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The Use of the Box Step Method in Discrete Optimization

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  • Roy E. Marsten

Abstract

The Boxstep method is used to maximize Lagrangean functions in the context of a branch-and-bound algorithm for the general discrete optimization problem. Results are presented for three applications: facility location, multi-item production scheduling, and single machine scheduling. The performance of the Boxstep method is contrasted with that of the subgradient optimization method.

Suggested Citation

  • Roy E. Marsten, 1975. "The Use of the Box Step Method in Discrete Optimization," NBER Working Papers 0086, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0086
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    1. Bernard P. Dzielinski & Ralph E. Gomory, 1965. "Optimal Programming of Lot Sizes, Inventory and Labor Allocations," Management Science, INFORMS, vol. 11(9), pages 874-890, July.
    2. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
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    4. Arthur M. Geoffrion, 1970. "Elements of Large-Scale Mathematical Programming Part I: Concepts," Management Science, INFORMS, vol. 16(11), pages 652-675, July.
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    Cited by:

    1. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    2. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    3. Hatem Ben Amor & Jacques Desrosiers & José Manuel Valério de Carvalho, 2006. "Dual-Optimal Inequalities for Stabilized Column Generation," Operations Research, INFORMS, vol. 54(3), pages 454-463, June.
    4. Kavinesh J. Singh & Andy B. Philpott & R. Kevin Wood, 2009. "Dantzig-Wolfe Decomposition for Solving Multistage Stochastic Capacity-Planning Problems," Operations Research, INFORMS, vol. 57(5), pages 1271-1286, October.

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