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

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

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Article ID: iaor20022818
Country: United Kingdom
Volume: 52
Issue: 11
Start Page Number: 1256
End Page Number: 1266
Publication Date: Nov 2001
Journal: Journal of the Operational Research Society
Authors: , , ,
Keywords: allocation: resources, networks
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.

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