A state dependent M/M/1 queue: A production-inventory model
This paper deals with a model of production and inventory control. The model incorporates a continuous-level production rate with a base-stock level inventory policy subject to fluctuating demand. The inventory level at time t is denoted by Y(t) and the base stock level by M. The quantity of interest here is \(U(t)=M-Y(t)\). The authors compute the stationary density of U(t) including the facility utilization and the mean time for U(t) to reach or exceed a given value. They analyze the production busy period of the facility, they compute the mean length of a production period and the mean time for a production busy period to end, given the current value of U(t). Finally, they compute the integral of U(t) during a busy period, and the distribution of the minimum inventory level.
scientific article; zbMATH DE number 4126984