Toward Fair and Sustainable Regional Development: A Multidimensional Framework for Allocating Public Investments in Türkiye

Abstract

Regional disparities pose persistent challenges for balanced and sustainable development in Türkiye, where provinces exhibit prominently heterogeneous socioeconomic structures, capacities, and investment needs. This study proposes an integrated, data-driven framework for allocating public investments across provinces by jointly addressing development efficiency and spatial equity. A dataset of 109 indicators for 81 provinces was compiled and standardized, and Principal Component Analysis, followed by multiple clustering algorithms (K-Means, Gaussian Mixture Model, Fuzzy C-Means), was used to derive robust provincial development profiles. National policy priorities were quantified through a document-based assessment of the 12th Development Plan (2024–2028), enabling the construction of nine strategic investment categories aligned with national objectives. These components were incorporated into a multi-objective optimization model formulated using the ε-constraint method, where total utility is maximized subject to an adjustable equity constraint based on a Gini-like parameter. Results reveal a clear efficiency–equity trade-off: low inequality tolerance yields uniform but low-return allocations, whereas relaxed equity constraints amplify concentration in high-capacity metropolitan provinces. Intermediate equity levels (G = 0.3–0.5) generate the most balanced outcomes, supporting both development potential and spatial cohesion. The proposed framework offers a transparent, reproducible decision support tool for more equitable and strategy-aligned public investment planning in Türkiye.

1. Introduction

There has been a fundamental debate in the regional development literature centered around the efficiency–equity trade-off. Numerous studies have demonstrated that dynamics that shape the economic performance of provinces and regions involve not only scale but also spatial structure, infrastructure quality, government capacity, and inequality mechanisms. For instance, Prud’homme and Lee (1999) [1] indicated that urban efficiency depends on population size together with sprawl, transport speed, and the effective labor market size impacted by them. This shows that well-governed cities having strongly integrated transportation infrastructure can achieve high labor productivity, similar to a metropolitan scale. Similarly, Melo et al. (2016) [2] confirmed in their comprehensive analysis on metropolitan regions of the U.S. that there has been a positive impact of agglomeration economies on productivity; however, this impact has quite limited coverage in spatial terms. According to their findings, a 10% rise in agglomeration yields only a 0.7% to 1.0% rise in labor productivity, and 80% of the productivity gain occurs only in the region of 20 min travel time to the center. Beyond this region, the impact of productivity gain drops rapidly, and this is named as a spatial decay mechanism by the authors. This study finds no statistical evidence that there exists an additional non-linear productivity premium among the metropolitan regions with a population greater than 1 million; therefore, this caused the failure of the widespread assumption that manipulating the growth of metropolitan regions additionally would generate disproportionate productivity.

Relying only on productivity-oriented strategies while spatially allocating government investments carries important risks. Prud’homme (1995) [3] specifies that with excessive decentralization, regions with low income capacity can fall further behind other regions, and in the long run, national integrity and growth rate can weaken as interjurisdictional disparities increase. Moreover, incentive and tax races that emerge due to interregional competition can deform resource allocation and trigger government incentives to accumulate more in developed regions. For this reason, if spatial inequalities are not managed properly, then substantial risk emerges in terms of inequity.

Castells-Quintana and Royuela (2017) [4] indicate that inequality in economic growth is not simply one-dimensional. They consider inequality as market inequality and structural inequality. Market inequality that stems from processes of the market can reinforce growth by entrepreneurship, innovativeness, and capital accumulation, whereas structural inequality that arises due to weakness of government institutions and high inequality of opportunities can suppress growth in the long run. This means that inequality does not conflict with economic growth all the time, and it can have a positive or negative impact with respect to governmental capacity and the dynamics of regional development.

Quality of government stands out as a critical determinant of the effectiveness of regional development policies. Rodríguez-Pose and Garcilazo (2015) [5] express that for public spending under the European Union’s cohesion policy to generate economic impact, regions must exceed a certain governmental quality threshold. They figure out that components like rule of law, control of corruption, and government effectiveness play a decisive role in returns on public investments. This result suggests that public investments should be evaluated not only by their amount but also by the governmental structure of the region in which they are implemented.

Alexiadis and Eleftheriou (2010) [6] show that the equity and efficiency relation does not always imply a conflict in their analysis of U.S. states. In low- and mid-level interregional inequality, a rise in spatial equity does not conflict with a rise in national economic efficiency; on the contrary, total productivity can be enhanced by mobilizing idle or underutilized resources. These findings emphasize the fact that with proper policy design, equity and efficiency objectives can reinforce each other.

Empirical studies in Türkiye offer a consistent picture in the context of the government investments and incentive policies. Saygılı and Özdemir (2021) [7] explain that components of physical, social, and financial infrastructure significantly clarify regional income disparities, and in particular, investments in physical infrastructure create strong positive effects on regional convergence. On the other hand, Saygılı (2020) [8] indicates that the investment incentive mechanism does not provide the expected income convergence in Türkiye, and the growth effect of incentives mainly concentrates on relatively high-income provinces. When these two studies are evaluated jointly, there is a need for a spatially sensitive, data-driven, and objective allocation model for public investments. When positive impacts of infrastructure investments and limited impacts of incentives are taken together, government investment allocations are not solely values; hence, they should be considered with the dynamics of capacity, need, and development potential of the province. This context serves as a strong motivation for the data-driven allocation framework proposed in this study.

The findings of Iammarino et al. (2019) [9] contain important insights for Türkiye, as they showed that regional development gaps no longer disappear by themselves and spatial inequalities tend to become persistent. In Türkiye, highly value-added employment and knowledge-intensive activities are concentrated in metropolitan areas, and the risk of falling into the “territorial trap” of mid- and low-income regions is rising. Therefore, directing public investment only into regions with high growth potential may weaken social cohesion and regional resilience at the national scale in the long run. Therefore, like the place-sensitive policies offered by Iammarino et al. (2019) [9], Türkiye needs funding policies that consider the distinct structural requirements of diverse regions and promote a more balanced and inclusive development pathway.

The aforementioned body of literature indicated that spatial allocation of government investments cannot be directed by a single dimension, especially in a socioeconomically heterogeneous country like Türkiye, where there exists a substantial divergence in development levels, infrastructure availability, government capabilities, and development potentials between provinces. Therefore, there is a need for a data-driven and reproducible framework for allocating government investments that systematically evaluates the dimensions of regional potential and regional need at the same time.

In this study, the aim is to propose a data-driven, multidimensional model that compromises the principles of equity–efficiency balance simultaneously. Therefore, the research questions that would be addressed in this study are as follows:

RQ1: 

How can the structural difficulties, development gaps, and socioeconomic requirements of provinces be consistently and objectively identified and compared?

RQ2: 

In order to promote national development goals, which key strategic investment areas should public authorities prioritize, and how should these domains be distinguished according to their effects on society and the region?

RQ3: 

How can government resources be distributed among provinces in a way that ensures both spatial cohesiveness and high-potential growth while maintaining a balance between regional equity and development efficiency?

In order to answer these research questions, this study employed an empirical methodological flow that combines comprehensive socioeconomic data collection with the systematic analysis of the province requirements and national policy prioritization. First of all, RQ1 is addressed by organizing and summarizing multidimensional indicators of all provinces in order to produce objective measures that reflect the development gaps, structural disadvantages, and potential strengths. In the second stage, in response to RQ2, using document-based content analysis, national development strategies—specifically the 12th Development Plan of Türkiye—were examined, and main strategic investment areas were determined. Then, these areas were subsequently categorized based on national and regional impacts. In the final stage, province-level requirement profiles and national priority areas are combined to build a consistent resource allocation framework to distribute investments under different efficiency–equity levels. This systematic approach to RQ3 provides an evidence-based assessment to distribute public funds in a way that promotes high return potential and yields regionally balanced outcomes.

To correctly position the theoretical and analytical framework of this study, a comprehensive review is required to comprehend how regional government investments are allocated, how the efficiency–equity trade-off has been handled, and which analytical approaches are employed. Existing studies demonstrate that public investments are heavily influenced by political, institutional, and spatial criteria in addition to economic efficiency standards. In addition to this, international policy frameworks like the EU Cohesion Policy are essential in order to reduce the disparities between regions’ spatial equity mechanisms. Recently, multidimensional data analysis, place-based strategies, and multi-objective optimization methods have been extensively used in the allocation of government investments for transparent and evidence-based decisions. Since this study combined the identification of needs at the provincial level, investment prioritization based on national plan priorities, and efficiency–equity balancing between provinces, it is vital to handle the contributions originating from different literature areas.

Table 1. Summary of key literature on regional public investment allocation.

