Ideal distribution route: An optimization approximation by using random search method

Abdu Afin Arsy, Faris Alaudin Shalih, Fulkan Kafilah Al Husein, Achmad Abdurrazzaq

Abstract


Distribution is the process of transferring goods from producers to consumers. In this process, both producers and consumers always expect a more efficient distribution system. One way to create an efficient distribution channel is by determining the ideal point for vital objects. By determining the ideal point, an optimal solution can be obtained in minimizing costs and improving the efficiency of the distribution system. This research discusses the determination of the ideal point using numerical optimization methods. Analytical and numerical approaches are used through the Modified Random Search method to formulate and analyze a mathematical model that can provide an optimal solution to the distribution problem. The proposed algorithm will be implemented to solve the energy distribution problem in the real environment. The aim is to test the effectiveness and accuracy of the proposed algorithm based on the solutions obtained. Based on the experimental results, distribution problems in general and energy distribution in particular are addressed better, and the distribution process is more efficient.


Keywords


Optimization; Random search; Numerical methods; Distribution

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References


Abdur, R. A., Tohir, M., Valentino, E., Imron, Z., & Taufiq, I. (2017). Buku guru matematika. Kementerian Pendidikan dan Kebudayaan. (ISBN 978-602-282-085-7).

Adam, S. P., Alexandropoulos, S. A. N., Pardalos, P. M., & Vrahatis, M. N. (2019). No free lunch theorem: A review. Approximation and Optimization: Algorithms, Complexity and Applications, 145, 57-82. https://doi.org/10.1007/978-3-030-12767-1_5

Akbari, M. & Haddadpour, H. (2019). Linear optimization methods for solving multi-objective optimization problems. Journal of Optimization in Industrial Engineering, 12(28), 27-34. 10.22094/joie.2019.1870499.1591

Amelia, L. (2013). Model optimasi produksi minyak sawit dan inti sawit menggunakan pendekatan hibrid sistem pakar kabur dan random direct search. Jurnal Inovisi, 9(2), 79–87.

Ayu Muchlisa, N., & Surianto, M. A. (2021). analisis saluran distribusi pada PT. Panahmas Dwitama Distrindo Jember. Jurnal Indonesia Sosial Sains, 2(12), 2059–2068. https://doi.org/10.59141/jiss.v2i12.480

Xue, B., Sun, C., Chu, H., Meng, Q., & Jiao, S. (2020). Method of electronic component location, grasping and inserting based on machine vision. 2020 International Wireless Communications and Mobile Computing (IWCMC), Limassol, Cyprus, 2020, pp. 1968-1971, doi: 10.1109/IWCMC48107.2020.9148099.

Battiti, R., & Brunato, M. (2019). Reactive search optimization: learning while optimizing. Springer. doi: https://doi.org/10.1007/978-3-319-91086-4_15

Bumblauskas, D., Mann, A., Dugan, B., & Rittmer, J. (2020). A blockchain use case in food distribution: Do you know where your food has been?. International Journal of Information Management, 52, 102008.

https://doi.org/10.1016/J.IJINFOMGT.2019.09.004

Rao, C. S. V. P., Pandian, A., Reddy, C. R., Bajaj, M., Jurado, F., and Kamel, S. (2023). Optimal Location of EV Parking Lot by MAOWHO technique in Distribution System. 2023 5th Global Power, Energy and Communication Conference (GPECOM), Nevsehir, Turkiye, 2023, pp. 103-107, doi: 10.1109/GPECOM58364.2023.10175745.

Carrizosa, E., Conde, E., Pascual, A., & Romero-Morales, D. (1997). Closest solutions in ideal-point methods. Advances in Multiple Objective and Goal Programming, 1, 274–281. doi: https://doi.org/10.1007/978-3-642-46854-4_30

Chandra, A., & Setiawan, B. (2018). Optimasi jalur distribusi dengan Metode Vehicle Routing Problem (VRP) optimizing the distribution routes using Vehicle Routing Problem (VRP) Method. Jurnal Manajemen Transportasi & Logistik, 5(2), 105-116. http://dx.doi.org/10.54324/j.mtl.v5i2.233

Trahan, D. H., & Wagon, S. (2018). Elementary differential equations and boundary value problems. The American Mathematical Monthly, 86:10, 599-612, DOI: 10.1080/00029890.1979.11994869

Dattorro, J. (2009). Convex optimization & euclidean distance geometry. California: Mεβoo Publishing.

