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An application of Lagrangian relaxation to a capacity planning problem under uncertainty

Author

Listed:
  • C Lucas

    (Brunel University)

  • S A MirHassani

    (Brunel University)

  • G Mitra

    (Brunel University)

  • C A Poojari

    (Brunel University)

Abstract

A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.

Suggested Citation

  • C Lucas & S A MirHassani & G Mitra & C A Poojari, 2001. "An application of Lagrangian relaxation to a capacity planning problem under uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(11), pages 1256-1266, November.
    • Handle: RePEc:pal:jorsoc:v:52:y:2001:i:11:d:10.1057_palgrave.jors.2601221
    DOI: 10.1057/palgrave.jors.2601221
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    Citations

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    Cited by:

    1. Alonso-Ayuso, Antonio & Carvallo, Felipe & Escudero, Laureano F. & Guignard, Monique & Pi, Jiaxing & Puranmalka, Raghav & Weintraub, Andrés, 2014. "Medium range optimization of copper extraction planning under uncertainty in future copper prices," European Journal of Operational Research, Elsevier, vol. 233(3), pages 711-726.
    2. Dulluri, Sandeep & Raghavan, N.R. Srinivasa, 2008. "Collaboration in tool development and capacity investments in high technology manufacturing networks," European Journal of Operational Research, Elsevier, vol. 187(3), pages 962-977, June.
    3. Gaivoronski, Alexei & Sechi, Giovanni M. & Zuddas, Paola, 2012. "Cost/risk balanced management of scarce resources using stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 214-224.
    4. Nasreddine Saadouli, 2021. "Stochastic programming model for production planning with stochastic aggregate demand and spreadsheet-based solution heuristics," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(4), pages 117-127.
    5. Schütz, Peter & Tomasgard, Asgeir & Ahmed, Shabbir, 2009. "Supply chain design under uncertainty using sample average approximation and dual decomposition," European Journal of Operational Research, Elsevier, vol. 199(2), pages 409-419, December.
    6. Josef Kallrath, 2005. "Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 339-373, November.
    7. Rastogi, Aditya P. & Fowler, John W. & Matthew Carlyle, W. & Araz, Ozgur M. & Maltz, Arnold & Büke, Burak, 2011. "Supply network capacity planning for semiconductor manufacturing with uncertain demand and correlation in demand considerations," International Journal of Production Economics, Elsevier, vol. 134(2), pages 322-332, December.
    8. Laureano Escudero & Araceli Garín & María Merino & Gloria Pérez, 2009. "BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 96-122, July.
    9. Laureano F. Escudero & María Araceli Garín & Celeste Pizarro & Aitziber Unzueta, 2018. "On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 865-888, July.
    10. Šárka Štádlerová & Sanjay Dominik Jena & Peter Schütz, 2023. "Using Lagrangian relaxation to locate hydrogen production facilities under uncertain demand: a case study from Norway," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    11. E Aghezzaf, 2005. "Capacity planning and warehouse location in supply chains with uncertain demands," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 453-462, April.

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