Study	Country/Context	Methodology	Main Focus	Key Findings
Yamano and Ohkawara (2000) [10]	Japan	Econometric modelling using regional production functions and simulation of alternative public investment allocation rules.	Efficiency–equity trade-off in the regional allocation of public investment; simulation of alternative allocation scenarios.	Public investment in Japan historically prioritizes equity over efficiency; marginal productivity of public capital is declining in depressed regions but rising in developed ones; efficiency-oriented allocation raises national GDP but increases regional inequality.
Castells and Solé-Ollé (2005) [11]	Spain	Dynamic panel data modelling, production function-based investment equation, political economy variables, inequality–efficiency trade-off estimation.	Determinants of regional infrastructure investment—equity, efficiency, and political drivers.	Efficiency considerations play only a limited role; infrastructure allocation is strongly shaped by regional needs and political incentives (electoral productivity, swing voters, pivotal regions).
Monastiriotis and Psycharis (2014) [12]	Greece	Descriptive and semi-parametric analysis.	Revealed allocation criteria (equity, efficiency, redistribution, geography) in regional public investment over time.	Public investment allocations in Greece show high inertia, lack of functional or spatial targeting, weak links to equity, efficiency, or redistribution, and no stable spatial patterns—suggesting unsystematic and ad hoc allocation practices.
Vasilakos et al. (2023) [13]	India	Panel data econometrics + comparative relative infrastructure specification based on a Dixit–Stiglitz-type theoretical model.	Impact of place-based public infrastructure (national highways, state highways, electricity-generating capacity) on firm location choices and regional economic performance.	National highways and electricity capacity significantly increase firm concentration and manufacturing output, while state highways show no robust effect; infrastructure differences between neighboring regions generate strong spatial spillovers.
Baffo et al. (2024) [14]	Italy	AHP-based MCDM.	Design and application of a sustainable public investment evaluation framework integrating economic efficiency, environmental sustainability, and social impact.	SEESIM provides a transparent, replicable, and multidimensional framework enabling policymakers to evaluate public projects holistically and ensure alignment with long-term sustainability goals.
Shang and Wang (2025) [15]	Belt and Road regions	Multi-objective optimization model + multi-factor analysis + AI-supported regional resource allocation.	Optimization of regional economic resource distribution under Belt and Road context.	Demonstrates that integrating multi-factor data with AI-driven optimization significantly improves the coherence, rationality, and effectiveness of regional resource allocation.
Lee (2022) [16]	South Korea	Dynamic panel + structural allocation model.	Determinants of regional infrastructure investment allocation.	Allocation is predominantly equity-oriented rather than efficiency-driven, influenced by political and fiscal factors.
Aray and Pacheco-Delgado (2020) [17]	Ecuador	Econometric panel data modelling grounded in a theoretical social welfare maximization framework.	Determinants of public investment allocation across provinces, considering efficiency, redistribution, congestion indicators, and political factors.	Central government partially balances efficiency and equity; investment grows faster in lower-income provinces and where productivity of investment is high, but political alignment also influences distribution.
Albalate et al. (2012) [18]	Spain	Econometric panel regressions using provincial transport investment data.	Determinants of regional infrastructure investment beyond the classic efficiency–equity framework, specifically testing the effect of political centralization.	Investment in network infrastructures (roads, rail) is strongly concentrated near the political capital (Madrid), independent of mobility demand or equity considerations; centralization emerges as a distinct and powerful allocation criterion.
Mikelbank and Jackson (1999) [19]	US—State of Ohio	Descriptive spatial analysis and data visualization.	Assessment of whether the distribution of public capital investment aligns with equity (worst-first rule) or efficiency (highest return regions) principles.	Public capital investment patterns in Ohio are overwhelmingly equity-driven: per capita investment is highest in the most socioeconomically distressed (high-poverty, high-unemployment) counties, while total investment levels concentrate in large urban counties where distress levels are also high.
Aray and Martinez-Vazquez (2024) [20]	Spain	Theoretical optimization model based on a Social Welfare Function + panel data econometrics.	Bridging the gap between theoretical and empirical criteria for public investment allocation, specifically introducing “output density” alongside efficiency and equity.	The derived theoretical model confirms that optimal allocation depends on efficiency, redistribution, and spatial criteria; empirical results for Spain show that policymakers heavily weight spatial output density, not just per capita output.
Beck et al. (2024) [21]	Global (71 advanced and emerging countries)	Local projections panel model using exogenous “globalization shocks”.	Re-visiting the “efficiency–equity trade-off” hypothesis in the context of globalization and economic integration shocks over the past 50 years.	Globalization shocks generally increase trade openness and often income (efficiency) but do not consistently lead to higher inequality (equity loss), challenging the assumption of a strict efficiency–equity trade-off.

summarizes the primary academic and political research related to this study and shows how each study handles the topic in terms of methodology and context.

The literature summarized in Table 1 indicates that in the regional allocation of public investments, efficiency–equity trade-offs, political motivations, institutional structure, and spatial differences are decisive. However, it can be seen that the vast majority of these studies are ex post econometric evaluations that attempt to explain the rationale behind current investment decisions, and they do not support a needs identification approach to define, in a holistic way, the multidimensional socioeconomic structure of the provinces. In light of the reviewed studies, it is evident that existing research largely focuses on descriptive or ex post econometric evaluations and does not provide a multidimensional, policy-aligned, and optimization-based allocation mechanism. The prior literature does not combine provincial needs identification, strategic investment prioritization, and normative efficiency–equity optimization within a single analytical framework. This gap highlights the necessity for an integrated, reproducible, and data-driven model capable of generating ex ante allocation recommendations rather than merely explaining past investment behaviors. Similarly, to the best of our knowledge, there are no studies that combine policy-based investment prioritization and data-driven provincial profiling under a single analytical framework to direct the investments to the appropriate strategic areas. Although there are studies in the existing literature that simultaneously consider efficiency and equity targets, none of them use a multi-objective optimization method to test these targets across different inequality tolerance levels and develop an applicable optimal allocation framework.

This research fills the relevant gap and offers three important contributions. Firstly, it measured the socioeconomic status of the provinces using Principal Component Analysis (PCA) and clustering-based profiles that are generated using 109 indicators. The provinces are then classified systematically and objectively based on regional requirements. Next, national development policies in the 12th National Development Plan of Türkiye were analyzed to build policy-weighted investment categories for nine strategic investment areas. Finally, a data-driven multi-objective optimization model was developed to handle efficiency and regional equity targets simultaneously, assess different Gini-like parameter levels, and produce an applicable public investment plan for provinces. Therefore, the study proposes a normative, reproducible, and spatially sensitive investment allocation mechanism that is quite different from the explanatory models in the existing literature.

2. Materials and Methods

In line with the development plans for Türkiye, which are prepared every 5 years, the central government identifies some specific sectors as prioritized investment areas and sets development targets for provinces or regions to accelerate development. However, there is often no systematic assessment approach to evaluate the current socioeconomic capacities of provinces, the development potentials, and the requirement level of sectors to implement these targets. The primary objective of this study is to provide a resource allocation model for government investments that takes efficiency and equity into account while utilizing the actual needs of each province with an objective, data-driven approach. Furthermore, if there exists a specific, high development opportunity in a province, this area can be supported by public investments to achieve long-term sustainability.

The methodological framework that was proposed in this study is composed of a multi-stage analytical structure, as illustrated in Figure 1. The process starts with data collection and standardization stages. A dataset composed of 109 indicators that are grouped under 10 categories was gathered for 81 provinces; then, the data were normalized so as to allow comparability across provinces. Later, PCA was applied to reduce high dimensionality and mitigate multicollinearity among variables. As a result of PCA, components representing 75% of the cumulative variance were preserved for further analysis. PCA was preferred because it produces orthogonal components, allowing subsequent clustering methods to operate on uncorrelated socioeconomic dimensions.

After PCA, for grouping the provinces based on their socioeconomic similarities, K-Means, Gaussian Mixture Model (GMM), and Fuzzy C-Means (FCM) methods were applied for clustering analysis. These methods were selected due to their complementary strengths in representing multidimensional socioeconomic structures. K-Means was included as a widely used and interpretable hard-clustering method, while GMM was used to account for probabilistic cluster memberships that capture transitional provincial characteristics. FCM was incorporated to reflect partial membership patterns in regions that do not fit neatly into discrete groups.

The resulting cluster profiles derived from the different methods were gathered to represent a robust representation for each province by combining weighted cluster profiles, reflecting partial membership of provinces across multiple clusters. In the next stage, public investment priorities were defined using the 12th Development Plan of Türkiye (for the years 2024 to 2028) by considering three dimensions, which are Policy Priority, Impact Area, and Regional Disparity. All this information was then converted to a Province × Investment Category matrix, and it was used as input for the multi-objective optimization.

In the final stage, the developed optimization model was designed to balance the trade-off between maximization of efficiency and minimization of inequality. Using the ε-constraint method, several scenario analyses were conducted to assess the relationship between efficiency and equity. Through this approach, the proposed methodology offers a holistic framework to allocate government resources in an equitable and sustainable way by considering existing capacities and potential development areas.

2.1. Data Processing and PCA-Based Dimensionality Reduction

In this study, 81 provinces of Türkiye were selected for the unit of analysis, and for each province, 109 socioeconomic indicators were collected. These indicators cover a wide range of dimensions, including economic performance, employment structure, education and health services, infrastructure, innovation capacity, environmental conditions, and quality of life. Data was gathered from national official resources like the Turkish Statistical Institute (TSI) and the Presidency of Strategy and Budget. In order to make the variables comparable with each other, these indicators, measured on different scales, were standardized.

The data used in the study were retrieved from open datasets provided by the Turkish Statistical Institute (TSI, 2024) [22]. All of them are accessible to the public in the regional statistics portal of TSI (https://data.tuik.gov.tr/, accessed on 30 April 2025). A full list of the indicators with category and subcategory classifications is presented in Appendix A—

Table A1. Province data with 109 indicators.

