Optimization of Tertiary Irrigation Network Using A Linear Program at D.I. Panggak Darat in Lingga District

The Panggak Darat Irrigation Area in Lingga Regency can irrigate 134.05 ha of rice fields. The problem that often occurs is that irrigation areas are not fully optimal for agricultural product productivity, so that an effort can be made to minimize the shortage of irrigation water and/or minimize the deviation of water release that can result from an optimal pattern of irrigation operations. The purpose of this study is to obtain an optimal operating pattern with better operating performance than the existing (planning). The analytical method used is an optimization technique using the LINDO program (linear programming). The objective function is to minimize the shortage of irrigation water. Evaluation of the operational performance of the optimized and existing reservoirs is carried out using simulation techniques. The results showed that the optimal operating pattern was obtained from the Objective Function with an average total release of reservoir water of 3.20 million m3, which can meet 100% of the irrigation water Requirements of an area of 134.05 ha of irrigation area that must be irrigated. The reliability of the optimization results is in the form of 100% irrigation reliability with a planting intensity of 300% with a rice-rice cropping pattern where the existing (planning) is a rice-rice-bero cropping pattern or a rice-bero cropping pattern with a cropping intensity of 200%. Optimization results from the objective function of minimizing the shortage of irrigation water provide better operating performance than the existing conditions, so as to increase agricultural productivity.


Introduction
Irrigation is an effort to provide and regulate water to support agriculture, the types of which include surface irrigation, swamp irrigation, underground water irrigation, pump irrigation, and pond irrigation (Ministry of PUPR, 2015).Irrigation is intended to support farming productivity to increase agricultural production in the context of national food security and community welfare, especially farmers which is realized through the sustainability of irrigation systems.
The need for water for all living things is an inseparable need in everyday life, water is an essential natural resource needed by humans and other living things, with water, the earth becomes a planet in the solar system that has life [1].Irrigation is the provision of water to the soil by using buildings and artificial channels for plant growth, so that during the dry season the plants do not lack water, and during the rainy season there is not excess water [2].The construction of the Panggak Darat Irrigation Area (D.I.) to meet the Requirements of irrigation water in Panggak Darat Village.To increase production in rice fields, a reliable irrigation system is needed, namely an irrigation system that can meet the IOP Publishing doi:10.1088/1755-1315/1343/1/012001 2 Requirements of irrigation water throughout the year.The planned planting pattern can be optimized using a linear program so that the planting intensity produces a maximum harvest compared to the existing planting pattern [3].
Panggak Darat Village, Lingga District, Lingga Regency is an agricultural area with a standard rice field area of 134,05 ha.The need for irrigation water meets the Requirements of the water distribution system, so an irrigation operation is needed that must be carried out correctly so that all water Requirements in the tertiary network can be met to the fullest.In the previous study, the regulation of fulfilling the Requirements of irrigation water used a water balance analysis which was based on the continuity of the flow mass.In the existing conditions (planning) the cropping intensity is 200% with a cropping pattern of rice-rice-bero or rice-crops-bero, so from the results of the previous study it was still possible to optimize it so that the irrigation area that could be served was wider with better cropping intensity on the tertiary plot.From the formulation of this research, it is obtained the formulation of how to provide optimum water for plants with the right conditions of quality, right space, and time effectively and economically to get maximum results in agriculture by paying attention to the irrigation system.The purpose of the research is to increase planting intensity from 200% to better so as to increase agricultural yields.

Methods
Research using linear programming equations with simple and complex equations can be solved using the LINDO (Linear Interactive Discrete Optimizer) Program package.For the cases of Objective Programs, which are modifications of the simplex method, they are almost the same as Linear Programs and the basic assumptions that apply to Linear Programs also apply to multiple Objective Programs, which can be solved using LINDO.The research was conducted at D.I Panggak Darat in Lingga District, Lingga Regency.The research data uses primary data for hydrological analysis.

