Sensitivity analysis for minimum weight base of a matroid

Numerous problems of combinatorial optimization can be formulated as problems of finding of the minimum weight base of a matroid, and then solved by the greedy type algorithms. The paper considers some post-optimality analysis questions for this problem. Given the minimum weight base we want to calculate the maximum increase and decrease of the weight of each matroid element which preserves the optimality of this base. A method for computing these data perturbations, i.e. tolerances of matroid elements, is given. This paper discusses also some other questions of post-optimal analysis which can be solved given the tolerances mentioned.