An application of Lagrangian relaxation to a capacity planning problem under uncertainty

C Lucas (), S A MirHassani, G Mitra () and C A Poojari
Additional contact information
C Lucas: Brunel University
S A MirHassani: Brunel University
G Mitra: Brunel University
C A Poojari: Brunel University

Journal of the Operational Research Society, 2001, vol. 52, issue 11, 1256-1266

Abstract: Abstract A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.

Keywords: Lagrangian relaxation; supply chain management; capacity planning; stochastic programming; scenario analysis (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (11)

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DOI: 10.1057/palgrave.jors.2601221

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