Model of Flexible Periodic Vehicle Routing Problem-Service Choice Considering Inventory Status
DOI:
https://doi.org/10.22219/JTIUMM.Vol22.No1.125-137Keywords:
Vehicle routing, Flexible Periodic , Branch-and-bound, inventory, FPVRPAbstract
Vehicle routing problems and inventory problems need to be integrated in order to improve performance. This research discusses the determination of vehicle routes for product delivery with periodic delivery times that are released at any time depending on the inventory status. A mixed-integer linear programming model in determining periodic flexible visiting vehicles' route considering inventory is proposed to solve this problem. This model also accommodates time window constraints, retailer warehouse capacity. The search for solutions was carried out using the branch-and-bound method with the help of Lingo 18.0. The mathematical model testing result saves shipping costs and inventory costs. In addition, the developing mathematical model offers the flexibility of visiting depending on the inventory status of the consumer. The sensitivity analysis of the model results in the vehicle capacity influence the total cost and routes formed.
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References
J.-F. Cordeau, G. Laporte, M. W. P. Savelsbergh, and D. Vigo, "Chapter 6 Vehicle Routing," in Handbooks in Operations Research and Management Science. vol. 14, C. Barnhart and G. Laporte, Eds., ed: Elsevier, 2007, pp. 367-428. https://doi.org/10.1016/S0927-0507(06)14006-2.
G. B. Dantzig and J. H. Ramser, "The Truck Dispatching Problem," Management Science, vol. 6, pp. 80-91, 1959. https://doi.org/10.1287/mnsc.6.1.80.
B. Eksioglu, A. V. Vural, and A. Reisman, "The vehicle routing problem: A taxonomic review," Computers & Industrial Engineering, vol. 57, pp. 1472-1483, 2009. https://doi.org/10.1016/j.cie.2009.05.009.
R. Lahyani, M. Khemakhem, and F. Semet, "Rich vehicle routing problems: From a taxonomy to a definition," European Journal of Operational Research, vol. 241, pp. 1-14, 2015. https://doi.org/10.1016/j.ejor.2014.07.048.
F. Alfredo Tang Montané and R. D. Galvão, "A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service," Computers & Operations Research, vol. 33, pp. 595-619, 2006. https://doi.org/10.1016/j.cor.2004.07.009.
A. Subramanian, L. M. A. Drummond, C. Bentes, L. S. Ochi, and R. Farias, "A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery," Computers & Operations Research, vol. 37, pp. 1899-1911, 2010. https://doi.org/10.1016/j.cor.2009.10.011.
C. Lagos, G. Guerrero, E. Cabrera, A. Moltedo, F. Johnson, and F. Paredes, "An improved Particle Swarm Optimization Algorithm for the VRP with Simultaneous Pickup and Delivery and Time Windows," IEEE Latin America Transactions, vol. 16, pp. 1732-1740, 2018. https://doi.org/10.1109/TLA.2018.8444393.
D. Gulczynski, B. Golden, and E. Wasil, "The split delivery vehicle routing problem with minimum delivery amounts," Transportation Research Part E: Logistics and Transportation Review, vol. 46, pp. 612-626, 2010. https://doi.org/10.1016/j.tre.2009.12.007.
M. Casazza, A. Ceselli, and R. Wolfler Calvo, "A branch and price approach for the Split Pickup and Split Delivery VRP," Electronic Notes in Discrete Mathematics, vol. 69, pp. 189-196, 2018. https://doi.org/10.1016/j.endm.2018.07.025.
Y. Dumas, J. Desrosiers, and F. Soumis, "The pickup and delivery problem with time windows," European Journal of Operational Research, vol. 54, pp. 7-22, 1991. https://doi.org/10.1016/0377-2217(91)90319-Q.
D. Favaretto, E. Moretti, and P. Pellegrini, "Ant colony system for a VRP with multiple time windows and multiple visits," Journal of Interdisciplinary Mathematics, vol. 10, pp. 263-284, 2007. https://doi.org/10.1080/09720502.2007.10700491.
P. Kirci, "On the Performance of Tabu Search Algorithm for the Vehicle Routing Problem with Time Windows," in 2016 IEEE 4th International Conference on Future Internet of Things and Cloud Workshops (FiCloudW), 2016, pp. 351-354. https://doi.org/10.1109/W-FiCloud.2016.77.
