Double Sources Queuing-Inventory System with Hybrid Replenishment Policy

A hybrid replenishment policy in double sources queuing-inventory system is proposed. If the inventory level drops to the reorder point s, then a regular order of the fixed volume Q = S − s is generated to a slow and cheap source, where S denotes the maximum size of the system’s warehouse. If the inventory level falls below a certain threshold value r, where r < s, then the system instantly cancels the regular order and generates an emergency order to a fast and expensive source where the replenishment quantity should be able to bring the inventory level back to S at the replenishment epoch. In addition to consuming customers, the system also receives destructive customers that do not require inventory but destroy them. The stability condition for the system under study is found, steady-state probabilities are calculated, and formulas for finding performance measures are proposed. The problem of minimizing the total cost of the system under the proposed hybrid replenishment policy is solved by choosing the appropriate values of the order point and the threshold value.