Multicriteria Analysis Model in Sustainable Corn Farming Area Planning

2.1. Land Suitability Analysis of Corn Plants

This analysis aims to determine land suitability by matching land characteristics with criteria for growing corn. The land suitability study for corn cultivation was conducted on land units obtained from overlaying data from the Soil Map, Slope Gradient from DEM SRTM, and Land Use for paddy fields specifically for fields planted with corn. Each land unit (Lu) is then matched with land suitability criteria from Puslitanak (Center for Soil and Agroclimatic Research) of the Agency for Agricultural Research and Development [15]. Land suitability classification is based on Food and Agriculture Organization (FAO) criteria, with classes S1 (very suitable), S2 (moderately suitable), S3 (marginally suitable), and N (not suitable).

2.2. Determination of Sub-criteria for Ecological, Social, and Economic Aspects

The relevant sub criteria will be identified through a literature review, consultation with experts, and discussions with stakeholders involved in sustainable agricultural planning. These sub-criteria will encompass aspects of sustainability in ecological, social, and economic dimensions. Data will be gathered from various sources, including secondary data from literature reviews [16, 17], data from relevant agencies or governmental institutions, and primary data from field surveys and interviews. Data collection methods will be tailored to each aspect under investigation.

2.3. Integration Analysis of Ecological, Economic and Social Aspects of Corn Farming Planning

The results of the land suitability analysis of corn crops are then collected sub criteria data from the ecological, social, and economic aspects of the sustainability of corn farming. The data that has been collected will be further analyzed using statistical methods and multivariate analysis techniques. Analysis will be conducted for each ecological, social, and economic aspect, considering the principles of sustainability, using the MDS method. The analysis is carried out with the ordination technique called RAP-Corn (Rapid Appraisal for Corn) modified from RAPFISH [18]. The ordination technique in MDS is based on the Euclidean Distance from the bad, medium, and good assessment results for each aspect sub-criteria. The ordination technique within MDS is based on Euclidean Distance. The regression technique described above is the ALSCAL algorithm [19]. Eq. (1) is written as:

(1)

The analysis is conducted in Microsoft Excel and is named RAP-Corn (Rapid Appraisal for Corn). This analysis represents an integrated approach to generate holistic assessments of sustainable corn farming area planning alternatives. The results of the MDS analysis will provide index values and sustainability status for ecological, economic, and social aspects (Table 1).

The results of the MDS analysis will provide leverage attributes for sustainability. These leverage attributes will be integrated into the AHP to gain a deeper understanding of the pairwise comparison structure found in the multidimensional analysis.

AHP is a multi-criteria decision-making method that employs a hierarchical approach to assign weights to variables. The goal of AHP is to prioritize alternatives more systematically based on identified preferences. This method uses a scale of values from 1 to 9 (Table 2) to depict the relative importance levels among attributes. Evaluation is performed using a pairwise comparison matrix where criteria and alternatives are assessed relative to the established goals. Matrix A (n x n) is created based on the number of criteria n (Eq. 2), then normalization is performed (Eq. 3), followed by eigenvector calculation (Eq. 4), Consistency Index (CI) calculation was performed in Equation 5, and Consistency Ratio (CR) calculation with Equation 6. The random index (RI) was calculated, according to Table 3. If the CR value > 1.0, it indicates poor consistency. If CR < 0.10, then the matrix is considered consistent and acceptable [20, 21].

(2)

(3)

(4)

Where W is the matrix weight of the criteria, λ _max is the largest eigenvalue

(5)

(6)

The goal of this integration is to obtain balanced weights, scores, and class values for each aspect in the assessment of planning alternatives on the criteria and sub-criteria of Ecological Sustainability (S-_Ecological), Economic Sustainability (S-_Economic), and Social Sustainability (S-_Social).

