Solving MDVRP Using Two-Step Clustering: A Case Study of Pharmaceutical Distribution in Tehran

Document Type : Research Paper

Authors

1 Department of Industrial Engineering & Management Systems, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran, Iran

2 Department of Industrial Engineering & Management Systems, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran, Iran

3 Industrial Engineering Department, Sharif University of Technology, 11155-1639 Tehran, Iran

Abstract

The healthcare sector has recently encountered significant challenges, including limited funding and intense competition. These issues have adversely impacted hospital supply chains, resulting in budget cuts, staffing shortages, and logistical difficulties. This study introduces a novel two-step clustering approach to address the multi-depot vehicle routing problem (MDVRP) in healthcare logistics, specifically focusing on optimizing the delivery of pharmaceutical supplies to hospital pharmacies in Tehran. The method begins with the K-means algorithm to identify optimal distribution centers in the first step. In the second step, K-means clustering, incorporating vehicle capacity and demand values, is applied to each distribution center to allocate demand points for each vehicle. The vehicle routes are then determined by solving the traveling salesman problem. By optimizing the number of distribution centers using the silhouette score, which resulted in a score of 0.3567 for four centers, the study shows that deploying five vehicles from four strategically located centers can meet the needs of Tehran hospitals with a total travel distance of 119.68 km. A comparative analysis with two alternative methods reveals that the proposed approach offers a 14% improvement in minimizing the total travel distance. This method not only helps identify optimal locations for new distribution centers but also develops efficient routing plans for pharmaceutical distribution, ultimately reducing costs and improving service quality within healthcare logistics.

