探討經濟生產批量模式含不良品重工之最佳決策

Optimal Lot-Size Decision for Economic Production Quantity Model with Defective Items Rework

王聖嘉(Sin-ga W.Chiu)

指導教授 ： 宮大川 ； 黃惠民

中原大學/工學院/工業工程研究所/博士(2004年)

https://doi.org/10.6840/cycu200400245

摘要

本研究探討隨機不良率與不良品重工之經濟生產批量模式的最佳化。在典型的EPQ模式中，完美生產狀況的假設在實際上近乎不可能。或許隨著時間，生產設備之狀況開始呈現疲憊、不穩定，或是基於其他因素，不良品的產生常常是不可避免的。本研究假設生產過程中不良率為隨機變數，且所有產出之不良品皆經過檢驗，而判別為兩大類；一類是可以重工的，另外一類則被判定為報廢品(將丟棄之)。重工程序緊接在正常批量生產程序之後，而重工程序亦被假設為不完美，在重工過程中有隨機性部分重工件會因修復失敗而成為報廢品。
本研究分析五種特定EPQ模式的不完美品質生產狀況，它們包含：(1)若產出之不良品皆判定為報廢品；(2)若產出之不良品皆判定為可重工修復者而進行重工修復；(3)若產出之不良品之一部分被判定為報廢品，而另一部分則被認定為可重工修復者而進行重工修復；(4)所有產出之不良品皆被判定為可重工，但有隨機性部分重工件會因修復失敗而報廢；(5)若產出之不良品狀況結合了以上所述之(3)與(4)，即產出之不良品有隨機性部分為報廢品，其餘為可重工者，但重工時又會有隨機性部分報廢品產生。
本研究分別建立以上五種特定EPQ模式的不完美品質生產狀況之數學模式，而成本分析中除了包含典型的EPQ模式之成本外，亦考慮報廢品之處理成本，重工件之持有成本，及重工件之修復成本。本研究以生產週期之期望值來因應因報廢品之隨機產出而造成生產週期長度亦具有隨機性。研究結果是依據存貨總成本之期望值最小化為目標，經微分而推導出各個模式之最佳經濟生產批量，並分別利用實例以說明其實際之應用。

關鍵字

不完美重工程序 ； 隨機不良品 ； 不完美品質 ； 重工修復 ； 經濟生產批量

並列摘要

This research considers optimal lot-size decision for Economic Production Quantity Model (EPQ) with defective items rework. The assumption of perfect quality production condition of the classical EPQ model is unrealistic. Due to process deterioration or other factors, the generation of defective items is inevitable. This study assumes that the defective rate is a random variable and all items produced are inspected. The imperfect quality items can fall into two groups, the repairable and the scrap. The reworking of the repairable defective items starts when the regular production process finishes in each cycle. The rework process is assumed to be imperfect, a random portion of reworked items fail and become scrap.
Five specific situations of EPQ model are examined in this research. They are situations where: (1) all defective items are scrap; (2) all defective items are reworked and can be repaired with an additional holding and reworking cost; (3) situation where the defective items fall into two groups, one is scrap and the other is repairable; (4) all defective items are reworked, however, a portion of them fail the reworking and become scrap; (5) An imperfect EPQ model combining the situations described by (3) and (4) above. Mathematical models are developed for each of the aforementioned situations, respectively. Disposal cost per scrap item and repairing and holding cost for each reworked item are included in the cost analysis. The renewal reward theorem is utilized in the proposed mathematical modeling to cope with the variable cycle length.
The optimal lot size that minimizes the expected overall costs is derived for each model, where shortages are not permitted. Numerical examples are provided demonstrate the ready and practical usages of our resulting models to the real-life manufacturing firms.

並列關鍵字

Manufacturing ； Production ； Imperfect Reworking ； EPQ ； Production lot size

參考文獻

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