2.4. Analysis of Sustainable Corn Farming Area Development

Sustainable corn development planning analysis is carried out through a spatial statistical analysis approach by performing mathematical calculations of the sustainability of ecological, economic, and social aspects with simple logarithms as follows:

(7)

(8)

(9)

The result of the above formula is then calculated through raster analysis of Sustainable Corn Farming Area Development Planning (SP-_Corn) with the following equation:

(10)

The equation yields value from the combined integration of sustainability pillars, which will then be divided into three priority classes of development. The categorization is based on natural breaks, the most accurate method for tabular data and has a picture of the smallest error volume based on the natural interval patterns of the data [22, 23]. This method calculates the Goodness of Variance Fit (GVF) with the following equation (Jenks, 1963):

(11)

SDAM (Sum of squared Deviations for Array Mean) indicates variance between classes; SDCM (Sum of squared deviations for Class Means) declares variance for each class.

3.1. Land Suitability Analysis

Land suitability analysis is an assessment of land quality regarding the suitability of cultivated crops, which influences its potential use as opportunities and challenges in managing and optimizing land productivity. The research results show that the land suitability class that dominates the study area is the S3 (Marginally Suitable) class with two subclasses, namely S3rf covering an area of 5,381.66 hectares and S3rfn covering an area of 559.43 hectares. The S3rf subclass reflects limitations on rooting media and nutrient retention factors, while S3rfn has additional constraints on nutrient availability factors. These findings indicate that most of the land in the study area is less suitable for maize farming without significant management intervention. The detail of land suitability class values is presented in Table 4, and the distribution area of the land suitability is presented in Fig. (1).

This land suitability includes various combinations of limiting factors such as drainage (r), base saturation (f), and k20 (n). Disturbed drainage can cause waterlogging, which is harmful to plant growth [24] and limits the choice of crops that can be planted. High base saturation can cause a variety of soil nutritional and physical problems that inhibit root development and nutrient uptake. An unbalanced k20 content can disrupt the nutritional balance of plants and affect productivity [25]. Therefore, careful management strategies are needed to overcome these limiting factors through effective drainage management, adjusting soil pH, or appropriate fertilization to improve land conditions and increase corn production potential [26, 27].

3.2. Multidimensional Scaling Analysis for Sustainable Corn Agricultural Development Planning

The data collection process through literature review and in-depth analysis has produced several important sub-criteria from ecological, economic, and social aspects. From an ecological perspective, the sub-criteria identified include the sustainability of natural resources, biodiversity, and the environmental impact of human activities [28, 29]. The economic aspect highlights sub-criteria such as efficient use of resources, potential for economic growth, and contribution to societal welfare [30]. Meanwhile, from a social perspective, sub-criteria include community involvement, social justice, and quality of life [31]. The identified criteria and sub-criteria are then subjected to a comprehensive evaluation, assessing their strengths and weaknesses, with assessments based on specific indicators.

These sub-criteria are utilized in the sustainability analysis of corn cultivation using the rap-corn ordination technique. This method is a statistical technique involving multidimensional transformation. The analysis can better illustrate the distribution and factors influencing the sustainability of corn cultivation in the study area. This ordination technique aids in understanding the complex patterns associated with sustainability aspects [32], as shown in the kite diagram (Fig. 2).

Based on the results of the rap-corn analysis on the kite diagram, the ecological dimension depicts less sustainability with an index value of 49.40%, indicating significant ecological imbalance and vulnerability. Meanwhile, the economic dimension index has a value of 61.69%, and the social dimension index is 61.26%, indicating relatively sustainable economic growth and improved community well-being. These results suggest that although some aspects achieve a relatively sustainable level, further efforts are needed to enhance ecological balance and reduce economic and social inequality to achieve a more holistic sustainability (Fig. 3a-c).

The assessment of the ecological dimension sustainability status involves 11 attributes (Fig. 3d). Leveraging attributes related to the ecological dimension index shows a root mean square (rms) value of 3.46 for soil organic carbon content suitability, 3.06 for biological agent utilization, and 1.3 for fertilization, which play crucial roles in determining the ecological sustainability of an agricultural system. These attributes are sensitive factors that need to be considered for improvement in practices supporting environmental sustainability. Improvements in fertilization and the use of organic materials can help reduce soil degradation, enhance crop productivity, and achieve better and more sustainable ecological balance [26, 27].