Water Availability
Hydrology is the study of the ins and outs and movement of water on the earth's surface.Hydrology is studied by people to solve problems related to water, such as water management, flood control, and planning of water structures [4].The availability of water in question is the availability of water in the river or what is more called the mainstay discharge.Mainstay debit is defined as weekly or semi-monthly average minimum debit.This weekly average or semi-monthly minimum debit is based on the average weekly or semi-monthly debit for a 20% probability of not being fulfilled [5].
The data needed for an analysis of water availability is monthly or daily discharge data with a long recording period, which is greater than the last 10 years [6] The scenario of the inflow discharge pattern group was carried out [7].If there is a post near the research location, then the model parameters can be estimated by means of calibration, then these parameters are used to convert rainfall data into discharge, semi-monthly rainfall data obtained from the Daik rain station.and the contribution of groundwater [8].Rice field water requirements for rice are determined by the following factors: 1. Land preparation, for calculating irrigation Requirements during land preparation, used the method developed by Van de Goor and Zijlsha (1968).The method is based on a constant water rate in l/s/ha during the land preparation period and produces the following formula: 3. Percolation and seepage are the downward movement of water from the unsaturated zone, which is compressed between the soil surface and the groundwater table (saturated zone).Percolation power (P) is the maximum possible percolation rate, which is affected by soil conditions in the unsaturated zone that lies between the soil surface and the groundwater table.On heavy clay soils with good puddling characteristics, the percolation rate can reach 1-3 mm/day.On lighter soils the percolation rate can be higher [9].4. Alternation of layers of water is done after fertilization.Replacement of the water layer is done as needed.
If no such schedule is available, perform 2 replacements, 50 mm each (or 3,3 mm/day for 1/2 month) for one month and two months after transplant. 5. Effective rainfall is determined by the amount of R80 which is the amount of rainfall that can be exceeded by 80% or in other words it is exceeded 8 times out of 10 events.In other words, the amount of rainfall that is smaller than R80 has a probability of only 20%.When expressed by the formula is as follows: where: R80 : Rainfall of 80%, n : Number of data, m : Rainfall rank selected.

Linear Program with LINDO Program
For cases of linear program equations, both simple equations and complex equations, including linear binary integer programs from quadratic programs, can be solved with the LINDO program package.Likewise, with the cases of the Objective Program which is a modification of the simplex method.The way to formulate an Objectives Program is almost the same as a Linear Program and the basic assumptions that apply to a Linear Program also apply to a Multiple Objectives Program.The LINDO Program Package (Linear Interactive Discrete Optimizer) was specifically designed by Linus Schrage, 1981.
Study of optimizing irrigation network cropping patterns with a Linear Program to get maximum profit from farming based on optimal planting area.For this analysis a linear program was used with the help of the LINDO 6.1 program.The results of this calculation are used to determine the area of rice fields that can be planted according to the type of plant and the growing season with the advantage of optimum farming yields [10].Detailed model formulation according to the operating system in utilizing reservoir water availability.The formulation of a mathematical equation to minimize the shortage of irrigation water against the irrigation water Requirements that must be met from the weir is as follows: ( 6 ) where: Zmin = total shortage of irrigation water minimized ‫ܫܣ݇‬ ௧ ି = lack of release of irrigation water Group I the t-month (KAIt on LINDO) ‫ܫܤ݇‬ ௧ ି = lack of release of irrigation water Group II the t-month (KAIt on LINDO) a a Constrain Function Solving cases of optimization of Linear Programs that contain several decision variables can be solved by the simplex method.The mathematical formulations of the case constraints must first be converted into the standard form of the simplex equation model.Rules for constructing the standard form of constraints [11].
Constraint functions are constraints in the operation of reservoirs which are expressed in the form of mathematical equations.Some mathematical equations for the constraint function of the Panggak Darat irrigation operating system are as follows: 1. Mathematical equation for reservoir water balance for each scenario group The condition of the initial storage volume is the same as the final storage volume of the reservoir, with the following equation: S0 = S24 S0 -S24 = 0 ( 8 ) where: It = reservoir inflow discharge according to scenario group year in t-month RLt = total release of reservoir water t-month Et = reservoir evaporation t-month SPt = reservoir runoff t-month St = reservoir storage volume at the end of t-month St-1 = reservoir volume at the beginning of t-month S0 = reservoir volume at the beginning of the year S12 = reservoir storage volume at the end of the year 2. At elevation conditions ≥ + 13,66 m to + 14,20 elevation, thus the condition of the reservoir at MOL irrigation ≤ St ≤ maximum inundation capacity.Total water release and maximum storage capacity are: RLt = PAIt + PBIt RLt -PAIt -PBIt = 0 ( 9 ) St ≤ 0 (10) where: PAIt = release of Group I irrigation water t-month PBIt = release of Group II irrigation water t-month 3. Shortage of irrigation water is assumed that the need for irrigation water is greater than the release of irrigation water, and excess irrigation water is assumed that the release is greater than the need in this case can be ignored (ignored).Therefore, to minimize the shortage of irrigation water release against the target amount of irrigation Requirements, the mathematical equation model can be recommended as follows: 4. The need for irrigation water is different for each month, while the land area is the same.To overcome the error on the Requirements scale, the following equation approach is recommended: 5. To anticipate excess inflow into the reservoir, the program allows runoff through the spillway.SPt ≥ 0 ( 1 5 ) 6.All decision variables cannot be less than zero or negative.
) Before the LINDO program package is applied, linear form equations as input must be prepared so that they can be decomposed into standard linear equations.From the reservoir water release system, it is known that the release of water to meet raw water Requirements is constant throughout the year, while the total release (raw water and irrigation) is a release through the intake with a maximum existing capacity limit.Thus, the mathematical equation can be formulated simply based on the release of irrigation water according to the cropping pattern.Several forms of formulation of mathematical equations that can be applied to the Panggak Darat irrigation system will be inputs for the analysis of the LINDO Program package.

