Cutting Some Trees to See the Forest

Most models of air and land combat use schemes of aggregation and disaggregation in representing combat systems, in spatial configuration, and in depicting the progress of a battle. For example, the use of firepower “scores” is an extreme case of aggregation of weapons into a single measure. Combining like systems into weapons categories — partial aggregation — is a common approach to representing a large number of aircraft or ground weapon types. This report explores different approaches to aggregation and what is known theoretically about aggregation and disaggregation in Lanchester combat models that in two dimensions are commonly called square-law models. It defines requirements for consistency between aggregate and higher-dimensioned models of this type. Some important conclusions are that aggregation should take into account the specific capabilities of the opponent (raising concern about many “scored” approaches that attempt to evaluate force components in isolation), and that partial aggregation (grouping “like” systems) and disaggregation of previously aggregated results can be done consistently only when certain restrictions of the relative attrition capabilities of weapon systems hold. When this is the case, specific nonarbitrary weightings can be determined for the partial aggregations.