在不良品可完全重工修復與非連續性配送之生產系統下探討最佳批量與配送次數決策

Optimal batch size and number of deliveries for EPQ model with non-continuous shipments and perfect rework process

鍾佳玲(Chia-Ling Chung)

指導教授 ： 王聖嘉

朝陽科技大學/管理學院/企業管理系/碩士(2009年)

摘要

本研究使用數學模式推導出不良品可完全重工修復與非連續性配送之生產系統下的最佳批量與配送次數決策。傳統的經濟生產批量模型是假設製造過程中的生產品質是完美且配送模式上為連續配送，但在現實中是不切實際且不合乎成本考量，因為實際生產過程中，不論是人為操作的失誤或機器發生故障當機，都導致不良品的產生以及成本的增加。因此本研究假設完美重工下，不良品皆可完全重工為良品，並考慮購買者的存貨成本，且進行定量多次配送產品給顧客，進而整合製造商與購買者的總合生產成本最小，運用Hessian Matrix Equation推導與驗證出最佳生產批量與最佳配送次數。所以本研究擬定三個部分，模式一為重工後配送且含購買者存貨成本之最佳生產批量及配送次數決策；模式二是重工前配送並含購買者存貨成本但重工時間小於一次配送時間之最佳生產批量及配送次數決策；模式三是重工前配送並含購買者存貨成本但重工時間大於一次配送時間之最佳生產批量決策。接著提出實例來做驗證，並對其參數做敏感度分析，以提供業界作為實際應用與決策上之參考依據。

關鍵字

最佳配送次數 ； 最佳生產批量 ； 非連續配送 ； 完美重工 ； 不良品 ； EPQ

並列摘要

This paper studies the optimal batch size and number of deliveries for EPQ model with non-continuous shipments and perfect rework process. Traditional Economic Production Quantity (EPQ) assumes that the production process is perfect and delivery policy is continuous. However, in real-life situations defect rate is inevitable and multiple shipments are commonly used. Therefore, this paper investigates a realistic production system with the following assumptions: (1) all defective items are repairable and will be repaired after regular production process ends; (2) the inventory costs of purchasers are also taken into consideration and the customer’s products are offered by the non-continuous shipments policy. This study integrates the manufacturer and buyer’ costs, uses Hessian Matrix equation is used to test the convexity of the cost function, and find the optimal production-shipment strategy that minimizes the total cost for such a realist production-inventory system.
The following mathematical models are about the EPQ model examined by rework and non-continuous shipments: Model 1 deals with the optimal batch size and number of deliveries with buyer’s inventory cost after the rework process. Model 2 investigates the delivery time starting before the rework process but the rework time is less than one delivery time. Mode 3 investigates the delivery time starting before the rework process but the rework time is more than one delivery time. The results of these models are verified. In addition, numerical examples with sensitivity analysis for optimal batch size and number of deliveries are provided to demonstrate its practical usage.

並列關鍵字

perfect rework ； defective item ； EPQ ； non-contin

參考文獻

[31] 王聖嘉，「探討經濟生產批量模式含不良品重工之最佳決策」，博士論文，中原大學工業工程研究所，台中(2003)。

[1] Agnihothri, S. R. & Kenett, Ron S. (1995). Impact of defects on a process with rework. European Journal of Operational Research, 80 (2), 308-327.

[2] Beatriz Abdul-Jalbar, Jose’ M. Gutie’ rrez, Joaquı’n Sicilia. (2007) An integrated inventory model for the single-vendor two-buyer problem. Int. J. Production Economics, 108, 246–258

[3] Bhaba R. S. & Gyana R. P. (1996).Optimal batch size and raw material ordering policy for a production system with a fixed-interval, lumpy demand delivery system. European Journal of Operational Research, 89, 593-608

[6] Diponegoro, A.S. & Bhaba R. (2006). Finite horizon planning for a production system with permitted shortage and fixed-interval deliveries. Computers & Operations Research, 33, 2387-2404