Keywords

Main Subjects

References

[1] J.K. Jain, S. Banerjee, J. Jain, G.S. Dangayach, G. Agarwal, Supply Chain Management: Literature Review and Some Issues, 2010. https://www.researchgate.net/publication/268361779.
[2] M. EL Midaoui, M. Qbadou, K. Mansouri, A novel approach of smart logistics for the health-care sector using genetic algorithm, Advances in Science, Technology and Engineering Systems 5 (2020) 1143–1152. https://doi.org/10.25046/aj0506138.
[3] A. Ghaffar, A. Rashidian, W. Khan, M. Tariq, Verbalising importance of supply chain management in access to health services, J Pharm Policy Pract 14 (2021). https://doi.org/10.1186/s40545-021-00352-5.
[4] M. Arora, Y. Gigras, Importance of Supply Chain Management in Healthcare of Third World Countries, International Journal of Supply and Operations Management 5 (2018) 101–106. www.ijsom.com.
[5] Sathyanarayanan S, K.S. Joseph, S.K.V. Jayakumar, A hybrid population seeding technique based Genetic Algorithm for stochastic Multiple Depot Vehicle Routing Problem, in: 2015 International Conference on Computing and Communications Technologies (ICCCT), IEEE, 2015: pp. 119–127. https://doi.org/10.1109/ICCCT2.2015.7292731.
[6] S. Zhang, W. Zhang, Y. Gajpal, S.S. Appadoo, Ant Colony Algorithm for Routing Alternate Fuel Vehicles in Multi-depot Vehicle Routing Problem, in: 2019: pp. 251–260. https://doi.org/10.1007/978-981-13-0860-4_19.
[7] S. Khoukhi, C. Bojji, Y. Bensouda, A review of medical distribution logistics in pharmaceutical supply chain, 2019.
[8] B. Bouziyane, B. Dkhissi, M. Cherkaoui, Multiobjective optimization in delivering pharmaceutical products with disrupted vehicle routing problem, International Journal of Industrial Engineering Computations 11 (2020) 299–316. https://doi.org/10.5267/j.ijiec.2019.7.003.
[9] C. Oliveira, J. Pereira, E. Santos, T.M. Lima, P.D. Gaspar, Optimization of the COVID-19 Vaccine Distribution Route Using the Vehicle Routing Problem with Time Windows Model and Capacity Constraint, Applied System Innovation 6 (2023). https://doi.org/10.3390/asi6010017.
[10]      M. de Magalh, J. Pinho de Sousa, Dynamic VRP in pharmaceutical distribution-a case study, 2006.
[11]      A. Perwira Redi, F. Rohmatul Maula, F. Kumari, N. Utami Syaveyenda, N. Ruswandi, A. Uswatun Khasanah, A. Chandra Kurniawan, J. Teuku Nyak Arief, K. Kby Lama, K. Jakarta Se latan, Simulated annealing algorithm for solving the capacitated vehicle routing problem: a case study of pharmaceutical distribution, Jurnal Sistem Dan Manajemen Industri 4 (2020) 41–49. https://doi.org/10.30656/jsmi.v4i1.2115.
[12]      E. Köse, B. Düzenlİ, S. Çakmak, D. Vural, Medicine distribution problem between pharmacy warehouse and pharmacies, Sādhanā 47 (2022) 171. https://doi.org/10.1007/s12046-022-01938-8.
[13]      Aji Thomas, Sushma Duraphe, Arvind Gupta, Harnessing the Power of Metaheuristic Algorithms for Optimal Logistics Management in Epidemic Response, International Journal of Engineering Technology and Management Sciences 7 (2023) 627–633. https://doi.org/10.46647/ijetms.2023.v07i04.087.
[14]      K.S. Harms, Single-Depot Vehicle Routing Problem for Home Delivery of Single-Depot Vehicle Routing Problem for Home Delivery of Pharmaceutical Products Pharmaceutical Products, 2013. https://scholarworks.wmich.edu/masters_theses.
[15]      C.-C. Chiou, W.-H. Ouyang, T.-Y. Lin, An Empirical Study of Vehicle Routing Problem with Clustering Approach for Medical Consumable Materials Delivery, in: Research and Developments in Engineering Research Vol. 1, B P International (a part of SCIENCEDOMAIN International), 2023: pp. 54–66. https://doi.org/10.9734/bpi/rader/v1/9716F.
[16]      G. Pérez Lechuga, Optimal logistics strategy to distribute medicines in clinics and hospitals, J Math Ind 8 (2018). https://doi.org/10.1186/s13362-018-0044-5.
[17]      Y. Ji, Optimal scheduling in home health care pharmacy-hospital-patient’s vehicle routing problem, in: ACM International Conference Proceeding Series, Association for Computing Machinery, 2019. https://doi.org/10.1145/3331453.3361310.
[18]      X. Shao, S. Lu, Optimizing Dual Distribution Scheme in Pharmaceutical Cold Chain for Cost and Carbon Emissions Reduction, Applied Sciences 13 (2023) 5524. https://doi.org/10.3390/app13095524.
[19]      M. Cieśla, B. Mrówczyńska, Problem of medicines distribution on the example of pharmaceutical wholesale, in: Mechanisms and Machine Science, Kluwer Academic Publishers, 2017: pp. 51–65. https://doi.org/10.1007/978-3-319-39020-8_4.
[20]      N. Mostafa, A. Eltawil, Solving the Heterogeneous Capacitated Vehicle Routing Problem using K-Means Clustering and Valid Inequalities, in: Rabat, Morocco, 2017.
[21]      A.N. Alfiyatin, W.F. Mahmudy, Y.P. Anggodo, K-means clustering and genetic algorithm to solve vehicle routing problem with time windows problem, Indonesian Journal of Electrical Engineering and Computer Science 11 (2018) 462–468. https://doi.org/10.11591/ijeecs.v11.i2.pp462-468.
[22]      H. Moussa, Using Recursive KMeans and Dijkstra Algorithm to Solve CVRP, ArXiv (2021).
[23]      R. He, W. Xu, J. Sun, B. Zu, Balanced K-means algorithm for partitioning areas in large-scale vehicle routing problem, in: 3rd International Symposium on Intelligent Information Technology Application, IITA 2009, 2009: pp. 87–90. https://doi.org/10.1109/IITA.2009.307.
[24]      J.R. Montoya-Torres, J. López Franco, S. Nieto Isaza, H. Felizzola Jiménez, N. Herazo-Padilla, A literature review on the vehicle routing problem with multiple depots, Comput Ind Eng 79 (2015) 115–129. https://doi.org/10.1016/j.cie.2014.10.029.
[25]      S.K. Routroy, S. Yadav, Vehicle routing problem: recent literature review of its variants, 2018.
[26]      M. El Midaoui, M. Qbadou, K. Mansouri, Logistics chain optimization and scheduling of hospital pharmacy drugs using genetic algorithms: Morocco case, International Journal of Web-Based Learning and Teaching Technologies 16 (2021) 54–64. https://doi.org/10.4018/IJWLTT.2021030104.
[27]      A. Burmakova, D. Kalibatienė, Applying Fuzzy Inference and Machine Learning Methods for Prediction with a Small Dataset: A Case Study for Predicting the Consequences of Oil Spills on a Ground Environment, Applied Sciences (Switzerland) 12 (2022). https://doi.org/10.3390/app12168252.
[28]      E.W. Steyerberg, M.J.C. Eijkemans, F.E. Harrell, J. Dik, F. Habbema, Prognostic modelling with logistic regression analysis: a comparison of selection and estimation methods in small data sets, 2000.
[29]      J.M. Lichtenberg, Simple Regression Models, 2016.
[30]      S. Rekabi, Z. Sazvar, F. Goodarzian, A machine learning model with linear and quadratic regression for designing pharmaceutical supply chains with soft time windows and perishable products, Decision Analytics Journal 9 (2023). https://doi.org/10.1016/j.dajour.2023.100325.
Advances in Industrial Engineering
Volume 58, Issue 1
June 2024
Pages 85-102

Files

Share

How to cite

Statistics