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A discrete EOQ problem is solvable in O(logn) time

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  • Kovalev, Alexandr
  • Ng, C.T.

Abstract

The Economic Order Quantity problem is a fundamental problem of inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible and demand occurs at a constant rate [lambda]. We prove that a discrete version of this problem, in which time and the product are discrete is solvable in O(logn) time, where n is the length of the time period where the demand takes place. The key elements of our approach are a reduction of the original problem to a discrete minimization problem of one variable representing the number of orders and a proof that the objective function of this problem is convex. According to our approach, optimal order sizes can take at most two distinct values: and , where k* is the optimal number of orders.

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  • 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.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:914-919
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    1. 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.
    2. Luca Bertazzi & Maria Speranza, 2001. "Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem," Annals of Operations Research, Springer, vol. 107(1), pages 33-49, October.
    3. 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.
    4. 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.
    5. 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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    Cited by:

    1. Li, Chung-Lun, 2009. "A new solution method for the finite-horizon discrete-time EOQ problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 412-414, August.
    2. Meyer, Anne & Amberg, Boris, 2018. "Transport concept selection considering supplier milk runs – An integrated model and a case study from the automotive industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 147-169.

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