Category	Subcategory	Indicator	Category	Subcategory	Indicator
Economic Performance/Macro Indicators	Macro-economic indicator	GDP per Capita, Value (2009-based) (2019–2023)	Economic Performance/Sectoral Composition of GDP	Professional, Technical and Support Services/GDP	Share of GDP (2009-Based) at Current Prices—M_N. Professional, Scientific, Technical, Administrative and Support Services (% change last year)
Economic Performance/Macro Indicators	Macro-economic indicator	GDP per Capita, Value (2009-based) (Average % Change)	Economic Performance/Sectoral Composition of GDP	Public, Education, Health, Social Services/GDP	Share of GDP (2009-Based) at Current Prices—OTQ. Public Administration, Defense, Education, Health and Social Services (% change last year)
Economic Performance/Macro Indicators	Macro-economic indicator	GDP per Capita, Value (2009-based) (% Change in Last Year)	Economic Performance/Sectoral Composition of GDP	Other Sectors/GDP	Share of GDP (2009-Based) at Current Prices—RTU. Other Services (% change last year)
Economic Performance/Macro Indicators	Agriculture, Forestry, and Fishing/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—A. Agriculture, Forestry and Fishing	Labor Market Indicators	Unemployment	Unemployment Rate (2024)
Economic Performance/Macro Indicators	Mining, Quarrying, and Other Industries/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—BTE. Mining, Quarrying and Other Industries	Labor Market Indicators	Unemployment	Unemployment Rate (2022–2024)
Economic Performance/Macro Indicators	Manufacturing Industry/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—C. Manufacturing Industry	Labor Market Indicators	Employment and Participation	Employment Rate (2024)
Economic Performance/Macro Indicators	Construction/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—F. Construction	Labor Market Indicators	Employment and Participation	Employment Rate (2022–2024)
Economic Performance/Macro Indicators	Trade, Transport, Accommodation, Food/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—GTI. Wholesale, Retail, Transport, Accommodation	Labor Market Indicators	Employment and Participation	Labor Force Participation Rate (2024)
Economic Performance/Macro Indicators	Information and Communication/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—J. Information and Communication	Labor Market Indicators	Employment and Participation	Labor Force Participation Rate (2022–2024)
Economic Performance/Macro Indicators	Finance and Insurance/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—K. Finance and Insurance Activities	Education Indicators	Years of Schooling	Mean years of schooling (2023)
Economic Performance/Macro Indicators	Real Estate Activities/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—L. Real Estate Activities	Education Indicators	Years of Schooling	Mean years of schooling, males (2023)
Economic Performance/Macro Indicators	Professional, Technical, and Support Services/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—M_N. Professional, Scientific, Technical Services	Education Indicators	Years of Schooling	Mean years of schooling, females (2023)
Economic Performance/Macro Indicators	Public, Education, Health, Social Services/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—OTQ. Public, Education, Health, Social Work	Education Indicators	Years of Schooling	Mean years of schooling, gender parity index (2023)
Economic Performance/Macro Indicators	Other Sectors/GDP	GDP Value (2009-based), Thousand TRY, Chain-linked Volume—RTU. Other Services	Education Indicators	Years of Schooling	Mean years of schooling (2019–2023)
Economic Performance/Growth Trends	Agriculture, Forestry, and Fishing/GDP	GDP YoY % Change (2009-Based, Chain Volume)— A. Agriculture, Forestry and Fishing (2019–2023)	Education Indicators	Years of Schooling	Mean years of schooling, males (2019–2023)
Economic Performance/Growth Trends	Mining, Quarrying, and Other Industries/GDP	GDP YoY % Change (2009-Based, Chain Volume)—BTE. Mining, Quarrying and Other Industries (2019–2023)	Education Indicators	Years of Schooling	Mean years of schooling, females (2019–2023)
Economic Performance/Growth Trends	Manufacturing Industry/GDP	GDP YoY % Change (2009-Based, Chain Volume)—C. Manufacturing Industry (2019–2023)	Education Indicators	Gender Parity Index	Mean years of schooling, gender parity index (2019–2023)
Economic Performance/Growth Trends	Construction/GDP	GDP YoY % Change (2009-Based, Chain Volume)—F. Construction (2019–2023)	Education Indicators	Educational Attainment (Age 15+)	Attained education level, population 15 years of age and over (2023), illiterate or literate without a diploma
Economic Performance/Growth Trends	Trade, Transport, Accommodation, Food/GDP	GDP YoY % Change (2009-Based, Chain Volume)—GTI. Trade, Transport, Accommodation and Food Services (2019–2023)	Education Indicators	Educational Attainment (Age 15+)	Attained education level, population 15 years of age and over (2023), primary and secondary School
Economic Performance/Growth Trends	Information and Communication/GDP	GDP YoY % Change (2009-Based, Chain Volume)—J. Information and Communication (2019–2023)	Education Indicators	Educational Attainment (Age 15+)	Attained education level, population 15 years of age and over (2023), university or other higher educational institutions
Economic Performance/Growth Trends	Finance and Insurance/GDP	GDP YoY % Change (2009-Based, Chain Volume)—K. Financial and Insurance Activities (2019–2023)	Education Indicators	Educational Attainment (Age 15+)	Attained education level, population 15 years of age and over (2023), master or doctorate
Economic Performance/Growth Trends	Real Estate Activities/GDP	GDP YoY % Change (2009-Based, Chain Volume)—L. Real Estate Activities (2019–2023)	Demographic Indicators	Population	Total Population (2024)
Economic Performance/Growth Trends	Professional, Technical, and Support Services/GDP	GDP YoY % Change (2009-Based, Chain Volume)— M_N. Professional, Scientific, Technical, Administrative and Support Services (2019–2023)	Demographic Indicators	Population	Male Population (2024)
Economic Performance/Growth Trends	Public, Education, Health, Social Services/GDP	GDP YoY % Change (2009-Based, Chain Volume)—OTQ. Public Administration, Defense, Education, Health and Social Work Activities (2019–2023)	Demographic Indicators	Population	Female Population (2024)
Economic Performance/Growth Trends	Other Sectors/GDP	GDP YoY % Change (2009-Based, Chain Volume)—RTU. Other Services (2019–2023)	Demographic Indicators	In-Migration	In-Migration to Regions (2024)
Economic Performance/Growth Trends	Agriculture, Forestry, and Fishing/GDP	GDP YoY % Change (2009-Based, Chain Volume)— A. Agriculture, Forestry and Fishing (Last year % change)	Demographic Indicators	Out-Migration	Out-Migration from Regions (2024)
Economic Performance/Growth Trends	Mining, Quarrying, and Other Industries/GDP	GDP YoY % Change (2009-Based, Chain Volume)—BTE. Mining, Quarrying and Other Industries (Last year % change)	Demographic Indicators	Dependency Ratios	Youth Dependency Ratio (Ages 0–14) (2024)
Economic Performance/Growth Trends	Manufacturing Industry/GDP	GDP YoY % Change (2009-Based, Chain Volume)—C. Manufacturing Industry (Last year % change)	Demographic Indicators	Dependency Ratios	Elderly Dependency Ratio (Ages 65+) (2024)
Economic Performance/Growth Trends	Construction/GDP	GDP YoY % Change (2009-Based, Chain Volume)—F. Construction (Last year % change)	Urbanization and Infrastructure	Densely Populated Areas	Densely Populated Areas (2024)
Economic Performance/Growth Trends	Trade, Transport, Accommodation, Food/GDP	GDP YoY % Change (2009-Based, Chain Volume)—GTI. Trade, Transport, Accommodation and Food Services (Last year % change)	Urbanization and Infrastructure	Intermediate-Density Areas	Intermediate-Density Areas (2024)
Economic Performance/Growth Trends	Information and Communication/GDP	GDP YoY % Change (2009-Based, Chain Volume)—J. Information and Communication (Last year % change)	Urbanization and Infrastructure	Thinly Populated Areas	Thinly Populated Areas (2024)
Economic Performance/Growth Trends	Finance and Insurance/GDP	GDP YoY % Change (2009-Based, Chain Volume)—K. Financial and Insurance Activities (Last year % change)	Urbanization and Infrastructure	Municipal Services Coverage	Proportion of Municipal Population Served by Waste Collection Services (%) (2022)
Economic Performance/Growth Trends	Real Estate Activities/GDP	GDP YoY % Change (2009-Based, Chain Volume)—L. Real Estate Activities (Last year % change)	Urbanization and Infrastructure	Municipal Services Coverage	Proportion of Municipal Population Served by Wastewater Treatment Plants (%) (2022)
Economic Performance/Growth Trends	Professional, Technical, and Support Services/GDP	GDP YoY % Change (2009-Based, Chain Volume)— M_N. Professional, Scientific, Technical, Administrative and Support Services (Last year % change)	Urbanization and Infrastructure	Municipal Services Coverage	Proportion of Municipal Population Served by Drinking and Utility Water Treatment Plants (%) (2022)
Economic Performance/Growth Trends	Public, Education, Health, Social Services/GDP	GDP YoY % Change (2009-Based, Chain Volume)—OTQ. Public Administration, Defense, Education, Health and Social Work Activities (Last year % change)	Urbanization and Infrastructure	Municipal Services Coverage	Proportion of Municipal Population Served by Drinking and Utility Water Supply Network (%) (2022)
Economic Performance/Growth Trends	Other Sectors/GDP	GDP YoY % Change (2009-Based, Chain Volume)—RTU. Other Services (Last year % change)	Urbanization and Infrastructure	Municipal Services Coverage	Proportion of Municipal Population Served by Sewerage Network (%) (2022)
Economic Performance/Sectoral Composition of GDP	Agriculture, Forestry, and Fishing/GDP	Share of GDP (2009-Based) at Current Prices—A. Agriculture, Forestry and Fishing (2019–2023)	Health Services	Health Infrastructure	Number of Physicians per 1000 People (2023)
Economic Performance/Sectoral Composition of GDP	Mining, Quarrying, and Other Industries/GDP	Share of GDP (2009-Based) at Current Prices—BTE. Mining, Quarrying and Other Industries (2019–2023)	Health Services	Health Infrastructure	Number of Hospitals (2023)
Economic Performance/Sectoral Composition of GDP	Manufacturing Industry/GDP	Share of GDP (2009-Based) at Current Prices—C. Manufacturing Industry (2019–2023)	Health Services	Health Infrastructure	Number of Hospital Beds (2023)
Economic Performance/Sectoral Composition of GDP	Construction/GDP	Share of GDP (2009-Based) at Current Prices—F. Construction (2019–2023)	Health Services	Health Infrastructure	Number of Hospital Beds per 100,000 People (2023)
Economic Performance/Sectoral Composition of GDP	Trade, Transport, Accommodation, Food/GDP	Share of GDP (2009-Based) at Current Prices—GTI. Trade, Transport, Accommodation and Food Services (2019–2023)	Economic Performance	Industry	Total Number of Industrial Enterprises (2023)
Economic Performance/Sectoral Composition of GDP	Information and Communication/GDP	Share of GDP (2009-Based) at Current Prices—J. Information and Communication (2019–2023)	Economic Performance	Agriculture	Crop Production Value (Thousand TL) (2021)
Economic Performance/Sectoral Composition of GDP	Finance and Insurance/GDP	Share of GDP (2009-Based) at Current Prices—K. Financial and Insurance Activities (2019–2023)	Economic Performance	Agriculture	Value of Livestock (Thousand TL) (2021)
Economic Performance/Sectoral Composition of GDP	Real Estate Activities/GDP	Share of GDP (2009-Based) at Current Prices—L. Real Estate Activities (2019–2023)	Economic Performance	Agriculture	Value of Animal Products (Thousand TL) (2020)
Economic Performance/Sectoral Composition of GDP	Professional, Technical, and Support Services/GDP	Share of GDP (2009-Based) at Current Prices—M_N. Professional, Scientific, Technical, Administrative and Support Services (2019–2023)	Economic Performance	Agriculture	Number of Cattle (Head) (2024)
Economic Performance/Sectoral Composition of GDP	Public, Education, Health, Social Services/GDP	Share of GDP (2009-Based) at Current Prices—OTQ. Public Administration, Defense, Education, Health and Social Services (2019–2023)	Economic Performance	Agriculture	Number of Sheep and Goats (Head) (2024)
Economic Performance/Sectoral Composition of GDP	Other Sectors/GDP	Share of GDP (2009-Based) at Current Prices—RTU. Other Services (2019–2023)	Economic Performance	Agriculture	Greenhouse Fruit and Vegetable Production (Tons) (2024)
Economic Performance/Sectoral Composition of GDP	Agriculture, Forestry, and Fishing/GDP	Share of GDP (2009-Based) at Current Prices—A. Agriculture, Forestry and Fishing (% change last year)	Economic Performance	Agriculture	Production of Cereals and Other Crops (Tons) (2024)
Economic Performance/Sectoral Composition of GDP	Mining, Quarrying, and Other Industries/GDP	Share of GDP (2009-Based) at Current Prices—BTE. Mining, Quarrying and Other Industries (% change last year)	Economic Performance	Agriculture	Total Cultivated Agricultural Area (Hectares) (2024)
Economic Performance/Sectoral Composition of GDP	Manufacturing Industry/GDP	Share of GDP (2009-Based) at Current Prices—C. Manufacturing Industry (% change last year)	Economic Performance	Tourism	Total Number of Overnight Stays (2021)
Economic Performance/Sectoral Composition of GDP	Construction/GDP	Share of GDP (2009-Based) at Current Prices—F. Construction (% change last year)	Economic Performance	Tourism	Total Number of Tourist Arrivals (People) (2021)
Economic Performance/Sectoral Composition of GDP	Trade, Transport, Accommodation, Food/GDP	Share of GDP (2009-Based) at Current Prices—GTI. Trade, Transport, Accommodation and Food Services (% change last year)	Economic Performance	Tourism	Number of Overnight Stays by Foreign Tourists (2021)
Economic Performance/Sectoral Composition of GDP	Information and Communication/GDP	Share of GDP (2009-Based) at Current Prices—J. Information and Communication (% change last year)	Economic Performance	Tourism	Number of Foreign Tourist Arrivals (People) (2021)
Economic Performance/Sectoral Composition of GDP	Finance and Insurance/GDP	Share of GDP (2009-Based) at Current Prices—K. Financial and Insurance Activities (% change last year)	Justice	Crime and Sentencing	Number of Convicted Prisoners by Province of Crime (2020)
Economic Performance/Sectoral Composition of GDP	Real Estate Activities/GDP	Share of GDP (2009-Based) at Current Prices—L. Real Estate Activities (% change last year)

