Cutting board distribution cost optimization by using the Clark and Wright saving heuristic algorithm (case study at PT Titan)
Keywords:
Distribution Problem, Clark and Wright Saving, Heuristic AlgorithmAbstract
One of the main challenges in PT Titan’s distribution process is the inaccurate determination of vehicle routes and improper selection of vehicle types and capacities, which leads to inefficient distribution costs. Although PT Titan already has a distribution route, the author proposed a more cost-effective alternative using the Clark and Wright Saving Heuristic, which efficiently solves vehicle routing problems by allowing a single vehicle to serve multiple agents in a single trip. The research aimed to identify the current distribution routes for cutting board products, apply the algorithm to improve them, and determine the most optimal routes after optimization. Graphs were used to visualize the revised distribution plan. The results showed two significant optimizations in mileage and cost. For the L300 and Ankle Box vehicles, mileage was reduced by 9 km, and distribution costs were reduced by 2.8% (Rp 250,000 per trip). Meanwhile, the Double ankle and L300 vehicles achieved a mileage reduction of 55.13%, corresponding to 1,386 km. They cost savings of 28.1% or Rp2.500,000 The final optimized routes consist of Route 1 (Depot–Klaten–Boyolali–Depot) and Route 2 (Depot–Bogor–Tangerang–Depot) using Doubel ankle vehicle, and Route 3 (Depot–Kuningan–Cikijing–Depot) using an L300 vehicle, resulting in a more efficient and cost-effective distribution system for PT Titan.
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[1] R. Hariyani, M. A. Misri and H. Handoko, "Implementasi Pewarnaan Graf Menggunakan Algoritma Welsh-Powell pada Peta Indonesia," JURNAL SILOGISME: Kajian Ilmu Matematika dan Pembelajarannya, vol. 9, no. 2, pp. 94-103, 2024.
[2] M. A. Misri, Struktur grup, Cirebon: cv. confident, 2017.
[3] M. A. Misri, K. H. Qadr and M. A. Rahmatullah, "SEIR Mathematical Model with the Use of Hand Sanitizers to Prevent the Spread of Covid-19 Disease," CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 9, no. 1, pp. 138-154, 2024.
[4] R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, New York, NY, USA: Wiley, 1989.
[5] G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, New York, NY, USA: Macmillan, 1941.
[6] J. Stewart, Calculus: Early Transcendentals, 8th ed., Boston, MA, USA: Cengage Learning, 2015.
[7] G. Strang, Linear Algebra and Its Applications, 5th ed., Belmont, CA, USA: Brooks/Cole, 2019.
[8] T. Tao, Analysis I, Oxford, UK: Oxford University Press, 2006.
[9] C. Bishop, Pattern Recognition and Machine Learning, New York, NY, USA: Springer, 2006.
[10] R. S. Sutton and A. G. Barto, Reinforcement Learning: An Introduction, 2nd ed., Cambridge, MA, USA: MIT Press, 2018.
[11] D. C. Montgomery, Design and Analysis of Experiments, 9th ed., Hoboken, NJ, USA: Wiley, 2019.
[12] L. C. Evans, Partial Differential Equations, 2nd ed., Providence, RI, USA: American Mathematical Society, 2010.
[13] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge, UK: Cambridge University Press, 2004.
[14] J. D. Logan, Applied Mathematics, 4th ed., Hoboken, NJ, USA: Wiley, 2013.
[15] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge, UK: Cambridge University Press, 2012.
[16] W. Rudin, Principles of Mathematical Analysis, 3rd ed., New York, NY, USA: McGraw-Hill, 1976.
[17] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, New York, NY, USA: Springer, 2010.
[18] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., New York, NY, USA: Springer, 2006.
[19] D. P. Bertsekas, Dynamic Programming and Optimal Control, 4th ed., Belmont, MA, USA: Athena Scientific, 2017.
[20] R. E. Kalman, "A new approach to linear filtering and prediction problems," Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45, 1960.
[21] J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton, NJ, USA: Princeton University Press, 1944.
[22] A. N. Kolmogorov, "Foundations of the theory of probability," Mathematical Reviews, vol. 1, no. 1, pp. 1–5, 1933.
[23] E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge, UK: Cambridge University Press, 2003.
[24] J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed., Upper Saddle River, NJ, USA: Prentice Hall, 2004.
[25] C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948.
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