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Mathematical models for planning support

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  • Kroon, L.G.
  • Zuidwijk, R.A.

Abstract

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator.

Suggested Citation

  • Kroon, L.G. & Zuidwijk, R.A., 2003. "Mathematical models for planning support," ERIM Report Series Research in Management ERS-2003-032-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.
    • Handle: RePEc:ems:eureri:332
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    References listed on IDEAS

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    1. Michael Pidd, 1999. "Just Modeling Through: A Rough Guide to Modeling," Interfaces, INFORMS, vol. 29(2), pages 118-132, April.
    2. Robert E. Bixby, 2002. "Solving Real-World Linear Programs: A Decade and More of Progress," Operations Research, INFORMS, vol. 50(1), pages 3-15, February.
    3. Nejib Ben-Khedher & Josephine Kintanar & Cecile Queille & William Stripling, 1998. "Schedule Optimization at SNCF: From Conception to Day of Departure," Interfaces, INFORMS, vol. 28(1), pages 6-23, February.
    4. Lingaya, Norbert & Cordeau, Jean-Françcois & Desaulniers, Guy & Desrosiers, Jacques & Soumis, Françcois, 2002. "Operational car assignment at VIA Rail Canada," Transportation Research Part B: Methodological, Elsevier, vol. 36(9), pages 755-778, November.
    5. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2001. "Simultaneous Assignment of Locomotives and Cars to Passenger Trains," Operations Research, INFORMS, vol. 49(4), pages 531-548, August.
    6. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
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    Cited by:

    1. von Corswant, F. & Wynstra, J.Y.F. & Wetzels, M., 2003. "In Chains? Automotive Suppliers and Their Product Development Activities," ERIM Report Series Research in Management ERS-2003-027-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.
    2. van den Berg, J.H. & van den Bergh, W.-M. & Kaymak, U., 2003. "Financial Markets Analysis by Probabilistic Fuzzy Modelling," ERIM Report Series Research in Management ERS-2003-036-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.

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    More about this item

    Keywords

    Planning; mathematical models; modeling process; optimization; planning support;
    All these keywords.

    JEL classification:

    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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