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A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem

Author

Listed:
  • Richard Freling

    (Formerly with Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands, and ORTEC Consultants B.V., Gouda, The Netherlands)

  • H. Edwin Romeijn

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611-6595)

  • Dolores Romero Morales

    (Saïd Business School, University of Oxford, Oxford OX 1HP, United Kingdom)

  • Albert P. M. Wagelmans

    (Econometric Institute, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

Abstract
In this paper, we propose a multiperiod single-sourcing problem (MPSSP), which takes both transportation and inventory into consideration, suitable for evaluating the performance of a logistics distribution network in a dynamic environment. We reformulate the MPSSP as a Generalized Assignment Problem (GAP) with a convex objective function. We then extend a branch-and-price algorithm that was developed for the GAP to this problem. The pricing problem is a so-called Penalized Knapsack Problem (PKP), which is a knapsack problem where the objective function includes an additional convex term penalizing the total use of capacity of the knapsack. The optimal solution of the relaxation of the integrality constraints in the PKP shows a similar structure to the optimal solution of the knapsack problem, that allows for an efficient solution procedure for the pricing problem. We perform an extensive numerical study of the branch-and-price algorithm.

Suggested Citation

  • Richard Freling & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2003. "A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem," Operations Research, INFORMS, vol. 51(6), pages 922-939, December.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:6:p:922-939
    DOI: 10.1287/opre.51.6.922.24914
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    References listed on IDEAS

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    1. H. Edwin Romeijn & Dolores Romero Morales, 2003. "An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 412-437, August.
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    Cited by:

    1. Zhalechian, M. & Tavakkoli-Moghaddam, R. & Zahiri, B. & Mohammadi, M., 2016. "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 182-214.
    2. Malaguti, Enrico & Monaci, Michele & Paronuzzi, Paolo & Pferschy, Ulrich, 2019. "Integer optimization with penalized fractional values: The Knapsack case," European Journal of Operational Research, Elsevier, vol. 273(3), pages 874-888.
    3. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    4. Gebennini, Elisa & Gamberini, Rita & Manzini, Riccardo, 2009. "An integrated production-distribution model for the dynamic location and allocation problem with safety stock optimization," International Journal of Production Economics, Elsevier, vol. 122(1), pages 286-304, November.
    5. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 407-429, June.
    6. Tancrez, Jean-Sébastien & Lange, Jean-Charles & Semal, Pierre, 2012. "A location-inventory model for large three-level supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 485-502.
    7. Wei Huang & H. Edwin Romeijn & Joseph Geunes, 2005. "The continuous‐time single‐sourcing problem with capacity expansion opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 193-211, April.
    8. Dinçer Konur & Joseph Geunes, 2019. "Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system," Annals of Operations Research, Springer, vol. 273(1), pages 527-559, February.

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