E jurnal Matematika

133-138

Authors: Ni Putu Prema Dewanti, Made Susilawati, I Gusti Ayu Made Srinadi

Poisson regression is a nonlinear regression which is often used for count data and has equidispersion assumption (variance value equal to mean value). However in practice, equidispersion assumption is often violated. One of it violations is overdispersion (variance value greater than the mean value). One of the causes of overdipersion is excessive number of zero values on the response variable (excess zeros). There are many methods to handle overdispersion because of excess zeros. Two of them are Zero Inflated Poisson (ZIP) regression and Zero Inflated Negative Binomial (ZINB) regression. The purpose of this research is to determine which regression models is better in handling overdispersion data. The data that can be analyzed using the ZIP and ZINB regression is maternal mortality rate in the Province of Bali. Maternal mortality rate data has proportion of zeros value more than 50% on the response variable. In this research, ZINB regression better than ZIP regression for modeling maternal mortality rate. The independent variable that affects the number of maternal mortality rate in the Province of Bali is the percentage of mothers who carry a pregnancy visit, with ZINB regression models ln⁡〖(μ_i)〗=2,7729-0,0247X_1 and logit (p_i )=-3,8670-0,0381X_1.

148-155

Authors: Gede Suryawan, Ni Ketut Tari Tastrawati, Kartika Sari

Companies which engaged in production activities such as Ramadhan Bakery would want optimal profit in their every production. The aim of this study was to find optimal profit and optimal combination of bread production (original chocolate bread, extra chocolate bread, rounding chocolate bread and mattress chocolate bread) that was produced by Ramadhan Bakery by applying Branch and Bound Algorithm method. Branch and Bound Algorithm is one method to solve Integer Programming’s problems other than Cutting Plane method. Compared with Cutting Plane method, Branch and Bound Algorithm method is more effective in determining the optimal value. As the result of this study showed that to get optimal profit, Ramadhan Bakery should produce 360 pcs of original chocolate bread, 300 pcs of extra chocolate bread, 306 pcs of rounding chocolate bread and 129 pcs of mattress chocolate bread with optimal profit amounts Rp. 1.195.624,00.. The profit will increase amounts 25,2 % than before.

164-169

Authors: Luh Gede Udayani, I Wayan Sumarjaya, Made Susilawati

Dependence relationship between two or more variables is an issue that is often studied in the science of probability and statistics. Pearson correlation is often the easiest option to measure dependencies between variables. It is well known, that Pearson correlation assumes that the variable under study must be normally distributed. However, in reality this is not the case; for example, data in fields such as climatology and meteorology, insurance, and financial. Copula is a tool that can be used to model the joint distribution because it does not require the assumption of normality of the data so that it is resilient against a wide range of data. In this study, we discussed the application of copula in modeling the structure of dependencies between two variables: the production of rice and El-Nino Southern Oscillation (ENSO) indicator per period in Tabanan Regency. The best dependency model structure is given by the Frank copula of the Archimedean copula family with estimation parameter, θ = 2,817 and the loglikelihood value of 3,47.

176-182

Authors: Ami Hilda Agustin, G.K. Gandhiadi, Tjokorda Bagus Oka

Fuzzy logic is a way to map an input space into an output space. The basic of fuzzy logic is fuzzy set theory. In the fuzzy set theory, the role of membership degree is important to determine the presence of elements in a set. Membership degree is the fundamental feature of reasoning in fuzzy logic. There are several methods that are often used in solving fuzzy inference system, one of them is fuzzy Sugeno method. The aim of this research is applications of fuzzy methods is to forecast to determine the selling price of used motorcycles. In determining the selling price of used motorcycles, there are several things that need to be considered, namely : the production year of the motorcycles, the physical condition of the motorcycles, the origin of the license plates, and the purchase price of the motorcycles. The calculation can be done by using Matlab program. The result obtained were then tested using the Mean Absolute Percentage Error (MAPE) by calculating difference between the selling price of dealer minus the selling price of fuzzy Sugeno then divided by the selling price of dealer. From the test result, MAPE value obtained was 5,64% . This indicates that error rate below 10%, so we can say the result of these calculation is considerably accurate.

