IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v284y2020i2d10.1007_s10479-018-2862-7.html
   My bibliography  Save this article

A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints

Author

Listed:
  • Majid Taghavi

    (Dalhousie University)

  • Kai Huang

    (McMaster University)

Abstract

In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stage stochastic mixed-integer programming model for the network capacity expansion problem. We assume that permanent capacity and spot market capacity are available, which can be used permanently or temporarily by the decision maker respectively. By relaxing the budget constraints, we propose a heuristic Lagrangian relaxation method to solve the problem. Two algorithms are developed to find tight upper bounds for the Lagrangian relaxation procedure. The experimental results show superior performance of the proposed Lagrangian relaxation method compared with CPLEX.

Suggested Citation

  • Majid Taghavi & Kai Huang, 2020. "A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints," Annals of Operations Research, Springer, vol. 284(2), pages 605-621, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:2:d:10.1007_s10479-018-2862-7
    DOI: 10.1007/s10479-018-2862-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2862-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-018-2862-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. R. Fulkerson, 1959. "Increasing the Capacity of a Network: The Parametric Budget Problem," Management Science, INFORMS, vol. 5(4), pages 472-483, July.
    2. Hanan Luss, 1982. "Operations Research and Capacity Expansion Problems: A Survey," Operations Research, INFORMS, vol. 30(5), pages 907-947, October.
    3. Inderfurth, Karl & Kelle, Peter & Kleber, Rainer, 2013. "Dual sourcing using capacity reservation and spot market: Optimal procurement policy and heuristic parameter determination," European Journal of Operational Research, Elsevier, vol. 225(2), pages 298-309.
    4. Francisco Barahona & Stuart Bermon & Oktay Günlük & Sarah Hood, 2005. "Robust capacity planning in semiconductor manufacturing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 459-468, August.
    5. Luss, Hanan, 1984. "Capacity expansion planning for a single facility product line," European Journal of Operational Research, Elsevier, vol. 18(1), pages 27-34, October.
    6. Shabbir Ahmed & Nikolaos V. Sahinidis, 2003. "An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion," Operations Research, INFORMS, vol. 51(3), pages 461-471, June.
    7. Inderfurth, Karl & Kelle, Peter, 2011. "Capacity reservation under spot market price uncertainty," International Journal of Production Economics, Elsevier, vol. 133(1), pages 272-279, September.
    8. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    9. Ahuja, R. K. & Batra, J. L. & Gupta, S. K. & Punnen, A. P., 1996. "Optimal expansion of capacitated transshipment networks," European Journal of Operational Research, Elsevier, vol. 89(1), pages 176-184, February.
    10. Yuri Levin & Mikhail Nediak & Huseyin Topaloglu, 2012. "Cargo Capacity Management with Allotments and Spot Market Demand," Operations Research, INFORMS, vol. 60(2), pages 351-365, April.
    11. Jan A. Van Mieghem, 2003. "Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments," Manufacturing & Service Operations Management, INFORMS, vol. 5(4), pages 269-302, July.
    12. Kai Huang & Shabbir Ahmed, 2009. "The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty," Operations Research, INFORMS, vol. 57(4), pages 893-904, August.
    13. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    14. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    15. Marí­n, íngel & Jaramillo, Patricia, 2008. "Urban rapid transit network capacity expansion," European Journal of Operational Research, Elsevier, vol. 191(1), pages 45-60, November.
    16. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    17. Bora Tarhan & Ignacio Grossmann & Vikas Goel, 2013. "Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution," Annals of Operations Research, Springer, vol. 203(1), pages 141-166, March.
    18. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
    19. Majid Taghavi & Kai Huang, 2016. "A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 600-614, December.
