Improved lower bounds for the capacitated lot sizing problem with setup times

We present new lower bounds for the capacitated lot sizing problem, applying decomposition to the network reformulation. The demand constraints are the linking constraints and the problem decomposes into subproblems per period containing the capacity and setup constraints. Computational results and a comparison to other lower bounds are presented.

[1]  Prabhakant Sinha,et al.  The Multiple-Choice Knapsack Problem , 1979, Oper. Res..

[2]  Laurence A. Wolsey,et al.  bc -- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems , 2000 .

[3]  G. D. Eppen,et al.  Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition , 1987, Oper. Res..

[4]  Z. Degraeve,et al.  Improved Lower Bounds for the Capacitated Lot Sizing Problem with Set Up Times , 2003 .

[5]  Alan S. Manne,et al.  Programming of Economic Lot Sizes , 1958 .

[6]  G. Nemhauser,et al.  Solving Multi-Item Capacitated Lot-Sizing Problems with Setup Times by Branch-and-Cut , 2000 .

[7]  William W. Trigeiro,et al.  Capacitated lot sizing with setup times , 1989 .

[8]  Laurence A. Wolsey,et al.  Uncapacitated lot-sizing: The convex hull of solutions , 1984 .

[9]  Harish C. Bahl,et al.  Capacitated lot-sizing and scheduling by Lagrangean relaxation , 1992 .

[10]  B. P. Dzielinski,et al.  Optimal Programming of Lot Sizes, Inventory and Labor Allocations , 1965 .

[11]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[12]  David Pisinger.  A minimal algorithm for the Multiple-choice Knapsack Problem , 1995 .

[13]  Wun-Hwa Chen,et al.  Analysis of relaxations for the multi-item capacitated lot-sizing problem , 1991 .

[14]  Marshall L. Fisher,et al.  An Applications Oriented Guide to Lagrangian Relaxation , 1985 .

[15]  Mathieu Van Vyve,et al.  A solution approach of production planning problems based on compact formulations for single-item lot-sizing models , 2004, 4OR.