indicates the distance between a waste source j and the nearest landfill; - wp
_{j}indicates the annual production of waste source j; - c
_{tr}indicates the cost per ton-km of transported waste (€/ton-km); - res
_{i}indicates the number of residents that have to be compensated for a landfill located in site i; - c
_{comp}is the annual compensation cost per ton of waste per resident (€/ton); - l
_{max}is the maximum number of landfills.

_{j}, is sent to the nearest landfill. Under this assumption, we can write:

_{i}(

**x**) = Σ

_{j}wp

_{j}a

_{i,j}(

**x**)

- a
_{i,j}(**x**) is equal to 1 if, under configuration**x**, site i is the nearest to source j (d_{i,j}= d_{j,min}), 0 otherwise, with d_{i,j}indicating the distance between site i and source j.

#### 3.2. Solution Algorithm

_{max}pointer variables, χ

_{k}, that assume an integer value between 0 and n, where n is the number of possible locations. Each pointer variable indicates site i, χ

_{k}= i, where a landfill is provided; otherwise, χ

_{k}= 0 indicates that the pointer variable is not associated to any site i and thus the number of landfills in this solution is lower than the maximum. Figure 1 shows an example of the above approach.

**x**can be represented by a vector of pointer variables,

**χ**, and the optimisation model can be formulated as follows:

**χ**

**= Arg**

^{opt}**min (Σ**

_{χ}_{i}yc

_{i}(w

_{i}(

**χ**)) x

_{i}(

**χ**) + Σ

_{j}d

_{j,min}(

**χ**) wp

_{j}c

_{tr}+ Σ

_{i}res

_{i}w

_{i}(

**χ**) c

_{comp})

_{k}≤ n ∀ k

_{k}integer ∀ k

_{k}χ

_{k}≥ 1

_{k}to 0. Set the objective function value to a very large number, M.

_{max}× n solutions.

_{max}× n).

## 4. Numerical Results

^{2}) has 551 municipalities, about 5.8 million inhabitants and its capital is Naples (about 1 million inhabitants). We assumed 551 waste sources, one per municipality, whose waste production was obtained from official data [56]. We also assumed 551 eligible sites, one inside each municipal area, and that a landfill located in an area will affect only people living in the same municipality. In Figure 3a the territories, with their centroid nodes, are reported, while Figure 3b reports the road network graph, representing about 6000 km of roads, used for calculating the distances between sources and eligible sites. All maps in this paper were generated with the software QGIS and are geo-referenced with the coordinate reference system WGS84/UTM Zone 32. Moreover, we have assumed a compensation cost equal to 0.0001 €/ton per resident and an average transportation cost of 0.4 €/ton-km (obtained from some regional tenders regarding waste management).

_{i}(w

_{i}(

**χ**)) = c

_{0}+ w

_{i}(

**χ**) c

_{1}(w

_{i}(

**χ**))

- c
_{0}is a fixed cost of the landfill (€/year); - c
_{1}is a variable cost per waste ton (€/ton-year), depending on w_{i}for considering the scale economy.

_{0}= 220,000 and c

_{1}(w

_{i}(

**χ**)) = 428.015 w

_{i}(

**χ**)

^{−0.209}.

_{1}(w

_{i}(

**χ**)) by substituting the value 428.015 with the following values: 600, 500, 400, 300, 200 and 100. Figure 6 shows the landfill year costs generated under such assumptions.

_{1}. As expected, solutions with more landfills correspond to lower amounts of the coefficient (5 or 4, if c

_{1}is between 100 and 300; between 1 and 3, if c

_{1}is between 400 and 600), i.e., lower construction/annual maintenance costs. On comparing the results with and without compensation costs, it can be shown that the total number of landfills does not differ so markedly (only in two cases does the model lead to a different number of landfills) although the number of inhabitants involved is very different. Some municipalities recur in the optimal solution; if we consider the compensation costs, this is due to a promising combination of position and inhabitants, while in the other case only the location influences the results.