Simulation Analysis
Reservoir operation simulation is carried out to evaluate reservoir system behavior and operating performance against optimization results and the existing rule curve.The simulation of the operation of the D.I Panggak Darat is carried out for a semi-monthly period, while the release of reservoir water is targeted for raw water and irrigation Requirements as well as river maintenance.
In the reservoir operation simulation process, several assumptions/approaches are made, including: 1. Beginning of operations in November-2, according to the cropping pattern in irrigated areas (rice-ricecrops).2. The reservoir is considered full at the start of operation of the reservoir [12].3. Monthly water loss (evaporation) is a function of the area of the inundation with existing evaporation height data.4. Release simulation based on water balance conditions where the volume of the final storage is not less than the minimum capacity and does not exceed the maximum capacity of the storage.This is an approach to meeting optimization/existing/Requirements release targets.
The law of water balance and reservoir release is formulated as follows: It = RLt + SPt + Et + St -St-1 (18) 5.The volume of the initial storage is the same as the volume of the final storage.6.The storage capacity at the end of the month is not allowed to be less than the minimum capacity.7. Overtopping occurs when the final storage volume exceeds the maximum capacity.Water that overflows through spillways is not considered as a resource that cannot be utilized or assumed to be excess [13].8. Irrigation operation failure occurs when the total supply of water demand allowed by the simulation analysis is less than the total discharge targeted by the optimization/existing/total demand analysis.

Research Stages
In carrying out research, a sequence of stages is needed to reduce errors and get maximum results in conducting analysis in research.The stages of the research can be seen in Figure 2.

Analysis of Water Availability
The location of the hydrology post is in Lingga District with a watershed area of 8,66 km 2 so it is necessary to calculate the rainfall flow to obtain the inflow discharge.For calculating linear program optimization using historical inflow discharge data from 2009-2022 obtained from BWS Sumatra IV Batam [14,15] as shown in Table 1.

