Coordinated and Joint Ordering Policies for Two Commodity Inventory System

We deal with the two commodity continuous review inventory system with two joint reordering policies. The maximum inventory level for the ith commodity is $S_i$ (i = 1, 2) units. It is assumed that demand for the ith commodity is of unit size and the demand time points form a Poisson process with parameter $\lambda_i$, i = 1, 2. The reorder level is fixed as $C_i$ for the ith commodity (i = 1, 2) . The ordering policy is to place an order for $P_i$ ($= S_i-c_i$) items for the ith commodity (i = 1, 2) when both the inventory levels are less than or equal to their respective reorder levels. If the total net inventory level drops to a prefixed level s, an order will be placed for $Q_i$ ($=S_i-s$) items for the ith commodity. The lead times are assumed to be negative exponential. Demands that occur during the stock-out periods are assumed to be lost. The joint inventory level for both commodities is obtained in the steady state. Various system performance measures in the steady state are derived.