如今，全球供應鏈的複雜性正在增加。因此，車輛路徑問題（VRP）在現實生活中的實用性，使其成為一個非常重要的議題。大部分客戶期望他們的需求可在特定的時間內完成，這稱為「時間窗」，由此可知，帶有時間窗的 VRP (VRPTW) 在實際應用中比一般的VRP 更具相關性。此外，綠色車輛路徑問題（GVRP）為VRP的延伸，它考慮了環境的影響並在環境和經濟成本中取得平衡。環境問題是影響地球永續性的一部分。然而，供應鏈複雜度的增加也是其更容易受到影響。另外，「彈性」被描述為供應鏈在中斷後恢復到初始狀態的能力，因此所有供應鏈都須具有彈性。
由於上述的因素，本研究採用多目標方法來解決兩階段 VRPTW 中的中斷問題，並具有兩個目標：第一個目標是最小化供應鏈總成本，而第二個目標是最小化供應鏈總碳排放量。此外，研究包括兩個階段：第一階段是假設供應鏈處於理想狀態，而第二階段則是假設供應鏈處於中斷狀態。另外，本研究提出了一種改善的MOPSO來解決問題。由於適應值不能決定哪種演算法更好，本研究使用質量指標來比較所有演算法。
最後根據計算結果，對於小型、中型和大型供應鏈網絡以及低、中、高中斷持續時間，改進的 MOPSO 具有最高的積載率和最低的空載率。因此，改進的 MOPSO 是解決兩階段中斷VRPTW的最佳演算法。

Nowadays, the complexity of the global supply chain is increasing. Thus, vehicle routing problem (VRP) has become a very important problem because of its practicality in real-world applications. Many customers have expectations that their demands should be delivered at a specific time interval, which is called time window. Thus, VRP with time windows (VRPTW) is more relevant than classical VRP in real-world applications. In addition, the green vehicle routing problem (GVRP) is an extension of the VRP that considers environmental impacts and harmonizing the environmental and economic costs. The environmental issue is important to be considered as part of the actions of taking care of earth sustainability. However, the increase in the supply chain complexity also leads to more vulnerability to disruptions. Resilience is described as the ability of the supply chain network to return to the initial condition after a disruption occurs, so all supply chain networks need to have resilience.
Therefore, a multi-objective method is processed to solve the disruption in two-stage VRPTW. There are two objectives of this study. The first objective is to minimize total supply chain cost, while the second one is to minimize the total supply chain carbon emission. This study consists of two stages. The first stage is the supply chain in ideal condition, while the second one is the supply chain in disrupted condition. This study proposes an improved MOPSO to solve the problem. As the fitness cannot decide which algorithm is better, this study uses the quality indicators to compare all of the algorithms.
Based on the computational result, for small-, medium-, and big-size supply chain networks and low, medium, and high disruption duration, improved MOPSO has the highest hypervolume and lowest spacing. Thus, it can be concluded that the improved MOPSO is the best algorithm to solve disruption in the two-stage VRPTW.

Abreu, D. V. H. S., González, P. H., Mauri, G. R., Ribeiro, G. M., Orrico, R. D., Campos Júnior, N. F. R., and Abramides, C. A., Network sensor location problem with monitored lanes: Branch-and-cut and clustering search solution techniques. Computers and Industrial Engineering, 150, 106827, 2020.
Azi, N., Gendreau, M., and Potvin, J. Y., An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. European Journal of Operational Research, 178(3), 755–766, 2007
Baniamerian, A., Bashiri, M., and Zabihi, F., A modified variable neighborhood search hybridized with genetic algorithm for vehicle routing problems with cross-docking. Electronic Notes in Discrete Mathematics, 66, 143-150, 2018.
Barbarosoglu, G., and Ozgur, D., A tabu search algorithm for the vehicle routing problem. In Computers and Operations Research, 26, 255-270, 1999.
Benjamin, A. M., and Beasley, J. E., Metaheuristics for the waste collection vehicle routing problem with time windows, driver rest period and multiple disposal facilities. Computers & Operations Research, 37(12), 2270-2280, 2010.
Bo, H., Chen, Y., Li, H., Han, P., and Qi, L., Time-sensitive supply chain disruption recovery and resource sharing incentive strategy. Journal of Management Science and Engineering, 6(2), 165–176, 2021.
Borhanazad, H., Mekhilef, Saad, Ganapathy, C. G., Modiri-Delshad, M., and Mirtaheri, A., Optimization of micro-grid system using MOPSO, Renewable Energy, 71, 295-306, 2014.
Cardoso, S. R., Paula Barbosa-Póvoa, A., Relvas, S., dan Novais, A. Q., Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty. Omega, 56, 53–73, 2015.