90-97

Authors: I Wayan Radika Apriana, Ni Ketut Tari Tastrawati, Kartika Sari

Cat Swarm Optimization (CSO) algorithm is a metaheuristic algorithm which is based on two behaviors of cat, seeking and tracing. CSO algorithm is used in solving optimization problems. One of the optimization problems which can be seen in daily life is Job Shop Scheduling Problem (JSSP). This study aimed to observe the performance of CSO algorithm in solving JSSP. This study focused on 5 job-12 machine cases. According to this study, CSO algorithm was effective in solving real case of JSSP in 5 jobs – 12 machines scheduling at CV Mitra Niaga Indonesia agriculture tools industry. In implementing CSO algorithm in JSSP, a correct parameter choosing could lead to an optimal result. On other hand, the greater the number of jobs or machines the more complex and difficult the JSSP that needed to be solved.

103-110

Authors: Palupi Purnama Sari, Made Susilawati, I Gusti Ayu Made Srinadi

This research was conducted to determine the variables that significantly influence nutritional status of children based on indicators that defined as height for age (H/A) and to classify children nutritional status into normal, short or very short categories. Height for age (H/A) is indicator used to describe the circumstances of malnutrition short. Short children (stunting) is children who fail to reach optimal growth. The secondary data was list of 116 data of children aged 24-59 months at UPT. Puskesmas Klungkung I in 2015. The method was used was ordinal logistic regression and bagging ordinal logistic regression. Based on the research results, it was obtained variables children body length at birth, birth weight, and length of mid-upper arm circumference (MUAC) in pregnant woman were significantly affects the nutritional status of children by the classification accuracy level of ordinal logistic regression 62,86% and misclassification 37,14%. Classification accuracy of ordinal logistic regression can be improved by bagging ordinal logistic regression method. Bagging works well on classification method which has unstable procedures. One of classification method which has unstable procedures is ordinal logistic regression. Bagging ordinal logistic regression method by 501 times replication capable to improve classification accuracy of ordinal logistic regression model from 62,86% to 68,57%, increased 5,71%.

117-125

Authors: I Putu Gede Dian Gerry Suwedayana, I Wayan Sumarjaya, Ni Luh Putu Suciptawati

The purpose of this research is to forecast the number of Australian tourists arrival to Bali (y_t) using Time Varying Parameter (TVP) model based on inflation of Indonesia (x_1t) and exchange rate AUD to IDR (x_2t) from January 2010 – December 2015 as explanatory variables. TVP model is specified in a state space model and estimated by Kalman filter algorithm. The result shows that the TVP model can be used to forecast the number of Australian tourists arrival to Bali because it satisfied the assumption that the residuals are distributed normally and the residuals in the measurement and transition equations are not correlated. The estimated TVP model is (y_t ) ̂=201.8253x_1t+8.903399x_2t. This model has a value of mean absolute percentage error (MAPE) is equal to 1.77% dan root mean square percentage error (RMSPE) is equal to 2.3418%. The number of Australian tourists arrival to Bali for the next five periods is predicted: 87,534; 86,708; 88,864; 90,651; and 88,077 (January - May 2016).

44-51

Authors: Merary Sianipar, Ni Luh Putu Suciptawati, Komang Dharmawan

Tourism demand is focused on estimating variables which influence tourist visit. The tourism demand that we discuss on this research is the tourism demand to Bali of the major tourism-generating country was Australia. The aim of this research is to analyze the relationship between tourist income and tourism price to tourism demand using VECM. VECM requires that the variables in the model must be stationary and fulfilled a cointegration condition. In order to make it valid, the stationarity of variables in the model have to be checked using ADF unit root test. In additon, cointegration between these variables are examined using Johansen’s cointegration test. The results of ADF unit root test show that indicated the tourist income, the tourism price and the tourism demand for Australia data are stationary in first lag or I(1). Cointegration test shows that all variables are cointegrated, i.e. have a long-run relationship. In the long-run, the tourist income and tourism price give positive effect to the tourism demand. This means, the increase of tourist income and tourism price will contribute to the increase in tourism demand. In addition, in the short-run, the tourist income and the tourism price give negative effect to the tourism demand. This means, the increase of tourist income and tourism price will contribute to the decrease in tourism demand. Keywords: ADF Unit Root Test, Johansen’s Cointegration Test, The Tourism Demand, The Tourist Income, The Tourism Price, Vector Error Correction Model.

