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2020 | 143 | 155-169
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Uncertain Semivariogram Model using Robust Optimization for Application of Lead Pollutant Data

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Semivariogram is a half variance diagram of the difference between observations at the location s_i with another location that is as far as h units of distance. Semivariogram is used to describe the correlation of observation sorted by location. This research discusses the theoretical Semivariogram for the Spherical, Gaussian, and Exponential Semivariogram models through the Linear Programming approach. Next, the Semivariogram parameter estimation is studied with the assumption that there are data uncertainties, called the Uncertain Semivariogram. The method used to overcome the uncertainty data is Robust Optimization. The Uncertain Semivariogram using Robust Optimization are solved using the box and ellipsoidal uncertainty set approach. The calculation of the application of the model was carried out using the R software. For the case study, the application of the model used secondary data of Lead pollutant data in the Meuse River floodplains on the borders of France and the Netherlands at 164 locations. Based on the calculation results, the Exponential theoretical Semivariogram model is obtained as the best Semivariogram model, because it has a minimum SSE. Furthermore, the application of the Uncertain Semivariogram model using Robust Optimization on the Semivariogram Exponential model of Lead pollutant data is carried out using the box and ellipsoidal uncertainty set approach which is to obtain computationally tractable results.
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  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang – 45363, Indonesia
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang – 45363, Indonesia
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang – 45363, Indonesia
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