Carvalho, H., Barroso, A. P., MacHado, V. H., Azevedo, S., and Cruz-Machado, V., Supply chain redesign for resilience using simulation. Computers and Industrial Engineering, 62(1), 329–341, 2012.
Chen, C., Demir, E., and Huang, Y., An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and delivery robots. European Journal of Operational Research, 294, 1164-1180, 2021.
Chen, J., Wang, H., and Zhong, R. Y., A supply chain disruption recovery strategy considering product change under COVID-19. Journal of Manufacturing Systems, 60, 920–927, 2021.
Chen, W., Zhang, Y., and Zhou, Y., Integrated scheduling of zone picking and vehicle routing problem with time windows in the front warehouse mode. Computers & Industrial Engineering, 163, 107823, 2022.
Christopher, M. dan Peck, H., Building the Resilient Supply Chain, The International Journal of Logistics Management, 15(2), 1–14, 2004.
Coello Coello, C. A., Pulido, G. T., and Lechuga, M. S., Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 256–279, 2004.
Craighead, C. W., Blackhurst, J., Rungtusanatham, M. J., dan Handfield, R. B., The Severity of Supply Chain Disruptions: Design Characteristics and Mitigation Capabilities, Decision Sciences, 38(1), 131–156, 2007.
Darom, N. A., Hishamuddin, H., Ramli, R., and Mat Nopiah, Z., An inventory model of supply chain disruption recovery with safety stock and carbon emission consideration. Journal of Cleaner Production, 197, 1011–1021, 2018.
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. In Ieee Transactions on Evolutionary Computation, 6(2), 182-197, 2002.
Dell’amico, M., Monaci, M., Pagani, C., and Vigo, D., Heuristic Approaches for the Fleet Size and Mix Vehicle Routing Problem with Time Windows. Source: Transportation Science, 41(4), 516–526, 2007.
Dixit, V., Seshadrinath, N., and Tiwari, M. K., Performance measures based optimization of supply chain network resilience: A NSGA-II + Co-Kriging approach. Computers and Industrial Engineering, 93, 205–214, 2016.
Fathi, M., Khakifirooz, M., Diabat, A., and Chen, H., An integrated queuingstochastic optimization hybrid Genetic Algorithm for a location-inventory supply chain network. International Journal of Production Economics, 237, 108139, 2021.
Fonseca-Galindo, J. C., de Castro Surita, G., Neto, J. M., de Castro, C. L., and Lemos, A. P., A multi-agent system for solving the Dynamic Capacitated Vehicle Routing Problem with stochastic customers using trajectory data mining. Expert Systems with Applications, 195, 116602, 2022.
Foroutan, A., Rezaeian, R., J., and Mahdavi, I., Green vehicle routing and scheduling problem with heterogeneous fleet including reverse logistics in the form of collecting returned goods. Applied Soft Computing Journal, 94, 106402, 2020.
Gholizadeh, H. and Fazlollahtabar, H., Robust optimization and modified genetic algorithm for a closed loop green supply chain under uncertainty: Case study in melting industry. Computers & Industrial Engineering, 147, 106653, 2020.
Guerreiro, A. P., Fonseca, C. M., and Paquete, L., The hypervolume indicator: problems and algorithms. ACM Computing Surveys. 54(6), 119, 2021.
Gutierrez, A., Dieulle, L., Labadie, N., and Velasco, N., A multi-population algorithm to solve the VRP with stochastic service and travel times. Computers and Industrial Engineering, 125, 144–156, 2018.
Hishamuddin, H., Sarker, R. A., and Essam, D., A recovery model for a two-echelon serial supply chain with consideration of transportation disruption. Computers and Industrial Engineering, 64(2), 552–561, 2013.
Hishamuddin, H., Sarker, R. A., and Essam, D., A recovery mechanism for a two echelon supply chain system under supply disruption. Economic Modelling, 38, 555–563, 2014.
Ishibuchi, H., Imada, R., Setoguchi, Y., and Nojima., How to specify a reference point in hypervolume calculation for fair performance comparison. Evolutionary Computation, 26(3), 411-440, 2018.
Jabir, E., Panicker, V. v., and Sridharan, R., Multi-objective Optimization Model for a Green Vehicle Routing Problem. Procedia - Social and Behavioral Sciences, 189, 33–39, 2015.
Jafarian, A., Rabiee, M., and Tavana, M., A novel multi-objective co-evolutionary approach for supply chain gap analysis with consideration of uncertainties. International Journal of Production Economics, 228, 107852, 2020.
Jean-François Cordeau Cordeau, J., Desaulniers, G., Desrosiers, J., Solomon, M. M., and Soumis, F., VRP with Time Windows, In P. Toth and Vigo, D (Eds), The Vehicle Routing Problem, Philadelphia: Society for Industrial and Applied Mathematics, 157-186, 2002.