The leveraged attributes related to the economic dimension (Fig. 3e) with an RMS value of 6.05 for profit, 6.25 for production per hectare, 6.25 for sales, and 6.12 for farmer income are crucial sensitive factors. Profitability is the main focus for farmers and increasing production per hectare is key to boosting agricultural product sales, thus increasing farmers' income [33]. Therefore, to enhance economic welfare in the agricultural sector, it is essential to consider and improve performance in terms of profit, production per hectare, sales, and farmer income.

The leveraged attributes from the social dimension (Fig. 3f) show an RMS value of 6.00 for the farmer welfare level. The farmer welfare level emphasizes the need for farmers to have sufficient access to resources and services that support their well-being [34]. Women's involvement in agricultural business, with a value of 6.18, highlights the crucial role of women in the agricultural sector and the overall economy [35]. The education level, with a value of 6.18, emphasizes that higher education can provide farmers with broader opportunities for more sustainable and efficient farming practices [36]. Meanwhile, the rms value for land ownership status is 6.0. Land ownership status can influence farmers' active involvement in managing and developing sustainable agricultural land [37]. Therefore, to improve social conditions and farmer welfare, it is essential to consider and enhance performance in terms of farmer welfare, women's involvement in agricultural business, education level, and land ownership status.

3.3. Weight Analysis of Ecological, Economic and Social Criteria

Integration of ecological, economic, and social aspects is an approach that considers the impact of activities or policies on the environment, economy, and society simultaneously. The AHP method is used to obtain scores and weights for relevant criteria in each attribute that acts as leveraged factors for sustainability from the results of the MDS analysis. The AHP results yield the weight values for each criterion (Table 5), with the ecological aspect having a weight of 0.63, the economic aspect with a weight of 0.26, and the social aspect obtaining a weight of 0.11.

The ecological aspect consists of 3 criteria, namely fertilization, organic material utilization, and soil organic carbon content suitability. The economic aspect includes 4 criteria: profit, production per hectare, sales per hectare, and farmer income per month. Meanwhile, the social aspect consists of 4 criteria, namely farmer welfare level, women's involvement in agricultural business, education level, and land ownership status (Table 6).

The AHP results produce a score for each indicator according to its importance in achieving the sustainability goals of corn farming. Fertilization received a score of 0.65, which reflects the effectiveness of fertilizer use in corn farming. Using appropriate fertilizer can minimize negative impacts on the environment [38, 39]. The use of organic materials received a score of 0.23, which shows the extent of the use of organic materials in corn fields. The use of organic materials can increase soil fertility, reduce the need for chemical fertilizers, and overall improve soil quality [38]. Meanwhile, the suitability of soil organic carbon content received a score of 0.12, which assesses the suitability of soil organic nutrients in supporting the growth of corn plants. The availability of sufficient nutrients in the soil is very important for optimal plant growth and plays a role in maintaining the balance of the soil ecosystem [39]. The AHP ecological sub-criteria class score values are presented in the following Tables: 7-9.

The AHP results from the economic aspect provide insight into the value of economic factor scores in the development of sustainable corn agriculture. The profit score obtained was 0.58 referring to the profitability of corn farming. High profits indicate that the business generates sufficient profits to support the sustainability of agricultural operations [40]. Production per hectare with a score of 0.20 shows the productivity of corn farming. High productivity is essential to

ensure agricultural operations are efficient and able to provide sufficient yields to meet market demand [41]. The sales score per hectare is 0.07. High sales volume indicates effective product marketing. Farmer income per month, with a score of 0.14, assesses whether the income earned by farmers each month is sufficient for their welfare. The AHP economic sub-criteria class score values are presented in the following Table: 10-14.

