Urban rent control: a decision support tool for the optimal resources allocation between Urban Forest Projects

Green areas in urban agglomerations are strategic resource for the sustainable city development. The implementation of Urban Forestry Projects (UFP) allows on the one hand to raise the environmental quality level, improving the microclimate and preserving biodiversity, on the other hand to promote urban regeneration and promote socio-economic development by creating eco-systemic s er vices for the population. The result is a more rational land use and an increase in real estate values. Although the EU Directives show the need to promote the sustainable territory growth through the recover y and redevelopment of the built environment, the implementation of investments based on eco-system logic is rarely counted as a priority action for the city, often preferring a different allocation of available resources. The present work aims first to define an indicators set useful to express the value components – financial, social, cultural and ecological- environmental – for the UFP. These indicator s are the reference terms for the characterization of an innovative protocol of multicriteria analysis for the public operator who wants to establish the optimal distribution of funds between UFP units in limited areas of the urban fabric. The protocol uses the algorithms of mathematical programming and is tested on a case study about urban areas to be redeveloped.


Integrated urban sustainable development
Since the end of the Second World War, the growth of many cities, both European and not, has often taken place in an uncontrolled manner, restoring over time a territory with: increasingly large, frayed and densely populated urban areas (urban sprawl); uncertain or even poor-quality real estate; insufficient services and infrastructure levels; limited green areas Green areas in urban agglomerations are strategic resource for the sustainable city development. The implementation of Urban Forestry Projects (UFP) allows on the one hand to raise the environmental quality level, improving the microclimate and preserving biodiversity, on the other hand to promote urban regeneration and promote socio-economic development by creating eco-systemic services for the population. The result is a more rational land use and an increase in real estate values. Although the EU Directives show the need to promote the sustainable territory growth through the recovery and redevelopment of the built environment, the implementation of investments based on eco-system logic is rarely counted as a priority action for the city, often preferring a different allocation of available resources. The present work aims first to define an indicators set useful to express the value componentsfinancial, social, cultural and ecological-environmentalfor the UFP. These indicators are the reference terms for the characterization of an innovative protocol of multicriteria analysis for the public operator who wants to establish the optimal distribution of funds between UFP units in limited areas of the urban fabric. The protocol uses the algorithms of mathematical programming and is tested on a case study about urban areas to be redeveloped. (Termorshuizen et al., 2007). In cities there are mixed settlement areas in terms of intended use, buildings density and population, in which there are often also empty urban areas consisting of areas not and / or partially built or abandoned. The spread and dispersion of settlements has led to the increasing occupation of originally agricultural land, natural or semi-natural, in favour of buildings and/or infrastructure (Torre et al., 2017). These factors negatively affect the city's urban organization for differentiation and alteration of ecological, environmental and urban income values, development of productive activities, quality, liveability and social equity of urban contexts (Morano et al., 2018). This has led, for some time, operators to look for more rational models of soil transformation and control urban income tools (e.g. mechanisms for the optimal resources allocation between alternative use destinations of existing physical and anthropic space; processes of expropriation of urban areas for public use; systems aimed at identifying the best location of productive activities) through new sustainable action strategies based on the integrated management of existing resources, both human and natural. To this end, according to the European Environment Agency (EEA), the territory must be considered as an integrated land system (EEA, 2018), in which the land use components are combined with those of the land cover (European Commission, 2/2007;EEA, 2018). Since 2007, with the Leipzig Charter (European Commission, 163/2007), the European Member States have promoted sustainable urban development policies through integrated design actions aimed mainly at the recovery and enhancement of the built environment, as well as the rehabilitation of degraded urban areas (European Commission, 2016). The objective is to favour interventions, both on the built up area and on free areas (not and/or partially built up), able to produce effects on society, economy, environment and culture (Konijnendijk et al., 2005;Asara et al., 2015;Gonzàles, 2017). In 2015, the United Nations approved the Global Agenda for Sustainable Development, setting out 17 Sustainable Development Goals (SdG) that Member States have agreed to pursue by 2030 (ONU, 2015). Among the SdGs, one of which is specifically aimed at «making cities and human settlements inclusive, safe, resilient and sustainable» (SdG 11), it is possible to identify some logical-functional relationships useful for defining intervention policies for integrated sustainable urban development (Fig. 1).
