Published by INFORMS/MAS Topics in Operations Research, 2001, 256 pages, ISBN #1-877640-16-6. Available to INFORMS members for $30.00 from the Book Series, "Topics in OR" [external link].
This book analyzes hundreds of historical battles to determine whether there are any consistent formulae for predicting combat effects. The results are positive and are incorporated in a spreadsheet battle model, which includes attrition, duration, advance, and victory. Attrition at the gross level is determined to follow neither the Lanchester Square Law nor the Lanchester Linear Law. Instead, attrition follows a law between the Linear Law and the Logarithmic Law. The model and all data are contained in the included CD.
The figure illustrates the provocative fact of patterns in historical battles: the battles follow an upward slope. Positive ln(Force Ratio) indicates more attackers than defenders are present. The red dots show that attackers are more likely to win than defenders when the force ratio favors them. However, attackers also win when the force ratio favors the defenders. The attackers are generally victorious below the sloping midline and the defenders win above the line.
The mathematics in this book is simple (not much above multiplying and dividing), most of the bulk is figures and tables, and the conclusions and caveats are summarized at the end. The model (included on the CD) runs on Lotus or Excel virtually instantaneously and only has a couple of dozen inputs.
More information is available on this website.
Published by MORS Military Operations Research Society, 1999, 172 pages, www.mors.org.
The Military Operations Research Society (MORS) held a workshop on Operations Other Than War (OOTW) analysis and model techniques on 28-30 January 1997 at MacDill Air Force Base, Florida. This book describes the workshop and its findings.
Published by The Canadian Peacekeeping Press, 1996, 300 pages, ISBN #1-896551-10-6.
Geo-political decisions can be critical determinants of success in war and peace. These decisions are based on predicted psychological and sociological responses by the various individuals and groups in the decision environment. For example, mental models are used in deciding whether to display our naval "presence" in a foreign port or whether a discussion on the golf course would be more effective. However, in constructing consistent policies over long periods of time that involve the conflicting interests of many countries, the complexities often overwhelm the mental models. In evaluating proposed actions, questions should address the immediate impact of an action, the long term impact, the potential for diverse impacts throughout the populations of interest, and the consequences of previous actions by other parties in the decision environment. A computer implementation that combines and extends the mental models might be useful; however, designing such an implementation is a hard problem. This paper presents a philosophical framework for modeling psycho-social attributes at the theater level and develops some of the necessary structure for a model.
Published by John Wiley & Sons, 1999, 205 pages, ISBN #0-471-98109-5.
Algorithms are used to describe the steps used in deciding treatments. Algorithms are most often diagrammed as flow charts, with decisions leading to procedures and further decisions. However, several other diagram types, or "languages," are appropriate in emphasizing different aspects of the algorithm. Gantt charts, influence diagrams, and decision trees are described as alternatives.
Published by MORS Military Operations Research Society, 1995, 594 pages, www.mors.org.
This article addresses the question of validating the homogenous Lanchestrian square law of attrition by the use of historical data (and by extension, other attrition models). Validating an attrition model means testing that model against reality. In this case, Lanchester's square law is tested against the data from the Inchon-Seoul campaign of the Korean War. The data are examined using three analysis techniques: linear regression, the Akaike Information Criterion (AIC), and Bozdogoan's Consistent AIC (CAIC). The data do not fit the assumption of a single, constant coefficient, homogeneous square law battle. The data do fit a set of three such battles (a new one every six or seven days); however, the data fit three constant-casualty-model battles just as well. The homogeneous Lanchester square law cannot be regarded as a proven attrition algorithm for warfare; however, the square law cannot be regarded as disproven either. Data on more battles are required to validate the square law or any other proposed attrition law.
The Lanchester square and linear laws do not provide good models of combat attrition as evidenced in historical data. A particular homogeneous, mixed, linear-logarithmic law, however, does provide a good approximation to the historical data. (This chapter precedes the one above; however, logically it should follow it.)
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