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We study the assignment problem with chance constraints (CAP) and its distributionally robust counterpart DR-CAP. We present a technique for estimating big-M in such a formulation that takes advantage of the ambiguity set. We consider a 0-1 bilinear knapsack set to develop valid inequalities for CAP and DR-CAP. This is generalized to the joint chance constraint problem. A probability cut framework is also developed to solve DR-CAP. A computational study on problem instances obtained from using real hospital surgery data shows that the developed techniques allow us to solve certain model instances and reduce the computational time for others. The use of Wasserstein ambiguity set in the DR-CAP model improves the out-of-sample performance of satisfying the chance constraints more significantly than the one possible by increasing the sample size in the sample average approximation technique. The solution time for DR-CAP model instances is of the same order as that for solving the CAP instances. This finding is important because chance constrained optimization models are very difficult to solve when the coefficients in the constraints are random. 

Ocean biogeochemistry involves the production and consumption of an array of organic compounds and halogenated trace gases that influence the composition and reactivity of the atmosphere, air quality, and the climate system. Some of these molecules affect tropospheric ozone and secondary aerosol formation and impact the atmospheric oxidation capacity on both regional and global scales. Other emissions undergo transport to the stratosphere, where they contribute to the halogen burden and influence ozone. The oceans also comprise a major sink for highly soluble or reactive atmospheric gases. These issues are an active area of research by the SOLAS (Surface Ocean Lower Atmosphere) community. This article provides a status report on progress over the past decade, unresolved issues, and future research directions to understand the influence of ocean biogeochemistry on gas-phase atmospheric chemistry. Common challenges across the subject area involve establishing the role that biology plays in controlling the emissions of gases to the atmosphere and the inclusion of such complex processes, for example involving the sea surface microlayer, in large-scale global models. 

We study the chance-constrained bin packing problem, with an application to hospital operating room planning. The bin packing problem allocates items of random sizes that follow a discrete distribution to a set of bins with limited capacity, while minimizing the total cost. The bin capacity constraints are satisfied with a given probability. We investigate a big-M and a 0-1 bilinear formulation of this problem. We analyze the bilinear structure of the formulation and use the lifting techniques to identify cover, clique, and projection inequalities to strengthen the formulation. We show that in certain cases these inequalities are facet-defining for a bilinear knapsack constraint that arises in the reformulation. An extensive computational study is conducted for the operating room planning problem that minimizes the number of open operating rooms. The computational tests are performed using problems generated based on real data from a hospital. A lower-bound improvement heuristic is combined with the cuts proposed in this paper in a branch-and-cut framework. The computations illustrate that the techniques developed in this paper can significantly improve the performance of the branch-and-cut method. Problems with up to 1,000 scenarios are solved to optimality in less than an hour. A safe approximation based on conditional value at risk (CVaR) is also solved. The computations show that the CVaR approximation typically leaves a gap of one operating room (e.g., six instead of five) to satisfy the chance constraint. Summary of Contribution: This paper investigates a branch-and-cut algorithm for a chance-constrained bin packing problem with multiple bins. The chance-constrained bin packing provides a modeling framework for applied operations research problems, such as health care, scheduling, and so on. This paper studies alternative computational approaches to solve this problem. Moreover, this paper uses real data from a hospital operating room planning setting as an application to test the algorithmic ideas. This work, therefore, is at the intersection of computing and operations research. Several interesting ideas are developed and studied. These include a strengthened big-M reformulation, analysis of a bilinear reformulation, and identifying certain facet-defining inequalities for this formulation. This paper also gives a lower-bound generation heuristic for a model that minimizes the number of bins. Computational experiments for an operating room planning model that uses data from a hospital demonstrate the computational improvement and importance of the proposed approaches. The techniques proposed in this paper and computational experiments further enhance the interface of computing and operations research. 

Abstract The discovery of carbon dots opens a new avenue to the applications of nanomaterials in biosensing and bioimaging. In this work, we develop simple methods to prepare carbon nanoparticles from xylose and to tune the photoluminescence (PL) characteristics of the xylose-derived carbon nanoparticles via the combination of three different processes: hydrothermal carbonization (HTC), annealing at 850 °C and laser ablation (LA) in a NH₄OH solution. The HTC-synthesized carbon dots (CDs) exhibit green emission under the 365 nm UV excitation, the annealing of the HTC-synthesized CDs leads to complete loss of the PL characteristics, and the LA processing of the annealed carbon nanoparticles recovers the PL characteristics with blue shift in comparison to the HTC-synthesized CDs under the same UV excitation. the PL characteristics of the HTC-CDs and the LA-CDs are dependent on theπ-π* transition of C-containing surface-functional groups andπ-π* and n-π* transitions of N-containing surface-functional groups, respectively, which are responsible for the difference in the PL characteristics between the HTC-synthesized CDs and the LA-processed CDs. The approaches demonstrated in this work provide a viable method to introduce and tune surface-functional groups on the surface of carbon nanoparticles. 

Biomass-derived carbon dots (CDs) are biocompatible and have potential for a variety of applications, including bioimaging and biosensing. In this work, we use ground soybean residuals to synthesize carbon nanoparticles by hydrothermal carbonization (HTC), annealing at high temperature, and laser ablation (LA) in a NH 4 OH solution. The carbon nanoparticles synthesized with the HTC process (HTC-CDs) exhibit photoluminescent characteristics with strong blue emission. The annealing of the HTC-processed carbon particles in the range of 250 to 850 °C causes a loss of the photoluminescent characteristics of the CDs without any significant change in the microstructure (amorphous structure) of the carbon particles. The LA processing of the annealed HTC-processed carbon particles introduces nitrogen-containing surface-functional groups and leads to the recovery of the photoluminescent features that are different from those of the HTC-CDs and dependent on the fraction of nitrogen in the surface-functional groups. The photoluminescence of both the HTC-CDs and LA-CDs is largely due to the presence of N-containing surface-functional groups. The quantum yield of the LA-CDs is more constant than that of the HTC-CDs under continuous UV excitation and does not exhibit a significant reduction after 150 min of excitation. The methods used in this work provide a simple and green strategy to introduce N-surface-functional groups to carbon nanoparticles made from biomass and biowaste and to produce stable photoluminescent CDs with excellent water-wettability.