An implicit enumeration algorithm for the all integer programming problem

In this paper an implicit enumeration algorithm is presented for solving the general integer programming problem. The algorithm is a generalization of algorithms of Balas and Geoffrion for solving 0-1 problems. In order that each variable may be treated directly, a special data structure has been designed. Based on this data structure, a procedure is developed which efficiently keeps track of the status of the algorithm and of the potential actions to be taken at any stage in the procedure. The concept of a ‘best’ surrogate constraint is extended and incorporated into the algorithm. The algorithm can be modified for solving mixed integer programming problems.