近年來電子商務蓬勃發展，使得配送作業逐漸受到電子商務業者或負責配送之第三方物流業者所重視。配送作業與與揀貨作業之間的關係最為密切且互相影響，過去學者已證實整合單一訂單揀貨與車輛排程能有效改善配送效率。然而在實務上，由於電子商務公司的配送中心需要處理大量訂單，通常採用批量揀貨策略而不是單一訂單揀貨策略。因此本研究探討具配送時間窗限制下整合批次揀貨與車輛排程問題之可行性，目標為最小化揀貨與配送成本。首先建立混合整數規劃模型，並透過最佳化軟體Gurobi求解小規模問題。而為了能夠解決大規模問題，我們另外提出禁忌搜尋演算法，並與Gurobi之最佳解驗證，透過小規模與大規模範例之測試後，證明禁忌搜尋法可在合理時間內求得高品質的可行解。本研究證實採用批次揀貨取代單一訂單揀貨於整合問題之效益，可有效減少1.7% 之揀貨與配送成本。期望能提供電子商務公司作為倉儲與物流管理之決策參考，進行更有效率之配送作業和人員調度，以達到作業人力與運輸成本的改善，並提高顧客服務品質。

The rapid development of e-commerce in recent years has led to an increase in the volume of order, and how to improve the efficiency of delivery becomes an important issue. To increase efficiency, picking and distribution operations should be considered simultaneously in an integrated problem since they are interrelated. In a real-world e-commerce context, since distribution centers have a large number of orders need to be handled, often a batch picking policy is applied instead of a single order picking policy. Therefore, this study focuses on the value of integrating batch picking and vehicle routing problem with time windows. The objective is to minimize total costs of the picking and distribution operations. First, a mixed integer programming model was constructed, and we use optimization solver, Gurobi, to solve the small-scale problems. In order to solve large-scale problems, we also proposed tabu search algorithm to solve the problem efficiently. It is proved that tabu search is able to find good solution in competitive computation time. We also proved an effective mathematical model of the integrated batch picking and the vehicle routing problem. Results show that using batch picking instead of single order picking in the integration problem leads to cost savings 1.7% on average. Thus, it is expected to provide e-commerce companies as a reference for warehousing and logistics management decisions. Both warehouse and distribution operations could be performed in an efficient way, improve labour costs as well as delivery costs and increased service levels.

Agatz, N. A. H., Fleischmann, M., & van Nunen, J. A. E. E. (2008). E-fulfillment and multi-channel distribution – A review. European Journal of Operational Research, 187(2), 339-356.
Alfa, A. S., Heragu, S. S., & Chen, M. (1991). A 3-OPT based simulated annealing algorithm for vehicle routing problems. Computers & Industrial Engineering, 21(1), 635-639.
Armentano, V. A., Shiguemoto, A. L., & Løkketangen, A. (2011). Tabu search with path relinking for an integrated production–distribution problem. Computers & Operations Research, 38(8), 1199-1209.
Barbarosoglu, G., & Ozgur, D. (1999). A tabu search algorithm for the vehicle routing problem. Computers & Operations Research, 26(3), 255-270.
Bodin, L., & Golden, B. (1981). Classification in vehicle routing and scheduling. Networks, 11(2), 97-108.
Bozer, Y. A., & Kile, J. W. (2008). Order batching in walk-and-pick order picking systems. International Journal of Production Research, 46(7), 1887-1909.
Chen, L., Bostel, N., Dejax, P., Cai, J., & Xi, L. (2007). A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal. European Journal of Operational Research, 181(1), 40-58.
Clarke, G., & Wright, J. W. (1964). Scheduling of Vehicles from a Central Depot to a Number of Delivery Points. Oper. Res., 12(4), 568-581.
Coyle, J. J., Bardi, E. J., & Langley, C. J. (2003). The Management of Business Logistics: A Supply Chain Perspective: South-Western/Thomson Learning.
Dantzig, G. B., & Ramser, J. H. (1959). The Truck Dispatching Problem. Management Science, 6(1), 80-91.
De Koster, M. B. M., Van der Poort, E. S., & Wolters, M. (1999). Efficient orderbatching methods in warehouses. International Journal of Production Research, 37(7), 1479-1504.
Dueck, G. (1993). New Optimization Heuristics: The Great Deluge Algorithm and the Record-to-Record Travel. Journal of Computational Physics, 104(1), 86-92.
Dueck, G., & Scheuer, T. (1990). Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. Journal of Computational Physics, 90(1), 161-175.
Elsayed, E. A. (1981). Algorithms for optimal material handling in automatic warehousing systems. The International Journal of Production Research, 19(5), 525-535.
