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.
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This research has been supported in part by the National Science Foundation Grant #1633196. The authors thank the editor and two anonymous referees for constructive comments.
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Dedicated to the memory of Maarten van der Vlerk.
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Xie, W., Ahmed, S. Distributionally robust simple integer recourse. Comput Manag Sci 15, 351–367 (2018). https://doi.org/10.1007/s10287-018-0313-1
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DOI: https://doi.org/10.1007/s10287-018-0313-1