In order to promote the cities sustainability (SdG 11), it is necessary to provide for actions both to address climate change (SdG 13) and to promote social inclusion (SdG 10), the citizens psycho-physical wellbeing (SdG 3) and economic growth (SdG 8). The pursuit of these objectives can take place through the production of eco-system services, distinct by the Millennium Ecosystem Assessment (MEA, 2005) in: Support and Regulating services (for the protection and differentiation of existing biotic communities), Provisioning services (for the economic growth of the territory) and Cultural services (for the people psychophysical well-being) (Fig. 2). In this perspective, urban forest interventions allow to raise the urban quality level as they lead to the creation of eco-systemic services useful for sustainable development in the environmental, economic and social city dimensions (Hansen et al., 2015;Ostoi et al., 2015). In general, Urban Forestry Projects (UFP) are interventions carried out inside and outside metropolitan areas that include trees in urban and peri-urban areas, including private ones, tree-lined avenues and urban parks of different sizes (Endreny, 2018). The European Union's Forest Strategy (European Commission 659/2013) defines urban and/or peri-urban forest interventions as «[...] multidisciplinary activities that include the design, planning, creation and management of trees, forests, which are usually physically linked to form a mosaic of vegetation within or near built-up areas» (Konijnendijk, 2006). Evidently, the general objectives are both the conservation of the environmental and natural component through less land consumption (Heal et al., 2005), the air quality improvement (Zengh et al., 2013) and the biodiversity conservation (Hardin and Jensen, 2007), and the economic growth of the area through commercial and/or productive activities useful to meet the needs of journal valori e valutazioni No. 27 -2020 Urban rent control: a decision support tool for the optimal resources allocation between Urban Forest Projects the community, as well as socio-cultural development by creating recreational spaces and offering services to the population (Donovan and Butry, 2011). Based on MEA classification, the Food and Agriculture Organization of the United Nations (FAO) has identified 10 Key Issues to be taken into account in the design phase for the execution of urban forest interventions (FAO, 2016). Each of the Key Issues can be expressed with an appropriate evaluation criterion, established on the basis of both the status quo of the intervention area and the effects generated on the urban reference context. It should be noted that in the literature are highlighted as the main effects generated by the UFP in terms of ecosystem services: pollutants removal, carbon storage, microclimate regulation , landscape improvement, biodiversity and soil protection, regulation of the water resources life cycle (Barò et al., 2014;Coutts et al., 2013). In the settlement transformation processes, the objective of producing multiple effects on the territory makes it necessary to pursue integrated logic, through initiatives that combine the plurality of project objectives with the ecosystem services of urban forestry. These are actions that take different forms according to the intervention scale: single building, block, urban districts of small/medium size, large land portions (Goméz-Baggethum et al., 2013). In the definition and evaluation of settlement transformation interventions that include urban forest actions, it is necessary to consider three Targets (Van Elegem et al., 2002): 1. provide citizens with a recreational space (Recreational targets); 2. encourage the territory development in respect of their economic and settlement vocations (Structure-Strengthening targets); 3. preserve the natural component of the area (Ecological targets). By highlighting the logical-functional relationships between Key Issues (FAO, 2016), eco-system services (MEA, 2005) and Targets (Van Elegem et al., 2002), it is possible to establish the prevailing Key Issues at the different project scales (Fig. 3). There are few examples of settlement transformation projects that include urban forest actions assessed in integrated eco-systemic way (Guarini et al., 2018;Nesticò et al., 2019). This is due to the operators interest in considering either only the financial consequences, or the environmental and social aspects separately, without therefore jointly taking into account the multidimensional effects produced by the initiatives. Only the use of different indicators makes it possible to carry out an integrated multidimensional evaluation in eco-systemic key (Wilson and Howarth, 2002). As in many application fields (Roy, 1981;Ishizaka and Nemery, 2013), also in the case of UFP, the multicriteria evaluation tools allow to solve, also through the use of specific software, decisional problems of choice concerning, for example, different ways of managing the forest resource (Wolfslehner et al., 2005), project alternatives for environmental protection (Stirn, 2006); the best location of urban forests (Van Elegem et al., 2002); ordering of project alternatives according to preestablished targets (Opricovic et al., 2007;Chu et al., 2007) and optimization solutionsf related to problems, for example, of resource allocation between investment alternatives (Guarini et al., 2018) and strategic land planning (Nesticò et al., 2019). In particular, the algorithms of Operational Research allow to solve (Ishizaka and Nemery, 2013) complex decision patterns with high number of variables and multiple objectives to be pursued simultaneously through the writing of linear expressions between the problem parameters, while respecting specific constraints (Guitouni et al., 1998).

