Determining Replenishment Lot Size and Shipment Policy in an EPQ Model with Quality Assurance: An Alternative Approach and Analysis

探討含品質保證的經濟生產批量模式之補貨批量與運送策略：另一種求解方法與分析

10.6186/IJIMS.2012.23.3.6

張宏吉(Hung-Chi Chang)

存貨 ； 經濟生產批量 ； 多次運送 ； 無微分最佳化方法 ； 不良品 ； Inventory ； EPQ ； multiple shipments ； derivatives-free optimization ； imperfect quality

International Journal of Information and Management Sciences

23:3（2012 / 09 / 01）

323 - 332

英文

本文分析在經濟生產批量模式中考慮品質保證議題並探討補貨批量與運送策略之現存研究。針對目標函數以補貨批量與運送次數為決策變數之模式，現存研究已運用傳統最佳化方法或代數解法，推導出決策變數為連續時之最佳解公式。本文則進一步展現,如何運用其他最佳化的方法，推導出決策變數為連續（補貨批量）與間斷（運送次數）以及模式最小總成本之封閉表示式。對於現存的研究，本文亦提出有用的補述，推導出執行多次運送策略的門檻值，並說明重要的參數對批量決策與運送策略的影響。

This paper analyzes several studies that address the replenishment lot size and multidelivery policy in an extended EPQ model with quality assurance. For a model in which the objective function is expressed in terms of lot size and number of shipments, previous studies have derived closed-form expressions for determining the optimal continuous values for both decision variables, using the classical optimization technique or algebraic method. In this paper, our aim is to show how to apply other optimization methods to derive explicit closed-form expressions, not only for the optimal lot size, but also for the optimal integer number of shipments and the minimum total cost of the model. Furthermore, we provide a helpful supplement to those related studies, specifically, a threshold for implementing multi-delivery policy and the effects of problem parameters on the lot size decision and shipment policy.

1. Hu, J.,Xu, R.,Guo, C.(2011).Fuzzy economic production quantity models for items with imperfect quality.International Journal of Information and Management Sciences,22,43-58.
   連結：
2. Banerjee, A.(1986).A joint economic-lot-size model for purchaser and vendor.Decision Sciences,17,292-311.
3. Carcía-Laguna, J.,San-José, L. A.,Cárdenas-Barrón, L. E.,Sicilia, J.(2010).The integrality of the lot size in the basic EOQ and EPQ models: Applications to other production-inventory models.Applied Mathematics and Computation,216,1660-1672.
4. Cárdenas-Barrón, L. E.(2011).The derivation of EOQ/EPQ inventory models with two backorders costs using analysis geometry and algebra.Applied Mathematical Modelling,35,2394-2407.
5. Cárdenas-Barrón, L. E.,Wee, H. M.,Blos, M. F.(2011).Solving the vendor-buyer integrated inventory system with arithmetic-geometric inequality.Mathematical and Computer Modelling,53,991-997.
6. Cárdenas-Barrón, L. E.,Wee, H. M.,Teng, J. T.(2011).A supplement to "Using the EPQ for coordinated planning of a product with partial backordering and its components".Mathematical and Computer Modelling,54,852-857.
7. Chen, K. K.,Wu, M. F.,Chiu, S. W.,Lee, C. H.(2012).Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework.Expert Systems with Applications,39,2232-2235.
8. Cheng, F. T.,Ting, C. K.(2010).Determining economic lot size and number of deliveries for EPQ model with quality assurance using algebraic approach.International Journal of the Physical Science,5,2346-2350.
9. Chiu, S. W.,Chen, K. K.,Lin, H. D.(2011).Numerical method for determination of the optimal lot size for a manufacturing system with discontinuous issuing policy and rework.International Journal for Numerical Methods in Biomedical Engineering,27,1545-1557.
10. Chiu, S. W.,Lin, H. D.,Wu, M. F.,Tang, J. C.(2011).Determining replenishment lot size and shipment policy in an EPQ model with delivery and quality assurance issues.Scientia Iranica Transactions E: Industrial Engineering,18,1537-1544.
11. Chiu, Y. S. P.,Lin, C. A. K.,Chang, H. H.,Chiu, V.(2010).Mathematical modeling for determining economic batch size and optimal number of deliveries for EPQ model with quality assurance.Mathematical and Computer Modelling of Dynamical Systems,16,373-388.
12. Goyal, S. K.(1976).An integrated inventory model for a single supplier-single customer problem.International Journal of Production Research,15,107-111.
13. Naddor, E.(1966).Inventory Systems.New York:John Wiley and Sons.
14. Porteus, E.(1986).Optimal lot sizing, process quality improvement, and setup cost reduction.Operations Research,34,137-144.
15. Rosenblatt, M J.,Lee, H. L.(1986).Economic production cycles with imperfect production processes.IIE Transitions,18,48-55.
16. Teng, J. T.(2009).A simple method to compute economic order quantities.European Journal of Operational Research,198,351-353.
17. Teng, J. T.,Cárdenas-Barrón, L. E.,Lou, K. R.(2011).The economic lot size of the integrated vendor-buyer inventory system derived without derivatives: A simple derivation.Applied Mathematics and Computation,217,5972-5977.
18. Warner, M.(Ed.)(1996).International Encyclopedia of Business and Management 4.London:Routledge.
19. Yano, C. A.,Lee, H. L.(1995).Lot sizing with random yields: A review.Operations Research,43,311-334.

1. 蔡登茂、林芷如(2015)。具回收料價格考慮之逆物流最適買賣整合生產存貨模式。臺灣企業績效學刊，8(2)，159-180。