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Continuous and Discrete Shipping Strategies for the Single Link Problem

Author

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  • Luca Bertazzi

    (University of Brescia, Department of Quantitative Methods, C.da S.ta Chiara, 50—25122 Brescia, Italy)

  • Maria Grazia Speranza

    (University of Brescia, Department of Quantitative Methods, C.da S.ta Chiara, 50—25122 Brescia, Italy)

Abstract

We consider the problem of shipping several products from a common origin to a common destination. Each product is offered at the origin and absorbed at the destination at a given constant rate. The objective of the problem is to determine a shipping strategy that minimizes the sum of the transportation and the inventory costs. We present a general framework of analysis from which we derive the known approaches with a continuous frequency and with a set of given frequencies as particular cases. Moreover, we derive from the general framework a new model for the case with discrete shipping times in which a shipment can take place at each discrete time instant. We prove that the optimal solutions of the three models can be ranked and that the distance between the optimal costs can be unlimited in the worst case. Finally, we evaluate, on the basis of a set of randomly generated problem instances, the "average" distance between the optimal solutions of the models.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:3:p:314-325
    DOI: 10.1287/trsc.36.3.314.7828
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    4. Maria Grazia Speranza & Walter Ukovich, 1994. "Minimizing Transportation and Inventory Costs for Several Products on a Single Link," Operations Research, INFORMS, vol. 42(5), pages 879-894, October.
    5. 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.
    6. S. Anily & A. Federgruen, 1990. "One Warehouse Multiple Retailer Systems with Vehicle Routing Costs," Management Science, INFORMS, vol. 36(1), pages 92-114, January.
    7. William L. Maxwell & John A. Muckstadt, 1985. "Establishing Consistent and Realistic Reorder Intervals in Production-Distribution Systems," Operations Research, INFORMS, vol. 33(6), pages 1316-1341, December.
    8. 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.
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    Cited by:

    1. 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).
    2. Dall'Orto, Leonardo Campo & Crainic, Teodor Gabriel & Leal, Jose Eugenio & Powell, Warren B., 2006. "The single-node dynamic service scheduling and dispatching problem," European Journal of Operational Research, Elsevier, vol. 170(1), pages 1-23, April.
    3. Bertazzi, Luca & Speranza, Maria Grazia, 2005. "Improved rounding procedures for the discrete version of the capacitated EOQ problem," European Journal of Operational Research, Elsevier, vol. 166(1), pages 25-34, October.
    4. Lap Mui Ann Chan & M. Grazia Speranza & Luca Bertazzi, 2013. "Asymptotic analysis of periodic policies for the inventory routing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 525-540, October.
    5. Z.N. Chen & C.K.M. Lee & W.H. Ip & G.T.S. Ho, 2012. "Design and evaluation of an integrated inventory and transportation system," Transportation Planning and Technology, Taylor & Francis Journals, vol. 35(4), pages 491-507, January.
    6. Timajchi, Ali & Mirzapour Al-e-Hashem, Seyed M.J. & Rekik, Yacine, 2019. "Inventory routing problem for hazardous and deteriorating items in the presence of accident risk with transshipment option," International Journal of Production Economics, Elsevier, vol. 209(C), pages 302-315.
    7. Bertazzi, Luca & Grazia Speranza, Maria, 2005. "Worst-case analysis of the full load policy in the single link problem," International Journal of Production Economics, Elsevier, vol. 93(1), pages 217-224, January.
    8. Kovalev, Alexandr & Ng, C.T., 2008. "A discrete EOQ problem is solvable in O(logn) time," European Journal of Operational Research, Elsevier, vol. 189(3), pages 914-919, September.
    9. Mirzapour Al-e-hashem, Seyed M.J. & Rekik, Yacine & Mohammadi Hoseinhajlou, Ebrahim, 2019. "A hybrid L-shaped method to solve a bi-objective stochastic transshipment-enabled inventory routing problem," International Journal of Production Economics, Elsevier, vol. 209(C), pages 381-398.
    10. Luca Bertazzi & Lap Mui Ann Chan, 2014. "Analysis of the Best Double Frequency Policy in the Single Link Problem with Discrete Shipping Times," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 286-309, October.
    11. Mohamed Salim Amri Sakhri & Mounira Tlili & Ouajdi Korbaa, 2022. "A memetic algorithm for the inventory routing problem," Journal of Heuristics, Springer, vol. 28(3), pages 351-375, June.
    12. 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.
    13. 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.
    14. Mirzapour Al-e-hashem, S.M.J. & Rekik, Yacine, 2014. "Multi-product multi-period Inventory Routing Problem with a transshipment option: A green approach," International Journal of Production Economics, Elsevier, vol. 157(C), pages 80-88.
    15. Luca Bertazzi & Lap Mui Ann Chan & Maria Grazia Speranza, 2007. "Analysis of practical policies for a single link distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 497-509, August.
    16. Tingting Ji & Shoufeng Ji & Yuanyuan Ji & Hongyu Liu, 2022. "Study on Sustainable Combined Location-Inventory-Routing Problem Based on Demand Forecasting," Sustainability, MDPI, vol. 14(23), pages 1-21, December.
    17. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.

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