Drug Distribution Cost Optimization with Vogel, Russel, and Northwest Corner Approaches

Authors

  • Miranthy Pramita Ningtyas Telkom University
  • Amalia Nur Alifah Telkom University
  • Helisyah Nur Fadhilah Sepuluh Nopember of Institute Technology

DOI:

https://doi.org/10.32938/jpm.v7i1.9501

Keywords:

VAM, RAM, NWC, Steppingstone, MODI

Abstract

The increase in annual turnover in a drug distribution company reflects positive growth but is often accompanied by a significant increase in operating costs that can reduce profit margins if not managed efficiently. This study aims to optimize distribution costs using a transportation method approach by comparing three initial solution methods, namely Vogel's Approximation Method (VAM), Russell Approximation Method (RAM), and Northwest Corner Method (NWC). The study was conducted at a drug distribution company with three central warehouses serving four distribution branches, based on distribution data for December 2024, which was arranged in the form of a transportation table. From the calculation results, the VAM method produced the lowest total distribution cost of IDR23,426,407. Evaluation of this solution was carried out using the Steppingstone method and the Modified Distribution Method (MODI) to determine whether the solution was optimal. The evaluation results show that all opportunity cost values ​​are positive, which means that no additional iterations or re-allocations are required so that the solution from the VAM method can be stated as an optimal solution. The novelty of this study lies in the integration of three initial solution methods with two optimal solution methods in one drug distribution case study, which has not been widely discussed in an integrated manner in previous studies. These findings provide strategic contributions to more precise and efficient logistics decision-making and support the sustainable operational growth of pharmaceutical distribution companies.

References

Abdelati, H. M. (2024). A new approach for finding an initial basic feasible solution to a transportation problem. Journal of Advanced Engineering Trends, 43(1), 77–85. https://doi.org/10.21608/jaet.2022.133374.1151

Agboola, O. O., Obembe, D. T., & Agarana, M. C. (2025). Application of Swarm Intelligence in Transportation System Optimisation. WSEAS Transactions on Information Science and Applications, 22, 74–82. https://doi.org/10.37394/23209.2025.22.8

Ahmed, S. S., Paul, G., Ramatu, A., Nafisat, S. B., & Usman, N. M. (2023). Application of Transportation Problem Models on Cattle Business in Niger State Using Russell’s Approximation Method. Journal of Applied Sciences and Environmental Management, 27(9), 1989–1994. https://doi.org/10.4314/jasem.v27i9.14

Al Khauzar Victorio, R., Yuliati, N., & Tondang, I. S. (2023). Improving the Optimization of Date Distribution Through Cost Eficiency using the Transportation Method Approach: Case Study PT. XYZ. International Journal of Multidisciplinary Research and Literature IJOMRAL, 2(5), 481–600. https://doi.org/10.53067/ijomral.v2i5

Amaliah, B., Fatichah, C., & Suryani, E. (2022). A Supply Selection Method for better Feasible Solution of balanced transportation problem. Expert Systems with Applications, 203. https://doi.org/10.1016/j.eswa.2022.117399

Annisa, & Mardiningsih. (2021). Analysis of Transportation Method in Optimization of Distribution Cost Using Stepping Stone Method and Modified Distribution. Journal of Mathematics Technology and Education, 1(1), 103–112. https://doi.org/10.32734/jomte.v1i1.7561

Castaneda, J., Ghorbani, E., Ammouriova, M., Panadero, J., & Juan, A. A. (2022). Optimizing Transport Logistics under Uncertainty with Simheuristics: Concepts, Review and Trends. Logistics, 6(3). https://doi.org/10.3390/logistics6030042

Drs. Siswanto, M. Sc. (2007). Operations Research, Jilid 1. Penerbit Erlangga.

Goodarzian, F., Kumar, V., & Ghasemi, P. (2021). A set of efficient heuristics and meta-heuristics to solve a multi-objective pharmaceutical supply chain network. Computers and Industrial Engineering, 158. https://doi.org/10.1016/j.cie.2021.107389

Handayani, S., Sari, R. F., & Aprilia, R. (2020). Optimization of Delivery Costs using Vogel’s Approximation Method (VAM) and Stepping Stone Method. In JMSCOWA (Vol. 1, Issue 1). https://pcijournal.org/index.php/jmscowa/article/download/5/1

Hidayat, R., & Saleh, Mgs. I. (2020). The Importance of Inventory Management in Pharmaceutical Practice. Open Access Indonesia Journal of Social Sciences, 3(1), 1–9. https://doi.org/10.37275/oaijss.v3i1.22

Hussein, H. A., & Shiker, M. A. K. (2020). A Modification to Vogel’s Approximation Method to Solve Transportation Problems. Journal of Physics: Conference Series, 1591(1). https://doi.org/10.1088/1742-6596/1591/1/012029

Kankarofi, R. H., Ayakubu, U., Sulaiman, I. M., Mamat, M., Sukono, & Saputra, M. P. A. (2021). Fertilizer Transportation Problem Using Vogel Approximation Method. IOP Conference Series: Materials Science and Engineering, 1115(1), 012005. https://doi.org/10.1088/1757-899x/1115/1/012005

