現今電子商務蓬勃發展，從顧客線上完成購買到交付的時間間隔逐漸縮短，甚至訂貨當日即需配送完成，這使零售商及物流業者面臨揀貨、配送作業壓力。揀貨及配送除成本考量之外，若於客戶期望的時間範圍內送達，可提升顧客的滿意度，進而提升業者競爭優勢，因此越來越受到重視。另一方面，在追求成本及時效性的前提之下，揀貨及配送從過去的單獨作業，轉變為整合問題，大幅的縮短從訂單成立到貨品送達的時間，使當日訂貨、當日送達得以實現。
過去整合問題研究中，主要追求成本最小，為因應現今顧客對於服務水準要求日趨增加，因此本研究同時考量配送偏誤時間最小化，這兩個目標彼此權衡，亦即成本越小時偏誤時間越大，反之亦然。綜觀過去相關文獻，針對整合揀貨以及配送車輛路徑問題，本研究為第一個同時考量成本及配送偏誤時間的雙目標研究。求解的部分，採用非支配排序基因演算法 (Non-dominated Sorting Genetic Algorithm II, NSGA-II) 法，透過此法求得柏拉圖最佳前緣，在演算法群體規模、迭代次數及變異率之參數的選擇方面，採用田口法找出最適合的參數組合。此外，亦透過傳統基因演算法求取單目標之解，驗證柏拉圖前緣的有效性。研究結果顯示，NSGA-II法所求得柏拉圖最佳前緣解能夠產生具代表性的非支配解，使得決策者能在不同目標權重下，按照所求得的解集合之中，選擇其所設定之成本及服務水準，並進而安排揀貨批次與配送路徑。

The rapid development of e-commerce in recent years has led to an increase in the volume of orders in small sizes, putting retailers and logistics operators under the pressure of picking and distribution operations. In addition, the delivery is completed within the time window that meets the customer's expectations. To achieve low-cost and on-time delivery services simultaneously, logistics companies need to find solutions that balance the two objectives and provide consumers with better satisfaction. Furthermore, it is known that the integration of order picking and delivery can further reduce the cost and time of the whole process. Therefore, this study intends to explore the bi-objective integrated batch picking and vehicle routing problem. The objectives are to minimize the total costs of the picking and distribution operations and minimize the total delivery time gap. We will construct a mathematical model and develop an efficient NSGA-II heuristic to solve the large-scale problem. Results show that the single-objective optimal solution cannot dominate the Pareto front obtained by the NSGA-II. It means that the Pareto front obtained in this study is competitive. Thus, it is expected to provide e-commerce companies as a reference for warehousing and logistics management decisions.

Abbass, H. A. (2002). The self-adaptive pareto differential evolution algorithm. Paper presented at the Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No. 02TH8600).
Ardjmand, E., Singh, M., Shakeri, H., Tavasoli, A., & Young II, W. A. (2021). Mitigating the risk of infection spread in manual order picking operations: A multi-objective approach. Applied Soft Computing, 100, 106953.
Coello, C. C., & Lechuga, M. S. (2002). MOPSO: A proposal for multiple objective particle swarm optimization. Paper presented at the Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No. 02TH8600).
Coyle, J., Bardi, E., & Langley, J. (2003). The Management of Business Logistics. (7th ed.). South-Western.
De Koster, M., Van der Poort, E. S., & Wolters, M. (1999). Efficient orderbatching methods in warehouses. International Journal of Production Research, 37(7), 1479-1504.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Drury, J. (1988). Towards more efficient order picking. IMM monograph, 1(1), 1-69.
Gupta, I., & Parashar, A. (2011). Study of Crossover operators in Genetic Algorithm for Travelling Salesman Problem. International Journal of Advanced Research in Computer Science, 2(4).
Ishibuchi, H., Matsumoto, T., Masuyama, N., & Nojima, Y. (2020). Many-objective problems are not always difficult for Pareto dominance-based evolutionary algorithms. In ECAI 2020 (pp. 291-298): IOS Press.
