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Optimal Programming of Lot Sizes, Inventory and Labor Allocations

Author

Listed:
  • Bernard P. Dzielinski

    (IBM Corporation, Yorktown Heights, New York)

  • Ralph E. Gomory

    (IBM Corporation, Yorktown Heights, New York)

Abstract

The economic lot size programming problem, as studied originally by A. S. Manne and later by B. P. Dzielinski, C. T. Baker and A. S. Manne, is the problem of making economic lot size, inventory and work force decisions in a multi-production process. When several thousand distinct items are involved, the large number of equations that result from the linear programming formulation makes computation infeasible. Also, a large number of variables are involved because of inclusion of alternative set-up sequences for each item. In this paper, the application of the Dantzig and Wolfe decomposition principle and a method for creating alternative set-up sequences as they are needed by means of a computation of the Wagner and Whitin type is described as a method for overcoming the computational difficulty. A digital computer program has been developed using these methods. The results of some experiments where production was planned for a large number of distinct items are described.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:9:p:874-890
    DOI: 10.1287/mnsc.11.9.874
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    Citations

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    Cited by:

    1. Bouchriha, Hanen & Ouhimmou, Mustapha & D'Amours, Sophie, 2007. "Lot sizing problem on a paper machine under a cyclic production approach," International Journal of Production Economics, Elsevier, vol. 105(2), pages 318-328, February.
    2. Bitran, Gabriel R. & Tirupati, Devanath., 1989. "Hierarchical production planning," Working papers 3017-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Zeger Degraeve & Raf Jans, 2007. "A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times," Operations Research, INFORMS, vol. 55(5), pages 909-920, October.
    4. Li, Yuchen & Liu, Ming & Saldanha-da-Gama, Francisco & Yang, Zaoli, 2024. "Risk-averse two-stage stochastic programming for assembly line reconfiguration with dynamic lot sizes," Omega, Elsevier, vol. 127(C).
    5. Roy E. Marsten, 1975. "The Use of the Box Step Method in Discrete Optimization," NBER Working Papers 0086, National Bureau of Economic Research, Inc.
    6. Degraeve, Z. & Jans, R.F., 2003. "Improved Lower Bounds For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-026-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Tom Vogel & Bernardo Almada-Lobo & Christian Almeder, 2017. "Integrated versus hierarchical approach to aggregate production planning and master production scheduling," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 193-229, January.
    8. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    9. Tao Wu & Zhe Liang & Canrong Zhang, 2018. "Analytics Branching and Selection for the Capacitated Multi-Item Lot Sizing Problem with Nonidentical Machines," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 236-258, May.
    10. Li, Yuchen & Saldanha-da-Gama, Francisco & Liu, Ming & Yang, Zaoli, 2023. "A risk-averse two-stage stochastic programming model for a joint multi-item capacitated line balancing and lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 304(1), pages 353-365.
    11. Degraeve, Z. & Jans, R.F., 2003. "A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-010-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    12. Reyes Zotelo, Yunuem & Mula, Josefa & Díaz-Madroñero, Manuel & Gutiérrez González, Eduardo, 2017. "Plan maestro de producción basado en programación lineal entera para una empresa de productos químicos || Master Production Scheduling Based on Integer Linear Programming for a Chemical Company," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 147-168, Diciembre.
    13. James R. Bradley & Bruce C. Arntzen, 1999. "The Simultaneous Planning of Production, Capacity, and Inventory in Seasonal Demand Environments," Operations Research, INFORMS, vol. 47(6), pages 795-806, December.
    14. S. Selcuk Erenguc & H. Murat Mercan, 1990. "A multifamily dynamic lot‐sizing model with coordinated replenishments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 539-558, August.
    15. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.

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