D. A. P. Putri, "Vehicle Routing Problem Dengan Time Window Untuk Multiple Product Dan Multiple Route Menggunakan Algoritma Sequential Insertion," Jurnal Teknik Industri, vol. 17, pp. 22-30, 2017. https://doi.org/10.22219/JTIUMM.Vol17.No1.22-30.
F. A. Gunadi, D. Lesmono, and K. Aritonang, "A Routing Model for Hybrid Hub-and-Spoke With Time Windows," Jurnal Teknik Industri, vol. 21, pp. 22-33, 2020. https://doi.org/10.22219/JTIUMM.Vol21.No1.22-33.
R. Russell and W. Igo, "An assignment routing problem," Networks, vol. 9, pp. 1-17, 1979. https://doi.org/10.1002/net.3230090102.
N. Christofides and J. E. Beasley, "The period routing problem," Networks, vol. 14, pp. 237-256, 1984. https://doi.org/10.1002/net.3230140205.
M. W. Carter, J. M. Farvolden, G. Laporte, and J. Xu, "Solving An Integrated Logistics Problem Arising In Grocery Distribution," INFOR: Information Systems and Operational Research, vol. 34, pp. 290-306, 1996. https://doi.org/10.1080/03155986.1996.11732310.
E. J. Beltrami and L. D. Bodin, "Networks and vehicle routing for municipal waste collection," Networks, vol. 4, pp. 65-94, 1974.
E. Hadjiconstantinou and R. Baldacci, "A multi-depot period vehicle routing problem arising in the utilities sector," Journal of the Operational Research Society, vol. 49, pp. 1239-1248, 1998. https://doi.org/10.1057/palgrave.jors.2600641.
J. Alegre, M. Laguna, and J. Pacheco, "Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts," European Journal of Operational Research, vol. 179, pp. 736-746, 2007. https://doi.org/10.1016/j.ejor.2005.03.063.
R. Liu, X. Xie, and T. Garaix, "Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics," Omega, vol. 47, pp. 17-32, 2014. https://doi.org/10.1016/j.omega.2014.03.003.
A. Rusdiansyah and D.-b. Tsao, "An integrated model of the periodic delivery problems for vending-machine supply chains," Journal of Food Engineering, vol. 70, pp. 421-434, 2005. https://doi.org/10.1016/j.jfoodeng.2004.05.073.
E. A. Silver, "An overview of heuristic solution methods," Journal of the Operational Research Society, vol. 55, pp. 936-956, 2004. https://doi.org/10.1057/palgrave.jors.2601758.
S. Pirkwieser and G. R. Raidl, "A variable neighborhood search for the periodic vehicle routing problem with time windows," in Proceedings of the 9th EU/meeting on metaheuristics for logistics and vehicle routing, Troyes, France, 2008, pp. 23-24.
V. C. Hemmelmayr, K. F. Doerner, and R. F. Hartl, "A variable neighborhood search heuristic for periodic routing problems," European Journal of Operational Research, vol. 195, pp. 791-802, 2009. https://doi.org/10.1016/j.ejor.2007.08.048.
P. K. Nguyen, T. G. Crainic, and M. Toulouse, "A hybrid generational genetic algorithm for the periodic vehicle routing problem with time windows," Journal of Heuristics, vol. 20, pp. 383-416, 2014. https://doi.org/10.1007/s10732-014-9244-3.
R. T. Moghaddam, A. M. Zohrevand, and K. Rafiee, "Solving a New Mathematical Model for a Periodic Vehicle Routing Problem by Particle Swarm Optimization," Transportation Research Journal, vol. 2, pp. 77-87, 2012.
D. Aksen, O. Kaya, F. Sibel Salman, and Ö. Tüncel, "An adaptive large neighborhood search algorithm for a selective and periodic inventory routing problem," European Journal of Operational Research, vol. 239, pp. 413-426, 2014. https://doi.org/10.1016/j.ejor.2014.05.043.
L. Trihardani and O. A. Candra Dewi, "Pengembangan Algoritma Hybrid Metaheuristik Untuk Penentuan Rute Pengiriman Produk Perishable," Jurnal Teknik Industri, vol. 18, pp. 191-206, 2017. https://doi.org/10.22219/JTIUMM.Vol18.No2.191-206.