. Since the dataset is extensively multidimensional and the indicators can be highly interrelated with each other, to eliminate the risk of multicollinearity and data redundancy, PCA was implemented. This method reduces the large number of indicators into principal components that capture the shared variance structure, which represent the provincial characteristics in a more compact and interpretable way. Therefore, socioeconomic differences between the provinces can be comparable with a simplified dataset.

After the PCA, the first 10 components that were derived from 109 indicators were able to explain 76% of the cumulative variance of 81 provinces, as shown in

Table 2. Interpretation of the principal components derived from 109 socioeconomic indicators across 81 provinces. Note: The symbols (+) and (–) indicate positive and negative loadings of the corresponding indicators on each principal component.

Component	Dominant Indicators	Main Theme	Interpretation
PC1	Higher education, hospitals, migration (+); agricultural GDP share (–)	Human Capital and Services	Urban–educated vs. agricultural–rural divide
PC2	Manufacturing share (–); public sector and dependency ratio (+)	Sectoral and Demographic Structure	Industrial vs. public service economies
PC3	Agricultural and livestock production (+); infrastructure and ICT (–)	Agro-Rural vs. Infrastructure	Rural production vs. urban service infrastructure
PC4	Employment and agriculture (+); industry share and unemployment (–)	Employment–Industrial Balance	Labor-intensive rural vs. industrial high-unemployment regions
PC5	Tourism and services (+); education duration (–)	Tourism–Service vs. Education	Tourism-driven economies vs. education-based provinces
PC6	Agricultural land and livestock (+); tourism intensity (–)	Agriculture vs. Tourism	Agricultural production regions vs. tourism-focused economies
PC7	Manufacturing and health (+); construction and real estate (–)	Productive Growth vs. Construction Cycle	Stable industrial/service growth vs. volatile construction-driven economies
PC8	Finance and public sector (+); agriculture, construction (–)	Sectoral Growth Volatility	Financially balanced vs. production-driven fluctuating economies
PC9	Water and sewerage coverage (+); retail/service growth (–)	Urban Infrastructure Quality	Developed infrastructure vs. rapidly expanding service economies
PC10	Manufacturing and finance growth (+); waste service coverage (–)	Sectoral Growth Diversity vs. Environmental Services	Multi-sectoral dynamic economies vs. infrastructure-focused stable regions

. These components reveal the multidimensional socioeconomic disparities between the provinces. The first component (PC1) represents the provincial differences in human capital, education level, and service infrastructure, whereas PC2 reflects the composition of economic sectors and demographic structure. PC3 and PC4 show the differences in agricultural production and employment characteristics; on the other hand, PC5 and PC6 distinguish between tourism-oriented and agriculture-oriented provincial economies. PC7 and PC8 capture the patterns in economic growth stability and fluctuations in sectors, while PC9 and PC10 report the differences in urban infrastructure and environmental service quality. These results show that the development of provinces cannot be depicted only by economic indicators but also by human capital, sectoral diversity, urban–rural structure, and infrastructure quality. These components serve as a basis for the clustering analysis and multi-objective optimization model applied in the subsequent stages of the study.

2.2. Clustering Analysis and Robust Profile Generation

Component scores for the provinces derived from PCA serve as a meaningful representation of socioeconomic characteristics. These representations enable the grouping of provinces with similar structural profiles using clustering. In this study, three different clustering methods were deployed: K-Means, Gaussian Mixture Model (GMM), and Fuzzy C-Means (FCM). Using these methods allows for both hard clustering with strict boundaries and probabilistic, transition-type memberships at the same time.

The K-Means algorithm assigns the provinces with similar socioeconomic specifications—derived from PCA—to the nearest centroids. The elbow method was used to calibrate the model, and 5-, 6-, and 7-cluster scenarios were evaluated. The elbow curve was used to examine the decrease in within-cluster sum of squares (WSS) as the number of clusters increased, thus helping to identify an optimal range. By using K-Means, the dominating clustering pattern can be seen, and large-scale development differences across provinces may be visualized.

The GMM approach provides a probabilistic classification assuming that each cluster follows an underlying Gaussian distribution. To determine the number of clusters, Bayesian Information Criterion (BIC) values were used, and the number was decided with the lowest BIC value. For each province, cluster membership probabilities were calculated, and using these probabilities, an uncertainty map was formed. This map spatially showed the probabilities that a province belongs to multiple clusters, and some provinces in transition regions like Konya, Adana, and Mersin could have mixed economic structures according to the results.

The FCM method is a “soft clustering” approach in which provinces can be assigned into clusters with a calculated membership degree (as a %). This membership degree value also guides the calculation of uncertainties while mapping the provinces to clusters. High uncertainties (such as membership values of 0.4 to 0.6) show that these provinces can belong to multiple development typologies simultaneously. Results were visualized on maps to distinguish the spatial consistency of the clusters. This method also supports the results of GMM and is used to capture the structural fluidity between clusters. For instance, some provinces can belong partially to multiple cluster profiles (such as 60% to Cluster 2, 35% to Cluster 3, and 5% to Cluster 1).