Aims work
In relation to what has been described above, the study aims to define a model of decision support that allows to identify the best allocation of available monetary resources between interventions to be developed in different urban districts according to the criteria of urban forestation, considering the eco-systemic effects produced by each of the investment alternatives examined. The model is relevant for the public operator who intends to pursue objectives of rational journal valori e valutazioni No. 27 -2020 land use, sustainable development of the territory and control of the formation of urban income, but also for the private operator who wants to increase the market value of real estate through operations to enhance the endowment of collective green. The following paragraph 2 describes the relations and logical-functional relations of correspondence between Key Issues, types of eco-systemic services and Targets and the indicators recognised in the literature to express the multiple effects deriving from settlement transformation interventions including urban forestation. Paragraph 3 shows the elements of characterization of the proposed model, illustrating: the algorithm of mathematical Programming used; the set of indicators selected for the application of the model; the methods of writing an algorithm of Continuous Linear Programming able to solve the problem of allocation of financial resources; the characterization of the optimization algorithm according to the syntax of the mathematical programming software AMPL. Paragraph 4 contains discussions on the analysis model, which is tested on a case-study. Finally, Section 5 provides conclusions and research perspectives.

URBAN FORESTRY PROJECTS. PERFORMANCE INDICATORS FOR SUSTAINABLE DEVELOPMENT
As shown above, Figure 3 relates: Key Issues, Ecosystem Services, Targets and Intervention Design Scales. In particular, the figure intends to highlight how each of the Key Issues can have a different value in the different scales of intervention and that, consequently, some of them can be assumed as prevailing objectives to be pursued. These are elements that make up a reference system useful for selecting the Key Issues during the design phase, which allow investments to be evaluated according to eco-systemic logic. For example, in the case of interventions in neighbourhoods, the prevailing Key Issues to be considered concern ecological-environmental (Food-Nutrition Security, Biodiversity Landscape, Mitigation Land-Soil Degradation), economic (Economic Benefits-Green Economy) and socio-cultural (Socio-Cultural Value) components.
Each Key Issue identified in this way corresponds to one or more performance indicators which, in relation to the evaluation question, make it possible to journal valori e valutazioni No. 27 -2020 Urban rent control: a decision support tool for the optimal resources allocation between Urban Forest Projects determine, qualitatively and/or quantitatively, the effects of the UFP to be achieved. Table 1 shows, in chronological order, the main indicators -collected through search queries on search engines (scopus, google scholar) -that the authors most considered in the literature on urban forest research have used to assess the impacts by UFP (Clark et al., 1997;De Groot et al., 2010;Dobbs et al., 2011;Kenney et al., 2011;Barron et al., 2016) A wide indicators set emerges, which sometimes, although referred to a similar performance, are named differently by various authors. These indicators allow both to characterize the context in which the intervention falls and to express a multi-criteria judgment on the eco-systemic services obtained through forestation (Goméz-Baggethun et al., 2013).
It should be noted that at the beginning of the second half of the last century, the indicators were mainly related to ecological-environmental evaluation issues (Clark et al., 1997;Dobbs et al., 2011;Kenney et al., 2011) and rarely of a financial, social or cultural nature ( Urban rent control: a decision support tool for the optimal resources allocation between Urban Forest Projects al., 2016). The latter begin to take on greater importance in the first decades of the 21st century, in relation to the growing attention paid to sustainable urban development issues.
