The value of multi-stage stochastic programming in capacity planning under uncertainty

Kai Huang; Shabbir Ahmed

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SPEPS Preprint

Author(s):	Kai Huang, Georgia Institute of Technology Shabbir Ahmed, Georgia Institute of Technology
Title:	The value of multi-stage stochastic programming in capacity planning under uncertainty
Date of Acceptance:	06.07.2005
Submission Date:	29.04.2005
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059913)
Keywords (eng):	Multi-stage stochastic programming, capacity planning, semiconductor tool planning, stochastic lot-sizing, analysis of algorithms
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Abstract (eng):

This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, we develop 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 (VMS) afforded over the two-stage approach. By exploiting a special lot-sizing substructure inherent in the problem, we develop an effient approximation scheme for the diffult multi-stage stochastic integer program and prove that the proposed scheme is asymptotically optimal. Computational experiments with realistic-scale problem instances suggest that the VMS for this class of problems is quite high. Moreover the quality and performance of the approximation scheme is very satisfactory. Fortunately, this is more so for instances for which the VMS is high.

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