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Title: The Maximum Semicontinuous Flow Problem
Abstract
This talk examines maximum proportional flow problems having node and arc capacities, along with semicontinuous flow restrictions. Semicontinuous flows are those that are either equal to zero, or are at least as large as some given lower bound. In maximum flow problems, all solutions can be decomposed into a set of origin-destination path flows. For semicontinuous flow problems, one can enforce the condition that the total amount of flow on each arc must satisfy semicontinuity constraints. Alternatively, one could seek to guarantee the existence of a flow decomposition such that the path flows satisfy semicontinuous restrictions. We focus on the latter problem in this presentation, and examine mathematical programming approaches for solving the problem based on column generation strategies. Furthermore, we examine a so-called dynamic flow variation of the problem. In the dynamic flow problem, origin-destination flows are scheduled over time, and any flows transmitted along an arc must persist on the arc for at least some minimum amount of time. This work is jointly authored by Mr. Robert Curry, an IE Ph.D. student at Clemson University.
Bio sketch
Dr. J. Cole Smith is Associate Provost of Academic Initiatives and Professor of Industrial Engineering at Clemson University. His research regards mathematical optimization models and algorithms, especially those arising in combinatorial optimization, and he has had the pleasure of collaborating with colleagues across many different disciplines. Dr. Smith’s awards include the Young Investigator Award from the ONR, the Hamid K. Elden Outstanding Young Industrial Engineer in Education award, the Operations Research Division Teaching Award, the 2014 Glover-Klingman prize for best paper in Networks, and the best paper award from IIE Transactions in 2007. He became a Fellow of IISE in 2018. Dr. Smith currently serves as the President of the INFORMS Computing Society, INFORMS Vice President for Publications, and IISE Senior Vice President for Continuing Education.