In this article, we examine the design of an evacuation tree, in which evacuation is subject to capacity restrictions on arcs. The cost of evacuating people in the network is determined by the sum of penalties incurred on arcs on which they travel, where penalties are determined according to a nondecreasing function of time. Given a discrete set of disaster scenarios affecting network population, arc capacities, transit times, and penalty functions, we seek to establish an optimal a priori evacuation tree that minimizes the expected evacuation penalty. The solution strategy is based on Benders decomposition, in which the master problem is a mixed-integer program and each subproblem is a time-expanded network flow problem. We provide efficient methods for obtaining primal and dual subproblem solutions, and analyze techniques for improving the strength of the master problem formulation, thus reducing the number of master problem solutions required for the algorithm's convergence. We provide computational results to compare the efficiency of our methods on a set of randomly generated test instances.

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality, introducing nonlinear, nonconvex constraints. We examine the Robust Two-Path Problem, which seeks to establish two paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case where both paths must be arc-disjoint and the case where arcs can be shared between the paths. We begin by proving the NP-hardness of these problems, and then examine various strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. We discuss the advantages and disadvantages of these methods, and conclude with computational results.

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Traditional engineering undergraduate research and design is typically seen in four-year institutions, restricted to junior-and senior-level students. In large institutions, freshman-and sophomore-level students are generally seen to be ill-equipped to take on complex projects, particularly while muddling through the basics of calculus, physics, and electronics. Our institution, McLennan Community College, through a partnership with the Council on Undergraduate Research (CUR), has been challenging that assumption. Students are being introduced to research and design methods in the very first semester and immediately take on projects that are challenging, and most importantly, relevant to the students themselves. The preliminary results are encouraging and indicate that an early focus on research can positively impact a students' academic and professional prospects.

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