Minimize shipping costs from multi-warehouse to multi-outlet with VAM and MODI
DOI:
https://doi.org/10.35335/mandiri.v14i3.506Keywords:
Distribution Cost Optimization, Modified Distribution Method (MODI), Operations Research, Transportation Problem, Vogel's Approximation Method (VAM)Abstract
Distribution costs are a dominant component in logistics operations, especially in multi-warehouse to multi-outlet delivery schemes involving variations in supply capacity, demand, and route costs. This study aims to minimize shipping costs by modeling the problem as a Transportation Problem (TP), generating an initial solution using Vogel's Approximation Method (VAM), and ensuring an optimal solution using the Modified Distribution Method (MODI). The case study was conducted in one planning period with input data in the form of a matrix of shipping costs per unit, supply capacity per warehouse, and demand per outlet (balanced condition). The results show that the baseline distribution cost is 4,898 (thousand IDR), while the initial VAM solution reduces the cost to 3,777 (thousand IDR). After optimality testing and improvements using MODI, the minimum cost is 3,605 (thousand IDR), with an additional improvement of 172 (thousand IDR) from the VAM solution. Compared to the baseline, the optimal solution provides savings of 1,293 (thousand IDR) or 26.40%, without violating the supply-demand constraint. These findings confirm that the VAM-MODI flow is effective as a fast, audit-friendly, and applicable end-to-end procedure for the preparation of minimum cost delivery plans in logistics companies.
References
Ackora-Prah, J., Acheson, V., Owusu-Ansah, E., & Nkrumah, S. K. (2023). A proposed method for finding initial solutions to transportation problems. Pakistan Journal of Statistics and Operation Research, 63–75. https://doi.org/10.18187/pjsor.v19i1.4196
Adianta, A., Saif, N., & Mussafi, M. (2024). Optimization of Transportation Distribution Costs Using Improved Vogel ’ s Approximation Method ( IVAM ) ( Case Study : PT . Sinar Putra Pertam ). 5(2), 417–428. https://doi.org/10.22441/ijiem.v5i2.27288
Amaliah, B., Fatichah, C., & Suryani, E. (2022). A supply selection method for better feasible solution of balanced transportation problem. Expert Systems with Applications, 203, 117399. https://doi.org/10.1016/j.eswa.2022.117399
Baller, R., Fontaine, P., Minner, S., & Lai, Z. (2022). Optimizing automotive inbound logistics: A mixed-integer linear programming approach. Transportation Research Part E: Logistics and Transportation Review, 163, 102734. https://doi.org/10.1016/j.tre.2022.102734
Carrabs, F., Cerulli, R., D’Ambrosio, C., Della Croce, F., & Gentili, M. (2021). An improved heuristic approach for the interval immune transportation problem. Omega, 104, 102492. https://doi.org/10.1016/j.omega.2021.102492
Correia, I., & Melo, T. (2022). Distribution network redesign under flexible conditions for short-term location planning. Computers & Industrial Engineering, 174, 108747. https://doi.org/10.1016/j.cie.2022.108747
Ghasemi, E., Lehoux, N., & Rönnqvist, M. (2024). A multi-level production-inventory-distribution system under mixed make to stock, make to order, and vendor managed inventory strategies: An application in the pulp and paper industry. International Journal of Production Economics, 271, 109201. https://doi.org/10.1016/j.ijpe.2024.109201
Guo, Y., Chen, R., Boulaksil, Y., & Allaoui, H. (2025). Modelling and solving sustainable supply chain network design based on graph autoencoder clustering algorithm. International Journal of Production Research, 63(24), 10000–10026. https://doi.org/10.1080/00207543.2025.2542506
Ho, G. T. S., Tang, V., Tong, P. H., & Tam, M. M. F. (2025). Demand-driven storage allocation for optimizing order picking processes. Expert Systems with Applications, 272, 126812. https://doi.org/10.1016/j.eswa.2025.126812
Hyder, J., & Hassini, E. (2025). Optimizing warehouse space allocation to maximize profit in the postal industry. Transportation Research Part E: Logistics and Transportation Review, 195, 103924. https://doi.org/10.1016/j.tre.2024.103924
Jiu, S., Wang, D., & Ma, Z. (2024). Benders decomposition for robust distribution network design and operations in online retailing. European Journal of Operational Research, 315(3), 1069–1082. https://doi.org/10.1016/j.ejor.2024.01.046
Madani, B., Saihi, A., & Abdelfatah, A. (2024). A systematic review of sustainable supply chain network design: Optimization approaches and research trends. Sustainability, 16(8), 3226. https://doi.org/10.3390/su16083226
Pratihar, J., Kumar, R., Edalatpanah, S. A., & Dey, A. (2021). Modified Vogel’s approximation method for transportation problem under uncertain environment. Complex & Intelligent Systems, 7(1), 29–40. https://doi.org/10.1007/s40747-020-00153-4
Riandari, F. (2025). A Unified Mathematical Framework for NWC , MODI , and Stepping Stone as Foundational Models in Optimal Transport Theory. Teknik Informatika C.I.T Medicom, 17(4), 183–195.
Riandari, F., & Sihotang, H. T. (2025). Distribution cost optimization: Comparison of NWC, MODI, and Stepping Stone methods in transportation problems. International Journal of Basic and Applied Science, 14(2), 85–96. https://doi.org/10.35335/ijobas.v14i2.688
Sepehri, A., Tirkolaee, E. B., Simic, V., & Ali, S. S. (2024). Designing a reliable-sustainable supply chain network: adaptive m-objective ε-constraint method. Annals of Operations Research, 1–32. https://doi.org/10.1007/s10479-024-05961-2
Shivani, & Rani, D. (2024). An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems. Soft Computing, 28(17), 9711–9734. https://doi.org/10.1007/s00500-024-09812-x
Wang, X., Zhan, L., Zhang, Y., Fei, T., & Tseng, M.-L. (2024). Environmental cold chain distribution center location model in the semiconductor supply chain: A hybrid arithmetic whale optimization algorithm. Computers & Industrial Engineering, 187, 109773.
Wireko, F. A., Dennis, I., Mensah, K., Nii, E., Aborhey, A., Appiah, S. A., Sebil, C., & Ackora-prah, J. (2025). Results in Control and Optimization The maximum range method for finding initial basic feasible solution for transportation problems. Results in Control and Optimization, 19(April), 100551. https://doi.org/10.1016/j.rico.2025.100551
Zehtabian, S. (2024). A fair multi-commodity two-echelon distribution problem. EURO Journal on Transportation and Logistics, 13, 100126. https://doi.org/10.1016/j.ejtl.2024.100126
Zhang, X., Chen, H., Hao, Y., & Yuan, X. (2024). A low-carbon route optimization method for cold chain logistics considering traffic status in China. Computers & Industrial Engineering, 193, 110304. https://doi.org/10.1016/j.cie.2024.110304
Zhang, Y., Lin, W.-H., Huang, M., & Hu, X. (2021). Multi-warehouse package consolidation for split orders in online retailing. European Journal of Operational Research, 289(3), 1040–1055. https://doi.org/10.1016/j.ejor.2019.07.004
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