As illustrated in Table 1, it is possible to assimilate certain indicators in relation to common performance (categories of performance indicators) into a single designation. These are first to be related to the ecosystemic service type and then to be associated with criteria and sub-criteria classes of various kinds. According to the logical scheme of Fig. 4, these criteria classes ( Fig. 4.f) can be traced back to the targets types according to: general objectives to be pursued ( Fig.  4.a), sustainability objectives ( Fig. 4.b) and eco-systemic service ( Fig. 4.c-d).
The complex system of relations between the elements of Figure 4 provides useful support for the construction of multicriteria evaluation models capable of expressing the effects of urban forestation in an eco-systemic key and its repercussions on land rents. As well known, these are models that allow us to rationalise choices driven by multiple and often conflicting objectives. With them, each objective is evaluated through appropriate evaluation criterion, in turn expressed through a specific indicator. In general, the result of a multi-criteria analysis is a qualitativequantitative evaluation profile, sometimes even linked to a single synthetic index. The models in question can be formulated using optimization algorithms which, as explained in Operational Research, often solve complex decisional problems through mathematical structures based on Continuous Linear Programming (CLP).

THE MODEL
As mentioned above, the paper objective is to define and test an evaluation model for the optimal allocation of available financial resources among UFP, in order to pursue the achievement at urban scale of uniform level of eco-systemic services in different neighbourhoods.
To this end, it is necessary to consider performance indicators capable of representing the three journal valori e valutazioni No. 27 -2020 sustainable dimensions (environmental, social and economic). The indicators selection should be made in the light of Figure 4, taking into account the case specificities to be solved. The indicators chosen in this way make it possible to define the state of the neighbourhood in terms of ex-ante and ex-post ecosystemic services. The values assumed by the indicators in each neighbourhood must be aggregated in order to obtain a synthetic evaluation index, called Total Value (TV), representative of the investment's capacity to pursue multiple urban forest objectives. The analysis algorithm is compiled in the syntax of "A Mathematical Programming Language" (AMPL). It is a language used to describe and solve mathematical programming problems, for example optimization ones (Zenios, 1993;Schoen, 2006), also with reference to urban regeneration interventions (Bekele et al., 2005;Bagstad et al., 2013;Nesticò and Sica, 2017). This language, based on a model file and data file, implements specific solvers (CPLEX, KNITRO, etc.) and adapts well to the modelling of decision-making cases in question (Fourerr et al., 1993;Gay, 1993).
Since it is a question of solving problems whose uncertainties assume real values (in the case, for example, of resources allocation between investments) and not only discrete (in the case, for example, of selection between investments for the construction of a Projects Portfolio), the evaluation algorithm is written in terms of the CLP according to AMPL rules (Vanderbei, 2014) with reference to urban regeneration interventions conducted with eco-systemic logic (Guarini et al., 2018).

Performance indicators for the model application
The indicators must measure the prevailing spread effects that UFP generate on the territory. Table 2 shows a possible selection of performance indicators. For each indicator is specified the: eco-systemic service type; Key Issue; measurement system; unit of measurement. The five performance indicators considered, as they are most frequently used in literature, are: 1) Canopy Cover, as «the percentage of land covered by the vertical projection of the canopies of the trees» (Jennings et al., 1999); 2) Water reserves presence, expressed as the area occupied by small and/or medium-sized water basins; 3) Native vegetation degree, capable of expressing the areas biodiversity to be regenerated according to number of existing tree species; 4) Income indicators, as measure of the development of productive activities in the urban area (Internal Rate of Return, Net Present Value or Return on Investment Time); 5) Area destined for recreational services, i.e. areas destined for cultural activities and socialrecreational services, with regard to the psycho-physical well-being of the residents.

