Analyzing the relationship between socio economic and environmental factors for building an integrated system supporting agricultural land use planning, a case study in soc trang province

THE MINISTRY OF EDUCATION AND TRAINING CAN THO UNIVERSITY SUMMARY OF THE DISSERTATION Major: Land Management Major Code: 62 85 01 03 NGUYEN HONG THAO ANALYZING THE RELATIONSHIP BETWEEN SOCIO-ECONOMIC AND ENVIRONMENTAL FACTORS FOR BUILDING AN INTEGRATED SYSTEM SUPPORTING AGRICULTURAL LAND USE PLANNING A CASE STUDY IN SOC TRANG PROVINCE Can Tho, 2021 THE PROJECT WAS COMPLETED IN CAN THO UNIVERSITY Supervisor: Assoc Prof Dr Nguyen Hieu Trung The dissertation was defended to the doctoral committee at college level Venue: Administration Building, Can Tho University Date and time: 14:00 PM, December 25, 2019 Reviewer 1: Assoc Prof Dr Le Van Trung Reviewer 2: Assoc Prof Dr Chau Minh Khoi Finding dissertation at: Learning resource center, Can Tho University Viet Nam National Library PUBLICATIONS Nguyen Hong Thao and Nguyen Hieu Trung, 2017 Establish open-source application for optimization agricultural land-use area Can Tho University, Journal of Science 52a, 62-71 https://doi.org/10.22144/ctu.jvn.2017.111 Nguyen Hong Thao, Nguyen Hieu Trung, Le Quang Tri, 2017 Establishing the model for supporting agricultural land use allocation - A case study in My Xuyen district, Soc Trang province Can Tho University, Journal of Science, Special issue: Environment and Climate change, 2017, 166-177 https://doi.org/10.22144/ctu.jsi.2017.065 Thao, N.H and Trung, N.H., 2018 Establishing an integrated model for supporting agricultural land use planning: A case study in Tran De district, Soc Trang province Can Tho University Journal of Science 54 (Special issue: Agriculture): 6271 https://doi.org/10.22144/ctu.jsi.2018.096 Nguyen Hong Thao, Nguyen Hieu Trung, Truong Chi Quang, Pham Thanh Vu, Phan Hoang Vu, Vuong Tuan Huy, Dang Kim Son, 2019 Application of optimizing algorithm and allocation of agricultural land use in the Mekong Delta Journal of Soil Science, Special issue 57, 97–102 Nguyen Hong Thao and Nguyen Hieu Trung, 2019 Using the Monte Carlo model to predict agricultural production areas for land use optimization Can Tho University, Journal of Science 55, Special issue: Environment and Climate change (2): 164-174 https://doi.org/10.22144/ctu.jsi.2019.143 CHAPTER INTRODUCTION 1.1 The necessity of the thesis The land use planning is based on a 10-year cycle and on the criteria of the Ministry of Natural Resources and Environment (Ministry of Natural Resources and Environment, 2014) The FAO's guiding procedures for land use planning process (FAO, 1981) consists of steps In which there are two steps that need to be emphasized to ensure the sustainable development, which are the natural land suitability assessment and socio-economic and environmental appraisal However, the step of alternative assessment of socio-economic factors often faces many difficulties because these conditions often changed from different regions, thus it difficult to apply by planners In order to alternative assessment of socio-economic factors, the authors used different methods such as multi-objective land assessment (Pham Thanh Vu et al., 2009), Analytic Hierarchy Process (AHP) in land use classification (Akıncı et al., 2013; Elaalem et al., 2010) The advantage of these methods is to propose the optimized area for agricultural land use types (LUTs) based on constraints However, there are limitations on result’s maps where many land use types are suitable for one land unit Therefore, it is necessary to research and develop a supporting software program to simplify the application process based on the identified socio-economic factors The request on optimal spatial arrangement of LUTs in agricultural land use planning is the most a big question of the planner Many studies have been carried out that can be listed are the methods applied for arranging LUTs based on MCA multicriteria analysis with GIS and on Cellular Automata (CA) (Le Canh Dinh, 2011) These methods have helped planners in their decision-making However, these current spatial arrangement methods not take into account specific impact factors on land use such as infrastructure for agriculture as well as the risk on implementation, capability investment of land use types Therefore, it is necessary to build a model of land use arrangement for agricultural production taking into account the socioeconomic factors and the influence of transport and canals systems, electric supply systems, neighborhood land use, and investment capacity of farmers as well as the rate of poor households in the local area affecting the spatial arrangement of agricultural land use types Since the advantages and shortcomings of relevant studies, it is necessary to fulfill the lag of previous studies Specifically, this thesis focuses on analyzing the relationship between socio-economic and