Two-commodity inventory system with retrial demand

This paper analyzes a two-commodity inventory system under continuous review. The maximum storage capacity for the ith commodity is Si(i=1,2).(i=1,2). It is assumed that primary demand for the ith commodity is of unit size and primary demand time points form a Poisson process. The reorder level is fixed as si for the i  th commodity and the ordering policy is to place order for Qi(=Si-si) items (i=1,2)(i=1,2) when both the inventory positions are less than or equal to their respective reorder levels. The lead time is assumed to be exponential. Both the commodities are assumed to be substitutable in the sense that at the time of zero stock of any one commodity, the other one is used to meet the demand. When the inventory position of both commodities are zero, any arriving primary demand enters into an orbit of infinite size. The orbiting demands in the orbit send out signal to compete for their demand which is distributed as exponential. The joint probability distribution for both commodities and the number of demands in the orbit is obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated numerically.