Shajin, D.; Benny, B.; Razumchik, R. V.; Krishnamoorthy, A. Discrete product inventory control system with positive service time and two operation modes. (English. Russian original) Zbl 1406.90012 Autom. Remote Control 79, No. 9, 1593-1608 (2018); translation from Avtom. Telemekh. 2018, No. 9, 59-78 (2018). Summary: Consideration is given to the Markov inventory control system of a discrete product of maximum volume \(S\) under the strategies \((s,Q)\) and \((s,S)\) with a positive service time. Upon arrival, the order is queued if the inventory level is positive or, otherwise, leaves the system unserviced. One server handles the queued orders one-by-one in the sequence of their arrival. If the inventory level exceeds \(s\), then the service time has the exponential distribution of intensity \(\mu\); otherwise, of intensity \(\alpha\mu\), \(0 < \alpha\leq 1\). The product in the inventory is consumed only at the instant when the service (of the order) ends. Inventory deficit is not allowed. When the inventory is empty new orders are not admitted into the system, and the service process of the queued orders (if any) is stopped. The lead time is assumed to be exponentially distributed. Analytical relations are established for the basic stationary performance characteristics of the system. Cited in 4 Documents MSC: 90B05 Inventory, storage, reservoirs 90B22 Queues and service in operations research 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) Keywords:inventory control system; positive service time; multiplicative representation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Sigman, K.; Simchi-Levi, D., Light traffic heuristic for an M/G/1 queue with limited inventory, Ann. Oper. Res., 40, 371-380, (1992) · Zbl 0798.90068 · doi:10.1007/BF02060488 [2] Melikov, A. A.; Molchanov, A. 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