Analysis of Irrigation Water Requirements
Analysis of Irrigation Water Requirements is done by calculating: 1. Evapotranspiration was calculated based on the Modified Penman method using climatological data from the Daik Climatology station closest to the irrigation area.Climatological data for the average Daik rain station sees Table 2. Evapotranspiration is used as data to carry out optimization simulations which is the average of outflow, namely water release, spillout and evapotranspiration in the mid-monthly period.
With the availability of data on evapotranspiration, plant coefficient, water requirements for saturation, percolation, change of water layers, effective rainfall, and irrigation efficiency, water can be obtained that must be supplemented from the dam intake gate.(3.33 mm/day for half a month and 2 months after initial planting).6.The proposed cropping pattern in the calculation of the water balance is: Rice-Rice-Crops with initial planting will be tried from November to January 7. Effective rainfall is calculated using semi-monthly rainfall data from the Daik rain station within the irrigated area.8. Irrigation efficiency see Table 3.The initial planting pattern is carried out every half month in one type of cropping pattern (rice-rice-secondary crops).With the availability of evapotranspiration data, crop coefficient, water requirement for saturation, percolation, water layer turnover, effective rainfall, and irrigation efficiency, it is possible to obtain water that must be supplied from the intake gate of the irrigation weir.
Optimization calculations with planned cropping patterns are carried out so that optimization in the form of cropping intensity produces a maximum harvest when compared to the existing cropping pattern [3].The results of the initial shift in the cropping pattern showed that the need for irrigation water with the start of planting in November-2 had the minimum requirement (Figure 3).The water requirement for irrigation is estimated for several cropping patterns and initial land preparation.For details on the calculation of irrigation water Requirements, see Table 4.This study used an analysis of the initial shift in cropping patterns with the minimum Requirements of the rice-rice-plants cropping pattern (Figure 4).

Linear Program Equations
The equation of the objective function and constraints as LINDO input is described as follows: -The equation minimizes the shortage of irrigation water release against the amount of irrigation demand target; -The need for irrigation water is different for each month, while the land area is the same.In order to overcome the error on the Requirements scale, the equation approach is recommended; -Non-negative requirements.

Linear Program Optimization Analysis
From the optimization results, irrigation can operate optimally with a total shortage of irrigation water (difference/deviation of not meeting the target requirement) of 0.00 million m 3 and from the total release can be known: 1. Reservoir operation pattern (Discharge Plan) Release plan is the result of optimization where the initial elevation of the reservoir operation is the same as the final elevation of the reservoir operation in one year.2. Fluctuations in the water level of the reservoir Is the water level elevation of the reservoir at the end of each period according to each scenario year group and the Objective Function performed?The results of solving problems with the LINDO program see Figure 5.
From the discharge and fluctuations in the water level of the reservoir resulting from the optimization, it shows that with the start of operation at an elevation of + 14.20 m, the condition for the period of water level rising (filling) starts from the beginning of November-2 to August-1 of the following year, while the period the water level recedes (empties) from August-2 to November-1, and the total water release is 3.20 million m 3 (Table 5).For a recapitulation of LINDO results from Figure 4, see Table 5.
From the results of the optimization carried out, it can be concluded that the optimum operating pattern of the optimization results gives the results of releasing the reservoir with optimum results according to the conditions of the inflow discharge group of the reservoir.The objective of minimizing the irregularities in the release of reservoir water turns out to only occur in the negative form of deviations in the release of irrigation water (lack of irrigation water) as is the aim of minimizing the shortage of irrigation water, so that excess (efficient) discharge does not occur.Besides that, the fulfilment of raw water Requirements is a constant priority throughout the year of operation.Because the distribution of irrigation water is influenced by the amount of irrigation water needed according to the type of plant in the growing season and its growth period, the amount of distribution of reservoir water release and irrigation water release will be different.

Irrigation Area Analysis
The area of the irrigation area irrigated from the weir according to the type of plant is the same in each operating period in one planting period (planting period).The total need for irrigation water supply from the weir is 3.20 million m 3 (Table 5).
By optimizing the Wet Year conditions, from a total release of irrigation water of 3.20 million m 3 (equivalent to 100% of the total requirement) can irrigate a total irrigation area of 134.05 ha, so that the average irrigation area that can be irrigated from water release irrigation is 134.05 ha/year (equivalent to 100%) where all irrigation water Requirements can be met.Table 5 is an analysis of the area of irrigation areas that can be irrigated according to the results of the optimization carried out.

Water Balance Analysis
From the analysis of the average area of irrigated areas that are irrigated from the release of reservoir water resulting from Optimization with the Objective Function of minimizing the shortage of irrigation water, it can be concluded that the entire ratio of the average area of irrigated areas can be irrigated.Specific water balance analysis for irrigation water withdrawal at the weir location in Figure 6.

