機器人智動揀貨系統(Robotic Mobile Fulfillment System, RMFS)系統為一新型貨到人倉儲系統，利用搬運車搬運可移動式貨架至工作站，讓揀貨人員揀貨，並主要應用於電子商務產業。RMFS系統的揀貨決策包含兩階段：任務產生以及任務指派與完成。考量揀貨流程的決策有順序性，越前段所做的決策會對揀貨績效有越大的影響，故本研究欲針對第一階段的任務產生做進一步的探討。
本研究探討主機板產業物流中心的RMFS之揀貨應用，其揀貨特色為：訂單量少、品項需求多且揀貨量多，並且相較於電商產業，需求較易預測。本研究考慮訂單需求量與貨架存量的限制，進行訂單與貨架選擇決策的最佳化。在已知多張訂單來到單一工作站揀貨下，以最小化選擇貨架總距離為目標，同步決定訂單的揀貨順序、貨架來到順序以及品項揀貨量。本研究建構混整數規劃進行求解，證明其為NP困難的問題，並使用best-first branch and bound進行搜尋，其中h值估計上本研究延伸set cover問題提出Interger property與Ratio property、剪枝策略則藉由貨架庫存與訂單需求的關係減少搜尋路徑，分枝策略為依照節點的揀貨狀態分為訂單與貨架分枝，藉由實驗驗證求解效率優於Gurobi算法。
實驗分析上，發現本研究方法對訂單數量以及貨架數量之參數敏感度高，隨著訂單數量增加，可求解的品項與貨架數量隨之減少，進一步的探討3張訂單的情境，將庫存總品項增加至2000種。有兩大發現，第一為在貨架數量與庫存品項增加下，求解時間並無顯著成長，原因為訂單數量少，容易產生可以使用剪枝策略的情況，減少搜尋節點，使求解效率加快；第二為隨著庫存品項與貨架數的增加，可成功求解的資料筆數減少，主要原因在於若無法使用剪枝策略，貨架分枝會產生大量節點，造成暫存空間不足，無法求解。

The Robotic Mobile Fulfillment System (RMFS) system is a new type of cargo-to-person warehousing system. It uses mobile robots to transport movable pods to workstations, allowing pickers to pick up goods, and is widely used in the e-commerce industry. The order picking process consists of two phases: “task generation” and “task assignment and completion”. Since order picking process is completed by sequential decisions and the decisions in the first phase have greater impact on the performance of order picking, task generation decisions are further discussed.
The orders in the computer industry warehouse usually requires large amount and many different types of items, and there are few orders every day. Comparing to e-commerce warehouse, demand in the computer industry warehouse is easier to be predicted.
Consider the quantity of order demand and inventory, this study aims to optimize order and pod selection problem. We focus on the picking process in single workstation, where all orders arrive at a time, with the goal of minimizing the total distance of the selected pods. We formulize the problem using mix integer programming and prove that this is an NP-hard problem and apply best-first branch and bound algorithm to optimize the problem. The result proves that the computation time of improved B&B outperforms Gurobi solver.
With regard to the characteristics of computer industry warehouse, we further discuss the case under 3 orders with at most 2000 inventory items. There are two major findings. The first is that the computational time does not increase significantly while the number of shelves and inventory items increase. Because the number of orders are small, and it can use the pruning rule more often, which speeds up the solving. The second is that as the number of inventory items increases, numbers of data that can be solved decreases. Seeing that pod branching may generate massive amount of nodes, which leads to the result of memory error.

摘要 I
Abstract II
誌謝 IV
目錄 V
圖目錄 VII
表目錄 XI
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究範圍與假設 3
1.4 研究架構 4
第二章 RMFS系統應用於主機板物流中心之問題分析 5
2.1 主機板產業物流中心簡介與特色概述 5
2.2 主機板產業物流中心之揀貨分析 10
2.3 RMFS系統於主機板產業物流中心的揀貨流程 30
2.4 RMFS系統於主機板產業物流中心的揀貨問題 32
第三章 文獻回顧 35
3.1 RMFS系統中訂單揀貨與貨架選擇相關文獻 35
3.2 Branch and bound文獻回顧 41
3.3 Set cover相關文獻回顧 44
第四章RMFS訂單與貨架選擇問題 48
4.1 問題分析 48
4.2 問題定義與數學模式 50
4.3 Best-first branch and bound研究方法 58
第五章 實驗與結果分析 82
5.1 Gurobi求解器與本研究之Best-first B&B演算法比較 82
5.2 實驗小結 94
第六章 結論與建議 95
6.1 結論 95
6.2 建議 96
參考文獻 98

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