Fitiyani, F., Away, Y., & A.Gani, T. (2018). Pengaruh inisialisasi populasi random search pada algoritma berevolusi dalam optimasi Travelling Salesman Problem (Tsp). Jurnal Nasional Komputasi dan Teknologi Informasi (JNKTI), 1(2). doi: 10.32672/jnkti.v1i2.770

García-Nava, P. E., Rodríguez-Picón, L. A., Méndez-González, L. C., & Pérez-Olguín, I. J. C. (2022). A study of stopping rules in the steepest ascent methodology for the optimization of a simulated process. Axioms, 11(10), 514. doi: https://doi.org/10.3390/axioms11100514

Hanafi, L., Rohmati, E., & Puspita, G. M. (2010). Penyelesaian numerik untuk menentukan nilai optimal pada american option dengan metode beda hingga Fully Implisit dan Crank-Nicolson. Limits: Journal Mathematics and Its Applications, 7(2). doi: http://dx.doi.org/10.12962/j1829605X.v7i2.1433

Harahap, M. K., & Khairina, N. (2017). Pencarian jalur terpendek dengan algoritma dijkstra. SinkrOn, 2(2), 18. doi: https://doi.org/10.33395/sinkron.v2i2.61

Hasmi, R. A. (2018). Optimasi perencanaan produksi dengan menggunakan metode linear programming pada CV. Aceh Bakery. Jurnal Optimalisasi, 1(1), 43–56. DOI:10.35308/jopt.v1i1.168

Hidayah, R. (2021). Strategi pemilihan lokasi terhadap kesuksesan usaha berbasis syariah. Skripsi. Jambi: Universitas Islam Negeri Sulthan Thaha Saifuddin.

James B. Riggs. (1988). An introduction to numerical methods for chemical engineers. Texas: Texas Tech University Press, Chapter 6

Kamal, N. Gramedia.com. Diakses tanggal 12 juli 2023. https://www.gramedia.com/literasi/pengertian-referensi/#Sumber_Referensi.

Kamus Besar Bahasa Indonesia

Kiki Setiawan, Dkk., (2018). Menghitung rute terpendek menggunakan algoritma A* dengan fungsi euclidean distance. Seminar Nasional Teknologi Informasi dan Komunikasi 2018, (ISSN: 2089-9815), 70–79.

Li, L. & Talwalkar, A. (2020). Random search and reproducibility for neural architecture search. PMLR: Proceedings of Machine Learning Research, 115:367-377, 2020.

Ranran, L. & Reynolds, A. (2020). Joint optimization of well locations, types, drilling order, and controls given a set of potential drilling paths. SPE Journal. 25. 10.2118/193885-PA.

Lubis, A. N. (2004). Peranan saluran distribusi dalam pemasaran produk dan jasa. Academia, 1–14. https://www.academia.edu/download/56449929/manajemen-arlina_lbs4.pdf

Martins, J. R., & Ning, A. (2021). Engineering design optimization. Cambridge University Press.

Moehle, N., Shen, X., Luo, Z. Q., & Boyd, S. (2019). A distributed method for optimal capacity reservation. Journal of Optimization Theory and Applications, 182(3), 1130–1149. https://doi.org/10.1007/s10957-019-01528-5

Nugraha, D. A., & Lian, K. L. (2019). A novel MPPT method based on cuckoo search algorithm and golden section search algorithm for partially shaded PV system. Canadian Journal of Electrical and Computer Engineering, 42(3), 173-182. doi: https://doi.org/10.1109/CJECE.2019.2914723

Pratama, M. A. (2019). Analisis pendistribusian yang efektif guna penjualan susu frisian flag pada CV. Sumber Makmur Metro ditinjau dari etika bisnis islam. Skripsi. Lampung: Institut Agama Islam Negeri (IAIN) Metro.

