Qualitative and quantitative analysis of the stability set of the first kind in parametric large scale integer linear programming problems

摘要

This paper presents a qualitative and quantitative analysis of the stability set of the first kind in large scale integer linear programming problems with real parameters in (1) The objective function, (2) The right-hand sides of the independent constraints and (3) Both the objective function and the right-hand sides of the independent constraints. The set of feasible parameters and the stability set of the first kind are redefined and analyzed for the above cases. In addition, a theory and an algorithm for the determination of the stability set of the first kind are given. Finally, an illustrative example for every case is given to clarify the developed theory and the algorithm.