Abstract:

In order to avoid the need to consider the relaxation linear programming problem in solving pure integer programming problem， an efficient new solution method for pure integer programming problem is proposed by using the indefinite equation theory in number theory and the estimation method for solving inequality equations. Through the derivation of two theorems， it is proved that the new solution method is feasible to solve pure integer programming problems. Taking the pure integer programming problem as an example， the cutting-plane method， the branch-and-bound method and the new solution method proposed are used to solve it respectively. The results show that compared with the cutting-plane method and branch-and-bound method， the new method is simpler for solving simple pure integer programming problems.

Key words:

"> pure integer programming">, number theory">, indefinite equation theory">, linear programming