Ozkan, SinemBulut, OnderDincer, Mehmet Cemali2026-04-072026-04-0720251476-93600160-568210.1080/01605682.2025.25893232-s2.0-105022718410https://hdl.handle.net/123456789/13802https://doi.org/10.1080/01605682.2025.2589323This study considers a production-inventory system with production start-up costs and parallel production lines. Production times are independent and identically distributed exponential random variables and demands are generated according to a stationary Poisson process. Production and inventory are controlled by the extended-two-critical-number policy. The system is modelled as an M/M/s make-to-stock queue and analysed for both lost sales and backordering cases. A renewal approach is developed to calculate the expected average system cost. Furthermore, an approximation is proposed to calculate the control parameters of the extended-two-critical-number policy. An extensive numerical study is conducted to illustrate the effects of changes in system parameters and the effectiveness of the proposed approximation. The analysis shows that the proposed approximation performs well across various system conditions.eninfo:eu-repo/semantics/closedAccessMake-to-stockProduction Start-up CostProduction and Inventory ControlMulti-Production LineRenewal TheoryArticle