Based on the results derived from clustering analysis, cluster profiles were evaluated by the average values of each indicator for the provinces in the specific cluster. In other words, each cluster represents the mean socioeconomic indicator levels of provinces sharing similar characteristics. In light of this, a characteristic subcategory profile vector (SPV) was produced for each cluster by calculating the average value of the indicators that fall into that category.

Using the SPVs, the outputs of the three clustering approaches (K-Means, GMM, and FCM) were combined for each province. As noted earlier, 5-, 6-, and 7-cluster K-Means, GMM, and FCM were used, and each generated an SPV for each province. In constructing the robust provincial profiles, these five SPVs were combined using an equal-weight averaging scheme. In this process, GMM posterior probabilities and FCM membership degrees were internally used as natural weights when computing their respective cluster profile vectors, whereas K-Means outputs contributed with equal weight across its three scenarios. Additionally, the 6- and 7-cluster K-Means scenarios were included to capture the finer structural distinctions observed in transitional provinces, as suggested by the probabilistic clustering results of GMM and FCM. This structure prevents any single clustering method from dominating the final profile and ensures a balanced representation of deterministic and probabilistic information.

This approach ensures the reduction in model-specific biases of individual clustering methods and the representation of provincial socioeconomic profiles in a more stable and reliable way. If any province had been assigned to the similar clusters in all five clustering methods, its vector would be stable; however, if it fell into different clusters, the averaging procedure would balance its representation and reflect its transitional nature.

Consequently, the robust SPV of each province was used as an input parameter to the optimization model (Efficiency vs. Equity Model). Therefore, investment allocation would not rely on a single clustering approach but on a harmonized data structure derived from multiple algorithms.

2.3. Setting Investment Priorities Based on the 12th Development Plan

The scoring process in this part of the study was conducted through a systematic review of the content of the 12th Development Plan of Türkiye (for the years 2024 to 2028) (SBB, 2023) [23], which is published by the Presidency of Strategy and Budget. The thematic emphasis, number of targets, and frequency of occurrence within the text were taken into consideration in the relevant parts of the plan (such as Strategic Goals, Transformation Areas, and Sectoral Action Plans). This approach of using document-based content assessment was preferred over using subjective expert opinion. In this way, investment domains were determined and scored objectively and in a reproducible manner using national policy documents.

Each investment category that originated from the national development plan was evaluated under three criteria: Policy Priority, Impact Area, and Regional Disparity. For each criterion, a scoring scale of 1 to 3 was applied. This scale was structured considering the thematic emphasis, policy context, and spatial impact potential reflected in the 12th Development Plan of Türkiye (2024–2028):

• Policy Priority (1–3): this demonstrates the degree to which the development plan strategically highlighted the investment area:
  • “High-priority” (3 points) areas are covered in the Priority Policies’ and Transformation Areas’ parts of the development plan and supported by independent action plans (such as Education, Industry and Technology, and Digitalization).
  • “Moderate-priority” (2 points) areas are mentioned in the plan in a limited number of targets.
  • “Low-priority” (1 point) domains are mentioned indirectly or have relatively low weight in the overall policy framework.
• Impact Area (1–3): this shows how widely the economic and social impacts of the investment are distributed over the region and sector:
  • “High-impact” (3 points) categories (like Education, Transportation) impact more than one sector and create regional synergy.
  • “Moderate-impact” (2 points) categories (like Tourism, Energy, and Agriculture) generate a strong regional impact; however, they show limited cross-sectoral diffusion.
  • “Low-impact” (1 point) categories (like Justice, Administration) represent investments whose influence is narrower in social and economic terms.
• Regional Disparity (1–3): this measures the potential impact of reducing interregional development gaps:
  • “High-potential” (3 points) categories (like Agriculture and Rural Development, Infrastructure, and Education) have a strong capacity to reduce regional asymmetries.
  • “Moderate-potential” (2 points) categories (like Industry, Digitalization) tend to concentrate in city centers; however, they provide moderate spatial diffusion.
  • “Low-potential” (1 point) categories (like Justice, Security) are more uniformly distributed across the country but have very limited ability to reduce spatial disparities among the provinces.

For each investment category, the scores assigned to each criterion are summed up to calculate the total weight (having values of 3 to 9), and based on these weights, total public funds were partitioned among the categories. This approach quantified the thematic orientations of the development plan as well as ensured consistency with national policy documents. In

Table 3. Determining investment priorities based on the 12th Development Plan (2024–2028).

Government Investment Areas	Policy Priority (1–3)	Impact Area (1–3)	Regional Disparity (1–3)	Total Weight
Education and Human Capital	3	3	3	9
Health and Social Services	3	3	2	8
Transportation Infrastructure	2	3	3	8
Industry and Technology Development	3	2	2	7
Agriculture and Rural Development	2	2	3	7
Energy and Environment	3	2	2	7
Digitalization and Information Society	3	2	2	7
Tourism and Cultural Development	2	2	2	6
Justice and Security Services	2	2	1	5

, the total weights of the categories are provided, along with the points taken from each criterion.

2.4. Calculating Province Investment Weights

In this stage, in order to quantify the relationships of each province and investment category, a Province × Investment Category matrix was constructed. This matrix shows the development potential or requirement level of each province in the corresponding investment area.

Step 1. Mapping subcategories to investment areas

Firstly, the 30 subcategories were mapped to the nine main government investment areas that were derived from the 12th Development Plan. This mapping was performed at two levels according to the impact of the subcategory on the investment domain:

• Direct effects: Subcategories classified as direct effects are those that influence an investment area through an immediate and domain-specific mechanism. These indicators represent capacities or needs that are directly targeted by the investment category and that can be altered through policy intervention within that domain. For example, “Years of Schooling” directly reflects educational attainment and therefore corresponds to the Education and Human Capital investment area.
• Indirect or supporting effects: Subcategories classified as indirect effects influence an investment domain through secondary, enabling, or demographic pathways rather than through a direct functional mechanism. These indicators shape the context within which an investment area operates and can affect the efficiency or effectiveness of public investments, but they are not themselves the primary target of such investments. For example, “Population Change” influences long-term demand for Health and Social Services, yet it is not a direct measure of health system capacity.

Mapping is shown in

Table 4. Mapping subcategories to government investment areas.

Government Investment Areas	Direct Effect	Indirect/Supporting Effect
Education and Human Capital	Years of Schooling Gender Parity Index Educational Attainment (Age 15+) Employment and Participation Unemployment	Public, Education, Health, Social Services/GDP Industry Information and Communication/GDP Manufacturing Industry/GDP Population Other Sectors/GDP
Health and Social Services	Health Infrastructure Dependency Ratios Public, Education, Health, Social Services/GDP	Municipal Services Coverage Unemployment Population In-Migration Out-Migration Gender Parity Index
Infrastructure and Transportation	Construction/GDP Trade, Transport, Accommodation, Food/GDP Intermediate-Density Areas Thinly Populated Areas Municipal Services Coverage	Densely Populated Areas Industry Tourism Population In-Migration Out-Migration Manufacturing Industry/GDP
Industry and Technology Development	Manufacturing Industry/GDP Industry Professional, Technical and Support Services/GDP Information and Communication/GDP Years of Schooling Educational Attainment (Age 15+)	Macro-Economic indicator Finance and Insurance/GDP Gender Parity Index
Agriculture, Food and Rural Development	Agriculture Agriculture, Forestry and Fishing/GDP Thinly Populated Areas	Municipal Services Coverage Dependency Ratios Out-Migration In-Migration
Tourism and Cultural Development	Tourism Trade, Transport, Accommodation, Food/GDP	Municipal Services Coverage Health Infrastructure Real Estate Activities/GDP
Energy and Environment	Municipal Services Coverage Industry Information and Communication/GDP Mining, Quarrying and Other Industries/GDP Manufacturing Industry/GDP	Population Densely Populated Areas Macro-Economic indicator
Justice and Security Services	Crime and Sentencing Unemployment Educational Attainment (Age 15+) Dependency Ratios	Densely Populated Areas Population
Digitalization and Information Society	Information and Communication/GDP Years of Schooling Educational Attainment (Age 15+)	Employment and Participation Professional, Technical and Support Services/GDP Other Sectors/GDP

.

Step 2. Direction and weighting of subcategories

For each relationship between subcategory and investment domain, the direction of the impact was determined:

• Subcategories with positive impacts (such as “Educational Attainment”, “Employment Rate”).
• Subcategories with negative impacts (such as “Unemployment”, “Crime Rate”).

Using the standardized subcategory $k$ scores in the robust SPV of each province $i$ (denoted as $v_{ik}$), the raw utility value (${\tilde{u}}_{ij}$) of province $i$ in the investment domain $j$ is calculated as below:

$${\tilde{u}}_{ij}={\sum }_{k\in D_j}{s}_k{v}_{ik}+0.5·{\sum }_{k\in I_j}{s}_k{v}_{ik}$$

(1)

where $D_j$ and $I_j$ represent directly and indirectly impacting subcategory sets, respectively. $s_k$ takes the value of +1 and −1 based on the positive or negative impacts of the subcategory on the investment domain. Indirect effects were evaluated with half weight (0.5) relative to the main impact.

