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

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  • 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.

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