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

Abstract

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.