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

Summary: The value of multi-stage stochastic programming in
capacity planning under uncertainty
Kai Huang and Shabbir Ahmed
School of Industrial & Systems Engineering
Georgia Institute of Technology
April 26, 2005
Abstract
This paper addresses a general class of capacity planning problems under uncer-
tainty, 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 ex-
pansion 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 efficient approximation scheme for the difficult multi-stage
stochastic integer program and prove that the proposed scheme is asymptotically op-
timal. Computational experiments with realistic-scale problem instances suggest that
the VMS for this class of problems is quite high. Moreover the quality and perfor-
mance of the approximation scheme is very satisfactory. Fortunately, this is more so

  

Source: Ahmed, Shabbir - School of Industrial and Systems Engineering, Georgia Institute of Technology

 

Collections: Engineering