The AHP results from the social dimension include four main indicators, each of which has its own score. Farmer welfare received a score of 0.56, which refers to the importance of a good level of farmer welfare in creating a productive work environment and supporting agricultural sustainability in the long term [42]. Women's involvement in agricultural businesses received a score of 0.27, which evaluates the extent to which women can increase productivity and sustainability in agricultural operations. Education level, with a score of 0.11, reflects how a higher level of education can help farmers adopt more innovative and sustainable agricultural practices [36]. Meanwhile, land ownership status received a score of 0.06, indicating that clear and guaranteed ownership status is very important to provide legal certainty to farmers and encourage long-term investment in agricultural development [43]. The AHP social sub-criteria class score values are presented in the following Tables: 15-19.

3.4. Analysis of Sustainable Corn Agricultural Development Planning

Sustainable corn agricultural development planning aims to create a balanced integration of ecological sustainability, economic profitability, and social welfare. Based on the AHP results, weights for criteria and scores for sub-criteria in the ecological, economic, and social aspects have been obtained.

With the weights for criteria and scores for sub-criteria as shown in Fig. (4), the formulation equation for sustainable corn agricultural development planning can be written as follows.

S-_Ecological = (0,65 x Fertilization Class Value) + (0,23 x Use of Organic Ingredients Class Value) + (0,12 x Soil Organic C Nutrient Suitability Class Value)

S-_Economic = (0,58 x Profit Class Value) + (0,20 x Production per hectare Class Value) + (0,07 x Sales per hectare Class Value) + (0,14 x Farmer's income per month Class Value)

S-_Social = (0,56 x Farmer welfare level Class Value + (0,27 x Involvement of women in agricultural business Class Value) + (0,11 x Level of education Class Value) + (0,06 x Land Ownership Status Class Value)

The equation above produces a cumulative value for each land unit which is spatially represented by a distribution of ecological sustainability values ranging from 0.49 to 0.65 (Fig. 5a). This range of values indicates that the area has serious environmental challenges. This relatively low value may indicate a land degradation problem that requires immediate intervention to prevent further damage. Actions in the form of implementing sustainable agricultural practices, or better management of natural resources are very necessary for sustainable agricultural resource management [44]. The economic sustainability value ranges from 16.85 to 20.03 (Fig. 5b); this shows that there is economic stability, but there is still potential inequality or economic challenges that need to be overcome. Policies that focus on equitable and inclusive economic development are essential to overcome unequal distribution of income and access to economic opportunities that hinder economic growth [45]. Social sustainability scores ranged from 4.11 to 54.65 (Fig. 5c), indicating very significant differences in social well-being and access to basic services in the region. These differences reflect gaps in welfare, education, land ownership and active involvement of women farmers. This inequality may be overcome by increasing access to resources, training, and inclusive empowerment programs, as well as policies that support gender equality and social welfare in the agricultural sector for sustainable development [37].

The formulation of the cumulative equation for the three pillars of sustainable development is as follows:

SP-_Corn = (0,63 x S-Ecological) +(0,26 x S-Economic) + (0,11 x S-Social)

The cumulative results above from the equation for the three pillars of sustainable development show a distribution of values ranging from 5.17 to 10.80. These values were then categorized into three priority classes using the natural break method which is known to be effective in grouping data based on its natural distribution to reduce variability within a group and maximize differences between groups [22, 23]. The First Priority Class is a distribution of land that is highly recommended for sustainable corn development which has a value range of 5.17 to 6.05 with an area of 1,614.17 hectares. The second priority class covers a value range of 6.05 to 7.73 with an area of 3,179.05 hectares, which can also be recommended. Meanwhile, the third priority class covers a value range of 7.73 to 10.80 with an area of 147.86 hectares, which requires serious consideration and attention to be used as a sustainable corn farming development area. Grouping land based on priority is a strategic step in planning sustainable corn farming areas that can be carried out in an informed and directed manner [46]. This is presented spatially in Fig. (6).