Robust Assignments via Ear Decompositions and Randomized Rounding

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling problems, where a set of tasks needs to be assigned to the available set of machines or personnel (resources), in a way that all tasks have assigned resources, and no two tasks share the same resource. In its nominal form, the resulting computational problem becomes the \emph{assignment problem} on general bipartite graphs. This paper deals with a robust variant of the assignment problem modeling situations where certain edges in the corresponding graph are \emph{vulnerable} and may become unavailable after a solution has been chosen. The goal is to choose a minimum-cost collection of edges such that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all tasks. We present approximation results and hardness proofs for this type of problems, and establish several connections to well-known concepts from matching theory, robust optimization and LP-based techniques.Comment: Full version of ICALP 2016 pape

Transportation Life Cycle Assessment Synthesis: Life Cycle Assessment Learning Module Series

The Life Cycle Assessment Learning Module Series is a set of narrated, self-advancing slideshows on various topics related to environmental life cycle assessment (LCA). This research project produced the first 27 of such modules, which are freely available for download on the CESTiCC website http://cem.uaf.edu/cesticc/publications/lca.aspx. Each module is roughly 15- 20 minutes in length and is intended for various uses such as course components, as the main lecture material in a dedicated LCA course, or for independent learning in support of research projects. The series is organized into four overall topical areas, each of which contain a group of overview modules and a group of detailed modules. The A and α groups cover the international standards that define LCA. The B and β groups focus on environmental impact categories. The G and γ groups identify software tools for LCA and provide some tutorials for their use. The T and τ groups introduce topics of interest in the field of transportation LCA. This includes overviews of how LCA is frequently applied in that sector, literature reviews, specific considerations, and software tutorials. Future modules in this category will feature methodological developments and case studies specific to the transportation sector