Latunde, T., Richard, J. O., Esan, O. O., & Dare, D. D. (2021). Optimal Value and Post Optimal Solution in a Transportation Problem. 3(3), 335–348. https://doi.org/10.12150/jnma.2021.335

Lim, H., & Rokhim, R. (2020). Factors affecting profitability of pharmaceutical company: an Indonesian evidence. Journal of Economic Studies, 48(5), 981–995. https://doi.org/10.1108/JES-01-2020-0021

Liu, S. (2022). Deconstruction of Road Logistics Transportation Cost Management Evaluation Based on Optimal Solution of Linear Programming. Mathematical Problems in Engineering, 2022. https://doi.org/10.1155/2022/5784053

M, M., T, M., & M, Dr. S. (2021). Comparative Study of Russel’s Approximation Method and Heuristic Method. International Journal of Creative Research Thoughts (IJCRT), 9(12). https://ijcrt.org/papers/IJCRT2112386.pdf

Niluminda, O., Niluminda, K. P. O., & Ekanayake, E. M. U. S. B. (n.d.). Modified Vogel’s Approximation Method to Solve Both Balanced and Unbalanced Transportation Problems. 2023. https://doi.org/10.5281/zenodo.10206936

Pratihar, J., Kumar, R., Edalatpanah, S. A., & Dey, A. (2021). Modified Vogel’s approximation method for transportation problem under uncertain environment. Complex and Intelligent Systems, 7(1), 29–40. https://doi.org/10.1007/s40747-020-00153-4

Pratiwi, N., & Siregar, R. (2021). Optimization of Crude Palm Oil Distribution Costs in PT. Perkebunan Nusantara III Using Vogel’s Approximation Method, Russel Approximation Method and Stepping Stone Method. In Journal of Mathematics Technology and Education (Vol. 1, Issue 1). https://doi.org/https://doi.org/10.32734/jomte.v1i1.6866

Putcha, C., Banerjee, A., Datta, D., Rivera Perez, I., Chan, B., & Pandey, P. (n.d.). Optimal Value Determination Using Traditional and Newly Developed Method Using Initial Basic Feasible Solution of North West & Russell Method. International Journal of Engineering Research and General Science, 10(4). www.ijergs.org

Ramakrishna, M., & Ashok, G. (2022). The Journal of Multidisciplinary Research (TJMDR) An initial basic feasible transportation solution based on the north-west corner rule programming in c. www.saap.org.in

Roschyntawati, A., Pujiwat, R., Upahita, D. P., Hendra, Y. N. R., Fajar, R., Saputro, M. I. A., & Kismanto, A. (2023). Application of North West Corner, least cost and Vogel’s approximation method for optimizing transportation cost of biodiesel between biofuel company and blending terminal. AIP Conference Proceedings, 2646. https://doi.org/10.1063/5.0113524

Stopka, O., Gross, P., Pečman, J., Hanzl, J., Stopková, M., & Jurkovič, M. (2022). Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study. Technologies, 10(4). https://doi.org/10.3390/technologies10040084

Sumathi, P., & Sathiabama, C. V. (2020). Minimizing the cost using an inventive proposal in transportation problems. IOP Conference Series: Materials Science and Engineering, 912(6). https://doi.org/10.1088/1757-899X/912/6/062065

Swaroop, K., S.B, B., Prasanthi, S., Goudanavar, P., Naveen, N. R., Sreeharsha, N., Meravanige, G., & Asif, A. H. (2025). Pro Transferosome Loaded Gefitinib Novel Tablet for pulmonary drug delivery: Optimization and characterization. Journal of the Indian Chemical Society, 102(1). https://doi.org/10.1016/j.jics.2024.101520

Szkutnik-Rogoż, J., & Małachowski, J. (2023). Optimization programming tools supporting supply chain management. Bulletin of the Polish Academy of Sciences: Technical Sciences, 71(3). https://doi.org/10.24425/bpasts.2023.145570

Wireko, F. A., Mensah, I. D. K., Aborhey, E. N. A., Appiah, S. A., Sebil, C., & Ackora-Prah, J. (2025). The maximum range method for finding initial basic feasible solution for transportation problems. Results in Control and Optimization, 19. https://doi.org/10.1016/j.rico.2025.100551

Yousefi Sarmad, M., Pishvaee, M. S., Jahani, H., Khaksar, S. M. S., & Ivanov, D. (2023). Integrated planning for a global pharmaceutical supply chain: an ambidexterity perspective. Annals of Operations Research. https://doi.org/10.1007/s10479-023-05554-5

Zabiba, M. S. M., Al-Dallal, H. A. H., Hashim, K. H., Mahdi, M. M., & Shiker, M. A. K. (2023). A New Technique to Solve the Maximization of the Transportation Problems. AIP Conference Proceedings, 2414. https://doi.org/10.1063/5.0114806

Downloads

Published

2025-07-31