Robust routing optimization for vehicle routing problem with stochastic demands and time windows
Considering uncertainty and time constraints in logistics planning
DOI:
https://doi.org/10.35335/emod.v16i2.61Keywords:
Logistics Planning, Robust Routing Optimization, Stochastic Demands, Time Windows, Vehicle Routing ProblemAbstract
This research addresses the challenge of robust routing optimization in the context of the Vehicle Routing Problem (VRP) with stochastic demands and time windows. The objective is to develop an effective logistics planning approach that considers demand uncertainty and time constraints in order to minimize costs and improve operational efficiency. A mathematical formulation is presented to model the problem, considering a robustness parameter to account for uncertainty in demand scenarios. The formulation incorporates binary decision variables to determine the routing plan and meet customer demands within specified time windows. A numerical example is provided to illustrate the application of the model, highlighting the impact of uncertainty and time window compliance on the routing plan and total expected cost. The results demonstrate the potential benefits of employing robust routing optimization, providing insights for logistics planners and decision-makers in designing more resilient and cost-effective routing strategies. Further research can explore advanced algorithms and real-world case studies to validate and enhance the proposed approach in practical logistics scenarios
References
Alamatsaz, K., Ahmadi, A., & Mirzapour Al-e-hashem, S. M. J. (2022). A multiobjective model for the green capacitated location-routing problem considering drivers’ satisfaction and time window with uncertain demand. Environmental Science and Pollution Research, 29(4), 5052–5071.
Allahyari, S., Yaghoubi, S., & Van Woensel, T. (2021). The secure time-dependent vehicle routing problem with uncertain demands. Computers & Operations Research, 131, 105253.
Balcik, B., & Yanıkoğlu, İ. (2020). A robust optimization approach for humanitarian needs assessment planning under travel time uncertainty. European Journal of Operational Research, 282(1), 40–57.
Baradaran, V., Shafaei, A., & Hosseinian, A. H. (2019). Stochastic vehicle routing problem with heterogeneous vehicles and multiple prioritized time windows: Mathematical modeling and solution approach. Computers & Industrial Engineering, 131, 187–199.
Bhuiyan, T. H., Roni, M., & Walker, V. (n.d.). Drone Fleet Deployment Optimization for Direct Delivery with Time Windows and Battery Replacements. Available at SSRN 4271364.
Bolanos, R., Escobar, J., & Echeverri, M. (2018). A metaheuristic algorithm for the multi-depot vehicle routing problem with heterogeneous fleet. International Journal of Industrial Engineering Computations, 9(4), 461–478.
Cacchiani, V., Qi, J., & Yang, L. (2020). Robust optimization models for integrated train stop planning and timetabling with passenger demand uncertainty. Transportation Research Part B: Methodological, 136, 1–29.
Calvet, L., Wang, D., Juan, A., & Bové, L. (2019). Solving the multidepot vehicle routing problem with limited depot capacity and stochastic demands. International Transactions in Operational Research, 26(2), 458–484.
Cao, E., Gao, R., & Lai, M. (2018). Research on the vehicle routing problem with interval demands. Applied Mathematical Modelling, 54, 332–346.
Chen, L., Chiang, W.-C., Russell, R., Chen, J., & Sun, D. (2018). The probabilistic vehicle routing problem with service guarantees. Transportation Research Part E: Logistics and Transportation Review, 111, 149–164.
Chien, C.-F., Dou, R., & Fu, W. (2018). Strategic capacity planning for smart production: Decision modeling under demand uncertainty. Applied Soft Computing, 68, 900–909.
Çimen, M., & Soysal, M. (2017). Time-dependent green vehicle routing problem with stochastic vehicle speeds: An approximate dynamic programming algorithm. Transportation Research Part D: Transport and Environment, 54, 82–98.
De La Vega, J., Munari, P., & Morabito, R. (2019). Robust optimization for the vehicle routing problem with multiple deliverymen. Central European Journal of Operations Research, 27, 905–936.
Errico, F., Desaulniers, G., Gendreau, M., Rei, W., & Rousseau, L.-M. (2018). The vehicle routing problem with hard time windows and stochastic service times. EURO Journal on Transportation and Logistics, 7, 223–251.