Step 3. Province–investment category normalization

Computed ${\tilde{u}}_{ij}$ values were transformed using min–max normalization to convert them into the [0,1] range using the following equation:

$$citydat{a}_{ij}={\displaystyle \frac{{\tilde{u}}_{ij}-\underset{i,j}{\min }{\tilde{u}}_{ij}}{\underset{i,j}{\max }{\tilde{u}}_{ij}-\underset{i,j}{\min }{\tilde{u}}_{ij}}}$$

(2)

As a result of this transformation, the province–category combination with the lowest values obtains 0, and the maximum value obtains 1. Even though raw utility value scales and values may vary, normalized $citydat{a}_{ij}$ values allow them to be comparable. Accordingly, positive effects correspond to higher values closer to 1, and negative effects translate into values closer to 0.

Step 4. Integration into the optimization model

The resulting $citydat{a}_{ij}$ matrix was used as benefit scores of the objective function value. These coefficients represent the efficiency component of the multi-objective optimization model by combining the socioeconomic performance profiles of the provinces with public investment priorities.

2.5. Multi-Objective Optimization: Efficiency vs. Equity Model

This study proposes a multi-objective optimization model for public-investment allocation that operates under two conflicting objectives:

(1)

Efficiency—maximizing the public utility of the total government investment.

(2)

Equity—minimizing the disparities in investment distribution across provinces.

Since these two objectives move in opposite directions due to their natures, a model was constructed using the ε-constraint method. In this method, while efficiency was preserved in the objective function, the equity objective was converted into a constraint whose value can be adjusted. The equity objective is applied using a G parameter that represents the inequality tolerance level. G was designed like a “Gini-like proxy” that determines the allowable difference between the maximum and minimum investment levels of provinces. Integrating the real Gini coefficient directly into the model would necessitate the calculation of absolute differences and pairwise sums to be incorporated into the model $\left|T_i-T_k\right|$, which would lead to a nonlinear optimization structure. For this reason, the Gini-like proxy constraint was preferred to reflect the impact of the Gini index while keeping the model in linear form. Solving the model for different G values can produce a Pareto front that exemplifies the trade-off between efficiency and equity. Thus, a systematic balance can be established between efficiency and equity.

• The mathematical model is formulated as below:
• Index Sets:

$i=1\dots M$: Provinces;

$j=1\dots N$: Investment categories;

$s=1\dots S$: Piecewise investment segments;

$c\left(i\right)$: The cluster to which province $i$ belongs.

• Parameters:

  $citydat{a}_{ij}$	Benefit score of allocating investment to province $i$ in category $j.$
  $w_s$	Weight factor representing diminishing returns for investment segment s (lower segments receive higher weights). $w_s\in \left(\mathrm{0,1}\right]$.
  $segBrea{k}_s$	Upper boundary (breakpoint) of segment s in the piecewise investment function.
  $minInves{t}_j$	Minimum required share for investment category j based on policy priorities. $minInves{t}_j\in \left[\mathrm{0,1}\right]$.
  $G$	Equity tolerance parameter, determining the maximum acceptable disparity between provinces. $G\in \left(\mathrm{0,1}\right]$.
  $B$	Total investment budget (normalized to 100).

Decision Variables:

$x_{ij}$	Total amount of investment allocated to province $i$ in category $j.$
$z_{ijs}$	Portion of investment $x_{ij}$ allocated to segment s (piecewise representation).
$T_i$	Total investment assigned to province $i$.
$x_{c\left(i\right),j}^{Cluster}$	Cluster-level investment plan for category $j,$ shared by all provinces within cluster $c(i$).

• Objective function:

$$\max {\sum }_i{\sum }_j{\sum }_{s}citydat{a}_{ij}·w_s·z_{ijs}$$

(3)

• Constraints:

• Piecewise segmentation

$$x_{ij}={\sum }_s{z}_{ijs} \forall i,j$$

(4)

$$z_{ijs}\le \left\{\begin{array}{c}segBrea{k}_s s=1\\ segBrea{k}_s-segBrea{k}_{s-1} s>1\end{array}\right.$$

(5)

2.

Cluster based allocation

$$x_{ij}=x_{c\left(i\right),j}^{Cluster} \forall i,j$$

(6)

3.

Budget constraint

$${\sum }_i{\sum }_j{x}_{ij}=100$$

(7)

4.

Minimum investment share per province–category

$$x_{ij}\ge 0.05·{\sum }_j{x}_{ij} \forall i,j$$

(8)

5.

Province-level min–max bounds

$$\min level\le {\sum }_j{x}_{ij}\le \max level \forall i$$

(9)

6.

Category-level minimum

$${\sum }_i{x}_{ij}\ge 100·minInves{t}_j \forall j$$

(10)

7.

Equity constraint (Gini-like proxy)

$$\underset{i}{\max }{T}_i-\underset{i}{\min }{T}_i\le G·\underset{i}{\max }{T}_i$$

(11)

$$T_i={\sum }_j{x}_{ij} \forall i$$

(12)

8.

Nonnegativity constraints

$$x_{ij}\ge 0, z_{ijs}\ge 0 \forall i,j,s$$

(13)

The objective function defined in Equation (3) aims to maximize the total utility of public investments. The benefit scores ($citydat{a}_{ij}$) were derived from a robust SPV, as mentioned in the preceding section. In order to represent the diminishing return structure of each investment in each piecewise segment (s), weight parameters ($w_s$) are incorporated.

Constraint (4) defines the relationship between the total investment variable ($x_{ij}$) and the segment-based investment variables ($z_{ijs}$). Each investment amount in each category is distributed over the segments to reflect the variance in shrinking marginal returns. In constraint (5), each segment is guaranteed to be below a predefined upper level (segBreaks). With this constraint, the effect of investment levels is to be reduced when a threshold is exceeded. Constraint (6) applies cluster-based allocation. All the provinces within the same socioeconomic cluster—having the same robust SPV—obtain the same investment share, and it also allows comparability across clusters. The total public investment budget is normalized (B = 100) in constraint (7). Total government investment is distributed over a fixed resource and this enables the proportional comparison across provinces and categories. Constraint (8) ensures a minimum investment share allocation for the province–investment combination. It prevents any province–investment share from being 0; in this instance, each category in a province obtains at least 5% of the overall investment in that province. Constraint (9) allows the lower and upper total investment boundaries of the provinces. This constraint avoids both oversaturation (excessive amount of investment) and underinvestment (insufficient funding) in a province. Based on the investment category priorities, a minimum category-level investment is applied in constraint (10). Minimum levels are obtained proportional to the scores shown in Table 3, which are based on the 12th Development Plan (for the years 2024–2028).

To prohibit the disparity among the provinces, a Gini-like proxy is used in equity constraint (11). This G parameter operates like an inequality tolerance coefficient that shows the maximum allowable disparity. This constraint makes sure that the difference between the maximum and minimum funded provinces does not exceed G. As noted earlier, to prevent converting the model into a nonlinear optimization problem, the real Gini index calculation, which requires pairwise absolute differences ($|T_i-T_k|$) to be estimated, is not preferred. In constraint 12, the total public fund for each province is defined, which is later used in equity constraint (11). Finally, constraint (13) is for nonnegativity.

3. Results

All PCA and clustering analyses were conducted in R (version 4.5.0) using RStudio 2025.05.0+496 “Mariposa Orchid”. The multi-objective optimization model was solved using IBM ILOG CPLEX 22.1.1.0. Supplementary Material SA includes full datasets, and Supplementary Material SB contains a reproducible R code snippet with all functions and steps required to replicate the results.

3.1. PCA and Clustering Descriptive Results

In this study, firstly, PCA was applied to the dataset containing 109 indicators for 81 provinces. As a result of PCA, the first 10 components describing 76% of the cumulative variance were selected for further analysis. These components represented the main structures of socioeconomic, demographic, and sectoral differences across provinces (see Table 2). The scores gathered from PCA were then used as input for the clustering methods.

The K-Means clustering approach was initially applied to the PCA output. Appropriate cluster numbers were determined using the Elbow method, and since the inflection point occurred beyond five clusters, the 5-, 6-, and 7-cluster scenarios were tested. These scenarios were selected so as to perform comparative analysis for provincial economic and social stability, growth levels, and sectoral variability. The K-Means results in Figure 2 indicated that clusters were formed based on similar provincial growth patterns. For instance, İstanbul was distinguished as a stand-alone cluster in all scenarios, because it does not show a statistically significant similarity to any other provinces in terms of socioeconomic structure, scale, sectoral diversity, and service capacity. On the other hand, the large coastal provinces İzmir and Antalya were placed in the same clusters in 5- and 6-cluster scenarios; however, in 7-cluster scenarios, they decomposed into different clusters, allowing the structural differences within themselves to emerge at a higher resolution.

As a second approach in clustering, the GMM method was employed. GMM relies on a model-based clustering approach where each cluster is assumed to be distributed with a Gaussian distribution. In practice, 1 to 9 cluster counts were tested, and even though the highest BIC value was concentrated around two clusters, the 5-cluster case provided similar statistical results and a more interpretable regional structure. The GMM approach generated membership probabilities for all provinces, and the uncertainty index was calculated based on the differences between the probabilities. This allowed for evaluating the strength of association of each province with the indicated cluster; moreover, an uncertainty map was created to visualize spatially. High certainty levels of the provinces indicated well-defined development profiles, whereas low certainty showed the transitional regions. Figure 3 illustrates the spatial results of the GMM analysis. Geographic spread of the clusters on the map revealed that high-probability industrial and service-oriented provinces were located in western Türkiye, while low-income and agriculture-oriented peripheral province clusters were in eastern regions. Additionally, intermediate uncertainty zones in Marmara and Central Anatolia more represented the transitional provinces with mixed structural characteristics lying between distinct economic typologies. With the help of the probabilistic nature of GMM, the results demonstrated that provinces could be associated with multiple development typologies, and the borders among the clusters were not always sharply defined but could be gradual.

