Multi-stage Stochastic Programming Models in Production Planning

dc.contributor.advisor Ahmed, Shabbir
dc.contributor.author Huang, Kai en_US
dc.contributor.committeeMember Shapiro, Alexander
dc.contributor.committeeMember White, Chelsea C., III
dc.contributor.committeeMember Sokol, Joel
dc.contributor.committeeMember Ergun, Özlem
dc.contributor.committeeMember Takriti, Samer
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2005-09-16T15:05:26Z
dc.date.available 2005-09-16T15:05:26Z
dc.date.issued 2005-07-13 en_US
dc.description.abstract In this thesis, we study a series of closely related multi-stage stochastic programming models in production planning, from both a modeling and an algorithmic point of view. We first consider a very simple multi-stage stochastic lot-sizing problem, involving a single item with no fixed charge and capacity constraint. Although a multi-stage stochastic integer program, this problem can be shown to have a totally unimodular constraint matrix. We develop primal and dual algorithms by exploiting the problem structure. Both algorithms are strongly polynomial, and therefore much more efficient than the Simplex method. Next, motivated by applications in semiconductor tool planning, we develop a general capacity planning problem under uncertainty. Using a scenario tree to model the evolution of the uncertainties, we present a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach. By exploiting the special simple stochastic lot-sizing substructure inherent in the problem, we design an efficient approximation scheme and show that the proposed scheme is asymptotically optimal. We conduct a computational study with respect to a semiconductor-tool-planning problem. Numerical results indicate that even an approximate solution to the multi-stage model is far superior to any optimal solution to the two-stage model. These results show that the value of multi-stage stochastic programming for this class of problem is extremely high. Next, we extend the simple stochastic lot-sizing model to an infinite horizon problem to study the planning horizon of this problem. We show that an optimal solution of the infinite horizon problem can be approximated by optimal solutions of a series of finite horizon problems, which implies the existence of a planning horizon. We also provide a useful upper bound for the planning horizon. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 856611 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/7164
dc.language.iso en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Resource allocation en_US
dc.subject Multistage stochastic programming
dc.subject Production planning
dc.subject Planning horizon
dc.subject Lot-sizing
dc.subject Capacity planning
dc.title Multi-stage Stochastic Programming Models in Production Planning en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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