DEVELOPING SUPPLY CHAIN NETWORK WITH PIECEWISE LINEAR TRANSPORTATION COST FOR A SMALL-AND-MEDIUM ENTERPRISE (SME) IN CILEGON

Authors

  • Bobby Kurniawan Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Ade Irman Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Akbar Gunawan Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Ani Umyati Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Evi Febianti Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Nuraida Wahyuni Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Putro Ferro Ferdinant Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Ratna Ekawati Department of Industrial Engineering, Sultan Ageng Tirtayasa University, Indonesia
  • Fellek Getu Tadesse School of Mechanical and Industrial Engineering, Ethiopian Institute of Technology-Mekelle, Ethiopia

DOI:

https://doi.org/10.29122/mipi.v15i2.4819

Keywords:

Supply chain network, piecewise linear function, convex-combination method, small and medium enterprise

Abstract

This study proposed a supply chain network for determining suppliers’ location in which the transportation costs are a piecewise linear function. The supply chain network consists of a production facility, suppliers, and customers. These types of costs are found in the fields of transportation, logistics, and purchasing discount. First, the supply chain network is formulated as the mixed-integer non-linear programming (MINLP) because piecewise linear transportation cost makes the model non-linear. Then, the model is transformed into a mixed-integer programming (MIP) model using the convex-combination method to overcome this nonlinearity. The model was used for solving the problem faced by a small and medium enterprise (SME) in Cilegon. The MIP was solved using the CPLEX software. Sensitivity analysis was carried to provide the SME with several alternatives in handling the suppliers’ location problem

References

M. Albareda-Sambola, E. Fernández and F. Saldanha-da-Gama, "The facility location problem with Bernoulli demands," Omega, vol. 39, p. 335–345, 2011.

A. Diabat, "A capacitated facility location and inventory management problem with single sourcing," Optimization Letters, vol. 10, p. 1577–1592, 2016.

X. Qi, "Order splitting with multiple capacitated suppliers," European Journal of Operational Research, vol. 178, p. 421–432, 2007.

S. Kameshwaran and Y. Narahari, "Non-convex piecewise linear knapsack problems," European Journal of Operational Research, vol. 192, p. 56–68, 2009.

S. Septiandre and N. Siswanto, "Penentuan Lokasi Gudang Penyangga Regional PT. “X” Wilayah Jawa Timur," Jurnal Studi Manajemen dan Bisnis, vol. 3, p. 184–194, 2016.

A. Montoya, M. C. Vélez–Gallego and J. G. Villegas, "Multi-product capacitated facility location problem with general production and building costs," NETNOMICS: Economic Research and Electronic Networking, vol. 17, p. 47–70, 2016.

G. R. Mauri, F. L. Biajoli, R. L. Rabello, A. A. Chaves, G. M. Ribeiro and L. A. N. Lorena, "Hybrid metaheuristics to solve a multi-product two-stage capacitated facility location problem," International Transactions in Operational Research, 2020.

X. Tang and J. Zhang, "The multi-objective capacitated facility location problem for green logistics," in 2015 4th International Conference on Advanced Logistics and Transport (ICALT), 2015.

A. Estrada-Moreno, A. Ferrer, A. A. Juan, A. Bagirov and J. Panadero, "A biased-randomised algorithm for the capacitated facility location problem with soft constraints," Journal of the Operational Research Society, vol. 71, p. 1799–1815, 2020.

H. Golpîra, "Optimal integration of the facility location problem into the multi-project multi-supplier multi-resource Construction Supply Chain network design under the vendor managed inventory strategy," Expert Systems with Applications, vol. 139, p. 112841, 2020.

M. Salahi and A. Jamalian, "Multi-Source Capacitated Plant Location Problem with Customer and Supplier Matching," Computational Mathematics and Modeling, vol. 26, p. 273–283, 2015.

L.-Y. Wu, X.-S. Zhang and J.-L. Zhang, "Capacitated facility location problem with general setup cost," Computers & Operations Research, vol. 33, p. 1226–1241, 2006.

Á. Corberán, M. Landete, J. Peiró and F. Saldanha-da-Gama, "The facility location problem with capacity transfers," Transportation Research Part E: Logistics and Transportation Review, vol. 138, p. 101943, 2020.

A. Diabat and E. Theodorou, "A location–inventory supply chain problem: Reformulation and piecewise linearization," Computers & Industrial Engineering, vol. 90, p. 381–389, 2015.

P. P. Repoussis and E. J. Alenezy, "Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm," Advances in Operations Research, vol. 2020, p. 5239176, 2020.

F. J. F. Silva and D. S. d. l. Figuera, "A capacitated facility location problem with constrained backlogging probabilities," International Journal of Production Research, vol. 45, p. 5117–5134, 2007.

K. Holmberg, "Solving the staircase cost facility location problem with decomposition and piecewise linearization," European Journal of Operational Research, vol. 75, p. 41–61, 1994.

T. R. L. Christensen, K. A. Andersen and A. Klose, "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, vol. 47, p. 428–438, 2013.

C. Xin, X. Liu, Y. Deng and Q. Lang, "An optimization algorithm based on text clustering for warehouse storage location allocation," in 2019 1st International Conference on Industrial Artificial Intelligence (IAI), 2019.

A. B. Keha, I. R. d. Farias and G. L. Nemhauser, "A Branch-and-Cut Algorithm without Binary Variables for Nonconvex Piecewise Linear Optimization," Operations Research, vol. 54, p. 847–858, 2006.

M. T. Ramos and J. Sáez, "Solving capacitated facility location problems by Fenchel cutting planes," Journal of the Operational Research Society, vol. 56, p. 297–306, 2005.

J. P. Vielma, S. Ahmed and G. Nemhauser, "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, vol. 58, p. 303–315, 2009.

Downloads

Published

13-09-2023

How to Cite

Kurniawan, B., Irman, A., Gunawan, A., Umyati, A., Febianti, E., Wahyuni, N., … Tadesse, F. G. (2023). DEVELOPING SUPPLY CHAIN NETWORK WITH PIECEWISE LINEAR TRANSPORTATION COST FOR A SMALL-AND-MEDIUM ENTERPRISE (SME) IN CILEGON. Majalah Ilmiah Pengkajian Industri; Journal of Industrial Research and Innovation, 15(2), 97–104. https://doi.org/10.29122/mipi.v15i2.4819

Issue

Vol. 15 No. 2 (2021): Majalah Ilmiah Pengkajian Industri; Journal of Industrial Research and Innovation

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Open Access Policy

MIPI provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.

MIPI by BRIN is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at http://ejurnal.bppt.go.id/index.php/MIPI