Akademik Veri Yönetim Sistemi
LOGIC JOURNAL OF THE IGPL, cilt.34, sa.3, 2026 (SCI-Expanded, Scopus)
This paper develops new closed form normal approximations for the ergodic distribution of a renewal-reward process $X(t)$ describing a semi-Markovian inventory model of type $(s, S)$. When demand sizes follow a Weibull distribution with shape parameter $\alpha \ge 3$, the renewal function can be well approximated by that of a normal distribution, as shown by Cui and Xie. We use this observation to derive a new numerical method for computing the ergodic distribution $Q_{X}(x)$ of the process $X(t)$. The resulting formulas are easy to evaluate and avoid repeated numerical computation of the Weibull renewal function. Numerical examples show that the approximations are accurate over a wide range of parameter values and that, as the replenishment threshold increases, the ergodic distribution of the inventory level approaches a uniform distribution.