考慮隨機維修及矯正時間與再製下損耗性產品之經濟生產模式

Economic production quantity models for deteriorating items with stochastic maintenance and corrective time and rework

慧珂特(I-Gede-Agus Widyadana)

指導教授 ： 黃惠民

中原大學/電機資訊學院/工業與系統工程研究所/博士(2011年)

https://doi.org/10.6840/cycu201100212

摘要

摘 要
近年來，存貨問題被廣泛地討論，其中生產系統的可靠度是存貨問題一個重要的議題，因為它會導致如庫存銷售損失或產品退貨的發生。因此、本研究將針對損耗性產品之不可靠生產系統，如：機器不可使用或故障等進行探討，並發展出經濟生產模式。
本研究共發展出五個損耗性產品的生產存貨模式，分述如下：由於機器會因某些原因，如：定期預防性維修而產生隨機性地不可用。因此、本研究的第一個模式探討機器在隨機性的發生不可用情況下的經濟生產模式，而銷售損失及補貨之情況亦將列入第一個模式考慮；第二個模式是考慮隨機性機器故障狀況下的經濟生產模式；第三個模式則整合第一、二模式，同時考慮隨機機器故障及隨機性機器故障。
另外、由於製程無法持續地生產良好品質的產品，導致有些產品被退貨，因此本研究在第四、五模式中討論影響產品品質的製程問題；第四個模式建立在後進先出系統下，假設瑕疵產品在正常生產結束時立即被再製（或重工）。但再製製程之後，機器將有一段隨機時間的維修。此一維修將導致機器不可用的狀況發生；相對地、在第五模式中，本研究考慮以先進先出系統取代後進先出，再次進行探討。在這五個模式中，機器的隨機不可用性將以兩種機率分配模式來考慮：上限及界限的機率分配。
由於本研究是探討在隨機性維護、修正時間及重工下的損耗性產品之經濟生產模式。數學模式有其複雜性，無法求得封閉式解，故運用Maple 8軟體以簡單搜尋方法求解。同時本研究假設所有模式符合凸性條件。
本研究中對每一模式均提供數值範例，敏感度分析中說明各關鍵參數的變化對生產時間及成本對生產所造成的影響。結果也顯示其中某些參數對最佳總成本及最佳生產時間有顯著的影響。最後、對應不可靠生產系統，本研究也提出一些管理上的見解。

關鍵字

故障機器 ； 重工製程 ； 預防性維修 ； 存貨 ； 損耗性產品

並列摘要

Inventory problems have been investigated extensively in recent years. One form of industrial issues causing inventory problems is production system reliability. Since production system is not continuously reliable, some consequences such as inventory lost sales, and product rejects can occur. Due to the condition, this research studies inventory models dealing with unreliable production system. The study develops economic production quantity (EPQ) models for deteriorating items under unreliable production systems such as machine unavailability and breakdown.
In this research, five production inventory models for deteriorating items are developed. The first model presents an EPQ model with random machine unavailability. Machine can be unavailable randomly due to some reasons such as regular preventive maintenance. Lost sales and backorder case are also included in the first model. The second model shows an EPQ model with random machine breakdown. Subsequently, the third model integrates the first and the second model. The third model considers both the random machine breakdown and random machine unavailability. While the fourth and fifth models deal with production process problems that affect the product’s quality. The production process can not consistently produce good quality products, hence some products are rejected. The fourth model assumes that defective products are reworked immediately at the end of the production process. This system is called as the last in first out (LIFO) system. After the rework process, the machine is maintained in random time where there is a possibility that the machine is not available when needed. Contrary, the fifth model considers the first in first out (FIFO) system instead of the LIFO system. From the first to the fifth model, two types of distribution models for random machine unavailability: upper-bound and bound distribution types are considered
This study develops EPQ models for deteriorating items with stochastic maintenance and corrective time, and rework. Since these mathematical models are complex, their closed form solutions cannot be derived. To solve the models, the simple search method is employed using Maple 8 software. All models are convex in the assumed conditions.
Numerical examples are provided for each model to illustrate the theorems. Sensitivity analyses are presented to demonstrate the effects of key parameters changes to production up time and cost. The results of the sensitivity analyses show that some parameters have significant effects on the optimal total cost and the optimal production time. Some management insights to handle unreliable production system are given in Chapter 8.

並列關鍵字

Rework process ； Breakdown machine ； Inventory ； Preventive maintenance ； Deteriorating items

參考文獻

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