Advanced Search
Article Contents
Article Contents

Approximate and exact formulas for the $(Q,r)$ inventory model

Abstract Related Papers Cited by
  • In this paper, new results are derived for the $(Q,r)$ stochastic inventory model. We derive approximate formulas for the optimal solution for the particular case of an exponential demand distribution. The approximate solution is within 0.29% of the optimal value. We also derive simple formulas for a Poisson demand distribution. The original expression involves double summation. We simplify the formula and are able to calculate the exact value of the objective function in $O(1)$ time with no need for any summations.
    Mathematics Subject Classification: Primary: 90B05; Secondary: 33F05, 34K28.


    \begin{equation} \\ \end{equation}
  • [1]

    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 7th printing, Applied Mathematics Series, National Bureau of Standards, Washington, DC., 1968.doi: 10.1119/1.1972842.


    R. B. S. Brooks and J. Y. Lu, On the convexity of the backorder function for an E.O.Q policy, Management Science, 15 (1969), 453-454.


    A. Federgruen and Y. -S. Zheng, An efficient algorithm for computing an optimal $(r,Q)$ policy in continuous review stochastic inventory systems, Operations Research, 40 (1992), 808-813.doi: 10.1287/opre.40.4.808.


    G. Gallego, New bounds and heuristics for ($Q,r$) policies, Management Science, 44 (1998), 219-233.doi: 10.1287/mnsc.44.2.219.


    R. Loxton and Q. Lin, Optimal fleet composition via dynamic programming and golden section search, Journal of Industrial and Management Optimization, 7 (2011), 875-890.doi: 10.3934/jimo.2011.7.875.


    J. O. Parr, Formula approximations to Brown's service function, Production and Inventory Management, 13 (1972), 84-86.


    D. E. Platt, L. W. Robinson and R. B. Freund, Tractable ($Q,R$) heuristic models for constrained service levels, Management Science, 43 (1997), 951-965.


    P. Zipkin, Foundations of Inventory Management, McGraw-Hill, New York, 2000.

  • 加载中

Article Metrics

HTML views() PDF downloads(202) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint