Analysis and optimization of hybrid replenishment policy in a double-sources queueing-inventory system with MAP arrivals

A hybrid replenishment policy in double sources queuing-inventory system with MAP flow of consumer customers is proposed. The service time of the consumer customer has a phase type distribution. If the inventory level drops to the reorder point s , then a regular order of volume 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 parameter r , where r < s , then the system instantly cancels the regular order and generates an emergency order to a fast and expensive source in accordance to “Up to S ” policy. The lead times to both sources have independent exponential distributions with different parameters. In addition to consumer customers, the system also receives destructive customers that do not require inventory but destroy them. The ergodicity 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 re-order point and the threshold parameter. Results of numerical experiments are demonstrated.