environmental factors affecting the choice of agricultural land use type in establishment optimization model; develop an integrated system that allows planners to build planning solutions based on land suitability, socio-economic conditions, infrastructure, and farmer’s ability to achieve optimal spatial location according to characteristics of each type of agricultural land use 1.2 Objectives Overall objective The research objective of the thesis is to analyze the main socio-economic environmental factors affecting the types of agricultural land use These factors can be used for building an integrated model to optimize the agricultural land use area and land use allocation That can help planners to improve the efficiency of land use planning Specific objectives Objective 1: Identify socio-economic and environmental factors affecting agricultural land use Objective 2: Building an application to optimize the area of agricultural land use types using open source tools Objective 3: Building an integrated model to optimize and allocate for agricultural land use map Objective 4: Application of the integrated model in agricultural land use planning 1.3 Contents of the study (1) Analyze the relationship between socio-economic and environmental factors for optimizing and allocating agricultural land use (2) Develop open source computer software for optimizing agricultural land (3) Building an integrated model in agricultural land use arrangement (4) Application of integrated models in formulating agricultural land use plans 1.4 Research objects and scope of the study Research objects The study focused on identifying the main socio-economic, environment factors that mainly affect the arrangement of agricultural land use types in land use planning Mathematical model in optimizing agricultural land area and spatial arrangement model of agricultural land use maps Scope of the study In terms of space, the thesis focusses on the research and experimental application of the integrated model in districts representing for ecological regions of Soc Trang province: Long Phu district where corresponds to the freshwater ecoregion, My Xuyen district where corresponds to the brackish water ecoregion outside the dike and Tran De that corresponds to the brackish water ecoregion inside the dike 1.4.1 The scientific meaning and applicability 1.4.2 Scientific meaning The thesis contributes new scientific points as follows: - Identifying main socio-economic and environment factors affecting the choice of agricultural land use types Relationships of these factors in land use optimization and land allocation mapping - Developing a computer software for solving optimizing agricultural land use with user interface This is a specialized tool for the management and planning of agricultural land use - Developing a model of spatial arrangement for land use mapping based on multicriteria evaluation Land use arrangement was based on economic priority level, land suitability and dominant characteristics of land use types, spatial correlation with social and environmental conditions as well as neighboring agricultural land use patterns, current land use status and infrastructure 1.4.3 Applicability The methods, tools and processes proposed from the results of the thesis is a useful reference for research at university, master and PhD level in Land Management The socio-economic, environmental factors and the integrated model could be used as a decision supporting tool for land use planning process that can help planners to improve quality of agricultural land use plans CHAPTER LITERATURE REVIEW 2.1 Factors affecting agricultural land use According to many studies on land use in general, including agricultural land use, is influenced by socio-economic and environment, policy factors (Lambin and Geist, 2007) Considering foreign studies related to this impact, Baker and Capel (2011) in the United States showed that there are three main factors: socio-economic, environmental issues that determine the distribution of agricultural cultivation In Europe, Cintina and Pukite (2018) show the economic, social and environmental, policy and management, technical and technological, subjective of farmers are the main affected factors In Vietnam, studies show that natural, socio-economic and environmental factors have a strong impact on land use and the implementation of land use planning In Vietnam, the study of Bui Anh Tuan et al (2013) in the case study in Son Tay Town (Hanoi) used regression statistics to evaluate which factors have a positive relationship affecting land use management The results show that land policies, support policies (capital, technology); soil properties; size of farm land, the role of media and information are the selected factors Huynh Van Dung (2017) assessed 14 socio-economic factors affecting the implementation of land use plan in Giong Rieng district, Kien Giang province by using AHP method The