P. M. Francis, K. R. Smilowitz, and M. Tzur, "The period vehicle routing problem and its extensions," in The vehicle routing problem: latest advances and new challenges, ed: Springer, 2008, pp. 73-102. https://doi.org/10.1007/978-0-387-77778-8_4.
T. Vidal, T. G. Crainic, M. Gendreau, N. Lahrichi, and W. Rei, "A Hybrid Genetic Algorithm for Multidepot and Periodic Vehicle Routing Problems," Operations Research, vol. 60, pp. 611-624, 2012. https://doi.org/10.1287/opre.1120.1048.
C. Archetti, E. Fernández, and D. L. Huerta-Muñoz, "The Flexible Periodic Vehicle Routing Problem," Computers & Operations Research, vol. 85, pp. 58-70, 2017. https://doi.org/10.1016/j.cor.2017.03.008.
R. Liu, X. Xie, V. Augusto, and C. Rodriguez, "Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care," European Journal of Operational Research, vol. 230, pp. 475-486, 2013. https://doi.org/10.1016/j.ejor.2013.04.044.
P. Francis, K. Smilowitz, and M. Tzur, "The Period Vehicle Routing Problem with Service Choice," Transportation Science, vol. 40, pp. 439-454, 2006. https://doi.org/10.1287/trsc.1050.0140.
A.-K. Rothenbächer, "Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures," Transportation Science, vol. 53, pp. 850-866, 2019. https://doi.org/10.1287/trsc.2018.0855.
C. Archetti, E. Fernández, and D. L. Huerta-Muñoz, "A two-phase solution algorithm for the Flexible Periodic Vehicle Routing Problem," Computers & Operations Research, vol. 99, pp. 27-37, 2018. https://doi.org/10.1016/j.cor.2018.05.021.
M. Darvish, C. Archetti, L. C. Coelho, and M. G. Speranza, "Flexible two-echelon location routing problem," European Journal of Operational Research, vol. 277, pp. 1124-1136, 2019. https://doi.org/10.1016/j.ejor.2019.04.002.
A. Estrada-Moreno, M. Savelsbergh, A. A. Juan, and J. Panadero, "Biased-randomized iterated local search for a multiperiod vehicle routing problem with price discounts for delivery flexibility," International Transactions in Operational Research, vol. 26, pp. 1293-1314, 2019. https://doi.org/10.1111/itor.12625.
F. Theurich, A. Fischer, and G. Scheithauer, "A Branch-and-Bound Approach for a Vehicle Routing Problem with Customer Costs," EURO Journal on Computational Optimization, p. 100003, 2021. https://doi.org/10.1016/j.ejco.2020.100003.
S. Poikonen, B. Golden, and E. A. Wasil, "A Branch-and-Bound Approach to the Traveling Salesman Problem with a Drone," INFORMS Journal on Computing, vol. 31, pp. 335-346, 2019. https://doi.org/10.1287/ijoc.2018.0826.
Y. Ngatilah, N. Rahmawati, C. Pujiastuti, I. Porwati, and A. Y. Hutagalung, "Inventory Control System Using Distribution Requirement Planning (DRP) (Case Study : Food Company)," in Journal of Physics: Conference Series, 2020, p. 032005. https://doi.org/10.1088/1742-6596/1569/3/032005.
R. Magdalena and T. Suli, "Forecasting Methods and Implementation of DRP (Distribution Requirement Planning) Methods in Determining the Master Production Schedule," IOP Conference Series: Materials Science and Engineering, vol. 528, p. 012049, 2019. https://doi.org/10.1088/1757-899X/528/1/012049.
I. Rizkya, K. Syahputri, R. M. Sari, I. Siregar, M. M. Tambunan, and Anizar, "DRP: Joint Requirement Planning in Distribution Centre and Manufacturing," in IOP Conference Series: Materials Science and Engineering, 2018, p. 012243. https://doi.org/10.1088/1757-899X/434/1/012243.
A. Saltelli, "Sensitivity Analysis for Importance Assessment," Risk Analysis, vol. 22, pp. 579-590, 2002. https://doi.org/10.1111/0272-4332.00040.
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