Stationary Characteristics for Renewal-Reward Process with Generalized Reflecting Barrier and Fuzzy Demands

Abstract

Renewal-reward processes with barriers are useful tools which are frequently applied in the fields of quantum physics as well as in some problems in various engineering areas. Especially, some problems in inventory theory can be modeled by means of renewal-reward processes with a generalized reflecting barrier. However, in inventory models, for instance, while predicting the distribution of the random variables such as demands or interarrival times, the entire distribution or some of its parameters can be fuzzy because of the vague information or some other subjective evaluations. Therefore, in this study, an inventory model is investigated by means of a renewal-reward process with a generalized reflecting barrier when the demands are fuzzy random variables. The aim of this study is to obtain exact expression and asymptotic expansions for the ?-cuts of ergodic distribution of the considered process which represents a fuzzy inventory model. Moreover, the asymptotic expansions for the ?-cuts of ergodic moments are derived. Particularly, a special case in which the demands have a Weibull distribution with a fuzzy parameter is studied in detail. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.