Wagner-Whitin動態經濟批量模式的主要目的乃是尋求總備置成本（Setup cost ）或總訂購成本（Ordering cost），總儲存成本（Holding cost ）以及總採購（或總生產）成本之和為最小。傳統Wagner-Whitin 批量模式假設備置成本為已知常數，很少致力於討論將備置成本視為參數對於經濟批量模式的影響，因此常導至較大之經濟批量，與現行市場上多種中小量需求的特質不一樣。本研究嘗試將備置成本視為參數，發展出一套成本路徑觀念以及延伸Wagner-Whitin 模式的演算法則，藉以提高演算效率。

日式零庫存批量生產方式縮短更換生產線的換模時間，相對降低備置成本；因此除了安全存量以外，各期基末存貨為0 ，但是大部分對於零庫存批量之研究都屬於文字性敘述，很少研究以數學方式進行研究[53]，缺乏理論性基礎，近來已有Porteus [33]，Zangwill等多位學者嘗試將備置成本視為參數，研究其對於經濟批量之影響。Zangwill曾討論穩定式降低備置成本對於Wagner-Whitin批量模式之影響，本研究則提出一種表達所有生產政策的新成本表示法；同時討論非穩定式降低備置成本對於Wagner Whitin模式批量之影響。無論備置成本的降低量為穩定式或非穩定式，我們都可以證明隨著備置成本降低量的增加，Wagner-Whitin 模式的總成本以及備置成本均將降低，同時亦可增加零庫存的基數，使得 Wagner-Whitin批旺模式趨向於零庫存批量模式。

本研究將備置成本視為參數，並討論Wagner-Whitin 批量模式滿足零庫存批量的條件，然後由總成本觀點比較兩模式優劣。由本研究可以探討零庫存的理論基礎並得知兩模式間之關係。結論顯示，相同生產或採購條件下Wagner批量模式優於零存批量模式；不同條件下零庫存批量模式不亞於Wagner-Whitin 批量模式，我們可以透過降低備置成本使得Wagner-Whitin 批量等於零庫存批量。

The goal in Wagner-Whitin''s dynamic lot sizing is to minimize the costs of inventory, setups and production. However, most of researcher observe that the setup and holding cost is fixed. Very few papers consider the setup cost as a parameter. This paper considers the setup cost as a parameter to develop a concept of cost-path and an extension of Wagner-Whitin model to increase the computational efficiency.

Zero Inventory (ZI) is a somewhat antithetical production philosophy which proposes cutting inventory to its lowest possible level (ideally zero). ZI philosophy is simple: to strive for the goals of ZI at the end of each period. Under ZI, the setup times should be reduced to a minimum. This will largerly reduce the setup cost. Zangwill provide a parametric algorithm for stationary setup cost reduction. This paper presents a new expression of total setup and holding costs for each policy and discusses a nonstationary setup cost redction. By adopting this new expression, we get a sufficient and necessary conditions such that ZI is the optimal policy in Wagner-Whitin model. No matter what setup cost reduction is stationary or nonstationary, the sum of all setup cost reduction of all periods which produce products increases when the amount of setup cost reduction increases. This result leads the optimal policy in Wagner-Whitin model closer to ZI.

This paper considers the setup cost as a paramenter. If all of the conditions in Wagner-Whitin lot size model and Zi model are equal, then the total cost of Wagner-Whitin lot size model is lower than that of Zi.

Otherwise, we can compare the two system with the unit total cost by different conditions. Most presentations of ZI have been descriptive with very few mathematical model of it. This paper seeks to demonstrate that reducing setup cost can move the economic lot size model towards ZI by mathematical method.

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