Design of Reliable Queue Systems in Complicated Logistics Networks by Using Mathematical Programming Methods

How to construct strong queuing schemes in a network logistics setting using mathematical programming will be considered in this paper. As global supply chains get increasingly complex, Effective management of queues at logistics hubs is crucial for business performance. This work provides a unifying structure which combines queueing models and mathematical programming methods to minimize waiting time, maximize capacity utilization, and optimizing the allocation of resources (e.g., servers) in an unknown demand environment. We employ both analytical models (e.g. M/M/c queueing systems) and simulation techniques developed by means of WinQSP software to explore performance measures under varying circumstances. For illustration, sortation systems of a realistic distribution center network have been placed in simulated. The computational results also show that our technology can reduce the average waiting time by 42% and increase the system's utilization rate by 28% compared to traditional methods by applying mathematical programming for optimal server scaling. The findings of the study will enable logistics managers to develop stable queuing systems that are responsive to demand fluctuation and service performance. This study bridges the gap between queuing theory and practical logistics applications, providing managers with actionable insights.