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Dynamic Capacity Acquisition and Assignment under Uncertainty

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  • Shabbir Ahmed
  • Renan Garcia

Abstract

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Shabbir Ahmed & Renan Garcia, 2003. "Dynamic Capacity Acquisition and Assignment under Uncertainty," Annals of Operations Research, Springer, vol. 124(1), pages 267-283, November.
    • Handle: RePEc:spr:annopr:v:124:y:2003:i:1:p:267-283:10.1023/b:anor.0000004773.66339.df
    DOI: 10.1023/B:ANOR.0000004773.66339.df
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    Citations

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    Cited by:

    1. Ilke Bakir & Natashia Boland & Brian Dandurand & Alan Erera, 2020. "Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 145-163, January.
    2. Can Li & Ignacio E. Grossmann, 2019. "A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables," Journal of Global Optimization, Springer, vol. 75(2), pages 247-272, October.
    3. 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.
    4. Amir Hossein Sadeghi & Ziyuan Sun & Amirreza Sahebi-Fakhrabad & Hamid Arzani & Robert Handfield, 2023. "A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design," Logistics, MDPI, vol. 7(1), pages 1-24, March.
    5. Zhili Zhou & Yongpei Guan, 2013. "Two-stage stochastic lot-sizing problem under cost uncertainty," Annals of Operations Research, Springer, vol. 209(1), pages 207-230, October.
    6. Lewis Ntaimo, 2010. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse," Operations Research, INFORMS, vol. 58(1), pages 229-243, February.
    7. Jakubovskis, Aldis, 2017. "Flexible production resources and capacity utilization rates: A robust optimization perspective," International Journal of Production Economics, Elsevier, vol. 189(C), pages 77-85.
    8. Jakubovskis, Aldis, 2017. "Strategic facility location, capacity acquisition, and technology choice decisions under demand uncertainty: Robust vs. non-robust optimization approaches," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1095-1104.
    9. Yelin Fu & Jianshan Sun & K. Lai & John Leung, 2015. "A robust optimization solution to bottleneck generalized assignment problem under uncertainty," Annals of Operations Research, Springer, vol. 233(1), pages 123-133, October.

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