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Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

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  • Luca Bertazzi
  • Maria Speranza

Abstract

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $$\frac{1}{2}$$ ( $$\sqrt 2 + 1/\sqrt 2 $$ )≈1.06 on classes of instances of high practical relevance. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:107:y:2001:i:1:p:33-49:10.1023/a:1014986628929
    DOI: 10.1023/A:1014986628929
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Lodree, Emmett Jr., 2007. "EOQ revisited: The case of unequal and integral order quantities," International Journal of Production Economics, Elsevier, vol. 105(2), pages 580-590, February.
    7. 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).
    8. Luca Bertazzi & Simona Cherubini, 2013. "An inventory-transportation system with stochastic demand," Computational Management Science, Springer, vol. 10(1), pages 1-20, February.
    9. 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.

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