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An iterative dynamic programming approach for the temporal knapsack problem

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  • Clautiaux, F.
  • Detienne, B.
  • Guillot, G.

Abstract

In this paper, we address the temporal knapsack problem (TKP), a generalization of the classical knapsack problem, where selected items enter and leave the knapsack at fixed dates. We model the TKP with a dynamic program of exponential size, which is solved using a method called Successive Sublimation Dynamic Programming (SSDP). This method starts by relaxing a set of constraints from the initial problem, and iteratively reintroduces them when needed. We show that a direct application of SSDP to the temporal knapsack problem does not lead to an effective method, and that several improvements are needed to compete with the best results from the literature.

Suggested Citation

  • Clautiaux, F. & Detienne, B. & Guillot, G., 2021. "An iterative dynamic programming approach for the temporal knapsack problem," European Journal of Operational Research, Elsevier, vol. 293(2), pages 442-456.
    • Handle: RePEc:eee:ejores:v:293:y:2021:i:2:p:442-456
    DOI: 10.1016/j.ejor.2020.12.036
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    References listed on IDEAS

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    1. Alberto Caprara & Fabio Furini & Enrico Malaguti, 2013. "Uncommon Dantzig-Wolfe Reformulation for the Temporal Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 560-571, August.
    2. Ruslan Sadykov & François Vanderbeck, 2013. "Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 244-255, May.
    3. Shunji Tanaka, 2012. "An Exact Algorithm for the Single-Machine Earliness–Tardiness Scheduling Problem," Springer Optimization and Its Applications, in: Roger Z. Ríos-Mercado & Yasmín A. Ríos-Solís (ed.), Just-in-Time Systems, chapter 0, pages 21-40, Springer.
    4. Ibaraki, Toshihide & Nakamura, Yuichi, 1994. "A dynamic programming method for single machine scheduling," European Journal of Operational Research, Elsevier, vol. 76(1), pages 72-82, July.
    5. Timo Gschwind & Stefan Irnich, 2017. "Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 541-556, March.
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    Cited by:

    1. Martinovic, J. & Strasdat, N. & Valério de Carvalho, J. & Furini, F., 2023. "A combinatorial flow-based formulation for temporal bin packing problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 554-574.
    2. Pereira, Jordi & Ritt, Marcus, 2023. "Exact and heuristic methods for a workload allocation problem with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 309(1), pages 387-398.

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