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Exact and Heuristic Solutions for a Shipment Problem with Given Frequencies


  • Luca Bertazzi

    () (Dipartimento di Metodi Quantitativi, University of Brescia, Italy)

  • Maria Grazia Speranza

    () (Dipartimento di Metodi Quantitativi, University of Brescia, Italy)

  • Walter Ukovich

    () (Dipartimento di Elettrotecnica, Elettronica ed Informatica, University of Trieste, Italy)


We consider the problem of shipping several products from an origin to a destination when a discrete set of shipping frequencies is available, in such a way that the sum of the transportation and inventory costs is minimized. This problem, which is known to be NP-hard, has applications in transportation planning and in location analysis. In this paper we derive dominance rules for the problem solutions that allow a tightening of the bounds on the problem variables and improve the efficiency of a known branch-and-bound algorithm. Moreover, we present some heuristics and compare them with two different modifications of an EOQ-type algorithm for the solution of the problem with continuous frequencies.

Suggested Citation

  • Luca Bertazzi & Maria Grazia Speranza & Walter Ukovich, 2000. "Exact and Heuristic Solutions for a Shipment Problem with Given Frequencies," Management Science, INFORMS, vol. 46(7), pages 973-988, July.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:7:p:973-988

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    References listed on IDEAS

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    Cited by:

    1. Faulin, Javier, 2003. "Applying MIXALG procedure in a routing problem to optimize food product delivery," Omega, Elsevier, vol. 31(5), pages 387-395, October.
    2. van Norden, Linda & van de Velde, Steef, 2005. "Multi-product lot-sizing with a transportation capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 165(1), pages 127-138, August.
    3. Luca Bertazzi, 2008. "Analysis of Direct Shipping Policies in an Inventory-Routing Problem with Discrete Shipping Times," Management Science, INFORMS, vol. 54(4), pages 748-762, April.
    4. Hua, N. Grace & Willems, Sean P., 2016. "Optimally configuring a two-stage serial line supply chain under the guaranteed service model," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 98-106.


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