Estimators of the Moments for the Inventory Model of Type (s, S)

The inventory model of type (s, S) is one of the most common used inventory models used in many problems of stock control. It is very important to know statistical characteristics such as the moments of the inventory model of type (s, S). However, since the moments of the inventory model of type (s, S) depend on the moments of demands, they cannot be obtained easily in most of the time. For this reason, we focus on the estimation problem of the moments of the inventory model of type (s, S). In this study, we obtain the estimators of the moments of this process initially. Afterwards, the asymptotic statistical properties of these estimators such as consistency, asymptotic unbiasedness and asymptotic normality are investigated. We also give a detailed numerical example of these estimators of the moments of the inventory model of type (s, S).[Gokpinar, Esra; Gamgam, Hamza; Gokpinar, Fikri] Gazi Univ, Dept Stat, TR-06500 Ankara, Turkey; [Khaniyev, Tahir] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06500 Ankara, Turkey; [Khaniyev, Tahir] Natl Acad Sci Azerbaijan, Inst Cybernet, AZ-1141 Baku, Azerbaija

On the Stationary Distribution for a Fuzzy Inventory Model of Type (s,S) with Inverse Gaussian Distributed Demands

In this study, we consider a fuzzy inventory model of type (s,S) with random demands having an inverse Gaussian distribution. We first show the monotonicity of the renewal function with respect to mean parameter. Thus we obtain the membership function of the fuzzy renewal function when the amount of demands is a random variable having an inverse Gaussian distribution with a fuzzy mean parameter by using the monotonicity property of renewal function. Making use of the membership function of the renewal function, we obtain the membership function of the fuzzy ergodic distribution of this process. We also present some numerical results obtained by using this membership function.[Khaniyev, Tahir; Turksen, I. Burhan] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06560 Ankara, Turkey; [Khaniyev, Tahir] Natl Acad Sci Azerbaijan, Inst Cybernet, AZ-1141 Baku, Azerbaijan; [Gokpinar, Fikri] Gazi Univ, Dept Stat, TR-06500 Ankara, Turkey; [Hanalioglu, Tagi] Bogazici Univ, Dept Ind Engn, Istanbul, Turkey; [Turksen, I. Burhan] Univ Toronto, Dept Mech & Ind Engn, Toronto, ON M5S 3G8, Canad