Optimising inventory in business environments: combining matrix analytic methods with a working vacation, cancellation policy and working breakdown

The inventory system of the single-server Markovian arrival process with working vacations, working breakdowns under a Bernoulli schedule, and cancellation policy are discussed. The server begins to go on a working vacation when there is no customer in the system even if the inventory level is positive. If any customers arrive while he is end of his working vacation time, a normal busy period begins. If not, he will simply remain idle in regular mode. When a system breaks down, it either offers slow service to the current customers with probability p or immediately undergoes a repair phase with probability q. We derive the invariant vector, busy period, waiting time distribution, total cost, and computation of performance measures using the matrix analytic technique.