考量變動訂購成本及持有成本之EOQ存貨模式

EOQ Models with Varying Ordering and Holding Costs

安博隆(Poltak-Tua Dorens-Ambarita)

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/碩士(2014年)

https://doi.org/10.6840/cycu201400256

摘要

摘要
產品庫存是公司的資產，並與公司的財務方面有密切的相關。因此，若無妥善的管理，庫存將會降低利潤。此後，存貨模式總是被用來設定為使總成本達到最小化。而且總成本為影響存貨模式之一重要參數。本研究提出一個EOQ存貨模式考慮到變動的訂購成本及持有成本使模式更符合現實情況。且本EOQ模式使用考慮缺貨 (允許缺貨補貨) 及不考慮缺貨(不允許缺貨補貨)兩種情況。主要目的為使總成本(TC)達到最小化。然而，此存貨模式以最佳存貨週期、經濟訂購量、及缺貨量為決策變數。
典型的最佳化方式是透過傳統的微積分求得目標函數之極大(小)值。因此，本研究透過微積分求解此存貨模式下的最佳存貨週期、經濟訂購量、及缺貨量之表示式並證明其存貨模式之凸性(convexity)。之後，透過一個數值範例說明此存貨模式之有效性及實用性，以及考量不同的訂購成本(α)及持有成本(β)下對於目標函數之敏感度分析，並用圖解與數值結果呈現參數改變對目標函數之影響。

關鍵字

變動訂購成本 ； EOQ存貨模式 ； 變動持有成本

並列摘要

Inventory is an important asset of a company, and its policy greatly influences the financial success of a company. Therefore, a company’s profit may decline due to inappropriately inventory management. Hence, inventory model should aim to minimize the total relevant inventory cost. Consequently, the total inventory cost becomes an important consideration and it affects the performance of a company. In this research, we propose a more practical EOQ models where the ordering cost and the holding cost are an increasing function of the ordering cycle length. Two EOQ models are developed. One considers no shortage environment and the other allows for shortage and backorder. The main objective of this research is to minimize the total inventory related costs. The optimum inventory cycle, the economic order quantity, and backorder size are the decision variables in this study. The classical optimization techniques using calculus technique with first-order and second-order derivatives have been performed to determine the optimum lot size, and to prove its convexity. To demonstrate the utility of the formulated models, and study the effect of the ordering cost (α)shape parameter and the holding cost (β) shape parameter on the optimal solution, numerical examples considering different value of α and β are given. Sensitivity analyses are also performed. They are presented graphically and numerically to illustrate the behavior of the models, and to determine the effects of the parameters changes. The numerical results show that our proposed models give smaller annual total costs than the traditional EOQ model. Finally, the results of the sensitivity analysis show that only the ordering cost parameter has a significant effect on the optimal total cost in both models.

並列關鍵字

EOQ models ； varying ordering cost ； varying holding cost

參考文獻

Abuo-El-Ata, M.O., Fergany, H.A., and El-Wakeel, M.F., 2003. Probabilistic Multi-Item Inventory Model with Varying Order Cost Under Two Restrictions: A Geometric Programming Approach, International Journal of Production Economics, 83, 223-231. Alamri, A.A. (2004). Economic Production Lot Size Inventory Models under Learning and Forgetting Effects. Department of Statistics and Operation Research at the College Science, King Saud University. Alfares, H.K., 2007. Inventory Model with Stock-Level Dependent Demand Rate and Variable Holding Cost, International Journal of Production Economics, 108 (1-2), 259-265. Arnold, J.R.T., Chapman S.N., Clive, L.M. (2008). Introduction to Materials Management (6thEdition). New Jersey: Pearson Prentice Hall. Darwish, M.A., 2008. EPQ Models with Varying Setup Cost, International Journal of Production Economics, 113 (1), 297-306. El-Wakeel,M.F., 2012. Constrained Backorders Inventory System with Varying Order Cost: Lead Time Demand Uniformly Distributed, Journal of King Saud University-Science, 24, 285-288. Ghasemi, N., and Nadjafi, B.A., 2013. EOQ Models with Varying Holding Cost, Hindawi Publishing Corporation, Journal of Industrial Mathematics, Vol. 2013, Article ID 743921, 7 pages. Giri,B.C., Goswami A., and Chaudhuri, K. S., 1996. An EOQ Model for Deteriorating Items with Time Varying Demand and Costs.Journal of the Operational Research Society, 47 (11), 1398–1405.

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Goh, M, 1992. Some Results for Inventory Models Having Inventory Level Dependent Demand Rate,International Journal of Production Economics. 27( 2), 155-160. Harris, F.W. 1913. How Many Parts to Make at Once, The Magazine of Management, 10(2), 135 -136, 152. Jaber, M.Y. (2009). Inventory Management Non-Classical Views. United States of America: Taylor and Francis Group. Jaber, M.Y. (2006). Lot Sizing for An Imperfect Production Process with Quality Corrective Interruptions and Improvements, and Redustion in Setups. Computers & Industrial Engineering, 51, 781-790.

Muckstadt, J.A., Sapra, A. (2010), Principles of Inventory Management when You are Down to Four, Order More. http://www.springer.com/978-0-387-24492-1. Mishra, V.K., Singh, L.S., Kumar, R. (2013). An Inventory Model for Deteriorating Items with Time-Dependent Demand and Time-Varying Holding Cost under Partial Backlogging. Journal of Industrial Engineering International, 9(4), 5 pages. Porteus, E.L. (1986). Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction, Operations Research. 34 (1), 137-144. Sarkar, B., Saren, S., Wee, H.M., 2013. An Inventory Model with Variable Demand, Component Cost, and Selling Price for Deteriorating Items, Economic Modeling, 30, 306-310. Waters, D. (2003). Inventory Control and Management (2nd Edition). Chichester: John Wiley & Sons. Wee, H. M., 2010. Inventory Systems Modeling & Research Methods.New York: Nova Science Publishers, Inc.