Optimization model growth and equalization of farmer’s income in the rotiklot dam service area on the border area of Indonesia-Timor Leste

The study aims to analyze optimization models of growth and income distribution. The study used a survey method in Fatuketi Village, Kakuluk Mesak District as the Rotiklot Dam service area, with a sample of 300 respondents. Data analysis uses a multi-objective linear programming model for growth and equal distribution of agricultural income. The results of the analysis show that an income of IDR 11,576,192.00 per year is an income that optimizes growth and income distribution. Optimizing growth and equal distribution shows that the average income of farmers in the first planting season was IDR. 4,132,108 and IDR. 7,444,084 in planting season II. The marginal land used is 300 ha with the volume of water needed to meet all plant needs as much as 1,986,565.16 m3. Agricultural income can still be increased for the third planting season because there is still excess water of 948,434.84 m3.


Introduction
The development of agricultural infrastructure that is being carried out is essentially a real effort to build the community's economy.The availability of agricultural infrastructure affects directly and indirectly in increasing agricultural and industrial production so as to maximize the income of a region [1,2].The development of agricultural infrastructure is very much needed in the process of economic development in a region because it encourages economic growth through increasing productivity, providing new jobs, and increasing per capita income.The availability of agricultural infrastructure is also able to move other economic sectors to develop, increase public consumption and encourage productive activities which directly and indirectly determine the economic growth of a region.
Development of agricultural infrastructure makes it easier for farmers to obtain maximum results from their farming activities.States that the development of irrigation infrastructure for agriculture increases regional economic growth.Increased economic growth has an impact on increasing income inequality, which in turn has an impact on disrupting sustainable economic growth [3].
Explained that border areas are classified as having a moderate level of investment inequality and tend to increase [4].The inequality in question is accumulated from differences in income between groups of society, and differences in access to available water resources; even though the government's investment in the development of agricultural infrastructure is meant for the welfare of its people equally.
The Rotiklot Dam, which has been operating since 2019, is in Fatuketi Village, Kakuluk Mesak District, Belu Regency is one of the real efforts of the central government in realizing the availability of water for agriculture.This is intended to be able to increase production and food security, as well as increase income and equal development in the border areas of Indonesia and Timor Leste.
Before the existence of the Rotiklot Dam in Fatuketi Village, farmers implemented one planting season in their farming business with commodities limited to rice and corn; However, now farmers have implemented two planting seasons due to the availability of adequate water with more varied commodities, namely rice, corn and horticulture.Apart from that, the availability of water from the Rotiklot Dam helps farmers expand their planting area so that there is an increase in production which has an impact on increasing farmers' income, as in previous findings from [5].
Increased income as an indicator of economic growth, which is also expected to increase income distribution; however, if access to land and water resources is owned by a group of people, it will have an impact on an increasingly high-income gap.Stated that income inequality that is left unchecked will create new problems such as economic inefficiency, high numbers of poor people, weakening social stability and solidarity as well as strengthening the political power of the rich which can create injustice in society [6,7].Therefore, this research aims to analyze the growth optimization model and income distribution in the Rotiklot Dam service area in the border region of Indonesia and Timor Leste.

Methods
The research was conducted in Fatuketi Village, Kakuluk Mesak sub-district in Belu Regency, which is the service area of the Rotiklot Dam.The population of this study is farmers who use irrigation water from the Rotiklot Dam for farming, with a total population of 4500 heads of farming families.The sample was determined using simple random sampling by considering the homogeneity of the population.The number of samples used was determined using the Isaac and Michael table at α = 10%, so the total sample was 300 heads of farming families.Primary research data were obtained from farmers in Fatuketi Village, while data were obtained from the Meteorology and Geophysics Agency.The data used are: economic data consisting of costs, selling prices and production of each commodity; and climatological data consisting of rainfall, humidity, temperature, wind speed, and solar radiation.
These data were analyzed using a multiple objective program to obtain optimal growth and equity of income by utilizing existing and marginal land and irrigation water resources at the Rotiklot Dam for two growing seasons.The stages of data analysis are presented in Figure 1.
Information: Vij: volume of irrigation water needed by farmer j for crop i V: volume of irrigation water available in the dam, which is 2,935,000 m 3 .This constraint is only applied in the season II because farmers use rainwater in the season I.
Obstacles to Equal Income.This constraint is to ensure that the addition of marginal land for each farmer provides equal distribution of income for all farmers.The model of the constraint function is 1  ≥ 0, 2  ≥ 0, 1  ≥ 0, 2  ≥ 0, , for all  dan  (10)

