不完美生產系統下，考量倉儲空間、重工、檢驗之經濟生產批量模式

An Economic Production Quantity Model for an Imperfect Production System in Consideration of Storage Space Capacity, Rework, and Inspection

薛竹媛(Chu-Yuan Hsueh)

指導教授 ： 宮大川

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2011年)

https://doi.org/10.6840/cycu201100939

摘要

傳統經濟生產批量考慮完美製程不會產出不良品，但與實際工廠內部真正所面臨到的問題有極大的落差。因此，本研究將放寬傳統EPQ基本假設，包括製程穩定、倉儲無上限等假設，當製程生產一段時間後，會受人為或非人為等外在因素影響，如操作不當、投料不妥、氣候等因素使製程從控制內(in-control)狀態轉為控制外(out of control)狀態，而以上等外在因素所產生的製程偏移時間為一隨機變數且服從指數分配，當一旦偏移後會產出固定比例的不良品數，於是本研究針對製程不穩定採取製程中之全檢策略，且對檢驗出的不良品進行重工與丟棄，並考慮原物料聯合補貨方面會受限於倉儲空間上限，發展出單位時間內總生產存貨成本最小化模式，其根據renewal reward 定理，即將一個生產存貨循環之期望總成本除以一個生產存貨循環之時間長度。而此模式考慮生產成本、整備成本、產品與原物料之庫存成本、重工成本、檢驗成本、丟棄成本及原物料補貨成本，以求得最佳生產週期時間與最佳原物料補貨週期數，再利用Algorithm1與前者結合bi-section方法之Mo- Algorithm1，比較分析兩個演算法之間的差異，並透過基因演算法驗證本模式之準確性。最後，透過範例數值代入本研究所推導出之數學模式中，比較兩種演算法之差異度，並透過調整某特定參數，進而觀察其變化關係。

關鍵字

聯合補貨 ； 丟棄 ； 重工 ； 不良品 ； 不完美製程 ； 倉儲上限

並列摘要

The traditional Economic Production Quantity (EPQ) considers the perfect production process without defects and space capacity limit. This research relaxes some EPQ assumptions which include perfect items and unlimited space capacity. As time goes on, the production process will shift from an in-control state to an out-of-control state. The elapsed time until the production process shifts is assumed to be a random variable with a known exponential distribution. Thus, a fixed portion of items produced is defective. This research is concerned with in-process inspection, rework, scrap, space capacity and economic joint replenishment quantity of raw material in a batch production system. The objective is to determine an optimal production cycle time and the replenishment quantity that minimize the expected average cost per unit of time. Then based on renewal reward theorem, expected average cost per unit of time can be obtained by dividing the expected total costs per renewal cycle to the expected duration of a renewal cycle. The bisection method is employed to find a near-optimal solution for the model. By approximating exponential function included in the objective function, a closed-form solution can be developed. A genetic algorithm heuristic is implemented to verify the effectiveness of the solution procedure we proposed in this research. Finally, to demonstrate the validity of the model, a numerical example is provided to illustrate the model. Meanwhile, sensitivity analysis is performed to give management insight.

並列關鍵字

JRP ； scrap ； rework ； imperfect production ； defective ； space capacity

參考文獻

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