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 在現代戰爭中，我們知道戰爭的勝利來源主要來自於一個重要的因素，即掌握由攻擊轉換為防守或者是由防守轉換為攻擊的重要時機。在本文中，我們除了介紹藍徹斯特直線律與平方律外，最主要是利用混合律來反映出第二次世界大戰中的阿登戰役，並與藍徹斯特原型方程式中之直線律與平方律求得之最小平方誤差和比較，進而瞭解德軍在此戰役中由攻擊轉換為防守的時間及德軍與盟軍雙方之耗損率，文內所建構混合律的數學模式中，即包含了雙方耗損率及攻守轉換時間等變數，這些變數幫助我們瞭解混合律的數學模式較直線律與平方律，更能反映出第二次世界大戰中阿登戰役的歷史資料。
 In modern warfare, many believe the decisive factor in winning a battle is seizing the right moment to shift from defense to attack, or vice versa. In this dissertation, the Lanchester Linear Law and Square Law are introduced, other than these, the Ardennes Campaign during World War II is reflected by means of the Mixed Law. In the meantime, through the minimum variation and comparison evaluated from Linear Law and Square Law in the Lanchester Original Form, we understand how was the time both German and Allied Army measured changing technique from attacking to defence and how was the Consumption Ratio for both of parties. The mathematical model in the Mix Law constructed in this dissertation, including the variations of the consumption ratio and shifting time from attacking to defending, showed more comprehension on mathematical model of Linear Law and Square Law, and reflected more historical information on the Ardennes Campaign during World War II.
 中文摘要...............................................................I 英文摘要...................................................................II 誌謝...........................................................III 目錄...............................................................V 圖目錄............................................................ VII 表目錄........................................................... VIII 第一章 緒論.......................................1 1.1研究動機...............................................1 1.2研究目的................................................2 1.3研究架構................................................3 第二章 文獻探討...................................5 2.1歷史背景回顧.......................................5 2.2藍徹斯特方程式緣起...............................11 2.3研究學者探討......................................12 2.4本研究模式及方法..................................15 第三章 模式建構與符號...................................17 3.1模式架構..................................................17 3.1.1直線律..............................................18 3.1.2 平方律..................................................20 3.2模式建構...........................................22 3.3符號說明...............................................23 3.4目標函數...............................................25 第四章 研究方法...............................................26 4.1模式推導.................................................26 4.2阿登戰役歷史資料........................................29 第五章 結論與建議...............................................31 5.1藍徹斯特方程式的優缺點...............................31 5.2結論建議..................................................31 5.3未來研究方向.............................................32 參考文獻............................................................37 作者簡介.................................................................40
 [1] 唐文漢(民八五)，兵力耗損理論用於作戰判斷之研究，國防管理學院資源管理研究所碩士論文。[2] 郭俊義（民七五）, “計算機模擬理論方法及其應用.” 宇航出版社,pp.271-275.[3] 孟昭宇著（民八八），「軍事作業研究」，第五章─藍徹斯特方程式應用於坦克作戰分析（微分方程估算戰損）。[4] Bracken, J, (1995), “Lanchester models of Ardennes Campaign.” , Naval Research Logistics, Vol. 42, pp. 559-577.[5] Brackney, H. (1959), “The Dynamics of Military Combat.” , Operation Research Vol. 7, pp. 30-44.[6] Deitchman, S. J. (1962),“A Lanchester model of guerrilla warfare.”Operation Research Vol. 10, pp. 818-827.[7] Engel, J. H. (1954),“A verification of Lanchester’s Law.”Operation Research Vol. 10, pp. 163-171.[8] Fricker, R. D. (1998),“Attrition models of the Ardennes Campaign.” Naval Research Logistics Vol. 45, pp. 1-22.[9] Helmbold, R. L. (1994),“Direct and Inverse Solution of the Lanchester Square Law with General Reinforcement Schedules.”European Journal of Operations Research Vol. 77, No. 3, pp. 486-495.[10] James G. Taylor (1974), “Lanchester-Type Model of warfare and Optimal Control.” Naval Research Logistics Quarterly 21, pp. 79-106.[11] James G. Taylor (1974), “Some Differential Game of Tactical Interest.” Operation Research Vol. 22, pp. 304-317.[12] James G. Taylor (1975), “On the Treatment of Force-Level Constraints in Time-Sequential Combat problem.” Naval Research Logistics Quart22, pp. 617-650.[13] James G. Taylor and G.G.Brown (1976), “Canonical Methods in the Solution of Variable.” Operation Research Vol. 24, pp. 44-69.[14] Lanchester, F. W. (1956),“Aircraft in Warfare. The Dawn of the Fourth Arm-No.V.” , Reprinted on pp. 2138-2148 of The World of Mathematics, vol. IV , J. Newman, Simon and Schuster, New York.[15] Lan, S. P., Wan, W. J., Chu, P. and Lin, P. H. (1998), “Fitting Lanchester’s Square Law to the Ardennes Campaign.”European Journal of Operation Research.[16] Morse, P. M. and Kimball, G. E. (1951), Methods of operations research, Wiley, New York.[17] Maybee, J. S. (1985), “The theory of combined-arms Lanchester-type models of warfare.”Naval Research Logistics Quarterly 32, pp. 225-237.[18] Peter Chu and Patrick S. Chen, (2000), “A simple method to fit Lanchester’s linear model for Ardennes Champaign.” Journal of Information & Optimization Sciences, Vol. 21, No. 3, pp. 421-427[19] Peter Chu and Patrick S. Chen, (2001), “Applying Lanchester’s Linear Law To Model the Ardennes Campaign.” Naval Research Logistics, Vol. 48.[20] R. H. Shudde, “Lanchester’s Theory of Combat” Chapter 6.[21] Samz, R. W. (1972), “Some comments on Engel’s ‘A verification of Lanchester’s Law.’”Operation Research Vol. 20, pp. 49-52.[22] Taylor, James G. (1981), “Force-On-Force Attrition Modeling.” Military Application-Section Operation Research Society of American, Arlington, VA.
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 1 兵力耗損理論用於作戰判斷之研究

 1 李咸亨（1998），山坡地建築專章與技術評議，地工技術，頁63-74。

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