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Review of some queueing models for managing inventories,backorders,and quality jointly in stochastic manufacturing systems

Kouikoglou Vasilis, Georgios Saharidis, Stratos Ioannidis

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This paper reviews some recent applications of queueing theory and convex analysis in determining customer admission, inventory, and quality control policies jointly in manufacturing systems that produce a single product to meet random demand. These problems have been addressed separately in the past. We consider admission and production control policies of the threshold type whereby the system produces until stock reaches a certain level and accepts orders until its backlog reaches another critical level. The problem is to find the optimal quality tolerances and the critical stock and backlog levels which maximize the mean profit rate of the system. We also examine a supply chain comprising two factories in series with external subcontractors, and we compare the benefit of determining the optimal base stocks for the two systems jointly rather than individually. From theoretical and numerical results, it appears that managing inventory levels, sales, and quality tolerances jointly achieves higher profit than independently determined control policies.

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