Lanchester Models for Irregular Warfare

Round 1

Reviewer 1 Report

In this work the author present a nice review about Lanchaster models focusing the attention on asymmentric combat models. Specifically, three irregular-warfare types are discussed: (1) those models that consider the level of situational awareness presented at both forces, (2) those models where the civilian population plays a fundamental role, and (3) those assymetric models where more than tow armies are involved.

It is an interesting review paper and, in my opinion, can be accepted for publication in this special issue. Nevertheless, the author must address the following:

(1) The summary and conclusions section must be improved.

(2) It could be of interest to present some future research lines.

(3) Explain the difference (advantages and disadvantages) between deterministic Lanchester models and stochastic Lanchester models.

Author Response

Thank you for reviewing the paper and for your comments.

1,2. I agree that the Introduction and Summary needed some beefing up. Please see P. 4 (Introduction), where I discuss the three main thrusts of the paper, and P. 28 (Summary) where I discuss possible direction for future research on Lanchester models.

3. I added a few sentences on stochastic Lanchester models at the end of Section 2.  

Reviewer 2 Report

The paper "LANCHESTER MODELS FOR IRREGULAR WARFARE" reviews the Legacy Lanchester equations used to model the mutual attritional dynamics of two opposing military forces. Moreover the Lanchester modeling is used by the author to present models that capture irregular warfare, such as insurgencies, highlight the role of target information in such conflicts, and capture multilateral situations where several players are involved in the conflict.

In my opinion the paper looks more like a review-paper then a research-paper, thus the Introduction part should be extended to cover the recent results on the more-way combat. The Summary part should also be updated to discuss the possible extensions of the Lanchester models.

Besides of the minor requests, the paper is interesting, technically sound and written in a good English.

Author Response

Thanks for reviewing and for the comments

Indeed, as stated in the Introduction, this is a review paper, summarizing about two decades of research on the application of Lanchester theory to irregular warfare. 

I agree that the Intro and Summary needed some beefing up. I added discussions in the Introduction (1) and Summary (7). In the Introduction I described the three main thrusts of the paper (P. 4) and in the summary I added a discussion about possible directions for Lanchester models' extensions (P. 28)

Reviewer 3 Report

It is an interesting review paper. It would be nice to see the discussion of whether or not multiple equilibria are possible for more complex models like (25), and stability of such equilibria.

Author Response

Thank you for your review and comment.

This is indeed a review paper summarizing about two decades of applications of Lanchester theory to irregular warfare.

Your comment regarding model extension is interesting and very appropriate. Thanks!

One possible extension of the model in (25) is to assume that the state forces (B) respond to the size of the insurgency (R) when deciding on reinforcement. Thus ALPHA is replaced by ALPHA(R). Suppose this function is linear, that is, ALPHA(R)=aR+b (b>=0) then if RHO>a we are back to the situation in (25) where RHO is replaced by a-RHO. If the reverse is true, the state forces keep growing and the insurgents are led to their demise. A nonlinear function could in principle lead to multiple equilibria.

I added a short discussion as the last paragraph of Section 5.

Reviewer 4 Report

see attachment

Comments for author File: Comments.pdf

Author Response

Dear Professor Volkmer,

Thank you for reviewing the paper and for your comments.

Indeed, the paper is a review paper, not a research one. It summarizes research on applying Lanchester models to current conflict situations - irregular warfare.

As you correctly point out, it is intended for readers with mathematical background who are interested in conflict modeling.

Thanks again,

Moshe Kress