59-66

Authors: Tjokorda Gde Agung Friska Adnyana, G. K. Gandhiadi, Desak Putu Eka Nilakusmawati

The aim of this research is to apply Fuzzy Analytic Hierarchy Process method to determine the dominant sectors of economy Bali Province. This research used survey data from respondents who understand about economy of Bali Province and Gross Regional Domestic Product (GRDP). The research variables consist of criteria and sub-criteria. The criteria consist of primary sector, secondary, and tertiary, while the sub-criteria consist of 9 sectors of the GRDP. Data processing is done by calculating the weighted average and arrange them into pairwise comparison matrices. Furthermore, the consistency ratio is checked. If consistency ratio less than 0.100 (CR<0.1), the elements of matrices is changed into triangular fuzzy scale and processed with synthetic extent to get the priority. Based on the result of research, the economy of Bali are dominated by tertiary sector in sector group, agriculture and forestry in sub-primary group, manufacturing industry in sub-secondary group, and trade, hotel and restaurant in sub-tertiary group.. Keywords: Economy, Sector, Fuzzy Analytic Hierarchy Process

76-81

Authors: Agust Wiras Ardi Kusuma, I Gusti Ayu Made Srinadi, Kartika Sari

One of multivariate analysis application was used to see the relationship between two or more quantitative variable and objects within. Multivariate analysis which used in this case is correspondence analysis. This paper will be done correspondence analysis application in order to see the characteristic of tourism business in Bali. In this study it can be seen the characteristic of tourism business in Bali in a form of illustration of tourism business situation of each regencies which mapped in two dimensional plots. The result was Karangasem, Buleleng, Gianyar, Jembrana, Tabanan, and Klungkung were in a group because they have the same development of tourism area business and accommodation service business. However tourism business that was developed in Denpasar and Badung was tour and travel and food and beverage business.

7-13

Authors: Ni Wayan Nining Ismiranti, I Putu Eka N. Kencana, I Komang Gde Sukarsa

The aim of this research is to find the alternative solutions that could be used to handle the traffic congestions in the Denpasar City and the priorities of each alternative. The main problem of this research is determining the appropriateness of alternatives and its criterias that could be used to set the priorities of the alternatives. Based on the interview with the transport experts of Denpasar City, there are three main factors that affect the traffic congestion i.e (1) the ratio of the volume of vehicles on the road capacity, (2) the existing traffic management, and the traffic regulation . The interviewee also suggest that there are six alternatives that can be used to handle traffic congestion. These alternatives are (1)improve the public transport system, (2) use technology to monitor and enforce the rules,(3) create a 3 in 1 rule, (4) create road pricing rule,(5) optimize the existing management in the road, and (6) create rule of road zoning. Based on the calculations by Analytic Network Process (ANP) method, improving the public transport system is the best alternative among others that is appropriate to handle traffic congestion in the Denpasar City.

22-26

Authors: Ni Putu Iin Vinny Dayanti, Ni Luh Putu Suciptawati, Made Susilawati

Ordinary Least Squares (OLS) Method is a good method to estimate regression parameters when there is no violation in classical assumptions, such as the existence of outlier. Outliers can lead to biased parameters estimator, therefore we need a method that can may not affected by the existence of outlier such as Minimum Covariance Determinant (MCD) and Least Median of Squares (LMS). However, the application of this method is less accurate when it is used for small data. To overcome this problem, it was aplicated bootstrap method in MCD and LMS to determine the comparison of bias in parameters which were produced by both methods in dealing outlier in small data. The used bootstrap method in this study was the residual bootstrap that works by resampling the residuals. By using 95% and 99% confidence level and 5%, 10% and 15% outlier percentage, MCD-bootstrap and LMS-bootstrap give value of parameter estimators which were unbias for all percentage of outlier. We also found that the widht of range which produced by MCD-bootstrap method was shorter than LMS-bootstrap method produced. This indicates that MCD-bootstrap method was a better method than LMS-bootstrap method. Keywords: outliers, bias, robust, Minimum Covariance Determinant, Least Median of Squares, bootstrap residual

32-37

Authors: Ni Luh Putu Ratna Dewi, I Nyoman Widana, Desak Putu Eka Nilakusmawati

Premium reserve is a number of fund that need to be raised by insurance company in preparation for the payment of claims. This study aims to get the formula of premium reserve as well as the value of the premium reserve for joint life insurance by using retrospective calculation method. Joint life insurance participants in this study are limited to 2 people. Calculations in this study is using Indonesian Mortality Table (TMI) 2011, joint life mortality tables, commutation tables, value of annuities, value of single premiums and constant annual premium and using constant interest rates of 5%. The results showed that by using age of the participant insurance joint life of x = 50 and y = 45 years and the premium payment period of t = 10 years, we obtained that the value of premium reserve from the end of the first year until the end of the 11th year has increased every year, while the value of premium reserves from the end of the 12th year and so on until a lifetime has decreased every year. Keywords: Joint Life Insurance, Premium Reserve, Retrospective