Results and discussion
Farmers in Fatuketi Village are traditional farmers with lower education and more than 10 years of experience.Farmers with these characteristics have low adaptability to technology [5-8].Before utilizing irrigation from the Rotiklot Dam, farmers in Fatuketi Village managed 157.25 ha of agricultural land by utilizing water resources that came from rainwater.Low rainfall causes farmers to apply only one growing season throughout the year.
Rotiklot Dam is able to meet irrigation water needs for agriculture of 2,935,000 m3.The irrigation water requirement for rice plants is 66.4 m3 per acre, while for corn plants it is 22.6 m3 per acre and horticultural crops 45.7 m3 per acre.The area of marginal land that has the potential to be used as agricultural land is 300 ha.Therefore, increasing planting area and planting intensity from one planting season to two planting seasons with the use of more varied commodities can be done thereby increasing farmers' income.This is in accordance with research by [9,10], that planting area increases production which has implications for farmer income.

Income growth analysis
Farmers' income in 2021 ranges from IDR. 144,000 to Rp. 2,880,000, -with an average of IDR.1,183,575.03.Farmers' income in 2022 ranges from IDR 150,000 to IDR 3,200,000.Based on the results of this analysis, there has been an increase in income between 2021 and 2022, ranging from IDR 1,500 to IDR 364,000 with an average of IDR 59,365.37.The percentage of revenue growth ranges from 1.01% to 16.28% with an average of 4.16%.The results of the analysis show that the increase in income is not accompanied by equal distribution of income as a result of the use of the Rotiklot Dam irrigation.The income gap is getting higher, as indicated by the standard deviation value which has increased from 637,530.96 in 2021 to 691,042.97 in 2022.Likewise, the comparison of the highest income to the lowest income has increased from 20 times to 21.33 times.
Optimization analysis using multiple objectives is needed so that increasing income is also accompanied by equal distribution of farmers' income in the Rotiklot Dam service area in the country's border areas.Stated that the development of agricultural infrastructure not only encourages economic growth but also encourages a more even distribution of income [11-14].

Optimizing growth and equal distribution of income
Optimization model analysis shows that to increase income as well as equalize income, farmers cultivate rice, corn and horticultural crops in planting seasons I and II.The planting area for each type of plant in planting seasons I and II, as well as water use consisting of planting season, I using rainwater and planting season II using irrigation water.Part of the marginal land is not distributed to be managed by farmers in the first and second planting seasons due to topography, considerations of maintaining environmental quality.The land area used in the first planting season was dominated by rice for existing land and marginal land.Land use for the second planting season tends to be more evenly distributed to rice, corn and horticulture with a wider distribution of land use for corn.
Table 1 also shows that the amount of irrigation water used to meet all agricultural needs in the second planting season is 1,986,565.16m3.This means that there are still 948,434.84m3 that have not been utilized, making it possible for farmers to implement the third planting season.The results of the analysis of the distribution of land use and irrigation water that will optimize growth and equal distribution of farmers' income in the Rotiklot Dam service area are shown in Table 1.

Figure 1 .
Figure 1.Stages of analysis of the programming model for growth and equalization of farmers' income in the rotiklot dam service area.

Table 1 .
Distribution of planting area and use of irrigation water.