Two sensitivity theorems in fuzzy integer programming

Authors:
A. S. Asratian;N. N. Kuzjurin
Affiliations:
Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden;Institute for System Programming, Russian Academy of Sciences, B. Kommunisticheskaya 25, 109004 Moscow, Russia
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

We consider the problem of estimating optima of covering integer linear programs with 0-1 variables under the following conditions: we do not know exact values of elements in the constraint matrix A but we know what elements of A are zero and what are nonzero, and also know minimal and maximal values of nonzero elements. We find bounds for variation of the optima of such programs in the worst and average cases. We also find some conditions guaranteeing that the variation of the optimum of such programs in the average case is close to 1 as the number of variables tends to infinity. This means that the values of nonzero elements in A can vary without significantly affecting the value of the optimum of the integer program.