Simple approximations for the reorder point in periodic and continuous review (s,S) inventory systems with service level constraints
Under classical assumptions it is shown that: \[ (1)\quad\int^{\infty}_{s}(x-s)h(x)dx\simeq (2\mu_ R)^{- 1}\{\int^{\infty}_{s}(x-s)^ 2\eta (x)dx-\int^{\infty}_{s}(x- s)^ 2\xi (x)dx\} \] where: h(x): probability density of \(Z+\xi\) where Z is the undershoot of the reorder point s at the review at which the tagged replenishment order is placed whereas \(\xi\) is for the total demand in the lead time of the tagged replenishment order; \(\eta\) (x): probability density of the total demand in the lead time plus review time; \(\xi\) (x): probability density of the total demand in the lead time; \(\mu_ R:\) average demand in the review time. The reorder point s is determined by solving equations derived from (1) using different service measures. Since only the first two moments of \(\mu\) and \(\xi\) are generally available, a two-moments fitting for these demand densities is proposed assuming that they are normal or gamma. Numerical results are given both for periodic and continuous reviews.
scientific article; zbMATH DE number 3873035
scientific article