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

G. Ayyappan and N. Arulmozhi

International Journal of Mathematics in Operational Research, 2025, vol. 31, issue 4, 465-497

Abstract: 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.

Keywords: Markovian arrival process; MAP; phase-type service; ( s , Q ) policy; working vacation; working breakdown; cancellation policy. (search for similar items in EconPapers)
Date: 2025
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