    20. Ganz, Zvi & Berman, Oded, 1992. "The capacity expansion problem in the service industry with multiple resource constraints," Socio-Economic Planning Sciences, Elsevier, vol. 26(1), pages 1-14, January.
    21. Sampath Rajagopalan & Jayashankar M. Swaminathan, 2001. "A Coordinated Production Planning Model with Capacity Expansion and Inventory Management," Management Science, INFORMS, vol. 47(11), pages 1562-1580, November.
    22. Solak, Senay & Clarke, John-Paul B. & Johnson, Ellis L. & Barnes, Earl R., 2010. "Optimization of R&D project portfolios under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 207(1), pages 420-433, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Majid Taghavi & Kai Huang, 2016. "A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 600-614, December.
    2. Hongmin Li & Stephen C. Graves & Woonghee Tim Huh, 2014. "Optimal Capacity Conversion for Product Transitions Under High Service Requirements," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 46-60, February.
    3. Torres-Rincón, Samuel & Sánchez-Silva, Mauricio & Bastidas-Arteaga, Emilio, 2021. "A multistage stochastic program for the design and management of flexible infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    4. Martínez-Costa, Carme & Mas-Machuca, Marta & Benedito, Ernest & Corominas, Albert, 2014. "A review of mathematical programming models for strategic capacity planning in manufacturing," International Journal of Production Economics, Elsevier, vol. 153(C), pages 66-85.
    5. Hahn, G.J. & Kuhn, H., 2012. "Simultaneous investment, operations, and financial planning in supply chains: A value-based optimization approach," International Journal of Production Economics, Elsevier, vol. 140(2), pages 559-569.
    6. Jodlbauer, Herbert & Altendorfer, Klaus, 2010. "Trade-off between capacity invested and inventory needed," European Journal of Operational Research, Elsevier, vol. 203(1), pages 118-133, May.
    7. Smirnov, Dina & van Jaarsveld, Willem & Atan, Zümbül & de Kok, Ton, 2021. "Long-term resource planning in the high-tech industry: Capacity or inventory?," European Journal of Operational Research, Elsevier, vol. 293(3), pages 926-940.
    8. Kai Huang & Shabbir Ahmed, 2009. "The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty," Operations Research, INFORMS, vol. 57(4), pages 893-904, August.
    9. Fatemeh Keshavarz-Ghorbani & Seyed Hamid Reza Pasandideh, 2022. "A Lagrangian relaxation algorithm for optimizing a bi-objective agro-supply chain model considering CO2 emissions," Annals of Operations Research, Springer, vol. 314(2), pages 497-527, July.
    10. Lijian Lu & Xiaoming Yan, 2016. "Capacity investment decisions under risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 218-235, April.
    11. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    12. Lee, Chia-Yen & Charles, Vincent, 2022. "A robust capacity expansion integrating the perspectives of marginal productivity and capacity regret," European Journal of Operational Research, Elsevier, vol. 296(2), pages 557-569.
    13. Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Qu, Xiaobo, 2021. "A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 143-160.
    14. Solak, Senay & Li, Zhuoxin & Gumus, Mehmet & Zhuo, Yueran, 2024. "A budgeting resource allocation model for capacity expansion," International Journal of Production Economics, Elsevier, vol. 273(C).
    15. Lara, Cristiana L. & Mallapragada, Dharik S. & Papageorgiou, Dimitri J. & Venkatesh, Aranya & Grossmann, Ignacio E., 2018. "Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1037-1054.
    16. Georgiadis, Patroklos & Athanasiou, Efstratios, 2013. "Flexible long-term capacity planning in closed-loop supply chains with remanufacturing," European Journal of Operational Research, Elsevier, vol. 225(1), pages 44-58.
    17. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    18. Woonghee Tim Huh & Robin O. Roundy, 2005. "A continuous‐time strategic capacity planning model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 329-343, June.
    19. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.
    20. Kelley, Morgan T. & Pattison, Richard C. & Baldick, Ross & Baldea, Michael, 2018. "An MILP framework for optimizing demand response operation of air separation units," Applied Energy, Elsevier, vol. 222(C), pages 951-966.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:284:y:2020:i:2:d:10.1007_s10479-018-2862-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.