Euchi, J., Zidi, S., & Laouamer, L. (2020). A hybrid approach to solve the vehicle routing problem with time windows and synchronized visits in-home health care. Arabian Journal for Science and Engineering, 45, 10637–10652.
Faiz, T. I., & Vogiatzis, C. (2022). A Robust Optimization Framework for Two-Echelon Vehicle and UAV Routing for Post-Disaster Humanitarian Logistics Operations. ArXiv Preprint ArXiv:2207.11879.
Fattahi, M., & Govindan, K. (2022). Data‐driven rolling horizon approach for dynamic design of supply chain distribution networks under disruption and demand uncertainty. Decision Sciences, 53(1), 150–180.
Gao, T., Erokhin, V., & Arskiy, A. (2019). Dynamic optimization of fuel and logistics costs as a tool in pursuing economic sustainability of a farm. Sustainability, 11(19), 5463.
Goel, R., Maini, R., & Bansal, S. (2019). Vehicle routing problem with time windows having stochastic customers demands and stochastic service times: Modelling and solution. Journal of Computational Science, 34, 1–10.
Goli, A., Aazami, A., & Jabbarzadeh, A. (2018). Accelerated cuckoo optimization algorithm for capacitated vehicle routing problem in competitive conditions. International Journal of Artificial Intelligence, 16(1), 88–112.
Ham, A. M. (2018). Integrated scheduling of m-truck, m-drone, and m-depot constrained by time-window, drop-pickup, and m-visit using constraint programming. Transportation Research Part C: Emerging Technologies, 91, 1–14.
Hosseinabadi, A. A. R., Vahidi, J., Balas, V. E., & Mirkamali, S. S. (2018). OVRP_GELS: solving open vehicle routing problem using the gravitational emulation local search algorithm. Neural Computing and Applications, 29, 955–968.
Hu, C., Lu, J., Liu, X., & Zhang, G. (2018). Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Computers & Operations Research, 94, 139–153.
Kim, S., Rasouli, S., Timmermans, H. J. P., & Yang, D. (2022). A scenario-based stochastic programming approach for the public charging station location problem. Transportmetrica B: Transport Dynamics, 10(1), 340–367.
Lu, D., & Gzara, F. (2019). The robust vehicle routing problem with time windows: Solution by branch and price and cut. European Journal of Operational Research, 275(3), 925–938.
Luan, J., Yao, Z., Zhao, F., & Song, X. (2019). A novel method to solve supplier selection problem: Hybrid algorithm of genetic algorithm and ant colony optimization. Mathematics and Computers in Simulation, 156, 294–309.
Mirzaei-Khafri, S., Bashiri, M., & Soltani, R. (2020). A ROBUST OPTIMIZATION MODEL FOR A LOCATION-ARC ROUTING PROBLEM WITH DEMAND UNCERTAINTY. International Journal of Industrial Engineering, 27(2).
Moons, K., Waeyenbergh, G., & Pintelon, L. (2019). Measuring the logistics performance of internal hospital supply chains–a literature study. Omega, 82, 205–217.
Mousavi, S. M., & Vahdani, B. (2017). A robust approach to multiple vehicle location-routing problems with time windows for optimization of cross-docking under uncertainty. Journal of Intelligent & Fuzzy Systems, 32(1), 49–62.
Norouzi, N., Sadegh-Amalnick, M., & Tavakkoli-Moghaddam, R. (2017). Modified particle swarm optimization in a time-dependent vehicle routing problem: minimizing fuel consumption. Optimization Letters, 11, 121–134.
Pagès‐Bernaus, A., Ramalhinho, H., Juan, A. A., & Calvet, L. (2019). Designing e‐commerce supply chains: a stochastic facility–location approach. International Transactions in Operational Research, 26(2), 507–528.
Paraskevopoulos, D. C., Laporte, G., Repoussis, P. P., & Tarantilis, C. D. (2017). Resource constrained routing and scheduling: Review and research prospects. European Journal of Operational Research, 263(3), 737–754.
Pasha, J., Dulebenets, M. A., Kavoosi, M., Abioye, O. F., Wang, H., & Guo, W. (2020). An optimization model and solution algorithms for the vehicle routing problem with a “factory-in-a-box.” Ieee Access, 8, 134743–134763.
