2026, Vol. 7, Issue 1, Part A

Service and production systems such as banking counters, healthcare registration units, and call centers operate under substantial uncertainty in arrivals, service rates, and cost parameters, while being required to meet explicit service-level targets. Classical queueingbased optimization typically assumes precisely known parameters, which limits its applicability in data-scarce or expert-driven environments. This paper addresses this gap by developing an integrated framework that combines fuzzy mathematical programming with queueing models, allowing congestion-aware decisions to be made under imprecise informatins.

Fuzzy parameters are modeled using membership functions, and system performance measures derived from queueing theory are embedded directly into the optimization layer through either α-cut decomposition or a satisfaction-level (λ) maximization approach. The resulting model captures trade-offs between operational cost and service quality while preserving interpretability of ambiguity. A real-world service-system case study, motivated by a single-station multi-server operational setting, demonstrates the practical implementation of the proposed framework.

Numerical results indicate that the integrated fuzzy-queueing approach yields solutions that are more robust and managerially transparent than crisp benchmarks, particularly when service-level constraints are critical. The framework supports informed staffing and capacity decisions and offers actionable insights for practitioners managing uncertainty in operational systems.