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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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.46.7.973.12032
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 46 (2000)
    Issue (Month): 7 (July)
    Pages: 973-988

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    Handle: RePEc:inm:ormnsc:v:46:y:2000:i:7:p:973-988
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    1. S. Anily & A. Federgruen, 1991. "Rejoinder to "Comments on One-Warehouse Multiple Retailer Systems with Vehicle Routing Costs"," Management Science, INFORMS, vol. 37(11), pages 1497-1499, November.
    2. Baita, Flavio & Ukovich, Walter & Pesenti, Raffaele & Favaretto, Daniela, 1998. "Dynamic routing-and-inventory problems: a review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(8), pages 585-598, November.
    3. Daganzo, Carlos F., 1988. "A comparison of in-vehicle and out-of- vehicle freight consolidation strategies," Transportation Research Part B: Methodological, Elsevier, vol. 22(3), pages 173-180, June.
    4. Bertazzi, Luca & Speranza, Maria Grazia & Ukovich, Walter, 1997. "Minimization of logistic costs with given frequencies," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 327-340, August.
    5. Robin Roundy, 1989. "Rounding Off to Powers of Two in Continuous Relaxations of Capacitated Lot Sizing Problems," Management Science, INFORMS, vol. 35(12), pages 1433-1442, December.
    6. Hall, Randolph W., 1985. "Determining vehicle dispatch frequency when shipping frequency differs among suppliers," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 421-431, October.
    7. Blumenfeld, Dennis E. & Burns, Lawrence D. & Diltz, J. David & Daganzo, Carlos F., 1985. "Analyzing trade-offs between transportation, inventory and production costs on freight networks," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 361-380, October.
    8. S. Anily & A. Federgruen, 1990. "One Warehouse Multiple Retailer Systems with Vehicle Routing Costs," Management Science, INFORMS, vol. 36(1), pages 92-114, January.
    9. Daganzo, Carlos F. & Newell, Gordon F., 1985. "Physical distribution from a warehouse: Vehicle coverage and inventory levels," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 397-407, October.
    10. Favaretto, Daniela & Pesenti, Raffaele & Ukovich, Walter, 2001. "Discrete frequency models for inventory management - an introduction," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 331-342, May.
    11. Peter L. Jackson & William L. Maxwell & John A. Muckstadt, 1988. "Determining Optimal Reorder Intervals in Capacitated Production-Distribution Systems," Management Science, INFORMS, vol. 34(8), pages 938-958, August.
    12. Donald Erlenkotter, 1989. "Note---An Early Classic Misplaced: Ford W. Harris's Economic Order Quantity Model of 1915," Management Science, INFORMS, vol. 35(7), pages 898-900, July.
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