results showed that the economic factor was assessed as important (the weight of 0.61) compared to the social factors which were 0.21 and environment was 0.18 The results showed that in terms of economic factor group, production cost was the most important factor of farmer with a weight of more than 50% compared to the other profit and market For social factors groups such as capital capacity, capital supporting, farming practices, technical assistance, job creation, land use planning In which, the ability of capital of farmers, the support of capital and farming practices were the important factors However, the studies of factors only for assessing which factors are important, but did not show the applicability in the selection of land use and land arrangement in land use planning 2.2 Optimization methods in agricultural land use planning Multi objective optimization is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously In land use planning, optimizing is used to estimate land use area based on the constraint between nature, socio-economy and environment (Nguyen Hai Thanh, 2005; Nguyen Hieu Trung et al., 2015) Optimization with single or multiple objectives is a method to find the best possible solution according to a certain requirement Actually, it is a decision-making supporting Decision-making is one of human activities and has been studied since the late 18th century The method of decision making includes the choice of development options; therefore, it is important in many fields of science including social science as well as natural science (Nguyen Nhu Phong, 2010a) It can be said that optimization is the most important quantitative tool for decision making (Nguyen Hai Thanh, 2005; Pham Thanh Vu et al., 2016) 2.3 Studies related to agricultural prediction Predictions are estimates and evaluations of future events, which are often uncertain The goal of forecasting is to use existing information in a best way to guide future activities Predictions are divided into two categories, qualitative and quantitative In which, qualitative methods are based on qualitative data such as opinions, judgments, professional experience of experts In contrast, the quantitative method is based on quantitative data collected over time series (Nguyen Nhu Phong, 2010a) Predictions based on the mathematical model need to analyze need large data source collected for building models Regarding simulation method in forecasting, according to Fishman (1997), Monte Carlo simulation method provides estimated solution based on statistical sampling method using computers This is a method of solving non-random problems by random sampling The samples are randomly selected and repeated several times to calculate the results according to the method of the given problem Therefore, the Monte Carlo method often provides an estimated solution with acceptable errors in the case of difficult to find the exact solution for the problem Many studies have been done to predict factors such as price, demand for agricultural products, and output of agricultural products, but choosing a feasible method is important to determine the threshold for production Forecasting production demand based on local production potential is more feasible than one for agricultural demand Agricultural productions from historical production areas in many years meet supply and demand mechanism of the market 2.4 Methods of agricultural land allocation in land use planning Riveira and Maseda (2006) reviewed models and application methods in land use planning There were two main stages: the land suitability assessment stage and the land allocation stage Land use allocation was an important step in the development of planning options, which answered questions about arrangement of LUTs Solutions and software for land use allocation according to environmental, socio-economic conditions The previous studies showed that land allocation solutions have been divided into the main groups: (i) Land allocation based on land suitability assessment (ii) Land allocation based on multi-criteria evaluation, but mainly on AHP method; (iii) Land allocation based on Cellular Automata Most researchers used the first method that based on natural factors (soil, terrain, and hydrology) to determine level of natural adaptation, suitable results showed in form of adaptive maps This kind of map provided information about multiple choices for a land mapping unit but it did not indicate where each land use type are located The approaches used the Cellular Automata (CA) method to analyze the land (Ligtenberg, 2010) According to Le Canh Dinh (2011), SALUP software has been developed based on CA model In which land use selection was based on determining on the current land use then using the spreading principle of Cellular Automata to arrange the land area until end of area need to be located The limitation of the pure CA method is that the selection