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We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained [...]

Vaccines are arguably the most important means of pandemic influenza mitigation. However, as during the 2009 H1N1 pandemic, mass immunization with an effective vaccine may not begin until a pandemic is well underway. In the U.S., state-level public health agencies are responsible for quickly and fairly allocating vaccines as they become available to populations prioritized to receive vaccines. Allocation decisions can be ethically and logistically complex, given several vaccine types in limited and uncertain supply and given competing priority groups with distinct risk profiles and vaccine acceptabilities. We introduce a model for optimizing statewide allocation of multiple vaccine types to multiple priority groups, maximizing equal access. We assume a large fraction of available vaccines are distributed to healthcare providers based on their requests, and then optimize county-level allocation of the remaining doses to achieve equity. We have applied the model to the state of Texas, and incorporated it in a Web-based decision-support tool for the Texas Department of State Health Services (DSHS). Based on vaccine quantities delivered to registered healthcare providers in response to their requests during the 2009 H1N1 pandemic, we find that a relatively small cache of discretionary doses (DSHS reserved 6.8% in 2009) suffices to achieve equity across all counties in Texas. [ABSTRACT FROM AUTHOR]

We study a stochastic interdiction model of Morton et al. IIE Transactions, 39 (2007):3-14 that locates radiation sensors at border crossings to detect and prevent the smuggling of nuclear material. In this model, an interdictor places sensors at customs checkpoints to minimize a potential smuggler's maximum probability of crossing a border undetected. We focus on a model variant in which the interdictor has different, and likely more accurate, perceptions of the system's parameters than the smuggler does. We introduce a model that is tighter and uses fewer constraints than that of Morton et al. We also develop a class of valid inequalities along with a corresponding separation procedure that can be used within a cutting-plane approach to reduce computational effort. Computational results demonstrate the effectiveness of our approach.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 91-100, 2014 [ABSTRACT FROM AUTHOR]