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A discussion of post-optimality and sensitivity analysis of linear integer programming problems through the construction of Hermitian bases. These bases are closely related to a Gaussian reduction for solving sets of linear equations. It is shown that from such a basis, the optimal integer solution for discrete changes in the constraint vector may be analyzed and bounds established for which the basis remains feasible. In addition, the effects of changes in the objective function can also be investigated. All of these analyses are direct extensions of linear programming post-optimality analysis applied to these special Hermitian bases. Other near optimal solutions can also be obtained.
V. Joseph Bowman (1972) studied this question.