Optimal Ordering Policy for a Deteriorating Item with Imperfect Quality and Partial Backordering

損耗性產品於存在不良品質情況下及允許部份欠撥補貨之最佳訂購政策

10.29977/JCIIE.200511.0007

游兆鵬(Jonas C. P. Yu)；黃惠民(Hui-Ming Wee)；陳振明(Jen-Ming Chen)

經濟訂購批量 ； 損耗性 ； 不良品質 ； 部份欠撥補貨 ； EOQ ； deterioration ； imperfect quality ； partial backordering

工業工程學刊

22卷6期（2005 / 11 / 01）

509 - 520

英文

由於消費者品質意識日益高漲的年代，企業對產品品質的管控、把關也日趨嚴格；防止不良品流入消費市場，最有效的方法，就是在執行供給前，做百分之百的品質檢查。本研究主要是考慮單一產品，此產品為一種服從「指數分配」的損耗性產品，亦即產品的損耗率是常數，不會隨時間而改變。產品在供給前經百分之百地檢查篩選後，不良品全數以低價轉賣。產品損失主要來自：一是本身的損耗，二是不良品質所造成的損失；就實際生活情況而言，不良品所造成的損失比較難預估，而損失所造成的缺貨，通常消費者允許部份欠撥補貨，但是倘若消費者不願意等待欠撥補貨，供應商可能因此而造成銷售的損失。本研究基於上述的假設建立一數學模式，並以軟體程式尋求最佳解以及部份欠撥補率的下限值，透過數值範例說明與敏感度分析來瞭解影響系統之關鍵因素，試圖尋求出最適當之訂購週期與訂購量，以達到單位利潤最大化。

This study develops a production-inventory model considering a deteriorating item with imperfect quality and partial backordering. Such implicit assumptions are reasonable in view of the fact that poor-quality items do exist during production. Defective items are usually picked up during the screening process. Shortages are partially backordered since not all customers are willing to wait for new replenishments of stocks. The impatient customer will result in lost sale. The analysis shows that our model is a generalization of the models in current literatures. Also, a lower bound on the back-ordered ratio is obtained to ensure concave of the net expected profit function. An algorithm and numerical analysis are used to illustrate the solution procedure. Computational results indicate that our model leads to more realistic results.

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