Title:
Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems

Simple item page
dc.contributor.advisor Ahmed, Shabbir
dc.contributor.advisor Nemhauser, George L.
dc.contributor.author Luedtke, James en_US
dc.contributor.committeeMember Cook, William J.
dc.contributor.committeeMember Gu, Zonghao
dc.contributor.committeeMember Parker, R. Gary
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2008-02-07T18:12:06Z
dc.date.available 2008-02-07T18:12:06Z
dc.date.issued 2007-07-30 en_US
dc.description.abstract In this dissertation we study several non-convex and stochastic optimization problems. The common theme is the use of mixed-integer programming (MIP) techniques including valid inequalities and reformulation to solve these problems. We first study a strategic capacity planning model which captures the trade-off between the incentive to delay capacity installation to wait for improved technology and the need for some capacity to be installed to meet current demands. This problem is naturally formulated as a MIP with a bilinear objective. We develop several linear MIP formulations, along with classes of strong valid inequalities. We also present a specialized branch-and-cut algorithm to solve a compact concave formulation. Computational results indicate that these formulations can be used to solve large-scale instances. We next study methods for optimization with joint probabilistic constraints. These problems are challenging because evaluating solution feasibility requires multidimensional integration and the feasible region is not convex. We propose and analyze a Monte Carlo sampling scheme to simplify the probabilistic structure of such problems. Computational tests of the approach indicate that it can yield good feasible solutions and reasonable bounds on their quality. Next, we study a MIP formulation of the non-convex sample approximation problem. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. Computational results indicate that large-scale instances can be solved using the strengthened formulations. Finally, we study optimization problems with stochastic dominance constraints. A stochastic dominance constraint states that a random outcome which depends on the decision variables should stochastically dominate a given random variable. We present new formulations for both first and second order stochastic dominance which are significantly more compact than existing formulations. Computational tests illustrate the benefits of the new formulations. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/19711
dc.publisher Georgia Institute of Technology en_US
dc.subject Integer programming en_US
dc.subject Stochastic programming en_US
dc.subject Chance constraints en_US
dc.subject Probabilistic constraints en_US
dc.subject Stochastic dominance en_US
dc.subject Capacity planning en_US
dc.subject.lcsh Mathematical optimization
dc.subject.lcsh Stochastic processes
dc.subject.lcsh Combinatorial probabilities
dc.title Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Nemhauser, George L.
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isAdvisorOfPublication cc31c1dc-5388-470a-9c3f-f8976a299674
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
luedtke_james_r_200712_phd.pdf
Size:
938.58 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Theses and Dissertations