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題名 | 動態經濟批量之探討--最低總成本法=A Study of Dynamic Economic Lot Size--Minimal Total Cost Approach |
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作者 | 黃士滔; 池福灶; | 書刊名 | 技術學刊 |
卷期 | 13:3 1998.09[民87.09] |
頁次 | 頁451-462 |
分類號 | 494.762 |
關鍵詞 | 總成本; 最低總成本法; 批量; Total cost; Minimal total cost approach; Lot size; |
語文 | 中文(Chinese) |
中文摘要 | 最小總成本(Least-Total-Cost, LTC)法是MRP系統中用以決定經濟批量常見的方 法之一,此方法是一種啟發式(Heuristic)的方法,所得到的解也只是近似解而不一定是最 佳解,但由於其易於使用的特性,使其在MRP系統中經常被提到。本文延伸總成本的觀念, 推導出具有良好遞迴關係的最低總成本(Minimal Total Cost, MTC)法,以決定動態經濟批 量的最佳解而非近似解。文中發展最低總成本法的觀念並提出數學模式以求得最佳之訂購批 量,並且推導出一些定理來簡化最低總成本法的求解過程,使其與LTC法一樣具有易於使 用的特性;另一方面,本文的MTC法可適用在各期單位儲存成本相等或不相等的情況,以 及各期訂購成本相等或不相等的情況,使得其具有較廣泛的適用性。 本文設計一個可使最低總成本法在計算上更簡易的表格,使經濟批量的求解工作,即使 不使用電腦也能很快速、很容易的求解動態經濟批量,滿足易於使用的特性。 本文除以實例配合上述的表格來說明MTC法之使用外,另透過實驗設計的方式,首先 證實MTC法不但具有LTC法易於使用的特性,而且所得到的批量解全部為最佳解優於LTC 法的部份最佳解;其次證實MTC法不但與Wagner-Whitin(W-W)法一樣可得到最佳解, 而且求解的速度比W-W法快很多,充分顯示本文的MTC法是一個良好且有效的方法,可 謂兼具LTC法與W-W法的優點(簡單易用且可得到最佳解)又沒有LTC法與W-W法的 缺點(不一定得到最佳解且計算繁瑣)。 |
英文摘要 | Least total cost (LTC) is popular method for determining economic lot sizes within MRP systems. The LTC method is a heuristic method, and it's results are an approximation. However, the special characteristics of LTC have made it's use common in MRP systems. This paper extends the total cost concept to create a process incorporating a recursive relation called the Minimal total cost (MTC) approach to determine the optimal, not approximate, dynamic economic lot size. This paper develops the MTC concepts and presents a mathematic model to obtain optimal order sizes. Moreover, it demonstrates several theorems to simplify MTC calculations while keeping the strength of the LTC method. The MTC method can be used whether the per unit carrying costs and ordering costs for each period are equal or not. These factors contribute to it's widespread applicability. This paper presents a useful table for the use of the MTC method which makes the work of determining dynamic economic lot sizes easier and quicker without using computer. An example, using this table, is provided to describe the MTC approach. Through experimental design, this paper proves that MTC approach is as easy to use as the LTC approach can obtain an optimal solution, not an approximation. This paper also proves that the MTC approach can obtain an optimal solution more quickly than the Wagner-Whitin(W-W)approach. Our results show that the MTC approach has the advantages of the LTC approach and W-W approach (ease of use and can obtain an optimal solution), without the disadvantages of the LTC approach and W-W approach(approximation and computational complexity). |
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