Fourment, M., & Gillings, M. R. (2008). A comparison of common programming languages used in bioinformatics. BMC bioinformatics, 9, 82-82.
Gademann, N., & Velde, S. (2005). Order batching to minimize total travel time in a parallel-aisle warehouse. IIE Transactions, 37(1), 63-75.
Gendreau, M., Hertz, A., & Laporte, G. (1994). A Tabu Search Heuristic for the Vehicle Routing Problem. Management Science, 40(10), 1276-1290.
Goetschalckx, M., & Ashayeri, J. (1989). Classification and design of order picking. Logistics World, 2(2), 99-106.
Gupta, D. K. (2002). Tabu Search for Vehicle Routing Problems (VRPs). International Journal of Computer Mathematics, 79(6), 693-701.
Henn, S., Koch, S., Doerner, K. F., Strauss, C., & Wäscher, G. (2010). Metaheuristics for the order batching problem in manual order picking systems. Business Research, 3(1), 82-105.
Henn, S., & Schmid, V. (2013). Metaheuristics for order batching and sequencing in manual order picking systems. Computers & Industrial Engineering, 66(2), 338-351.
Henn, S., & Wäscher, G. (2012). Tabu search heuristics for the order batching problem in manual order picking systems. European Journal of Operational Research, 222(3), 484-494.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. science, 220(4598), 671-680.
Kohl, N. (1995). Exact methods for time constrained routing and related scheduling problems. Kgs. Lyngby: Technical University of Denmark.
Krajewska, M. A., & Kopfer, H. (2009). Transportation planning in freight forwarding companies: Tabu search algorithm for the integrated operational transportation planning problem. European Journal of Operational Research, 197(2), 741-751.
Le-Duc, T., & De Koster, R. M. (2007). Travel time estimation and order batching in a 2-block warehouse. European Journal of Operational Research, 176(1), 374-388.
Lenstra, J. K., & Kan, A. H. G. R. (1981). Complexity of vehicle routing and scheduling problems. Networks, 11(2), 221-227.
Li, F., Golden, B., & Wasil, E. (2007). A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 34(9), 2734-2742.
Lin, S. (1965). Computer solutions of the traveling salesman problem. The Bell System Technical Journal, 44(10), 2245-2269.
Low, C., Chang, C.-M., Li, R.-K., & Huang, C.-L. (2014). Coordination of production scheduling and delivery problems with heterogeneous fleet. International Journal of Production Economics, 153, 139-148.
Low, C., Li, R.-K., & Chang, C.-M. (2012). Integrated scheduling of production and delivery with time windows. International Journal of Production Research - INT J PROD RES, 51, 1-13.
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, 1-19.
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.
Ratliff, H. D., & Rosenthal, A. S. (1983). Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem. Operations Research, 31(3), 507-521.
Roodbergen, K., & De Koster, R. (2001). Routing methods for warehouses with multiple cross aisles. International Journal of Production Research - INT J PROD RES, 39, 1865-1883.
Rosenkrantz, D., Stearns, R., & Ii, P. (1977). An Analysis of Several Heuristics for the Traveling Salesman Problem. SIAM J. Comput., 6, 563-581.
Russell, R. A., & Urban, T. L. (2008). Vehicle routing with soft time windows and Erlang travel times. Journal of the Operational Research Society, 59(9), 1220-1228.
Schubert, D., Scholz, A., & Wäscher, G. (2018). Integrated order picking and vehicle routing with due dates. OR Spectrum, 40(4), 1109-1139.
Shen, C.-W., Hung, Y.-C., & Lin, Y.-S. (2019). A Nearest-based Clustering Adjustment Algorithm for the Capacitated Vehicle Routing Problem. Journal of the Chinese Institute of Transportation, 31(4), 449-480.
Solomon, M. M. (1987). Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints. Operations Research, 35(2), 254-265.
Tarantilis, C. D., Kiranoudis, C. T., & Vassiliadis, V. S. (2004). A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. European Journal of Operational Research, 152(1), 148-158.
Toth, P., & Vigo, D. (1997). An Exact Algorithm for the Vehicle Routing Problem with Backhauls. Transportation Science, 31, 372-385.
Toth, P., & Vigo, D. (2003). The Granular Tabu Search and Its Application to the Vehicle-Routing Problem. INFORMS Journal on Computing, 15(4), 333-346.
Ullrich, C. A. (2013). Integrated machine scheduling and vehicle routing with time windows. European Journal of Operational Research, 227(1), 152-165.
Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013). Heuristics for multi-attribute vehicle routing problems: A survey and synthesis. European Journal of Operational Research, 231(1), 1-21.
Yu, M., & de Koster, R. B. M. (2009). The impact of order batching and picking area zoning on order picking system performance. European Journal of Operational Research, 198(2), 480-490.
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.