# OPTIMIZATION OF RICE INVENTORY USING FUZZY INVENTORY MODEL AND LAGRANGE INTERPOLATION METHOD

• Eka Susanti Science Doctoral Program, Mathematic and Natural Science, Universitas Sriwijaya, Indonesia
• Fitri Maya Puspita Department of Mathematics, Universitas Sriwijaya, Indonesia
• Evi Yuliza Department of Mathematics, Universitas Sriwijaya, Indonesia
• Siti Suzlin Supadi Institute of Mathematics Sciences, University of Malaya, Malaysia
• Oki Dwipurwani Department of Mathematics, Universitas Sriwijaya, Indonesia
• Novi Rustiana Dewi Department of Mathematics, Universitas Sriwijaya, Indonesia
• Ahmad Rindarto Department of Mathematics, Universitas Sriwijaya, Indonesia
Keywords: Fuzzy EOQ, Lagrange Interpolation, Trapezoidal Fuzzy Number

### Abstract

Interpolation is a method to determine the value that is between two values and is known from the data. In some cases, the data obtained is incomplete due to limitations in data collection. Interpolation techniques can be used to obtain approximate data. In this study, the Lagrange interpolation method of degree 2 and degree 3 is used to interpolate the data on rice demand. A trapezoidal fuzzy number expresses the demand data obtained from the interpolation.  The other parameters are obtained from company data related to rice supplies and are expressed as trapezoidal fuzzy numbers. The interpolation accuracy rate is calculated using Mean Error Percentage (MAPE). The second-degree interpolation method produces a MAPE value of 30.76 percent, while the third-degree interpolation has a MAPE of 32.92 percent. The quantity of order  respectively  202677 kg, 384610 kg, 1012357 kg, 1447963 kg, and a Total inventory cost of Rp. 129231797951.

### References

S. Sanni and B. O. Neill, “Computers & Industrial Engineering Inventory optimisation in a three-parameter Weibull model under a prepayment system,” Comput. Ind. Eng., vol. 128, no. December 2018, pp. 298–304, 2019.

X. Luo and C. Chou, “International Journal of Production Economics Technical note : Solving inventory models by algebraic method,” Int. J. Prod. Econ., vol. 200, no. March, pp. 130–133, 2018.

S. M. Mousavi and D. Ph, “Optimizing a location allocation-inventory problem in a two-echelon supply chain network : A modified Fruit Fly optimization algorithm,” Comput. Ind. Eng., 2015.

J. Rezaeian, S. Haghayegh, and I. Mahdavi, “Designing an Integrated Production / Distribution and Inventory Planning Model of Fixed-life Perishable Products,” J. Otimization Ind. Eng., vol. 19, pp. 47–59, 2016.

Y. Perlman and I. Levner, “Perishable Inventory Management in Healthcare,” J. Serv. Manag., vol. 2014, no. February, pp. 11–17, 2014.

E. Susanti, R. Sitepu, K. Ondhiana, and W. D. Wulandari, “Optimization of Inventory Level Using Fuzzy Probabilistic Exponential Two Parameters Model,” J. Mat. MANTIK, vol. 7, no. 2, pp. 124–131, 2021.

L. E. Cárdenas-barrón, A. A. Shaikh, S. Tiwari, and G. Treviño-garza, “An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit,” Comput. Ind. Eng., vol. 139, p. 105557, 2020.

A. A. Shaikh, M. A. A. Khan, G. C. Panda, and I. Konstantaras, “Price discount facility in an EOQ model for deteriorating items with stock-dependent demand and partial backlogging,” Int. Trans. Oper. Res., vol. 26, no. 4, pp. 1365–1395, 2019.

L. E. Cárdenas-Barrón, A. A. Shaikh, S. Tiwari, and G. Treviño-Garza, “An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit,” Comput. Ind. Eng., vol. 139, no. December 2018, p. 105557, 2020, doi: 10.1016/j.cie.2018.12.004.

F. Geng and X. Wu, “Reproducing Kernel Functions Based Univariate Spline Interpolation,” Appl. Math. Lett., vol. 122, p. 107525, 2021.

M. Hasanipanah, D. Meng, B. Keshtegar, N. T. Trung, and D. K. Thai, “Nonlinear Models Based on Enhanced Kriging Interpolation for prediction of Rock Joint Shear Strength,” Neural Comput. Appl., vol. 33, no. 9, pp. 4205–4215, 2021.

S. Tayebi, S. Momani, and O. Abu Arqub, “The Cubic B-Spline Interpolation Method for Numerical Point Solutions of Conformable Boundary Value Problems,” Alexandria Eng. J., vol. 61, no. 2, pp. 1519–1528, 2022.

P. Lamberti and A. Saponaro, “Multilevel Quadratic Spline Quasi-Interpolation,” Appl. Math. Comput., vol. 373, 2020.

G. I. Gandha and D. Nurcipto, “The Newton’s Polynomials Interpolation Based-Error Correction Method for Low-Cost Dive Altitude Sensor in Remotely Operated Underwater Vehicle (ROV),” J. Infotel, vol. 11, no. 1, p. 1, 2019.

L. Zou, L. Song, X. Wang, T. Weise, Y. Chen, and C. Zhang, “A New Approach to Newton-Type Polynomial Interpolation with Parameters,” Math. Probl. Eng., vol. 2020.

S. Raubitzek and T. Neubauer, “A fractal interpolation approach to improve neural network predictions for difficult time series data,” Expert Syst. Appl., vol. 169, no. August 2020, p. 114474, 2021.

C. M. Păcurar and B. R. Necula, “An Analysis of COVID-19 Spread based on Fractal Interpolation and Fractal Dimension,” Chaos, Solitons and Fractals, vol. 139, p. 110073, 2020.

H. Ochoa, O. Almanza, and L. Montes, “Fractal-interpolation of seismic traces using vertical scale factor with residual behavior,” J. Appl. Geophys., vol. 182, p. 104181, 2020.

S. Maity, S. K. De, and S. P. Mondal, A study of an EOQ model under lock fuzzy environment, vol. 7, no. 1. Springer Singapore, 2019.

T. Nadu and T. Nadu, “Fuzzy Inventory EOQ Optimization,” Int. J. Electr. Eng. Technol., vol. 11, no. 8, pp. 169–174, 2020.

R. Patro, M. M. Nayak, and M. Acharya, “An EOQ Model for Fuzzy Defective Rate with Allowable Proportionate Discount,” Opsearch, vol. 56, no. 1, pp. 191–215, 2019.

S. K. De, “Solving an EOQ Model under Fuzzy Reasoning,” Appl. Soft Comput., vol. 99, p. 106892, 2021.

K. Kalaiarasi, M. Sumathi, H. M. Henrietta, and A. S. Raj, “Determining the Efficiency of Fuzzy Logic EOQ Inventory Model with Varying Demand in Comparison with Lagrangian and Kuhn-Tucker Method Through Sensitivity Analysis,” J. Model Based Res., vol. 1, no. 3, pp. 1–12, 2020.

Q. Huang, K. Zhang, J. Song, Y. Zhang, and J. Shi, “Adaptive Differential Evolution with a Lagrange Interpolation Argument Algorithm,” Inf. Sci. (Ny)., vol. 472, pp. 180–202, 2019.

Published
2023-09-30
How to Cite

E. Susanti, “OPTIMIZATION OF RICE INVENTORY USING FUZZY INVENTORY MODEL AND LAGRANGE INTERPOLATION METHOD”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1215-1220, Sep. 2023.
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Articles