Distributionally robust simple integer recourse

Weijun Xie () and Shabbir Ahmed ()
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Weijun Xie: Virginia Tech
Shabbir Ahmed: Georgia Institute of Technology

Computational Management Science, 2018, vol. 15, issue 3, No 3, 367 pages

Abstract: Abstract The simple integer recourse (SIR) function of a decision variable is the expectation of the integer round-up of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two-stage stochastic linear programming. Structural properties and approximations of SIR functions have been extensively studied in the seminal works of van der Vlerk and coauthors. We study a distributionally robust SIR function (DR-SIR) that considers the worst-case expectation over a given family of distributions. Under the assumption that the distribution family is specified by its mean and support, we derive a closed form analytical expression for the DR-SIR function. We also show that this nonconvex DR-SIR function can be represented using a mixed-integer second-order conic program.

Keywords: Distributionally robust; Stochastic integer recourse; Mixed integer conic program (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10287-018-0313-1

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