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

Authors: G. Ayyappan; N. Arulmozhi

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Puducherry Technological University, Puducherry, India

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.

DOI: 10.1504/IJMOR.2025.148075

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.4, pp.465 - 497

Received: 04 Oct 2023
Accepted: 07 Oct 2023
Published online: 25 Aug 2025 *

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