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A robust approach to a class of uncertain optimization problems with imprecise probabilities

In this paper a class of discrete optimization problems with uncertain costs is discussed. The uncertainty is modeled by providing a discrete scenario set, in which each scenario represents a possible realization of the element costs (the problem parameters). It is assumed that a partial information about scenario occurrence probabilities is also available. Namely, each such a probability is known to belong to a given closed interval. Several criteria for choosing a solution, such as the expected value, the value at risk, the conditional value at risk, and the tail α-mean are considered. A solution minimizing one of these criteria for the worst possible probability distribution in scenario set is computed. The computational complexity of the problems under consideration is explored. Some exact and approximation algorithms for them are proposed.