降低長鞭效應一直是供應鏈管理中相當重要的議題，長鞭效應產生之主要原因有五項︰需求預測、批次訂購、價格變動、短缺賽局與前置時間。衡量長鞭效應的指標有許多種，其中Gilbert(2005)所提出來的訂貨端的長鞭效應指標與存貨端的長鞭效應指標能用來衡量長鞭效應的影響程度。而上述五項長鞭效應的因子都與存貨政策有關。存貨政策的主要目標在於決定何時訂購以及訂購數量，其中，何時訂購又分為週期訂購與再訂購點之訂購，前者之存貨水準是被動的，後者之存貨水準則主動做為再訂購之依據。而訂購數量可以是採用經濟訂購量模式，或是達到安全庫存量的訂購模式。這些不同的存貨政策都會影響供應商對銷售端需求的反應，也就是長鞭效應的幅度大小，因此，本研究針對四種不同的存貨政策，分析其長鞭效應指標與存貨管理成本的表現，提出建議的存貨政策方案。
　　本研究根據Gilbert所提出的訂貨端與存貨端長鞭效應的指標，利用系統模擬的方法，模擬四種存貨政策運作過程，並從產生的資料中求算需求標準差、存貨標準差、訂貨標準差與需求預測標準差，進而得到訂貨端與存貨端長鞭效應指標值。本研究並分析四種存貨政策在前置時間、移動平均期數與訂購週期之參數改變情況下，長鞭效應指標值的變化情形。管理者可以藉由調整參數之設定，達到降低長鞭效應的影響，然而卻存在降低訂貨端長鞭效應反而使得存貨端長鞭效應增加之兩難問題，因此管理者可同時考量存貨管理成本的因素，以期找出符合企業目標的最佳決策。

An important issue of supply chain management is to reduce bullwhip effect. The main five causes of bullwhip effect are demand forecast updating, order batching, price fluctuation, rationing and shortage gaming, and lead time. There are many methodologies to quantify the effect of bullwhip effect, one of these is brought up by Gilbert(2005), using the ratio of the standard deviation of the inventory to standard error of the forecast as a measure of the bullwhip effect on the inventory, and using the ratio of the standard deviation of orders to that of demand as a measure of the bullwhip effect on orders. The five causes of bullwhip effect are concerned with inventory policies. Inventory policies are ways that manager decide “when to pass an order” and “how many to order”. “When to pass an order” means “reorder point”, it can be “continuous review system” or “period review system”. “How many to order” can be the classical “economy order quantity (EOQ)” model or the “order-up-to a target” model. Different inventory policies have different contribution to the bullwhip effect. Therefore, the paper focuses on the effect of bullwhip effect in the condition of four different inventory policies, and analysis the values of the bullwhip effect on orders and that on inventory.
The paper simulates four inventory policies via system simulation methodology. By using programming language “visual basic for application (VBA)”, it’s can output time series data. These data are used to get the values of the bullwhip effect on orders and that on inventory. This paper also analyzes the changes of the bullwhip effect when lead time, the term of moving average and the term of order period changed. It’s found that to decrease the bullwhip effect on orders and the bullwhip effect on inventory at the same time is not possible in most cases. So, managers can also consider inventory cost, and choose the best way to fit the enterprises’ goal.

張有恆，＂現在物流管理＂，華泰文化，2005。
顏憶茹、張淳智，＂物流管理－原理、方法與實例＂，前程文化，2001。
Box, G. E. P. and Jenkins, G. M., Times Series Analysis: Forecasting and Control, Prentice Hill, 3rd Edition, 1994.
Chang, Y. and Makatsoris, H., International Journal of Simulation, Vol. 2, No.1, 2001.
Chatfield, D. C., Kim, J. G., Harrison, T. P., and Hayya, J. C., The bullwhip effect- Impact of stochastic lead time, information quality, and information sharing: A simulation study, Production and Operations Management, Vol. 13, No. 4, pp.340-353, 2004.
Chen, F., Drenzner, Z., Ryan, J. K., and Simchi-Levi, D., Quantifying the bullwhip effect in a simple supply chain: The impact of forecasting, lead times, and information, Management Science, Vol. 46, No. 3, pp. 436-443, 2000.
Dejonckheere, J., Disney, S. M., Lambrecht, M. R., and Towill D. R., Measuring and avoiding the bullwhip effect: A control theoretic approach, European Journal of Operational Research, Vol. 147, pp. 567-590, 2003.
Forrester, J. W., Industrial Dynamics, M.I.T. Press and John Wiley and Sons, Cambridge, Mass., 1961.
Ganeshan, R., “Managing supply chain inventories: A multiple retailer, one warehouse, multiple supplier model”, International Journal of Production Economics, Vol. 59, 1999.
Gilbert, K., An ARIMA supply chain model, Management Science, Vol. 51, No. 2, pp. 305-310, 2005.
Ingalls, R.G., “The value of simulation in modeling supply chains”, Proceedings of the Winter Simulation Conference, 1998.
, M. and Rusjan, B., The effect of replenishment policies on the bullwhip effect: A transfer function approach, European Journal of Operational Research, Vol. 184, pp. 946-961, 2008.
Kelepouris, T., Miliotis, P., and Pramatari, K., The impact of replenishment parameters and information sharing of the bullwhip effect: A computational study, Computers & Operations Research, Vol. 35, pp. 3657-3670, 2007.
Law, A., Simulation modeling and analysis, The McGraw-Hill, 4th Edition, 2006.
Lee, H. L., Padmanabhan, V., and Whang, S., The bullwhip effect in supply chains, Sloan Management Review, Spring 38(3), pp. 93-102, 1997a.
Lee, H. L., Padmanabhan, V., and Whang, S., Information distortion in supply chain: The bullwhip effect, Management Science, Vol. 43, No. 4, pp. 546-558, 1997b.
Ljung, G. M. and Box, G. E. P., On a measure of lack of fit in time series models, Biometrika, Vol. 65, pp. 297-303, 1978.
Metters, R., Quantifying the bullwhip effect in supply chains, Journal of Operations Management, Vol. 15, pp. 89-100, 1997.
Silver, E. A., Pyke, D. F., and Peterson, R., Inventory Management and Production Planning and Scheduling, John Wiley & Sons Inc, 3rd Edition, 1998.
Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E., Designing and Managing the Supply Chain: Concepts, Strategies And Case Studies, The McGraw-Hill, 2nd Edition, 2003.
Sterman, J. D., Modeling managerial behavior: Misperceptions of feedback on a dynamic decision making experiment, Management Science, Vol. 35(3), pp. 321-339, 1989.
Whybark, D.C. and Yang, S., Positioning inventory in distribution systems,
International Journal of Production Economics, Vol. 45, pp. 271-278, 1996.
Wright, D., and Yuan, X., Mitigating the bullwhip effect by ordering policies and forecasting methods, International Journal of Production Economics, Vol. 113, pp.587-597, 2008.