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題名 | 考慮數量折扣的動態經濟批量=Dynamic Economic Lot Size with Quantity Discount |
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作者 | 池福灶; 黃士滔; | 書刊名 | 技術學刊 |
卷期 | 14:2 1999.06[民88.06] |
頁次 | 頁235-246 |
分類號 | 494.762 |
關鍵詞 | 經濟批量; 數量折扣; 遞迴關係; 總成本變化量; 成本路徑; Economic lot size; Quantity discount; Recursive relation; Variation of total cost; Cost-path; |
語文 | 中文(Chinese) |
中文摘要 | 單階多期需求系統的經濟採購批量可藉由Wagner-Whitin(W-W)演算法則求得最佳 解,但若再考慮數量折扣因素。 則 W-W 法相關定理無法使用,且顯得更加複雜難解。本文 考慮單一數量折扣因素,修正 W-W 法路徑表達方式, 以路徑節點表示總成本變化量,架構 出前後期之間具有良好遞迴關係的總成本路徑模式,藉以建立考慮數量折扣因素的最佳經濟 批量演算模式,解決複雜難解的困擾,並以表格方式說明所建立數學模式的求解過程,讓使 用者依表格即可進行求解。考慮各期需求在可分割成二批來進行採購的複雜狀況下,文中透 過樹狀狀態分析及動態規劃觀念,藉以了解各種可行採購政策的特性及所產生的總成本變化 量; 經由所建立的成本路徑觀念,計算各節點所代表的數量折扣狀態的總成本變化量及各路 徑總成本,而成功的建立路徑中前後節點之間的總成本關係式,此一關係式在前後節點之間 具有良好的遞迴關係,可減少演算時的加法項數。配合前述的遞迴關係及相關公式,建立一 表格以閩述此一模式的計算過程,使易於求解。 |
英文摘要 | The algorithm of Wagner-Whitin (W-W) gives an optimal solution for the undiscounted dynamic lot-sizing problem. A discounted problem requires complex computation, and the theorems of Wagner-Whitin can not be applied to the quantity discount problem. Taking into consideration the single discount level, we modify the expression of the Wagner-Whitin algorithm. Using the path node to represent the variation of total cost, we establish a cost-path model, which has a good recursive relation between two adjacent periods, to obtain an optimal solution. A table is designed to illustrates the computational tional process developed by the mathematical model. We assume that the demand at each period may be separated into two lots for purchasing. This paper uses tree-structure analysis and the dynamic programming approach to obtain the property and the variation of the total cost for each feasible policy. By using the cost-path concept, we compute the variation of the total cost for each node and the total cost for each path. A good recursive relation between two adjacent nodes is developed to reduce the number of addition items. A table solution is designed to describe the recursive relation between two adjacent nodes and the computational process. |
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