Abstract:
Many transportation and logistics problems—such as freight routing, lot sizing, and capacity allocation—are naturally modeled as mixed-integer linear programs (MILPs). These models capture operational realities including discrete decisions, capacity limits, and service constraints, but they can become computationally intractable at scale—especially when model inputs (e.g., demand or travel times) are uncertain. In this talk, we present improvements in cut-based decomposition methods for solving large scale stochastic MILPs. First, we show that integer L-shaped cuts—computationally cheap but often viewed as weak—belong to the family of Lagrangian cuts, which are typically stronger but harder to compute. Second, we address dual degeneracy in cut generation, where multiple optimal dual solutions may produce weak cuts. We propose a normalization approach that selects dual solutions yielding stronger, Pareto-optimal cuts. Finally, we compare normalization with regularization-based alternatives, showing that normalization can recover cuts produced by regularization, while the converse need not hold.
Bio:
Akul Bansal is a Ph.D. student in the Department of Industrial Engineering and Management Sciences at Northwestern. His research interests include mixed-integer, large-scale, and stochastic optimization.
Torene Harvin
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