The mathematical methods of analysis play an increasingly significant role in planning military operations. The matrix differential equations educed on the basis of Lanchester combat models for describing the heterogeneous force combat engagements were studied. An investigation was conducted on the campaign superiority parameter derived directly from the control matrix and the initial value of the state variables without solving the equations. Battle outcome prediction, military decision support, force deployment optimization and fire allocation programming have been discussed with an air-combat example to demonstrate the important applications of the campaign superiority parameter. Evaluation of superiority parameter as well as Lanchester equations is presented in the conclusion.