NDLI: Irreducible Infeasible Subsystem Decomposition for Probabilistically Constrained Stochastic Integer Programs

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Irreducible Infeasible Subsystem Decomposition for Probabilistically Constrained Stochastic Integer Programs

Content Provider	Semantic Scholar
Author	Arrubla, Gallego Andrés, Julian
Copyright Year	2013
Abstract	This dissertation explores methods for finding irreducible infeasible subsystems (IISs) of systems of inequalities with binary decision variables and for solving probabilistically constrained stochastic integer programs (SIP-C). Finding IISs for binary systems is useful in decomposition methods for SIP-C. SIP-C has many important applications including modeling of strategic decision-making problems in wildfire initial response planning. New theoretical results and two new algorithms to find IISs for systems of inequalities with binary variables are developed. The first algorithm uses the new theory and the method of the alternative polyhedron within a branch-and-bound (BAB) approach. The second algorithm applies the new theory and the method of the alternative polyhedron to a system in which zero/one box constraints are appended. Decomposition schemes using IISs for binary systems can be used to solve SIP-C. SIP-C is challenging to solve due to the generally non-convex feasible region. In addition, very weak lower (upper) bounds on the objective function are obtained from the linear programming (LP) relaxation of the deterministic equivalent problem (DEP) to SIP-C. This work develops a branch-and-cut (BAC) method based on IIS inequalities to solve SIP-C with random technology matrix and random righthandside vector. Computational results show that the LP relaxation of the DEP to SIP-C can be strengthened by the IIS inequalities. SIP-C modeling can be applied to wildfire initial response planning. A new methodology for wildfire initial response that includes a fire behavior simulation model, a wildfire risk model, and SIP-C is developed and tested. The new methodology assumes a known standard response needed to contain a fire of given size. Likewise, this methodology is used to evaluate deployment decisions in terms of the
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://oaktrust.library.tamu.edu/bitstream/handle/1969.1/151296/GALLEGOARRUBLA-DISSERTATION-2013.pdf;sequence=1
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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