Kuhn, H., Schubert, D., & Holzapfel, A. (2020). Integrated order batching and vehicle routing–a general adaptive large neighborhood search algorithm. European Journal of Operational Research.
Li, J. T., Liu, K., & Qin, K. (2020). Research on Order Batching Problem of Intelligent Warehouse Picking System. Paper presented at the Proceedings of the Seventh International Forum on Decision Sciences.
Li, M., & Yao, X. (2019). Quality evaluation of solution sets in multiobjective optimisation: A survey. ACM Computing Surveys (CSUR), 52(2), 1-38.
Mohammadi, S., Al-e-Hashem, S. M., & Rekik, Y. (2020). An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company. International Journal of Production Economics, 219, 347-359.
Moons, S., Braekers, K., Ramaekers, K., Caris, A., & Arda, Y. (2019). The value of integrating order picking and vehicle routing decisions in a B2C e-commerce environment. International Journal of Production Research, 57(20), 6405-6423.
Moons, S., Ramaekers, K., Caris, A., & Arda, Y. (2018). Integration of order picking and vehicle routing in a B2C e-commerce context. Flexible Services and Manufacturing Journal, 30(4), 813-843.
Petersen, C. (2009). An evaluation of order picking policies for mail order companies. Production and Operations Management, 9, 319-335.
Purshouse, R. C., & Fleming, P. J. (2002). Why use elitism and sharing in a multi-objective genetic algorithm? Paper presented at the Proceedings of the 4th Annual Conference on Genetic and Evolutionary computation.
Ramaekers, K., Caris, A., Moons, S., & van Gils, T. (2018). Using an integrated order picking-vehicle routing problem to study the impact of delivery time windows in e-commerce. European Transport Research Review, 10(2), 1-11.
Schmid, V., Doerner, K. F., & Laporte, G. (2013). Rich routing problems arising in supply chain management. European Journal of Operational Research, 224(3), 435-448.
Schubert, D. (2020). Integrated order picking and vehicle routing operations–Literature review and further research opportunities. Available at SSRN 3631748.
Schubert, D., Scholz, A., & Wäscher, G. (2018). Integrated order picking and vehicle routing with due dates. OR Spectrum, 40(4), 1109-1139.
Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3), 221-248.
Srivastava, G., Singh, A., & Mallipeddi, R. (2021). NSGA-II with objective-specific variation operators for multiobjective vehicle routing problem with time windows. Expert Systems with Applications, 176, 114779.
Statista. (2019). E-commerce worldwide - Statistics & Facts. Retrieved from https://www.statista.com/topics/871/online-shopping/
Tompkins, J. A., White, J. A., Bozer, Y. A., & Tanchoco, J. M. A. (2010). Facilities planning: John Wiley & Sons.
Wang, C.-S., & Uzsoy, R. (2002). A genetic algorithm to minimize maximum lateness on a batch processing machine. Computers & Operations Research, 29(12), 1621-1640.
Yeh, L.-T. (2020). Using Tabu Search for Integrated Batch Picking and Vehicle Routing Problem. National Cheng Kung University Department of Transportation & Communication Management Science,
Zhang, J., Wang, X., & Huang, K. (2016). Integrated on-line scheduling of order batching and delivery under B2C e-commerce. Computers & Industrial Engineering, 94, 280-289.
Zhang, J., Wang, X., & Huang, K. (2018). On-line scheduling of order picking and delivery with multiple zones and limited vehicle capacity. Omega, 79, 104-115.
Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712-731.
Zhao, P., Liu, F., Guo, Y., Duan, X., & Zhang, Y. (2021). Bi-Objective Optimization for Vehicle Routing Problems with a Mixed Fleet of Conventional and Electric Vehicles and Soft Time Windows. Journal of Advanced Transportation, 2021.
Zhao, P., Luo, W., & Han, X. (2019). Time-dependent and bi-objective vehicle routing problem with time windows. Advances in Production Engineering & Management, 14(2), 201-212.
Zhou, Y., & Wang, J. (2015). A local search-based multiobjective optimization algorithm for multiobjective vehicle routing problem with time windows. IEEE Systems Journal, 9(3), 1100-1113.