algorithm did not consider the characteristics of infrastructure, social practices, and investment capacity of each land use type to be arranged CHAPTER RESEARCH METHODOLOGY 3.1 Method for analyzing the relationship of socio-economic-environment factors affecting agricultural land use These kinds of data were collected for analyzing the relationship of socioeconomic-environment factors affecting agricultural land use: Land use statistics and land use maps of districts Long Phu, Tran De and My Xuyen in 2005, 2010 and 2015; Socio-economic statistics from 2010 to 2018; The annual agricultural reports of Long Phu, Tran De and My Xuyen districts from 2015 to 2018 Household survey to collect information on agricultural production, socioeconomy and environment affected land use The number of interviews was determined based on formula Yamane (1967) 𝑁 (1) 𝑛= + 𝑁𝑒 Where N: total agricultural households; e: sample error Number of agricultural households of districts in the study area is about 55,000 households, sample error is selected as 6%, and thus, the number of samples n calculated was 276 samples Considering the number of samples of similar studies by according to the district and province levels of Le Quang Tri et al., (2013); Thai Phu Vinh et al., (2015); Santiphop et al (2012) The total number of interviews in districts was rounded up to 45 households / LUT Therefore, the total number of famers for surveying is 315 households Descriptive statistical methods (Mann, 1995) was used to determine average values and standard deviations for quantitative economic indicator as profits of land use types; Qualitative social indicators include: education level, intensive farming level, production capital, technological and scientific transferring; farmer's risk assessment, infrastructure requirements for production; impact of agricultural land use types as environmental qualitative factor 3.2 Methods of building the integrated model The integrated model, named ST-IALUP (Soc Trang- Integrated model for supporting Agricultural Land Use Planning), was a combination of various tools where input and output data were well connected The integrated model provided agricultural land area estimation, agricultural land area optimization software - LandOptimizer, and land use allocation model - ST-LUAM The principle of integration was shown in Figure 3.2 Figure 3.1 Integrated model ST-IALUP Figure 3.2 showed the connection of components of the integrated model named Using Monte Carlo method is to estimate the land use areas of limited land use types Estimated land use areas were exported to a CSV file containing the area of the LUTs in the predicted over years This data source was used as constraint value in LandOptimizer This software gives optimized area for each LUT and was connected to the land allocation model, ST-LUAM, which performs land use solution maps 3.2.1 Agricultural land use area estimating In terms of estimating land use area, this thesis focused on analyzing three types of agricultural production: vegetables, fruit and aquaculture Cultivating area was estimated based on Monte Carlo simulation method which was applied as the diagram in Figure 3.3 In which, data of area of annual crops, fruit and aquaculture from 20102010 were loaded into the model Figure 3.2 Estimating the cultivated area using Monte Carlo method Next, historical of cultivated area was analyzed to get frequency of occurrence This frequency data was normalized For each LUT, model generate cultivated values of next years by generating a random frequency in the range [0, 1] This random number was used to get the cultivating area according with frequency where area values were classified After that, the model checks condition to stop simulation, if it is false the calculated area value will be returned to the list of area values the next simulation cycle 3.2.2 Method for developing agricultural land use optimization LandOptimizer software was built using the programming language Visual Basic.Net on Windows operating system The main steps of software development were shown in Figure 3.4 Figure 4.3 Number of workdays for LUTs during the year 4.2.3.2 Relationship between infrastructure and land use The survey results showed that local agricultural production was facing problems such as: (i) water supplied and drainage due to distance from canals, (ii) difficulty in transporting materials and travel due to narrow or unpaved roads, (iii) affecting farming practices due to saline leakage from shrimp ponds to rice fields Particularly for aquaculture, besides natural conditions such as land and water, people still faced difficulties in production due to lack of electricity or weak operation of equipment, thus affecting production efficiency Figure 4.4 Infrastructure requirements of LUTS The three LUTs such as two rice crops, three rice crops and rice-shrimp, are the types affected by neighbor land uses Especially for