Using Mathematical Programming to Analyze and Improve Robust Queue Management in Healthcare Systems

Efficient management of patient queues is essential in healthcare systems to ensure timely care, optimize resource utilization, and enhance patient satisfaction. Mathematical programming, particularly when applied in conjunction with queuing theory and optimization models, provides a rigorous framework for analyzing and improving healthcare service delivery. This approach involves modeling arrivals and service processes, applying queuing models (such as single-server, multi-server, and priority queues), and formulating optimization objectives—often to minimize total costs, patient waiting times, or resource idling. Recent research demonstrates that combining queuing theory with mixed-integer programming and simulation techniques enables healthcare managers to allocate resources dynamically, set staffing levels, and assign priorities among different patient categories. For example, the use of mixed-integer programming can determine the optimal number of servers, beds, and service rates based on patient flow and priority needs, striking a balance between reducing waiting times for critical cases and controlling operational costs. These mathematical models also account for practical constraints and stochastic variability inherent in clinical settings. Applications span emergency departments, outpatient clinics, and even pharmacy and blood service centers—showing significant improvements in system efficiency, reduced patient wait times, and enhanced overall care quality. Thus, mathematical programming is a powerful decision-support tool for queue management, offering evidence-based strategies to address congestion and resource allocation challenges in complex healthcare environments.