Purcell, E. J. & Varberg, D. (1995). Kalkulus dan geometri analitis jilid 1. Alih Bahasa, I Nyoman Susila.; Bana Kartasasmita (Edisi 8 Jilid 1). Jakarta: Erlangga.

Rao, S. S. (2019). Engineering optimization: theory and practice. John Wiley & Sons. doi: 10.1002/9781119515592

Rasheed, M., Shihab, S., Rashid, T., & AL-Farttoosi, O. A. A. (2021). Comparison study between classic chord and inverse quadratic interpolation methods. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Page-184. doi: https://doi.org/10.29304/jqcm.2021.13.1.781

Rebentrost, P., Schuld, M., Wossnig, L., Petruccione, F., & Lloyd, S. (2019). Quantum gradient descent and Newton’s method for constrained polynomial optimization. New Journal of Physics, 21(7), 073023. doi: 10.1088/1367-2630/ab2a9e

Reza Ahmadzadeh (2023). Random Search Algorithm (https://www.mathworks.com/matlabcentral/fileexchange/38630-random-search-algorithm), MATLAB Central File Exchange. Retrieved February 16, 2023.

Ridha P. E., Marisa M. D., & Hidayati, R. (2020). Menggunakan metode simulated annealing (studi kasus: PD Bumi Jaya Indah Kota Pontianak). In Coding: Jurnal Komputer dan Aplikasi, 8(3). doi: https://doi.org/10.26418/coding.v8i3.42409

Soetopo, W. (2004). Teknik simulasi untuk optimasi random search dengan menerapkan relaksasi pada perbaikan fungsi tujuan. Jurnal Teknik, 79

Steven C. C. & Raymond P. C. (2003). Numerical Methods for Engineers: With Software and Programming Applications, 4th edition. New York: McGraw-Hill Company Inc, Part Four

Sunarya, U. & Haryanti, T. (2022). Perbandingan kinerja algoritma optimasi pada metode random forest untuk deteksi kegagalan jantung. Jurnal Rekayasa Elektrika, 18(4), 241–247. doi: 10.17529/jre.v18i4.26981

Takata, H. (2019). Transaction costs and capability factors in dual or indirect distribution channel selection: An empirical analysis of Japanese manufacturers. Industrial Marketing Management, 83, 94–103. https://doi.org/10.1016/J.INDMARMAN.2018.11.003

Wang, Y., Zhao, N., Jing, H., Meng, B., & Yin, X. (2016). A novel model of the ideal point method coupled with objective and subjective weighting method for evaluation of surrounding rock stability. Mathematical Problems in Engineering, 2016. doi: 10.1155/2016/8935156

Wijaya, F. S. (2019). Optimalisasi pelaksanaan maintenance armada pt. hidup sejahtera Sentosa. Doctoral dissertation. Universitas Muhammadiyah Gresik.

Wiyanti, D, T. (2013). Algoritma optimasi untuk penyelesaian travelling salesman problem. Jurnal Transformatika, 11(1), 1-6. doi: 10.26623/transformatika.v11i1.76

Xiong, F., Wei, B., & Xu, F. (2022). Identification of arch dam mechanical parameters based on sensitivity analysis and Hooke–Jeeves algorithm optimization. Structures, 46, 88-98. doi: https://doi.org/10.1016/j.istruc.2022.10.052

Yang, J., & Kim, Y. (2020). A hybrid random search optimization algorithm for global optimization problems. Journal of Applied Mathematics and Computing, 63(1-2), 173-186 doi: 10.1007/s12190-020-01438-5

Yao, J., Zhang, X., & Murray, A. T. (2019). Location optimization of urban fire stations: Access and service coverage. Computers, Environment and Urban Systems, 73, 184–190. doi: https://doi.org/10.1016/J.COMPENVURBSYS.2018.10.006

Yoash Levron (2023). Minimization of a function by random iterative search (https://www.mathworks.com/matlabcentral/fileexchange/40276-minimization-of-a-function-by-random-iterative-search), MATLAB Central File Exchange. Retrieved February 16, 2023.




DOI: http://dx.doi.org/10.24042/djm.v7i1.21580

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