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Inspired by its success for their continuous counterparts, the standard approach to deal with mixed-integer recourse (MIR) models under distributional uncertainty is to use distributionally robust optimization (DRO). We argue, however, that this modeling choice is not always justified, since DRO techniques are generally computationally extremely challenging when integer decision variables are involved. That is why we propose a fundamentally different approach for MIR models under distributional uncertainty aimed at obtaining models with improved computational tractability. For the special case of simple integer recourse (SIR) models, we show that tractable models can be obtained by pragmatically selecting the uncertainty set. Here, we consider uncertainty sets based on the Wasserstein distance and also on generalized moment conditions. We compare our approach with standard DRO and discuss potential generalizations of our ideas to more general MIR models. An important side-result of our analysis is the derivation of performance guarantees for convex approximations of SIR models. In contrast with the literature, these error bounds are not only valid for continuous distribution, but hold for any distribution., Comment: 35 pages, 5 figures

While stress visualization within 3-dimensional particles would greatly advance our understanding of the behaviors of complex particles, traditional photoelastic methods suffer from a lack of available technology for producing suitable complex particles. Recently, 3D-printing has created new possibilities for enhancing the scope of stress analysis within physically representative granules. Here, we investigate and evaluate opportunities offered by 3D-printing a single particle with a complex external shape with photoelastic properties. We report the results of X-ray computed tomography and 3D-printing, combined with traditional photoelastic analysis, to visualize strain for particles ranging from simple 2D discs to complex 3D printed coffee beans, including with internal voids. We find that the relative orientation of the print layers and the loading force affects the optical response of the discs, but without a significant difference in their mechanical properties. Furthermore, we present semi-quantitative measurements of stresses within 3D-printed complex particles. The paper outlines the potential limitations and areas of future interest for stress visualization of 3-dimensional particles.

Multiple syringe exchange programs serve the Chicago metropolitan area, providing support for drug users to help prevent infectious diseases. Using data from one program over a ten-year period, we study the behavior of its clients, focusing on the temporal process governing their visits to service locations and on their demographics. We construct a phase-type distribution with an affine relationship between model parameters and features of an individual client. The phase-type distribution governs inter-arrival times between reoccurring visits of each client and is informed by characteristics of a client including age, gender, ethnicity, and more. The inter-arrival time model is a sub-model in a simulation that we construct for the larger system, which allows us to provide a personalized prediction regarding the client's time-to-return to a service location so that better intervention decisions can be made with the help of simulation.

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current optimal power flow (ACOPF) problem has been considered challenging since the 1960s due to its nonconvexity. Linear approximation of the AC power flow system sees pervasive use, but does not guarantee a physically feasible system configuration. In recent years, various convex relaxation schemes for the ACOPF problem have been investigated, and under some assumptions, a physically feasible solution can be recovered. Based on these convex relaxations, we construct a robust convex optimization problem with recourse to solve for optimal controllable injections (fossil fuel, nuclear, etc.) in electric power systems under uncertainty (renewable energy generation, demand fluctuation, etc.). We propose a cutting-plane method to solve this robust optimization problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound.

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen-Van Leeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the deterministic arrivals case.

We present new Hubble Space Telescope (HST)-NIC3, near-infrared H-band photometry of globular clusters (GC) around NGC 4365 and NGC 1399 in combination with archival HST-WCPC2 and ACS optical data. We find that NGC 4365 has a number of globular clusters with bluer optical colors than expected for their red optical to near-infrared colors and an old age. The only known way to explain these colors is with a significant population of intermediate-age (2-8 Gyr) clusters in this elliptical galaxy. In contrast, NGC 1399 reveals no such population. Our result for NGC 1399 is in agreement with previous spectroscopic work that suggests that its clusters have a large metallicity spread and are nearly all old. In the literature, there are various results from spectroscopic studies of modest samples of NGC 4365 globular clusters. The spectroscopic data allow for either the presence or absence of a significant population of intermediate-age clusters, given the index uncertainties indicated by comparing objects in common between these studies and the few spectroscopic candidates with optical to near-IR colors indicative of intermediate ages. Our new near-IR data of the NGC 4365 GC system with much higher signal-to-noise agrees well with earlier published photometry and both give strong evidence of a significant intermediate-age component. The agreement between the photometric and spectroscopic results for NGC 1399 and other systems lends further confidence to this conclusion, and to the effectiveness of the near-IR technique., Comment: Accepted for publication in ApJ Letters