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The uniform distribution product: an approach to the inventory model using R

Author

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  • Amílcar Oliveira
  • Teresa Oliveira
  • Antonio Seijas-Macías

Abstract

In this work the probability density function (PDF) for the product of two uniformly distributed random variables is explored under the implementation of a new procedure in R language. Based on the Rohatgi theorem for the theoretical form of the product, different possibilities for the range of values of the limits of both distributions are considered. As an application, the management of a $ (Q,r) $ (Q,r) inventory model with the presence of lead-time and uniform demand forecasts is considered. Solution to this model looks up to minimize the total costs through the variables Q (reorder quantity) and r (the reorder point), and not always exists an analytical solution of the problem. We show a graphical procedure for the simulation results and a more exactly analytical solution. Implementation in R is straightforward.

Suggested Citation

  • Amílcar Oliveira & Teresa Oliveira & Antonio Seijas-Macías, 2018. "The uniform distribution product: an approach to the inventory model using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 284-297, January.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:2:p:284-297
    DOI: 10.1080/02664763.2016.1275531
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    References listed on IDEAS

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    1. Chandrasekhar Das, 1976. "Approximate Solution to the (Q, r) Inventory Model for Gamma Lead Time Demand," Management Science, INFORMS, vol. 22(9), pages 1043-1047, May.
    2. Dettmann, Carl P. & Georgiou, Orestis, 2009. "Product of n independent uniform random variables," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2501-2503, December.
    3. Glen, Andrew G. & Leemis, Lawrence M. & Drew, John H., 2004. "Computing the distribution of the product of two continuous random variables," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 451-464, January.
    4. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.
    5. Chandrasekhar Das, 1976. "Explicit formulas for the order size and reorder point in certain inventory problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 25-30, March.
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