A production queueing-inventory system with two-customer and a server subject to breakdown

• Published in: Annals of operations research Vol. 331; no. 2; pp. 1089 - 1117
• Main Authors: Kocer, Umay Uzunoglu, Ozkar, Serife
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2023; Springer; Springer Nature B.V
• Subjects: Breakdown; Business and Management; Combinatorics; Cost function; Customer services; Customers; Inventory control; Inventory management; Markov processes; Operations research; Operations Research/Decision Theory; Original Research; Parameter sensitivity; Probability; Probability distribution; Probability distribution functions; Queuing theory; Random variables; Theory of Computation; Turkey; 90B22; Bright-Taylor algorithm; Server breakdown; LDQBD; Two types of customers; 90B05; 60K25; Optimization; Queueing-inventory
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-023-05275-9

A queueing-inventory system where the server is subject to breakdown is examined. The products in inventory are provided by production. Two different types of customers are considered. Each customer type arrives in the system according to a Poisson process with different parameters. There is only one server and the service time follows an exponential distribution. Service may be interrupted randomly due to breakdowns. There may be minor or major breakdowns and after the recovery process, the priority customer class gets service first. The described system is formulated as a level-dependent quasi-birth-death process (LDQBD). The stationarity condition is provided and the steady-state probabilities are calculated. A comprehensive numerical study is presented that examines the sensitivity of the performance measures to the change of system parameters and also investigates the optimal inventory policy according to the considered cost function.