The multi-objective decision-making structure model
Multi-objective decision problems can be solved in linear programming terms, which defines a logicaloperational system of the type: where an objective function C(x), the constraints system (φ m ) and the variables vector x appear. In general, multi-objective problems can be of: • continuous optimization, if the vector x has values in R n ; journal valori e valutazioni No. 27 -2020 84 '"#$ ( )"***)"$ + % , #()"***)"-% #$ ( )"***)"$ + %"."/ #()"***)"-% $"""0 ! • whole (or discrete) optimization, when the variables considered assume values in Z n . In all cases, it is important to choose the solver algorithm, which in the CLP often coincides with simplex algorithm, able to determine the optimal solution through an iterative search process. Specifically, starting with an evaluation function f of the type: is associated to every possible alternative of the Decision Domain (D) an index, image of the data characterizing the nature state of the system, defined in the field of the real numbers R. To vary of the function f, the choice criteria can vary, also for a same evaluation problem. For example, function f can return the Total Value (TV) for each element of the domain (Vercellis, 2008). In particular, the Expected Value criterion, both monetary and non-monetary, is frequently used to support analysis in stochastic decision-making systems. It formalizes the heuristic idea of Average Value of the Decision (Di), which depends on the occurrence probability Pr (GOAL j ) for each nature state Si of the system S, fruit of formulated evaluations with regard to the Goal j-th (G j ) to be reached, and to the data characterizing the state of nature (Si, G j ) of the i-th system. Thus the terms "occurrence probability" and "weight" assume the same meaning. In mathematical terms, relationships apply: con i = 1, … , n j = 1, … , m The expected value EV for the S system is therefore:

Analysis alghoritm
The use of continuous linear programming logics therefore makes it possible to solve the resources distribution problem between urban areas undergoing requalification through UFP. Specifically, each area is evaluated with m criteria (with m>1) expressed through the corresponding selected performance indicators. These uniquely characterize the i-th area, so as to return the Total Value TV (both initial and expected) as a linear combination of the values by each indicator. The specific evaluation problem can be solved considering a mathematical model according to which the decision to assign a part ε i of the available resources to the project for the i-th area depends on the Δ TV i , that is the difference between TV i_fin and TV i_in of the i-th area subjected to the i-th project. In other words, the values TV i_fin and TV i_in correspond to the Total Value of the i-th area respectively after and before the allocation of resources to the forestation project for the AREAi. Depending on the rate of resources i assigned to the i-th area such that: (1) the calculation of the TV fin responds to a simple mathematical formulation of the type: (2) Equation (2) specifies the analytical relationship between the final value TV i_fin of the i-th area and the independent problem variable ε i to be solved (Fig. 5). In accordance with equalisation principle, the condition is laid down: (3) which can also be written in the form: This condition leads to the allocation of more financial resources to urban areas with the most serious shortcomings in terms of eco-systems and serious development delays. The equality tie between all the TV i_fin allows to obtain from (5) the financial resources rates i necessary for the increases of value Δ TV i of the areas: Once the total budget available has been established, if Ci is the investment cost of the i-th forest project, the formal relationships in the (5) ensure that the (6) is always respected: Implemented in AMPL using CPL algorithms, the model summarized in (5) assumes the structure of Table 3. Ultimately, the n neighbourhoods to be regenerated (set NEIGHBOURHOODS) are evaluated according to the selected sustainability indicators (set INDICATORS). Each district is assigned a resources rate (RATES set) according to the budget available and increase in Total Value (param Δ TV) to be achieved through UFP.
The numeric values of the initial TV of the i-th area (param TVin) are PARAMETERS of the system to be resolved.
Once the problem unknowns have been established (var ε {i in NEIGHBOURHOODS} >= 0), the objective function is written.: This function is subject to the COSTRAINTS on the value increase of the i-th area: s.t. (subject to) constraint 1 : TV (i-1)_fin = TV i_fin = TV (i+1)_fin

CASE STUDY
Six city districts are considered to be regenerated through UFP financed by distribution of available public resources. The objective is to ensure the optimal use of the available budget (assumed at € 4,200,000) with the aim of maximizing and homogenizing the eco-systemic effects that the projects generate on the territory and to make less different the values of the urban income. This according to equalization principles aimed at achieving uniform final levels of urban quality.
