On a continuous review production-inventory problem (Q761232)

The author considers a single product production-inventory system, where both the input into the inventory and the demand for the product follow a Poisson process. As soon as the stock level reaches S, the machine is shut off. It is put back into operation as soon as the stock level drops down to s. The machine itself is subject to failure; life time is exponentially distributed, repair time has an arbitrary distribution. As a main result, the inventory level is studied as a function of time. In particular, its asymptotic behaviour is derived. Furthermore, some related problems are investigated and an asymptotic cost rate is introduced, which may be employed to determine s and S in an optimal way.