The Lanchester (n, 1) problem

Abstract

We discuss the background of the Lanchester (n, 1) problem, in which a heterogeneous force of n different troop types faces a homogeneous force. We also present a more general set of equations for modelling this problem, along with its general solution. As an example of the consequences of this model, we take the (2, 1) case and solve for the optimal force allocation and fire distribution in a (2, 1) battle. Next, we present examples that demonstrate our model's advantages over a previous formulation. In particular, we point out how different forces may win a battle, depending on the handling and interpretation of the model's solution. Lastly, we present a variant of the Lanchester square law which applies to the (2, 1) case.

Keywords:

• Lanchester problem
• optimisation

Acknowledgements

We thank the referees for their valuable suggestions, and their comments concerning Lanchester's original work. This research has been supported in part by the US Army Research Development and Engineering Command, Simulation Technology Center, Contract #N61339-02-C-0107.