The parameters values that define the problem, i.e. the attributes that express the equipment of eco-systemic services in each neighbourhood before the intervention, are given in Table 4. The normalization operation is carried out by comparing each attribute journal valori e valutazioni No. 27 -2020 Urban rent control: a decision support tool for the optimal resources allocation between Urban Forest Projects to the corresponding maximum value found, as in Table 5.
On the basis of the normalised data obtained, the implementation of the proposed model makes it possible to obtain for each neighbourhood the initial TV in ) as the sum of the parameter values (last column of Table 5). The final total value of TV fin is set at 5.00 for all the neighbourhoods to be redeveloped through forestation. It corresponds to the highest value of TV for each intervention area. It is obtained from the sum of the highest values that each indicator can assume in correspondence with the i-th district. By specifying in AMPL the ciplex solver that implements the simplex algorithm, we obtain the resources rates ε i to be assigned to the areas to be upgraded. These rates correspond to the budget portions to be allocated to individual districts in order to maximize the total increase in urban quality Δ TV. The ε i obtained by the analysis algorithm, on the basis of which the monetary amounts are attributed to each project, are summarized in Table 6. It is evident that the highest values of ε i , therefore the greater monetary amounts, concern the areas with lower levels of TV in . In the application, in fact, the sums of € 1,131,060 and of € 1,008,000 concern respectively the districts 6 and 4, that have the lowest TV in , that is 1,17 and 1,77. This means allocating greater financial resources to the city areas with the greatest development delays. According to equalisation principle, which leads to guaranteeing the same final TV fin level of urban quality to all the districts considered, the values of the i provided by the model produce the maximum Total Value.

CONCLUSION
The integration between natural and built environment orients the territory planning towards strategies of urban sustainability. In this perspective, the inclusion of new green areas in consolidated urban contexts (Urban Forestry Projects) allows to pursue multiple objectives in a sustainable key through services aimed at favouring the places economy, improve the population welfare, promote environmental protection and rational land use. This with effects of greater uniformity of urban income values, especially between cities areas with low liveability levels.
To evaluate forest initiatives, it is necessary to develop evaluation tools to support public administrations. So it is possible to identify the best allocation of available monetary resources among project alternatives on areas to renewal in relation to a more homogeneous ecosystem services level.
With the present work, with the present work, defined a set of indicators according to the evaluation problem to be solved and the project scale of interest, the algorithm that defines the economic investigation model is proposed. The characterization of the model makes use of the Continuous Linear Programming principles, implemented in A Mathematical Programming Language (AMPL) that allow to consider indicators of multiple nature (financial, environmental, socio-cultural) to define an overall value of the area subject to UFP. This value is important for estimating the budget rates to be allocated to each district. This is done in compliance with the criterion of urban equalization, which consists in balancing the overall final values of each district with the aim of standardizing the quality of settlement between different city portions and consequently the values of the urban income. The role of the proposed investigation and evaluation tool is evident, as also from the case study developed, which demonstrates its effectiveness and ease of use. Specifically, the model lends itself to solving complex decision-making systems with a high number of journal valori e valutazioni No. 27 -2020  variables and multiple data, generally expressed on different evaluation scales. This is the case, for example, where it is necessary to establish priority list of project alternatives to be implemented in the urban environment, and when it is necessary to estimate the increase in eco-systemic value for each type of service in the i-th area subjected to UPF in order to achieve more uniform values of urban income. Through the proposed instrument, each alternative is evaluated in an integrated eco-systemic key, and the mechanism for selecting and/or measuring the variation of the type of eco-systemic service is conducted with a view to minimising the disparity in wealth (environmental, social and economic) between parts of the same city. In order to allocate the available financial resources among project alternatives, the model provides as output the rate to be allocated to the single initiative. It should be noted that the results obtained by the analysis algorithm do not provide any estimation of the urban return of the areas. It is in fact a comparison between areas to be redeveloped in compliance with the principles of equalization and with the aim of obtaining uniformity of eco-system values.  