A Lagrangian Relaxation Approach for Multi-Echelon Capacitated Lot-Sizing

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Abstract

This paper proposes a Lagrangian relaxation approach toward the solution of the multistage lot-sizing problem with multiple constrained resources in general product structures. Dualizing the resource constraints this problem results in an uncapacitated problem that can be solved efficiently by reformulating it as a simple facility location representation. The Lagrangian dual costs are updated by subgradient optimization. A Lagrangian based heuristic procedure to generate good solutions for the problem is also proposed. Numerical results are presented for some test problem instances of differing sizes.<BR>(Lot-sizing; Capacity constraints; Echelon stocks; Lagrangian relaxation)

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