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Production and Sales Planning with Limited Shared Tooling at the Key Operation

Author

Listed:
  • Gerald G. Brown

    (Naval Postgraduate School)

  • Arthur M. Geoffrion

    (University of California, Los Angeles)

  • Gordon H. Bradley

    (Naval Postgraduate School)

Abstract

The focus of this paper is multiperiod production and sales planning when there is a single dominant production operation for which tooling (dies, molds, etc.) can be shared among parts and is limited in availability. Our interest in such problems grew out of management issues confronting an injection molding manufacturer of plastic pipes and fittings for the building and chemical industries, but similar problems abound in the manufacture of many other cast, extruded, molded, pressed, or stamped products. We describe the development and successful application of a planning model and an associated computational approach for this class of problems. The problem is modeled as a mixed integer linear program. Lagrangean relaxation is applied so as to exploit the availability of highly efficient techniques for minimum cost network flow problems and for single-item dynamic lot-sizing type problems. For the practical application at hand, provably good solutions are routinely being obtained in modest computing time to problems far beyond the capabilities of available mathematical programming systems.

Suggested Citation

  • Gerald G. Brown & Arthur M. Geoffrion & Gordon H. Bradley, 1981. "Production and Sales Planning with Limited Shared Tooling at the Key Operation," Management Science, INFORMS, vol. 27(3), pages 247-259, March.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:3:p:247-259
    DOI: 10.1287/mnsc.27.3.247
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    Citations

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    Cited by:

    1. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2016. "Optimal control of queueing systems with non-collaborating servers," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 79-110, October.
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-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.
    3. Gerald G. Brown & Robert F. Dell & Ray L. Davis & Richard H. Duff, 2002. "Optimizing Plant-Line Schedules and an Application at Hidden Valley Manufacturing Company," Interfaces, INFORMS, vol. 32(3), pages 1-14, June.
    4. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.

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