Optimization of planting pattern plan in Logung irrigation area using linear program

Logung irrigation area is located in Kudus Regency, Central Java Province, Indonesia. Irrigation area with 2810 Ha of extent is getting water supply from Logung dam. Yet, the utilization of water at Logung dam is not optimal and the distribution of water is still not evenly distributed. Therefore, this study will discuss about the optimization of irrigation water utilization based on the beginning of plant season. This optimization begins with the analysis of hydrology, climatology and river discharge in order to determine the irrigation water needs. After determining irrigation water needs, six alternatives of planting patterns with the different early planting periods, i.e. 1st November, 2nd November, 3rd November, 1st December, 2nd December, and 3rd December with the planting pattern of rice-secondary crop-sugarcane is introduced. It is continued by the analysis of water distribution conducted using linear program assisted by POM-Quantity method for Windows 3 with the reliable discharge limit and the available land area. Output of this calculation are to determine the land area that can be planted based on the type of plant and growing season, and to obtaine the profits of harvest yields. Based on the optimum area of each plant species with 6 alternatives, the most optimum area was obtained at the early planting periods on 3rd December with the production profit of Rp 113.397.338.854,- with the planting pattern of rice / beans / sugarcane-rice / beans / sugarcane-beans / sugarcane.


Introduction
Indonesia is one of the country in the world that has a large agriculture field. Horticultural crops have important and strategic roles in national and regional development, such as improving food sustainability, gross domestic product (GDP), income sources, and regional and national economies. Agriculture has become an attractive factor for upstream and downstream industry growth that huge contribution to national economic growth. One of the irigation area that should support this task is Logung Irrigation Area. This located in the Logung River, Kudus Regency, Central Java. Logung Irrigation Area, which has an area of 2810 Ha gets water supply from Logung River. Recently, the performance of this irrigation area tend to decrease because of uneven distribution of water. It becomes even worst by unpredictable rainy seasons that cause drought during the dry season and flooded during the rainy season. Therefore, such a method is introduced in order to solve this problem and to increase the crops productions, especially during dry season.
One of the method introduced to improve agricultural products in Logung irrigation area is by regulating a best way of water distribution. This method is done based on linier programming approach. By this methods, the water demand can be adjusted depend upon the water availability in Logung Dam. The aplicability of linier programming in case of water resources optimization has already introduced by Frizzone et.al [1], Jakovskis [2] Wafa Dipalla [3], Anieting [4] Pearson and McRoberts [5] and Suhardono [6]. The water demmand is determined by planting pattern. Optimal planting pattern arrangement simulated based on the type of plants and water

Methods
This part explaines the step on reaching the aim of research. Starting with collecting, reading and understanding some related references, follows by data collection, application of some formula and data analysis of water need. Finally it ended with optimization step, that consist of variation on the beginning of planting pattern and calulation of harvest yields benefit.

Literature review
On reaching the aim of study, some basic knowledge should be understood well. The basic knowledge has been learned on undergraduate lectures that consist of hydrology, hydraulics, irrigation and optimazion stage aspects [9]. The basic design of channel and its operation sourced to design criterium of irrigation channel [10], while the operation of Logung Dam is stated on Design of Logung Dam [11]. The aplicability of linier programe on optimation of water resources case is already proved by many experts [1,2,3,4,5,6] as mentions above.

Data collection and analysis
The data used in this study consist of Catchment and Irrigation area data, Hydrology and Hydraulic Data. Firstly the data of the catchment area and Logung river. The most important thing is the data of discharge. The 10 days measurement data of discharge from 2006 up to 2015 are available. Based on this data then the discharge distribution can be determined. Total area of irrigation field as the study area is an important parameter to be known, besides the type of crops, crops limitation and crop's water need . By knowning this, the scenario of optimation can be determined. The climatology data is also needed to calculate water balance not only in the field but also in irrigation intake and dam.

Optimization of planting patterns
Based on the result of water needs analysis from each alternative of planting pattern and reliable volume, it becomes the input of Linear Program to obtain the optimum planting pattern. The stage of finding optimum planting pattern is shown on Figure 1

Results and discussion
After calculation, some result should be analysis in order to support the optimization model. The outcme analysis are reliable discharge, water balance, waterneed for irrigation and harvest yields.

Hydrological analysis
This part explaines the process of hydrologic analysis. Based on discharge data of Logung River (

Water balance
Climatological calculation is calculated in order to determine the magnitude of plant evapotranspiration. The parameters should be consider on this calculation are air temperature, wind speed, relative humidity and duration of solar irradiance. The available data of climatology is from 1993 up to 2014. The result of calculation called as the potential evapotranspiration is shown at Table 3. Based on this table, the water balance can be estimated.

Effective Rainfall Calculations
Firstly, the rainfall station should be available on study area. There are three rainfall station : Rahwatu Station, Gembong Station, Tanjungrejo Station. To know the amount of surface runoff, the area of rainfall influence can be determined using Thiessen Polygon method. If the land use and rainfall intensity are known, then free surface discharge can be calculated.    The average rainfall calculation using Thiessen polygon in 2014 was shown in the following table:   I  II  III  I  II  III  I  II  III  I  II  III  I  II  III  I  II  III   1 I  II  III  I  II  III  I  II  III  I  II  III  I  II  III  I  II  III   1

Source: Calculation Result
After obtaining the average rainfall, an effective rainfall calculation for rice, secondary crops, and sugarcane are calculated. The result of calculation can be seen at Table 7.  I  II  III  I  II  III  I  II  III  I  II  III  I  II  III  I  II  III   1 I  II  III  I  II  III  I  II  III  I  II  III  I  II  III  I  II  III   1     The alternative calculations for planting pattern in the optimization study are as follows: • Alternative 1: the beginning of planting on 1 st November • Alternative 2:the beginning of planting on 2 nd November • Alternative 3: the beginning of planting on 3 rd November • Alternative 4: the beginning of planting on 1 st December • Alternative 5: the beginning of planting on 2 nd December • Alternative 6: the beginning of planting on 3 rd December Table 11, Table 12 and Table 13 show the water need in difference time of the beginning of planting time.

. Analysis of harvest yield
Harvest yields are the result of net income from crops harvesting by farmers. It is define as net income, that can be found as the difference between the gross production and production cost. Table  14 shows the basic calculation of harvest yields for Kudus Area.

Mathematical Model for Optimization
The linier programe classified the parameter of optimation as functional purpose and function constraints. Two approaches are used as basic assumption : maximize based on land area and water need. The optimization model equations used in this study are as follows: Functional purpose Maximize based on land area Z = Xp1 + Xw1 + Xp2 + Xw2 + Xp3 + Xw3 + Xt

Analysis of Optimization Results
The optimization analysis is based on two objectives, i.e. the maximum area and maximum profit. Iterative analysis is conducted using POM-QM for Windows 3.
The iteration data result using POM-QM program for Windows 3 obtained the optimum area data on each plant type with each alternative planting pattern. Then, it can be known the planting intensity in every planting season. Moreover, the extent area data will obtain the results of agricultural production annually. Table 16 shows that the greatest profit of production is obtained in alternative 6 with the early planting periods on the 3 rd December.