As the third clustering method, the FCM approach was applied. FCM is a soft clustering approach in which a province can be associated with multiple clusters with different membership percentages. This approach especially provided more realistic clustering for socioeconomically transitional provinces (like Adana, Konya, Kayseri). A fuzzification parameter m was chosen as 2, which is in the suggested standard range and ensures a reasonable level of cluster overlap. FCM results provided the primary cluster assignment together with the membership percentages. The derived uncertainty surface showed the tendency of the provinces to be associated with multiple development typologies. Figure 4 illustrates the membership uncertainty map derived from the results of FCM analysis. In the map, provinces are shown with different color intensities based on their membership percentages to the indicated primary cluster. Dark tones represented low uncertainty with high membership in a single dominant cluster, whereas light tones with high uncertainty corresponded to transitional provinces that belonged to multiple clusters with similar probabilities. In particular, provinces with mixed economic structures like Konya, Adana, Kayseri, and Gaziantep had high uncertainty levels. These provinces displayed hybrid structures that developed in industry and service sectors while simultaneously maintaining significant agriculture and traditional production characteristics. FCM results also confirmed the probabilistic transitions observed in GMM and revealed that clusters are not separate from each other, and there are regions of gradual transition zones in Türkiye.

In the two probabilistic methods, namely GMM and FCM, the cluster membership information reflected the strength of belonging to a cluster for a province; the results were assessed with weighted representation rather than hard cluster assignment. In GMM analysis, the posterior cluster probabilities were used to calculate cluster centroids with weighted cluster averages. Likewise, membership degrees created by FCM illustrated the assignment of provinces to multiple clusters, and these figures contributed to the calculation of fuzzy-weighted cluster centroids. Finally, three K-Means clustering results combined with GMM and FCM weighted cluster results were averaged to form a robust provincial subcategory vector in the succeeding stage. This approach enabled the incorporation of inter-cluster uncertainty in a data-driven way and also reduced the model-specific bias arising from any individual algorithm. Overall, the PCA-based three-stage clustering approach provided a multidimensional classification of the socioeconomic structures of provinces and synthesized the complementary information produced by each method to form robust provincial profiles. These profiles were used as core input data for the optimization model.

3.2. Robust Provincial Profiles and Investment Potentials

The results obtained from the clustering approaches were then used to calculate the robust provincial profiles that summarize the province structure using 30 subcategories. For each province, three K-Means scenarios, GMM, and FCM results produced an SPV composed of the average values of the clusters to which the province was assigned. For instance, in

Table 5. Calculation of robust provincial profile for Izmir province.

		Subcategories
		#1	#2	#3	#4	…	#8	#9	#10	…	#30
	Cluster	Agriculture	Agriculture, Forestry and Fishing/GDP	Construction/GDP	Crime and Sentencing	…	Employment and Participation	Finance and Insurance/GDP	Gender Parity Index	…	Years of Schooling
K-Means (5 Clusters)	2	2.2482	0.3045	0.0892	1.9298		0.5995	0.3928	1.1698		1.4481
K-Means (6 Clusters)	2	1.6538	0.3605	0.3925	1.3322		0.5072	0.1461	1.2137		0.9578
K-Means (7 Clusters)	6	2.4676	0.2854	0.0284	1.9759		0.3073	0.4678	1.0340		1.4565
Gaussian Mixture Model	2	1.6817	0.0117	0.3454	2.9556		0.6841	1.3417	1.2634		1.5434
Fuzzy C-Means	5	0.4132	0.0348	0.1254	0.3676		0.1463	−0.0700	0.5119		0.3881
Robust SPV	Average	1.6929	0.1994	0.1962	1.7122		0.4489	0.4557	1.0386		1.1588

, the robust SPV computed for İzmir province is shown. In the table, the cluster assignment for each method and the relevant subcategory averages for that cluster are displayed. In the GMM and FCM, since the provinces were not sharply assigned to a cluster, the vectors were calculated based on weighted cluster averages. In other words, weighted cluster averages were constructed by using posterior probabilities (in GMM) and membership degrees (FCM). Then, the resulting five SPVs were again averaged to derive a single robust SPV containing values for 30 subcategories for each province. While merging the results of different clustering approaches, a balanced dataset representing the provincial socioeconomic situation by deterministic and probabilistic information was assembled.

The robust SPVs not only captured the current socioeconomic position of each province but also its potential future investment capacity. These robust SPVs built up a Province × Subcategory (matrix of 81 × 30), which was later used to calculate $citydat{a}_{ij}$(matrix of 81 × 9) to be employed in the optimization model.

3.3. Scenario-Based Optimization and Equity–Efficiency Trade-Off

For each government investment area, minimum investment thresholds were determined using the policy weights derived proportionately from the 12th Development Plan, as shown in Table 3. In the model, these minimum threshold ratios were scaled to 80% of the total investment budget. This ratio supported maintaining the data-driven policy alignment of the model while providing optimization flexibility. This structure guaranteed a minimum support level for the investment domains, but at the same time, the remaining 20% was distributed freely according to the dynamics of efficiency–equity trade-off.

In order to explain the results of the optimization model, ten provinces with distinctly different socioeconomic profiles were selected. Selected provinces with their strengths and weaknesses are displayed in

Table 6. Provincial investment profiles: strong and weak dimensions.

Province	Strong Dimensions	Weak Dimensions	Profile Summary
İstanbul	Infrastructure and Transportation; Industry and Technology; Digitalization and Information Society	Agriculture and Rural Development; Education	Highly industrialized and digitalized metropolitan hub; national economic core with low agricultural capacity.
Ankara	Health and Social Services; Education and Human Capital; Infrastructure and Transportation	Tourism and Cultural Development; Agriculture	Administrative and educational capital; balanced development with strong social infrastructure.
İzmir	Infrastructure and Transportation; Industry and Technology; Agriculture; Tourism	Justice and Security; Digitalization (Moderate)	Diversified regional economy integrating industry, tourism, and agriculture; balanced investment potential.
Antalya	Tourism and Cultural Development; Infrastructure and Transportation	Education; Industry and Technology	Tourism-driven coastal province; high seasonal economy and logistics focus.
Gaziantep	Industry and Technology; Agriculture and Rural Development; Energy and Environment	Tourism; Digitalization	Export-oriented industrial hub of Southeastern Anatolia; strong manufacturing base with growing energy sector.
Kayseri	Industry and Technology; Infrastructure and Transportation; Energy and Environment	Tourism; Digitalization	Industrial and trade-oriented central Anatolian city; high production and logistics potential.
Eskişehir	Education and Human Capital; Industry and Technology; Energy and Environment	Agriculture; Justice and Security	University and innovation-oriented province; strong RandD and human capital base.
Van	Education; Health and Social Services; Agriculture and Rural Development	Industry and Technology; Digitalization	Underdeveloped eastern province with high potential in public services and rural development.
Tunceli	Education; Health and Social Services	Industry and Technology; Infrastructure and Transportation	Small-scale province with strong public service provision and limited industrial capacity.
Rize	Agriculture and Rural Development (Tea Sector); Health and Social Services	Industry and Technology; Digitalization	Coastal and agriculture-oriented province; limited diversification beyond primary sectors.

. Figure 5 shows the investment distribution in these provinces for various equity tolerance levels (Gini-like proxy values between 0 and 1). At the G = 0 level, the model provides a fully egalitarian allocation structure, and all provinces take approximately the same share from the overall public fund. Even though this approach removed the inter-provincial disparity, provinces with high capacities (like İstanbul, Ankara, İzmir) were limited in terms of using their potential contributions to the efficiency.

When G is between 0.3 and 0.5, there was a more balanced distribution between efficiency and equity, where the relative strength of the provinces started to reflect more on the investment plan. For instance, provinces with strong industry and production capacities like Kayseri, Gaziantep, and İzmir took a higher investment share, whereas service and agriculture-oriented provinces such as Van, Tunceli, and Rize continued to receive a more stable but comparatively lower share. This range can be considered as an optimum trade-off zone for the system, where efficiency increase was achieved while maintaining equity.

When G was increased to the 0.7–1 range, the equity constraint became substantially relaxed, and efficiency was promoted in the model solution. In this case, government investment was oversaturated in provinces with high capacity (such as İstanbul, Ankara); however, less developed regions like Tunceli and Van fell to very low investment levels. This leads to the conclusion that when the equity constraint is weakened, Regional Disparity escalates rapidly, and highly uneven spatial outcomes could occur.

In general, when Figure 5 and Table 6 are evaluated, it is evident that each province exhibits distinct investment responses to the allocation model based on its structural strengths (such as tourism for Antalya, industry for Kayseri and Gaziantep, basic public services for Van and Tunceli). This pattern indicates that the model successfully captures multidimensional growth profiles and provides a powerful tool for policy makers that clearly visualizes the efficiency–equity trade-off.

All 109 indicators used in this study are included in the Supplementary Material. Additionally, all investment allocation results that were produced for the complete range of equity tolerance levels (Gini-like proxy between 0, 0.1, 0.2, …, 1) are also presented in the Supplementary Material:

• Supplementary Material—SA: Raw indicator dataset containing the original provincial values for all 109 indicators.
• Supplementary Material—SC: Investment allocation tables for each G value, including both category-level and total investment allocations for all provinces.

