On solving discrete optimization problems with one random element under general regret functions

Diptesh Ghosh, Pranab K. Mandal, Shubhabrata Das

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    Abstract

    In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and define an optimal solution as one having the least possible risk. We show that for discrete optimization problems with one random element and with min-sum objective functions a least risk solution for the stochastic problem can be obtained by solving a non-stochastic counterpart where the latter is constructed by replacing the random element of the former with a suitable parameter. We show that the above surrogate is the mean if the stochastic problem has only one symmetrically distributed random element. We obtain bounds for this parameter for certain classes of asymmetric distributions and study the limiting behavior of this parameter in details under two asymptotic frameworks.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages17
    Publication statusPublished - 2005

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1784
    ISSN (Print)0169-2690

    Keywords

    • METIS-227058
    • IR-65968
    • EWI-3604
    • MSC-90C31

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