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Exact and Heuristic Solutions for a Shipment Problem with Given Frequencies

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  • 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)

Abstract

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
    DOI: 10.1287/mnsc.46.7.973.12032
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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. Bertazzi, Luca & Moezi, Sarem Deilami & Maggioni, Francesca, 2021. "The value of integration of full container load, less than container load and air freight shipments in vendor–managed inventory systems," International Journal of Production Economics, Elsevier, vol. 241(C).
    4. Lawrence C. Leung & Yer Van Hui & Yong Wang & Gang Chen, 2009. "A 0--1 LP Model for the Integration and Consolidation of Air Cargo Shipments," Operations Research, INFORMS, vol. 57(2), pages 402-412, April.
    5. Sara Martins & Pedro Amorim & Bernardo Almada-Lobo, 2018. "Delivery mode planning for distribution to brick-and-mortar retail stores: discussion and literature review," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 785-812, December.
    6. Haiqing Song & Vernon N. Hsu & Raymond K. Cheung, 2008. "Distribution Coordination Between Suppliers and Customers with a Consolidation Center," Operations Research, INFORMS, vol. 56(5), pages 1264-1277, October.
    7. 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.
    8. Milind Dawande & Srinagesh Gavirneni & Sridhar Tayur, 2006. "Effective Heuristics for Multiproduct Partial Shipment Models," Operations Research, INFORMS, vol. 54(2), pages 337-352, April.
    9. 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.
    10. Luca Bertazzi & Maria Grazia Speranza, 2002. "Continuous and Discrete Shipping Strategies for the Single Link Problem," Transportation Science, INFORMS, vol. 36(3), pages 314-325, August.

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