rice-shrimp, if surrounding households raise shrimp or hold salt water in the pond, then neighboring rice-growing households will not be able to cultivate or achieve low yields For shrimp and fruit farming, the most priority was strong electric power source to operate machinery, followed by the need to be located near the road as well as the influence neighbor LUTs In fact, if they want to cultivate aquaculture products, the neighboring households must also cultivate the same style, which will bring about high efficiency About 20% of people agreed that vegetables and fruits should be located near rivers and canals However, vegetables and fruit needed to be located near the road due to the 12 farming behaviors of farmers 4.2.4 Environmental factors affecting agricultural land use 4.2.4.1 Risk of LUTs Besides natural characteristics of land, risk factors in production of land use types that were assessed by people through four levels such as high risk, medium risk, and low risk and non-risk as shown in Figure 4.5 (a) (b) Figure 4.5 Risks of use types (a) and environmental benefits of LUTs (b) Risk factors include more or less uncertainty about productivity, prices and weather risks Figure 4.5 showed that over 60% of the people assessed the shrimp farming style with highest risks in production On the contrary, about 50% of people think of using two rice crops or two rice crops – vegetable provided low-risk or no-risk crops In the case of fruit and vegetables, the average risk was assessed because the risk of farming depends only on the market, and the yield and weather not usually affect these LUTs 4.2.4.2 Environmental benefits of LUTs The analysis results show that the use patterns such as two rice crops, two rice crops-vegetable, rice - shrimp were assessed to be good for the environment In contrast, three rice crops, shrimp and vegetables were evaluated as not good for the environment At a level that was not good for the environment, vegetables has the highest rate of bad environmental among the LUTs The shrimp was only assessed to be medium to the environment The results of these assessments will be used to set goals in the application of agricultural land use optimization 4.2.5 Summary of main factors affecting agricultural land use The specific socio-economic factors surveyed had different impacts on LUT For applying these factors in building an integrated model to support land use planning, these factors are ranked based on the statistical results for main purposes The order of applicability of these factors was presented in Table 4.2 Each factor was considered to serve for one purpose: optimize land use area and allocate agricultural land use Table 4.2 Summary of the influence of factors on agricultural land use 13 Factors Detailed Profit Economic Capacity of investment No of labors Road systems Social Road systems Neighboring LUT Land suitability Affecting LUTs and it orders Applied LUT 7, LUT 6, LUT 5, LUT 4, LUT 3, LUT 1, LUT LUT 7, LUT 6, LUT 5, LUT 4, LUT 3, LUT 1, LUT LUT 5, LUT 7, LUT 3, LUT 6, LUT 1, LUT 4, LUT LUT 5, LUT6, LUT 7, LUT 1, LUT 4, LUT3, LUT LUT 5, LUT 6, LUT 7, LUT 4, LUT3, LUT 1, LUT LUT 7, LUT 4, LUT 1, LUT 3, LUT Based on Land suitability order Optimization Allocation Optimization Allocation Allocation Allocation Optimization LUT6, LUT 7, LUT 1, LUT 5, LUT Optimization 4, LUT 3, LUT Benefit of LUT 2, LUT 4, LUT 3, LUT 1, LUT Optimization environmnent 6, LUT 5, LUT Thus, in the optimizing agricultural land use area software, factors such as natural adaptation, profitability, number of labors, risk level, and benefit level of environment were used These factors were considered as the objectives of the optimization model according to single goal or multiple goals The priority order of LUTs for each element was different, there are opposite situations Therefore, the application of optimization model will help balance the impact of these factors on the overall results For the allocation of agricultural land use, factors including investment capacity, transport infrastructure, canals and requirements of neighboring LUTs The order of the LUTs was ranked based on the results of the survey analyzed and considered in the land arrangement The combined results show that LUT (Shrimp) and LUT (Fruit) are prioritized to be located near roads, canals and rivers, where investment was possible, compared to other kind of land use This feature was considering for two regions: For brackish areas, shrimp was prioritized to be arranged in priority areas, near roads, rivers and canals, in areas with investment potential, then it gradually spreads out, followed by rice - shrimp arranged For fresh water region, vegetables and fruit are prioritized to be located near roads, canals and rivers and investment able areas, followed by rice - vegetable and rice (LUT 1, LUT 2) Environment Risk of LUT 4.3 Building an integrated ST-IALUP model The results in previous session