Normal approximations for the ergodic distribution of a semi-Markovian inventory model of type (s,S)
Logic Journal of the IGPL, cilt.34, sa.3, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 3
- Basım Tarihi: 2026
- Doi Numarası: 10.1093/jigpal/jzag007
- Dergi Adı: Logic Journal of the IGPL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
- Anahtar Kelimeler: ergodic distribution, inventory model of type (s,S), normal approximation, Weibull distribution
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Hayır
Özet
This paper develops new closed form normal approximations for the ergodic distribution of a renewal–reward process (Formula presented) describing a semi-Markovian inventory model of type (Formula presented). When demand sizes follow a Weibull distribution with shape parameter (Formula presented), 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 (Formula presented) of the process (Formula presented). 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.