Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data

Eka Susanti, Oki Dwipurwani, Dian Cahyawati, Novi Rustiana Dewi, Husnul Khotimah, Wahyuni Apria Ningsih

Abstract


A common problem in inventory planning is the uncertainty of demand. One technique for determining the demand approximation value is the fractal interpolation. The aim of this study is to develop a fractal interpolation technique using a Fractal Interpolated Function constructed by the affine function that forms the Box Fractal shape. The developed method is applied to interpolate rice demand data based on prices at a rice milling factory. Mean Absolute Percentage Error (MAPE) is used to measure the accuracy of the interpolation results. For the n^{th} iteration, the number of boxes formed is 5^n, and the number of pairs of points is 4×5^n. Based on the rice demand data from one of the factories, the best MAPE was obtained at the $6^{th}$ iteration, with a value of 16.319%, which falls into the good category. Based on the data used, the affine function forming the Box Fractal as a Fractal Interpolated Function can be applied in fractal interpolation techniques.

Keywords


Box Fractal; Demand; Fractal; Fractal Interpolation.

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DOI: https://doi.org/10.18860/cauchy.v11i1.38905

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