Structural approach to parametric analysis of an IP problem: On the case of the right-hand side

In this paper, we define a stepsize to parametrize the right-hand side of an integer programming problem. Based on the properties of the defined stepsize, we derive an algorithm for solving families of integer linear programming problems with the right-hand side in the form of {b->} + • {b->}′, where {b->} and {b->}′ are vectors and the single parameter • is a scalar. The proposed algorithm is appliable to the cases when the vector {b->}′ consists of positive and/or negative components. A complexity analysis of solving the entire problem is done with numerical examples.