showed the relationship of natural, socioeconomic, environment factors in optimizing the area of land use and agricultural land use allocation A newly integrated model called ST-IALUP (Soc Trang- Integrated model for supporting Agricultural Land Use Planning) was built This integrated model was built with the following tools: (i) Agricultural production area estimating model used to determine boundary conditions of production areas that need for land use optimization; (ii) A new software to optimize the area of agricultural land use according to constraints related to natural, socio-economic and environment 14 conditions; (iii) Agricultural land use mapping model for LUTs that have been optimized 4.3.1 Modeling area for agricultural production The input data for model collected that were production area of vegetables, fruit and aquaculture in districts was collected from period 2010-2018 The simulation was repeated 10.000 times to determine the mean and the standard deviation from the replicate simulation data Figure 4.6 shown the area of the LUTs analyzed Figure 4.6 Estimated area of vegetables, fruit trees and aquaculture products to 2030 The results of Monte Carlo analysis in Figure 4.6 showed that the area of vegetable land in 2030 is 14.868 ± 894 ha, the area of fruit is 8,799 ± 136 and the area of aquaculture land is 16.697 ± 2.540 The mean area of vegetable and fruit did not change much However, the standard deviation value of vegetables is about 900 and aquaculture area was more than 2.500 These values and its range various ranges will be used as constraint values in optimization 4.3.2 Developing software for agricultural land use optimization Based on the socio-economic factors affecting the land use area, LandOptimizer software was built to optimize land use area for each land mapping unit based on these factors Source and packaged program have been uploaded in to website: https://github.com/nhthao/LandOptimizer 4.3.2.1 Designing the input for the software For the input data, depending on equation programming options, the input data includes: land unit maps, land use suitability of LUTs, profit, number of labor, environment benefit rate, and limited area for LUTs The profit was based on land suitability level of LUTs in land units Profit was standardized directly on LandOptimizer as shown in Figure 4.7 15 Figure 4.7 Standardize profit on LandOptimizer The output data of LandOptimizer were in Excel format that showed the area of LUTs per land unit For the most part, each land unit could have different LUTs The results data sheet was also exported to CSV format as input data for the land use allocation tool 4.3.2.2 Developing optimization objectives Optimizing with single goal The objective optimization function is set in the case of optimizing an objective such as adaptation or profit optimization The objective functions in equations (4) and (5) are used in the case of adaptive optimization and profit optimization of land use types for each land unit 𝑛 𝑚 (4) Maximizing Land suitability level ∑ ∑ 𝑇𝑁𝑖𝑗 𝑋𝑖𝑗 → 𝑀𝑎𝑥 𝑖=1 𝑗=1 𝑛 𝑚 Maximizing profit ∶ ∑ ∑ 𝐿𝑁𝑖𝑗 𝑇𝑁𝑖𝑗 𝑋𝑖𝑗 → 𝑀𝑎𝑥 (5) 𝑖=1 𝑗=1 Multi-objective optimization function: The objectives were maximizing the profit, land suitability, number of local labor used, environmental benefit rate, minimizing risk of LUTs 𝑛 𝑚 𝑛 𝑚 𝑛 𝑚 𝑤1 ∑ ∑ 𝐿𝑁𝑖𝑗 𝑇𝑁𝑖𝑗 𝑋𝑖𝑗 + 𝑤2 ∑ ∑ 𝑀𝑇𝑗 𝑋𝑖𝑗 + 𝑤3 ∑ ∑ 𝐿𝐷𝑗 𝑋𝑖𝑗 𝑖=1 𝑗=1 𝑛 𝑚 𝑖=1 𝑗=1 (6) 𝑖=1 𝑗=1 − 𝑤4 ∑ ∑ 𝑅𝑅𝑗 𝑋𝑖𝑗 → 𝑀𝑎𝑥 𝑖=1 𝑗=1 Where : i = n, n: index of land units; j = m, with m the index of LUTs Xij: Area of LUTj in land unit i LNij: Profit of LUTj in land unit i (unit: million VND / ha) LDj: the number of working days of LUTj / 16 MTj: Environmental benefit coefficient of LUTj Farmer’s assessments of environmental benefits of LUTs RRj: Risk coefficient of LUTj This is the LUTj productivity risk indicator The smaller the risk value gave greater contribution to the goal function Wi: The weight of the objectives In this study, the assumption of equalweighted goals is set by default to with the meaning that the goals in the multiobjective function have the same priority These weights can be adjusted for increasing (moving toward 1) or decreasing (moving towards 0) depending on the priority of the local goals for the local development orientation Constraint equations Constraint of the total area of LUTs per land use units must be less than or equal to the area of land unit (Inequalities 7) 𝑛 𝑚 (7) ∑ ∑ 𝑋𝑖𝑗 ≤ area of 𝑙𝑎𝑛𝑑 𝑢𝑛𝑖𝑡i 𝑖=1 𝑗=1 The total labor demand of the LUTs cannot exceed the local agricultural labor resources ∑𝑛𝑖=1 ∑𝑚 (8) 𝑗=1 𝐿𝐷𝑗 𝑋𝑖𝑗 ≤ Total working days The minimum of each agricultural product to supply (system of inequation 9) (9) ∑ 𝑋𝑖𝑗 𝑁S𝑗 ≥ Minimum production of LUT k NSj: Yield of LUTs that provode the product k j = l ( LUTs that provide product k) k = p (type of products) The maximum of each agricultural product to supply (10) ∑ 𝑋𝑖𝑗 𝑁S𝑗 ≤ Maximum production of LUT k Total area of LUTj