Improve Fuzzy Inventory Model of Fractal Interpolation with Vertical Scaling Factor
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Keywords:
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Fractal Interpolation, Vertical Scaling Factor, Fuzzy, Inventory Model
Abstract
The inventory model is used to determine the optimal inventory of a product. In certain cases, parameters in the inventory model are uncertain. Fractal interpolation techniques can be used to overcome parameter with uncertainty. Fractal interpolation results are affected by the fractal interpolation function and the vertical scaling factor. The vertical scaling factor is positive and less than 1. In this study, fractal interpolation techniques are introduced with variations in vertical scaling factor to overcome the uncertainty of demand data in inventory models. Furthermore, the interpolation results are used in fuzzy inventory models and expressed by Trapezoidal Fuzzy Number. This paper considers an inventory model with varying demand to optimize rice inventory. Based on the data obtained, the accuracy level will increase for the vertical scaling factor values close to 1. Optimal rice inventory of each successive fuzzy parameter is 1447963, 1013914, 504950, 215312. If the cost parameter is increased, then the amount of inventory is decreases.
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Thinakaran, N., Jayaprakas, J., & Elanchezhian, C. (2019). Survey on inventory model of EOQ & EpQ with partial backorder problems. Materials Today: Proceedings, 16, 629–635.
Tyada, K. R., Chand, A. K. B., & Sajid, M. (2021). Shape preserving rational cubic trigonometric fractal interpolation functions. Mathematics and Computers in Simulation, 190, 866–891.
Baicoianu, A., Pacurar, C. M., & Paun, M. (2021). A concretization of an approximation method for non-affine fractal interpolation functions. Mathematics, 9(7).
Balasubramani, N. (2017). Shape preserving rational cubic fractal interpolation function. Journal of Computational and Applied Mathematics, 319, 277–295.
Çalışkan, C. (2021). A simple derivation of the optimal solution for the EOQ model for deteriorating items with planned backorders. Applied Mathematical Modelling, 89, 1373–1381.
Chakraborty, A., Maity, S., Jain, S., Mondal, S. P., & Alam, S. (2021). Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem. Granular Computing, 6(3), 507–521.
Geng, F., & Wu, X. (2021). Reproducing Kernel Functions Based Univariate Spline Interpolation. Applied Mathematics Letters, 122, 107525.
Han, T., Yang, Y., & Huang, G. (2021). Vertical Scaling optimization Algorithm for a Fractal Interpolation Model of Time Offsets Prediction in Navigation Systems. Applied Mathematical Modelling, 90, 862–874.
Hemalatha, S., & Annadurai, K. (2020). A fuzzy EOQ inventory model with advance payment and various fuzzy numbers. Materials Today: Proceedings.
Huang, Q., Zhang, K., Song, J., Zhang, Y., & Shi, J. (2019). Adaptive Differential Evolution with a Lagrange Interpolation Argument Algorithm. Information Sciences, 472, 180–202.
Kalaiarasi, K., Sumathi, M., Henrietta, H. M., & Raj, A. S. (2020). Determining the Efficiency of Fuzzy Logic EOQ Inventory Model with Varying Demand in Comparison with Lagrangian and Kuhn-Tucker Method Through Sensitivity Analysis. Journal of Model Based Research, 1(3), 1–12.
Laura, S. M. (2020). A fuzzy inventory model with green environment by controlling carbon emissions. Malaya Journal of Matematik, 8(4), 1454–1457.
Liao, H., & Li, L. (2021). Environmental sustainability EOQ model for closed-loop supply chain under market uncertainty: A case study of printer remanufacturing. Computers and Industrial Engineering, 151(April).
Lisan, S. (2018). Safety stock determination of uncertain demand and mutually dependent variables. International Journal of Business and Social Research, 8(3), 01–11.
Navascués, M. A., Katiyar, S. K., & Chand, A. K. B. (2020). Multivariate Affine Fractal Interpolation. Fractals, 28(7).
Ochoa, H., Almanza, O., & Montes, L. (2020). Fractal-interpolation of seismic traces using vertical scale factor with residual behavior. Journal of Applied Geophysics, 182, 104181.
Onyenike, K. (2022). A Study on Fuzzy Inventory Model with Fuzzy Demand with No Shortages Allowed using Pentagonal Fuzzy Numbers. 7(3), 7–11.
Păcurar, C. M., & Necula, B. R. (2020). An Analysis of COVID-19 Spread Based on Fractal Interpolation and Fractal Dimension. Chaos, Solitons and Fractals, 139.
Rani, S., Ali, R., & Agarwal, A. (2019). Fuzzy Inventory Model for Deteriorating Items in a Green Supply Chain with Carbon Concerned Demand. In Opsearch (Vol. 56, Issue 1). Springer India.
Raubitzek, S., & Neubauer, T. (2021). A fractal interpolation approach to improve neural network predictions for difficult time series data. Expert Systems with Applications, 169(August 2020), 114474.
Ri, Song Il. (2018). A new idea to construct the fractal interpolation function. Indagationes Mathematicae, 29(3), 962–971.
Ri, M. G., Yun, C. H., & Kim, M. H. (2021). Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus. Chaos, Solitons and Fractals, 150, 111177.
Ri, Songil. (2017). A New Nonlinear Fractal Interpolation Function. Fractals, 25(6), 1–12.
Ri, SongIl. (2020). Fractal functions on the Sierpinski Gasket. Chaos, Solitons and Fractals, 138, 110142.
Russel, E., Wamiliana, Warsono, Nairobi, Usman, M., & Elfaki, F. A. M. (2023). Analysis Multivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia. Science and Technology Indonesia, 8(1), 144–150.
Shaikh, A. A., Khan, M. A. A., Panda, G. C., & Konstantaras, I. (2019). Price discount facility in an EOQ model for deteriorating items with stock-dependent demand and partial backlogging. International Transactions in Operational Research, 26(4), 1365–1395.
Shee, S., & Chakrabarti, T. (2020). Fuzzy Inventory Model for Deteriorating Items in a Supply Chain System With Time Dependent Demand Rate. International Journal of Engineering Applied Sciences and Technology, 5(1), 558–569.
Susanti, E., Dwipurwani, O., Sitepu, R., Wulandari, & Natasia, L. (2019). Triangular fuzzy number in probabilistic fuzzy goal programming with pareto distribution. Journal of Physics: Conference Series, 1282(1).
Tahami, H., & Fakhravar, H. (2020). A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order. European Journal of Engineering Research and Science, 5(10), 1179–1185.
Thinakaran, N., Jayaprakas, J., & Elanchezhian, C. (2019). Survey on inventory model of EOQ & EpQ with partial backorder problems. Materials Today: Proceedings, 16, 629–635.
Tyada, K. R., Chand, A. K. B., & Sajid, M. (2021). Shape preserving rational cubic trigonometric fractal interpolation functions. Mathematics and Computers in Simulation, 190, 866–891.
Authors
Eka Susanti, Fitri Maya Puspita, Siti Suzlin Supadi, Evi Yuliza, & Ahmad Farhan Ramadhan. (2023). Improve Fuzzy Inventory Model of Fractal Interpolation with Vertical Scaling Factor. Science and Technology Indonesia, 8(4), 654–659. https://doi.org/10.26554/sti.2023.8.4.654-659
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