Irrigation Operation Simulation
Then a simulation of irrigation operations was carried out for various conditions of cropping intensity and Q outflow (half-monthly irrigation) with the results shown in Table 6.Based on the simulation results in Table 6, for weirs with irrigation benefits, the irrigation area is 134.05 ha.The rice-rice-secondary cropping pattern with a cropping intensity of 300% has a reliability level of 100%.However, the failure of water supply for the Requirements of irrigation areas can be tolerated up to 20% of the total requirement, so the proposed cropping pattern is a rice-rice-plants cropping pattern with a cropping intensity of 300%.This study shows: 1.Before the existence of irrigation weirs, agricultural activities depended only on rain with the planting season during the rainy season and only with the rice cropping pattern I. 2. Based on the results of planning and the current existing conditions, the cropping pattern used is rice-rice- bero or rice-crops-bero so that optimization can still be carried out from the existing conditions.3. The simulation results from the optimization results show that the operation pattern with the rice-riceplants planting season with the beginning of planting November 2 (Group.1)and December 1 (Group.2) can be applied to increase the productivity of agricultural products.

Conclusion
From the calculation results it can be concluded as follows: 1.The objective function is used to minimize the shortage of irrigation water with a total release that can serve the irrigation water Requirements of 3,20 million m 3 throughout the year of irrigation operation.2. The simulation results of irrigation operations based on optimization results with a linear program are as follows: a.The results of the optimization of the linear program.The objective function of minimizing the shortage of irrigation water shows that all irrigation water Requirements can be met for an area of 134,05 ha, so based on the results of the analysis of irrigation areas it is 100%.b.Simulations can be used to determine the performance of irrigation operations resulting from the optimization of the linear program as a guideline for the operation of reservoirs, in which irrigation reliability is obtained from simulation results with optimized reservoirs reaching 100% with a cropping intensity of 300% with a rice-rice-crops cropping pattern where the existing cropping pattern is rice-rice-bero or rice-crops-bero with a planting intensity of 200%.3. The operation of irrigation with the optimization method actually provides optimum results with a different operating pattern from the existing one and can increase the productivity of agricultural products and planting intensity. 4. From the results of the study indicate that the optimum operating pattern can be obtained from the optimization analysis of the Objective Function to minimize the shortage of irrigation water can be applied.

Figure 1 .
Figure 1.Research Location and Daik Rain Station2.2Irrigation Water RequirementsThe need for irrigation water is the volume of water needed to meet evaporation Requirements, water loss, water Requirements for plants by taking into account the amount of water provided by nature through rain ) where: IR = Need for irrigation water at the rice field level (mm/day), M = Water requirement to replace water loss due to evaporation and percolation in saturated rice fields.‫ܯ‬ = ‫ܧ‬ + ܲ ( 2 ) where: Eo = Evaporation of open water taken 1.1 ETo during land preparation (mm/day), P = Percolation (mm).‫ܭ‬ = ‫.ܯ‬ܶ/ܵ ( 3 ) where: T = Land preparation period (days) S = Water requirement, for saturation add a 50 mm layer of water 2. Consumptive use is the need for water used by plants to carry out photosynthesis calculated by the following formula: ‫ܶܧ‬ = ‫ܭ‬ ‫ܶܧݔ‬ ( 4 ) where: Kc = Crop coefficient, ETo = Potential evapotranspiration (modified Penman) (mm/day).

Figure 3 .
Figure 3. Graph of Average Annual Water Requirements according to the Wal of the Planting Pattern

Table 2 .
Evapotranspiration Calculation of Penman Monteith Method (mm/day) Plant type and growth factor (Kc), ½ monthly period.a 200 mm saturation, 50 mm flooding other than evaporation and percolation.a Replacement of 50 mm puddle at 1 month and 2 months after planting 3. The amount of Percolation is determined at 2 mm/day.4. The need for groundwater treatment a Saturation number 200 mm; rice without bero a Saturation number 250 mm; rice fields bero more than 2.5 months 5. Water changes were carried out 2 times, 50 mm each

Table 3 .
Irrigation Network Efficiency

Table 4 .
Results of Analysis of Irrigation Water Requirements