Grado Department of Industrial and Systems Engineering

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https://hdl.handle.net/10919/24217

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Browsing Grado Department of Industrial and Systems Engineering by Subject "0102 Applied Mathematics"

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    Regret in the Newsvendor Model with Demand and Yield Randomness
    Chen, Zhi; Xie, Weijun (Wiley, 2021-07-28)
    We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally robust optimization approach to hedge against all distributions that are sufficiently close to a uniform and discrete distribution of empirical data, where closeness is measured by the type-∞ Wasserstein distance. We adopt the minimax regret decision criterion to assess the optimal order quantity that minimizes the worst-case regret. Several properties about the minimax regret model, including optimality condition, regret bound, and the worst-case distribution, are presented. The optimal order quantity can be determined via an efficient golden section search. We extend the analysis to the Hurwicz criterion model, which generalizes the popular albeit pessimistic maximin model (maximizing the worst-case expected profit) and its (less noticeable) more optimistic counterpart—the maximax model (maximizing the best-case expected profit). Finally, we present numerical comparisons of our data-driven minimax regret model with data-driven models based on the Hurwicz criterion and with a minimax regret model based on partial statistical information on moments.
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    Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs
    Bansal, Manish; Zhang, Yingqiu (Springer, 2021-01-22)
    In this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple integer variables using conic mixed integer rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1–20, 2008), thereby extending their result for a simple polyhedral conic mixed integer set with single constraint and one integer variable. We then introduce two-stage stochastic p-order conic mixed integer programs (denoted by TSS-CMIPs) in which the second stage problems have sum of lp-norms in the objective function along with integer variables. First, we present sufficient conditions under which the addition of scenario-based nonlinear cuts in the extensive formulation of TSS-CMIPs is sufficient to relax the integrality restrictions on the second stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We utilize scenario-based CMIR cuts for TSS-CMIPs and their distributionally robust generalizations with structured CMIPs in the second stage, and prove that these cuts provide conic/linear programming equivalent or approximation for the second stage CMIPs. We also perform extensive computational experiments by solving stochastic and distributionally robust capacitated facility location problem and randomly generated structured TSS-CMIPs with polyhedral CMIPs and second-order CMIPs in the second stage, i.e. p= 1 and p= 2 , respectively. We observe that there is a significant reduction in the total time taken to solve these problems after adding the scenario-based cuts.