For a class of optimal decision making problems of warfare systems with force resource complementary, the
definitions of the empty type winning strategy and non-empty type winning strategy are proposed based on a defined winning
theory of warfare systems. By means of Lanchester equation, the sufficient conditions for the existence of two strategies are
presented. Nonlinear optimization technology is used to solve the corresponding optimal decision making problems for
winner, and the optimal strategies is obtained, which ensures the victory of the decision maker in conflicts, and the maximum
value of index performance is obtained. Numerical examples show the feasibility of the proposed optimal winning strategies.

Lanchester equation;winning theory;empty type winning strategy;non-empty type winning strategy;force
resource complementary;nonlinear optimization