4. Discussion and Implications

Upon the examination of the existing literature, it can be seen that studies on the distribution of regional public investments are largely based on descriptive, econometric, or ex post evaluative approaches. For instance, Yamano and Ohkawara (2000) [10] analyze the dynamics of the efficiency–equity trade-off in investment allocation; Castells and Solé-Ollé (2005) [11] decompose the components of equity, efficiency, and political factors affecting investment. Similarly, Monastiriotis and Psycharis (2014) [12] demonstrate that public investment allocation processes in Greece exhibit significant inertia and non-systematic patterns. Moreover, recent cross-country evidence challenges the inevitability of this conflict; for instance, Beck et al. (2024) [21] find that globalization shocks do not consistently lead to higher inequality, suggesting that the efficiency–equity trade-off may not be as strict as traditionally assumed. This literature generally demonstrates that public investment is often shaped not only by economic efficiency signals but also by geographic, political, or redistributive dynamics.

Another important observation is that most of the existing studies evaluate past investment distributions in specific country contexts with econometric models (e.g., South Korea, Lee, 2022 [16]; Greece, Monastiriotis and Psycharis, 2014 [12]; Ecuador, Aray and Pacheco-Delgado, 2020 [17]; Spain, Albalate et al., 2012 [18]). These studies show that investments are often made not only according to the efficiency criterion, but are also shaped according to the dynamics of politics, redistribution, congestion, or centralization. Recently, Aray and Martinez-Vazquez (2024) [20] have advanced this theoretical landscape by proposing a general model that integrates output density alongside per capita income to bridge the gap between theoretical frameworks and empirical allocation criteria. However, the main limitation of these models is that they cannot produce an optimal distribution recommendation going forward. In other words, the question of “which provinces should receive how much investment” is not determined using the context of multidimensional data, spatial heterogeneity, policy-based weightings, or any efficiency–equity optimization framework.

Additionally, some studies analyze how investment allocation varies by infrastructure type or spatial spillovers. For example, Vasilakos et al. (2023) [13] examine how place-based infrastructure investments (like investments in national highways and electricity capacity) shape firms’ location preferences and regional performance in India, whereas Albalate et al. (2012) [18] show that transport infrastructure investments in Spain are strongly influenced by political centralization. However, a common limitation of these studies is that they are limited to describing current investment decisions and do not produce ex ante optimal allocations.

MCDMs, which have emerged in recent years, have been developed by AI-supported optimization or multi-objective allocation models (Baffo et al., 2024 [14]; Shang and Wang, 2025 [15]) that contribute to the development of more systematic decision-making mechanisms, but most of these studies are sectoral, project-level, or regional. None of them solves the problem of province-level investment allocation in an entire country in an integrated manner with both a multidimensional indicator set and an equity constraint (G-parameter).

The contribution of this study emerges precisely in this gap. This study offers an original contribution by integrating the three approaches discussed separately in the literature:

(1)

Province-level needs identification: With PCA + multiple clustering algorithms (K-Means, GMM, FCM), the socioeconomic structures of the provinces were extracted as robust provincial profiles. This approach goes beyond only income-level-based criteria and represents the multidimensional capacity and need structures of the provinces.

(2)

Policy-aligned investment prioritization: The document-based content assessment for the 12th Development Plan is a policy-integrated investment classification that is rarely used in the literature. Thus, investment categories were modeled in a quantified manner in line with national strategies.

(3)

Normative multi-objective optimization: The model, which includes an adjustable equity constraint (G-parameter), clearly reveals efficiency–equity trade-off behavior at different inequality tolerance levels. In this respect, this study offers a normative and practical decision support tool by going beyond the explanatory character of the previous literature.

This study is distinct in the literature since it addresses the issue of “how should investments be distributed?” in a data-driven, policy-consistent, reproducible, and optimization-based framework, whereas the existing studies only address the question “why are investments distributed in this way?” This approach has produced a model that considers the multidimensional development profiles of provinces, generates alternative scenarios at different G levels, and offers a transparent and analytical balance between spatial equity and development efficiency.

In conclusion, this study makes a strong contribution to the literature in three respects:

i.

The transition from ex post explanatory models to an ex ante optimization approach.

ii.

The transition from one-dimensional indicators to the use of multidimensional provincial profiles.

iii.

The transition from general regional analyses to province-specific investment allocation.

This integration provides a strong methodological framework for a more objective, transparent, and strategy-aligned distribution of public funds in countries with high regional heterogeneity like Türkiye. The integrated approach put forward by this study (a framework consisting of PCA-based needs identification, policy-aligned investment prioritization, and normative multi-objective optimization) produces important methodological, academic, and policy design implications.

By integrating several analytical methods that are dispersed throughout the literature into a single cohesive model, this study offers a number of methodological implications. First, the use of multidimensional indicator sets demonstrates that the development discrepancies between provinces cannot be explained by one-dimensional indicators. Provinces can now be represented with strong provincial profiles thanks to the combination of PCA and three distinct clustering methods; as a result, both probabilistic and deterministic data were gathered in an integrated data structure.

Secondly, the normative multi-objective optimization model used in the study represents a design approach that is rarely used in public investment allocation studies. Modeling the equity–efficiency trade-off with the ε-constraint method makes it possible to produce systematic and reproducible solutions at different equity levels. In this respect, this study goes beyond the literature based solely on descriptive or econometric results and provides a strong methodological framework for prescriptive decision-making.

Third, the derivation of the Province × Investment Category matrix from both provincial profiles and policy-based weights is an important methodological contribution to how multi-layered data integration can be incorporated into the modeling process. This structure provides a scalable modelling framework that can be easily adapted to other country contexts in future studies.

This study enhances the literature on regional development economics and public investment allocation with important main academic implications. First, it brings an ex ante optimization-oriented perspective instead of the ex post explanatory approach seen in existing studies. Thus, it has become possible not only to explain investment behaviors but also to generate optimal allocation recommendations. Secondly, the study evaluates the development levels of provinces based not only on economic indicators but also on multiple areas such as human capital, infrastructure, sectoral composition, social services, and the environment. This multidimensional approach offers a more comprehensive and realistic evaluation than classifications based on single indicators (such as GDP per capita) common in the literature. Additionally, use of the equity element modeled as a G-parameter allows the spatial equity–efficiency trade-off to be examined under different tolerance levels. Thus, the question of “how much inequality is acceptable?”, which is frequently discussed in the literature but rarely modeled quantitatively, has become directly testable. In this respect, this study makes a valuable contribution to the spatial economics and public finance literature.

The findings of this study have important implications for policy makers in public policy design. First, robust provincial profiles provide a more objective basis for needs-based allocation by revealing structural differences that are not visible at first glance. This approach makes it possible to direct public investments not only based on past trends or political motivations but also through objective capacity and requirement analysis. Secondly, the fact that the investment category weights are based on the content analysis of the 12th Development Plan ensures that the model works in an integrated manner with the national strategy. This method creates a transparent and accountable structure for policy-consistent allocation, which offers a justification for minimum investment levels in high-priority areas such as Education, Industry, and Digitalization. Furthermore, scenario analyses based on different levels of equity offered by the model allow decision-makers to compare efficiency-oriented, equity-oriented, or balanced policy options. This feature helps public investment planning not only to increase total benefit, but also to be designed in accordance with the goals of spatial cohesion and balanced territorial development. A limitation of this study is that province-level historical public investment data are not publicly disclosed by the relevant ministries, which prevents direct empirical validation of the model through comparison with past allocation patterns. This limitation also highlights the need for systematic collection and publication of province-level investment data by governmental institutions to enable future impact assessment.

Finally, the fact that the entire dataset and model outputs are presented in a reproducible manner shows that this study is a feasible decision support tool in terms of policy design. This structure allows for rapid evaluation of different policy scenarios for national planning institutions.

5. Conclusions

This study proposes an integrated methodological framework for allocating public investments at the provincial level in Türkiye in a more objective, data-driven, and policy-aligned manner. In the study, the multidimensional dataset created using 109 socioeconomic indicators was reduced with PCA; then, K-Means, Gaussian Mixture Model, and Fuzzy C-Means methods were used together to obtain robust provincial profiles reflecting the structural similarities of the provinces. These profiles provided a database that holistically represents the development levels, structural capacities, and potentials of the provinces in different sectors.

Thematic areas highlighted in the 12th Development Plan were identified using a document-based content analysis, converted into investment categories, and weight coefficients were developed for these categories in order to improve adherence to national development strategies. The province-specific development profiles and national strategic priorities obtained were combined in a multi-objective optimization model, and the efficiency–equity balance was analyzed at different inequality tolerance levels.

The results of the model revealed that the spatial distribution of public investment showed high sensitivity to the equity–efficiency relationship. At low G values, the model produces a more equitable distribution, while at high G levels, investments are largely concentrated in provinces with high capacities. It has been observed that at medium inequality tolerance (G ≈ 0.3–0.5), both the potential returns of developed provinces can emerge and also a distribution structure that maintains spatial balance is possible. This result demonstrates that preferred policy areas can be modeled based on the different planning objectives.

This study contributes to the literature in terms of (i) defining multidimensional requirements and capacities at the provincial level, (ii) integrating national strategic priorities into investment categories in an analytical way, and (iii) using a normative optimization approach that can adjust the equity–efficiency balance. The results imply that data-driven approaches in public investment planning can be helpful in the development of more consistent and transparent mechanisms that consider Regional Disparity.

However, the model is limited by the scope of the available dataset and the indicators chosen. Future studies may contribute to expanding the proposed framework by adding a time dimension, incorporating spatial interaction models, or evaluating complementarities between investment types. Despite this, this study provides a reproducible, adaptable, and evidence-based assessment tool for policy analysis and strategic planning processes.