mission, 2016). L'obiettivo è di favorire interventi, sia sull'edificato sia su aree libere (non e/o parzialmente edificate), in grado di produrre effetti sulla società, l'economia, l'ambiente e la cultura (Konijnendijk et al., 2005;Asara et al., 2015;Gonzàles, 2017). Nel 2015 l'Organizzazione delle Nazioni Unite ha approvato l'Agenda Globale per lo Sviluppo Sostenibile, definendo 17 Sustainable development Goals (SdG) che gli Stati Membri hanno concordato di perseguire entro il 2030 (ONU, 2015). Tra gli SdG, uno dei quali specificamente indirizzato a «rendere le città e gli insediamenti umani inclusivi, sicuri, resilienti e sostenibili» (SdG 11), è possibile individuare alcune relazioni logico-funzionale utili a definire politiche d'intervento per lo sviluppo urbano sostenibile integrato (Fig. 1). Allo scopo di promuovere la sostenibilità delle città (SdG 11), occorre prevedere azioni volte sia ad affrontare il cambiamento climatico (SdG13), sia a favorire l'inclusione sociale (SdG 10), il benessere psico-fisico dei cittadini (SdG 3) e la crescita economica (SdG 8). Il perseguimento di tali obiettivi può avvenire con la produzione di servizi eco-sistemici, distinti dalla Millennium Ecosystem Assessment (MEA, 2005) in: Servizi di supporto e regolazione (per la tutela e la differenziazione delle comunità biotiche esistenti), Servizi di approvvigionamento (per la crescita economica del territorio) e Servizi culturali (per il benessere psico-fisico delle persone) (Fig. 2). In questa prospettiva, gli interventi di forestazione urbana consentono di innalzare il livello di qualità urbana in quanto conducono alla creazione di servizi eco-sistemici utili allo sviluppo sostenibile nelle dimensioni ambientale, economica e sociale della città (Hansen et al., 2015;Ostoi et al., 2015). In generale, per Urban Forestry Projects (UFP) s'intendono interventi realizzati dentro e fuori le aree metropolitane che ricomprendono gli alberi presenti nelle aree urbane e peri-urbane, incluse quelle private, i viali alberati and i parchi urbani di diversa dimensione (Endreny, 2018 (Van Elegem et al., 2002), risulta possibile stabilire le Key Issues prevalenti alle diverse scale progettuali (Fig. 3). Sono pochi gli esempi di progetti di trasformazione insediativa che comprendono azioni di forestazione urbana valutati in maniera eco-sistemica integrata (Guarini et al., 2018;Nesticò et al., 2019). Ciò per l'interesse degli operatori a considerare o soltanto le ricadute finanziarie, oppure disgiuntamente gli aspetti ambientali e sociali, senza portare quindi in conto insieme gli effetti multidimensionali prodotti dalle iniziative. Soltanto l'uso di indicatori di varia natura permette di effettuare una valutazione integrata-multidimensionale in chiave eco-sistemica (Wilson and Howarth, 2002). Come in molti campi di applicazione (Roy, 1981;Ishizaka and Nemery, 2013) anche nel caso dii UFP gli strumenti di valutazione multicriteriale permettono di risolvere, anche tramite l'utilizzo di specifici software, problemi decisionali di scelta riguardanti, ad esempio, diverse modalità di gestione della risorsa forestale (Wolfslehner et al., 2005), alternative progettuali di difesa ambientale (Stirn, 2006); la migliore localizzazione delle foreste urbane (Van Elegem et al., 2002); ordinamento tra alternative di progetto secondo target prestabiliti (Opricovic et al., 2007;Chu et al., 2007) e ottimizzazione delle soluzioni relative a problemi, ad esempio, di allocazione di risorse tra alternative d'investimento (Guarini et al., 2018) e pianificazione strategica del territorio (Nesticò et al., 2019). In particolare, gli algoritmi della Ricerca Operativa consentono di risolvere (Ishizaka and Nemery, 2013) schemi decisionali complessi con un alto numero di variabili e obiettivi plurimi da perseguire simultaneamente attraverso la scrittura di espressioni lineari tra i parametri del problema, pur nel rispetto di specifici vincoli (Guitouni et al., 1998).