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A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

Suresh Bolusani(bsuresh***at***lehigh.edu)
Stefano Coniglio(s.coniglio***at***soton.ac.uk)
Ted Ralphs(ted***at***lehigh.edu)
Sahar Tahernejad(sahar***at***lindo.com)

Abstract: We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.

Keywords: Multilevel optimization, Multistage optimization with recourse, Integer Programming, Duality, Branch-and-Cut, Decomposition

Category 1: Other Topics (Game Theory )

Category 2: Stochastic Programming

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation: COR@L Laboratory Technical Report 20T-005, Lehigh University, http://coral.ie.lehigh.edu/~ted/files/papers/MultistageFramework20.pdf

Download: [PDF]

Entry Submitted: 04/16/2020
Entry Accepted: 04/16/2020
Entry Last Modified: 04/16/2020

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