On a continuous review production-inventory problem

This paper considers a one-product, one-machine production-inventory problem operating under an (s, S) policy that identifies a semi-regenerative process and expressions for the probability mass function for the inventory process at any time and in the stationary regime are obtained.

Abstract

This paper considers a one-product, one-machine production-inventory problem operating under an (s, S) policy. The production facility may be set up and in production, shut down and idle or failed and under repair. Back-order is not permitted. By identifying a semi-regenerative process, expressions for the probability mass function for the inventory process at any time and in the stationary regime are obtained. The distribution for the total duration of idleness of the machine upto any time is derived. Cost analysis is also indicated.