Pasha, J., Nwodu, A. L., Fathollahi-Fard, A. M., Tian, G., Li, Z., Wang, H., & Dulebenets, M. A. (2022). Exact and metaheuristic algorithms for the vehicle routing problem with a factory-in-a-box in multi-objective settings. Advanced Engineering Informatics, 52, 101623.
Prakash, S., Kumar, S., Soni, G., Jain, V., & Rathore, A. P. S. (2020). Closed-loop supply chain network design and modelling under risks and demand uncertainty: an integrated robust optimization approach. Annals of Operations Research, 290, 837–864.
Qian, H., Guo, H., Sun, B., & Wang, Y. (2022). Integrated inventory and transportation management with stochastic demands: A scenario-based economic model predictive control approach. Expert Systems with Applications, 202, 117156.
Rabbani, M., Bosjin, S., Yazdanparast, R., & Saravi, N. (2018). A stochastic time-dependent green capacitated vehicle routing and scheduling problem with time window, resiliency and reliability: a case study. Decision Science Letters, 7(4), 381–394.
Santos, M. J., Curcio, E., Mulati, M. H., Amorim, P., & Miyazawa, F. K. (2020). A robust optimization approach for the vehicle routing problem with selective backhauls. Transportation Research Part E: Logistics and Transportation Review, 136, 101888.
Sazvar, Z., Zokaee, M., Tavakkoli-Moghaddam, R., Salari, S. A., & Nayeri, S. (2021). Designing a sustainable closed-loop pharmaceutical supply chain in a competitive market considering demand uncertainty, manufacturer’s brand and waste management. Annals of Operations Research, 1–32.
Seakhoa-King, S. (2019). Enhancing value in time-sensitive service delivery systems using intelligent scheduling.
Shi, Y., Boudouh, T., & Grunder, O. (2017). A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand. Expert Systems with Applications, 72, 160–176.
Shi, Y., Boudouh, T., & Grunder, O. (2019). A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times. Transportation Research Part E: Logistics and Transportation Review, 128, 52–95.
Shi, Y., Zhou, Y., Ye, W., & Zhao, Q. Q. (2020). A relative robust optimization for a vehicle routing problem with time-window and synchronized visits considering greenhouse gas emissions. Journal of Cleaner Production, 275, 124112.
Smith, D., & Srinivas, S. (2019). A simulation-based evaluation of warehouse check-in strategies for improving inbound logistics operations. Simulation Modelling Practice and Theory, 94, 303–320.
Sreedevi, R., & Saranga, H. (2017). Uncertainty and supply chain risk: The moderating role of supply chain flexibility in risk mitigation. International Journal of Production Economics, 193, 332–342.
Stodola, P., Michenka, K., Nohel, J., & Rybanský, M. (2020). Hybrid algorithm based on ant colony optimization and simulated annealing applied to the dynamic traveling salesman problem. Entropy, 22(8), 884.
Sun, L., Pan, Q., Jing, X.-L., & Huang, J.-P. (2021). A light-robust-optimization model and an effective memetic algorithm for an open vehicle routing problem under uncertain travel times. Memetic Computing, 13, 149–167.
Tan, B., Chen, H., Zheng, X., & Huang, J. (2022). Two-stage robust optimization dispatch for multiple microgrids with electric vehicle loads based on a novel data-driven uncertainty set. International Journal of Electrical Power & Energy Systems, 134, 107359.
Wu, D., & Wu, C. (2022). Research on the time-dependent split delivery green vehicle routing problem for fresh agricultural products with multiple time windows. Agriculture, 12(6), 793.
Xu, T., Ren, Y., Guo, L., Wang, X., Liang, L., & Wu, Y. (2021). Multi-objective robust optimization of active distribution networks considering uncertainties of photovoltaic. International Journal of Electrical Power & Energy Systems, 133, 107197.
Yang, T., Wang, W., & Wu, Q. (2022). Fuzzy demand vehicle routing problem with soft time windows. Sustainability, 14(9), 5658.
Zhang, H., Zhang, Q., Ma, L., Zhang, Z., & Liu, Y. (2019). A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows. Information Sciences, 490, 166–190.
Zhang, J., Yu, M., Feng, Q., Leng, L., & Zhao, Y. (2021). Data-Driven Robust Optimization for Solving the Heterogeneous Vehicle Routing Problem with Customer Demand Uncertainty. Complexity, 2021, 1–19.
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