Matheuristics for the Temporal Bin Packing Problem

  • Fabio FuriniEmail author
  • Xueying Shen
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 62)


We study an extension of the Bin Packing Problem , where items consume the bin capacity during a time window only. The problem asks for finding the minimum number of bins to pack all the items respecting the bin capacity at any instant of time. Both a polynomial-size formulation and an extensive formulation are studied. Moreover, various heuristic algorithms are developed and compared, including greedy heuristics and a column generation based heuristic. We perform extensive computational experiments on benchmark instances to evaluate the quality of the computed solutions with respect to strong bounds based on the linear programming relaxation of the proposed formulations.


Temporal bin packing problem Heuristic algorithms Column generation 



The authors want to thank Professor Paolo Toth and Professor Ivana Ljubic for stimulating discussions on the topic and for their contributions.


  1. 1.
    M. Bartlett, A.M. Frisch, Y. Hamadi, I. Miguel, S.A. Tarim, C. Unsworth, The temporal knapsack problem and its solution, in Proceedings of the 2nd International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR 2005) (2005), pp. 34–48Google Scholar
  2. 2.
    P. Bonsma, J. Schulz, A. Wiese, A constant-factor approximation algorithm for unsplittable flow on paths. SIAM J. Comput. 43(2), 767–799 (2014)CrossRefGoogle Scholar
  3. 3.
    A. Caprara, F. Furini, E. Malaguti, Uncommon Dantzig-Wolfe reformulation for the temporal knapsack problem. INFORMS J. Comput. 25(3), 560–571 (2013)CrossRefGoogle Scholar
  4. 4.
    A. Ceselli, G. Righini, M. Salani, A column generation algorithm for a vehicle routing problem with economies of scale and additional constraints. Transp. Sci. 43(1), 56–69 (2009)CrossRefGoogle Scholar
  5. 5.
    E.G. Coffman Jr., M.R. Garey, D.S. Johnson, Approximation algorithms for bin-packing—an updated survey, in Algorithm Design for Computer System Design (Springer, Vienna, 1984), pp. 49–106Google Scholar
  6. 6.
    E.G. Coffman Jr., J. Csirik, G. Galambos, S. Martello, D. Vigo, Bin packing approximation algorithms: survey and classification, in Handbook of Combinatorial Optimization, ed. by P.M. Pardalos, D. Du, R.L. Graham (Springer, New York, 2013), pp. 455–531CrossRefGoogle Scholar
  7. 7.
    F. Furini, E. Malaguti, R. Medina Durán, A. Persiani, P. Toth, A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size. Eur. J. Oper. Res. 218(1), 251–260 (2012)CrossRefGoogle Scholar
  8. 8.
    P.C. Gilmore, R.E. Gomory, A linear programming approach to the cutting-stock problem. Oper. Res. 9(6), 849–859 (1961)CrossRefGoogle Scholar
  9. 9.
    P.C. Gilmore, R.E. Gomory, A linear programming approach to the cutting stock problem - part II. Oper. Res. 11(6), 863–888 (1963)CrossRefGoogle Scholar
  10. 10.
  11. 11.
    D. Johnson, Near-optimal bin packing algorithms. Ph.D. dissertation, Department of Mathematics, M.I.T., Cambridge, MA (1973)Google Scholar
  12. 12.
    S. Lavoie, M. Minoux, E. Odier, A new approach for crew pairing problems by column generation with an application to air transportation. Eur. J. Oper. Res. 35(1), 45–58 (1988)CrossRefGoogle Scholar
  13. 13.
    S. Martello, P. Toth, Knapsack Problems: Algorithms and Computer Implementations (Wiley, New York, 1990)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.PSLUniversité Paris-DauphineParis Cedex 16France
  2. 2.Decision BrainParisFrance

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