Kennedy, J., and Eberhart, R. C., A discrete binary version of the particle swarm algorithm, IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, 5, 4104-4108, 1997
Ke-Wei, J., San-Yang, L., and Xiao-Jun, S., A hybrid algorithm for time-dependent vehicle routing problem with soft time windows and stochastic factors. Engineering Applications of Artificial Intelligence, 109, 104606, 2022.
Khanduzi, R., and Sangaiah, A., K., A fast genetic algorithm for a critical protection problem in biomedical supply chain networks. Applied Soft Computing Journal, 75, 162-179, 2019.
Kolen, A. W. J., Rinnooy Kan, A. H. G., and Trienekens, H. W. J. M., Vehicle routing with time windows. Operations Research, 35(2), 266–273, 1987.
Kurihara, K., Li, Y. L., Nishiuchi, N., and Masuda, K., Flow shop scheduling for separation model of set-up and net process based on Branch-and-Bound method. Computers and Industrial Engineering, 57(2), 550–562, 2009.
Kyriakakis, N. A., Sevastopoulos, I., Marinaki, M., and Marinakis, Y., A hybrid Tabu search – Variable neighborhood descent algorithm for the cumulative capacitated vehicle routing problem with time windows in humanitarian applications. Computers & Industrial Engineering, 164, 107868, 2022.
Mandal, P., and Mondal, S. C., Multi-objective optimization of Cu-MWCNT composite electrode in electro discharge machining using MOPSO-TOPSIS, Measurement, 169, 108347, 2021.
Ogden, J. A., Petersen, K. J., Carter, J. R., Carey, W. P., and Monczka, R. M., Supply Management Strategies for the Future: A Delphi Study. The Journal of Supply Chain Management, 41(3), 29-48, 2005.
Olgun, B., Koç, Ç., and Altıparmak, F., A hyper heuristic for the green vehicle routing problem with simultaneous pickup and delivery. Computers and Industrial Engineering, 153, 107010, 2021.
Paul, S. K., Sarker, R., and Essam, D., Managing risk and disruption in production-inventory and supply chain systems: A review. In Journal of Industrial and Management Optimization, 12(3). 1009–1029, 2016.
Paul, S. K., Sarker, R., and Essam, D., A quantitative model for disruption mitigation in a supply chain. European Journal of Operational Research, 257(3), 881–895, 2017.
Prescott-Gagnon, E., Desaulniers, G., Drexl, M., Rousseau, L., European Driver Rules in Vehicle Routing with Time Windows. Transportation Science, 44(4), 455–473, 2010.
Rabbani, M., Navazi, F., Asl, H. F., and Balali, M. H., A sustainable transportation-location-routing problem with soft time windows for distribution systems. Uncertain Supply Chain Management, 6, 229-254, 2018.
Soleimani, H., Chaharlang, Y., and Ghaderi, H., Collection and distribution of returned-remanufactured products in a vehicle routing problem with pickup and delivery considering sustainable and green criteria. Journal of Cleaner Production, 172, 960–970, 2018.
Srinivas, N., and Deb, K., Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3), 221–248, 1994.
Srivastava, G., Singh, A., and Mallipeddi, R., NSGA-II with objective-specific variation operators for multiobjective vehicle routing problem with time windows. Expert Systems With Applications, 176, 114779, 2021.
Talbi, E., Metaheuristics: From Design to Implementation. New Jersey: Wiley and sons, Inc., 2009.
Tang, C. S., Perspectives in supply chain risk management. In International Journal of Production Economics, 103(2), 451–488, 2006.
Toth, P. and Vigo, D., An overview of vehicle routing problem, In P. Toth and Vigo, D (Eds), The Vehicle Routing Problem, Philadelphia: Society for Industrial and Applied Mathematics, 2002.
Wang, Y., Ran, L., Guan, X., Fan, J., Sun, Y., Wang, H., Collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups. Expert Systems with Applications,197, 116690, 2022.
Worawattawechai, T., Intiyot, B., Jeenanunta, C., and Ferrell, W. G., A learning enhanced golden ball algorithm for the vehicle routing problem with backhauls and time windows. Computers and Industrial Engineering, 168, 108044, 2022.
Xu, Z., Elomri, A., Pokharel, S., and Mutlu, F., A model for capacitated green vehicle routing problem with the time-varying vehicle speed and soft time windows. Computers and Industrial Engineering, 137, 106011, 2019.
Yang, W., Ke, L., Wang, D. Z. W., and Lam, J. S. L., branch-price-and-cut algorithm for the vehicle routing problem with release and due dates. Transportation Research Part E: Logistics and Transportation Review, 145, 102167, 2021.
Zulvia, F. E., Kuo, R. J., and Nugroho, D. Y., A many-objective gradient evolution algorithm for solving a green vehicle routing problem with time windows and time dependency for perishable products. Journal of Cleaner Production, 242, 118428, 2020.