基因分群之經濟訂購量模式—多物料及多分公司存貨管理

Abstract

傳統經濟訂購量（Economic Order Quantity，EOQ）模型旨在探討單一廠商訂購處理單一物料的最佳化行為。然在實務應用上，許多廠商擁有多家分公司，而其所訂購處理之物料也都非僅有一種，不同分公司針對各種物料雖可利用EOQ模型分別計算各分公司各種物料之最佳訂購量及頻次，但若能針對同一種物料採取聯合訂購以享受數量折扣，並將不同種類物料進行集中倉儲，以發揮倉儲及運輸之經濟規模特性，將可使總成本有效降低。基此，本文建立多物料多分公司之最佳存貨模型，以求解使總成本（包含訂購、倉儲、配送及購買等四項成本）最低之各種物料最佳訂購比例，以及各種物料的訂購與倉儲方式。 基於訂購及倉儲兩個層面，本文研擬四種存貨策略，分別為「獨立訂購分散倉儲」（方式1）、「獨立訂購集中倉儲」（方式二）、「聯合訂購分散倉儲」（方式三），以及「聯合訂購集中倉儲」（方式四），並推導此四種方式下總成本最低時之各項物料訂購量，及進行四種存貨方式之比較分析與成本相關參數之敏感度分析。之後，利用分群方式將物料予以分群之後，就各群採取適用之存貨方式。分群方式主要有兩種，一為傳統統計分群方式，另一為基因演算法分群方式。 本研究利用一簡例及案例分別進行存貨模式之驗證。結果發現，若統一利用同一存貨方式，採用方式四的情況下，在訂購、倉儲及運送成本方面最低；而方式三則在購買成本上最低。若採取分群方式，統計分群的方式與不予分群的方式相差39,776,908 元，差異為0.68%。基因分群與不予分群方式相差41,091,964元，差異為0.71%。故利用基因分群的方式可較統計分群方式容易研擬出最佳之存貨策略。

In solving the single material and single firm inventory problem, many researches often use the traditional economic ordering quantity (EOQ) models to compute the optimal solution. In practice, however, many firms or industrials have its own branches, and also order many materials. We can compute the ordering quantity and ordering rate of each branch for each material individually by EOQ models. However, if we take jointly ordering for single material, we can have the benefit of quality discounts. And that, if we store many materials at the same time, we can develop the economies of scale of warehousing and distributing, so that we can effectively decrease the inventory cost. In this paper, we propose multi-item and multi-branch inventory models. The objective of the model is to find out the optimal ordering rate with the minimum inventory cost and individual inventory alternative of each material. Base on two aspects of ordering and warehousing, we propose four alternatives. They are separated ordering and decentralized warehousing, separated ordering and centralized warehousing, joint ordering and decentralized warehousing, joint ordering and centralized warehousing alternative, and we use them to compute the ordering rate of materials and the inventory cost. The result of tested example indicates that it is better adopting joint ordering than separated ordering. And we also find out that centralized warehousing is better than decentralized warehousing when the warehousing coefficient is less than 0.83. Due to different price, volume, and total demand of materials, it doesn’t necessary to unite the inventory alternative to any material or branch. Therefore, we integrate genetic clustering algorithm and EOQ models. We use genetic clustering algorithm to cluster all the materials, and find the best inventory alternative to each group. The result of case study (50 materials, 4 branches) indicates that adopting genetic clustering algorithm is better than traditional clustering method or non-clustering.