## 5. Discussion

_{i}(w

_{i}(

**χ**)). In this second case, a specific study on the economic value of such impacts has to be preliminarily conducted.

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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With Compensation Costs | Without Compensation Costs | |
---|---|---|

Number of landfills | 2 | 2 |

Municipalities | Massa di Somma; Giungano | Casoria; Battipaglia |

Total inhabitants | 6702 | 128,440 |

Transportation costs | 34,274,833 | 30,270,389 |

Landfill annual costs | 54,311,274 | 55,754,544 |

Compensation costs | 1,312,718 | − |

Objective function value | 89,898,825 | 86,024,933 |

Coeff. | With Compensation Costs | Without Compensation Costs | |
---|---|---|---|

100 | Number of landfills | 5 | 5 |

Municipalities | Bellizzi; Carinaro; Pietradefusi; San Sebastiano al Vesuvio; Sant’Egidio del Monte Albino | Aversa; Capaccio; Napoli; Pietradefusi; Sant’Egidio del Monte Albino | |

Total inhabitants | 41,202 | 1,061,188 | |

Transportation costs | 21,349,521.53 | 19,291,800.69 | |

Landfill annual costs | 17,018,714.56 | 17,055,619.52 | |

Compensation costs | 2,168,097.22 | - | |

Objective function value | 40,536,333.30 | 36,347,420.21 | |

200 | Number of landfills | 5 | 5 |

Municipalities | Capaccio; Carinaro; Pietradefusi; San Sebastiano al Vesuvio; Sant’Egidio del Monte Albino | Benevento; Casavatore; Pompei; Salerno; Vallo della Lucania | |

Total inhabitants | 50,444 | 247,902 | |

Transportation costs | 21,206,069.45 | 21,448,200.66 | |

Landfill annual costs | 32,918,528.70 | 31,482,230.56 | |

Compensation costs | 2,326,336.09 | - | |

Objective function value | 56,450,934.24 | 52,930,431.21 | |

300 | Number of landfills | 5 | 4 |

Municipalities | Bellizzi; Carinaro; Celle di Bulgheria; Pietradefusi; San Sebastiano al Vesuvio | Benevento; Casavatore; Salerno; Torre Orsaia | |

Total inhabitants | 34,215 | 216,131 | |

Transportation costs | 22,913,058.23 | 24,290,867.40 | |

Landfill annual costs | 47,126,152.86 | 43,748,060.61 | |

Compensation costs | 2,173,152.10 | - | |

Objective function value | 72,212,363.19 | 68,038,928.02 | |

400 | Number of landfills | 3 | 3 |

Municipalities | Giungano; Massa di Somma; Pietradefusi | Battipaglia; Casavatore; Pietradefusi | |

Total inhabitants | 9072 | 71,795 | |

Transportation costs | 30,418,540.86 | 26,547,423.82 | |

Landfill annual costs | 54,645,985.51 | 55,576,136.54 | |

Compensation costs | 1,239,271.64 | - | |

Objective function value | 86,303,798.02 | 82,123,560.36 | |

500 | Number of landfills | 2 | 2 |

Municipalities | Giungano; Massa di Somma | Battipaglia; Casavatore | |

Total inhabitants | 6724 | 69,447 | |

Transportation costs | 34,274,833.33 | 30,109,769.18 | |

Landfill annual costs | 63,371,526.24 | 65,128,788.33 | |

Compensation costs | 1,312,717.53 | - | |

Objective function value | 98,959,077.10 | 95,238,557.51 | |

600 | Number of landfills | 1 | 2 |

Municipalities | Massa di Somma | Casoria; Agropoli | |

Total inhabitants | 5444 | 99,123 | |

Transportation costs | 39,204,346.81 | 32,079,796.38 | |

Landfill annual costs | 70,697,991.09 | 75,959,521.84 | |

Compensation costs | 1,397,663.58 | - | |

Objective function value | 111,300,001.49 | 108,039,318.22 |

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**MDPI and ACS Style**

Gallo, M.
An Optimisation Model to Consider the NIMBY Syndrome within the Landfill Siting Problem. *Sustainability* **2019**, *11*, 3904.
https://doi.org/10.3390/su11143904

**AMA Style**

Gallo M.
An Optimisation Model to Consider the NIMBY Syndrome within the Landfill Siting Problem. *Sustainability*. 2019; 11(14):3904.
https://doi.org/10.3390/su11143904

**Chicago/Turabian Style**

Gallo, Mariano.
2019. "An Optimisation Model to Consider the NIMBY Syndrome within the Landfill Siting Problem" *Sustainability* 11, no. 14: 3904.
https://doi.org/10.3390/su11143904