Service operations across health care, banking and supply chain logistics face persistent congestion challenges where staffing decisions must simultaneously satisfy cost constraints and service-quality targets, yet classical single-objective M/M/c models address only one dimension at a time, concealing the inherent cost–service trade-off. This paper aims to develop the QS-MOO framework to expose the full Pareto frontier of this trade-off, enabling managers to make informed server-allocation decisions across heterogeneous business environments.
Grounded in Erlang-C analytical theory and extended through phase-type service distributions and discrete-event simulation (DES), the QS-MOO framework incorporates stochastic arrival modelling, non-stationary demand approximation via the stationary independent period-by-period (SIPP) method and a Pareto-front optimization engine based on NSGA-II. Parameter ranges are drawn from the established queueing literature to demonstrate cross-sectoral applicability.
The framework consistently identifies Pareto-optimal server configurations that balance waiting-time minimization and cost containment. The convex trade-off frontier is most sensitive to arrival-rate variability and service-time coefficient of variation and least sensitive to queue discipline in high-volume settings.
Operations managers can deploy the Pareto front as a decision-support instrument, selecting server configurations aligned with cost constraints and service-level agreements. The modular architecture supports cross-sectoral application, including healthcare systems, banking operations and supply chain networks, thereby enhancing its adaptability to diverse operational contexts.
This study contributes a generalizable QS-MOO architecture bridging analytical and simulation-based queueing, formally treats the bi-objective cost–service trade-off via Pareto-front theory, extends Erlang-C to phase-type and non-stationary settings and integrates NSGA-II with stochastic DES alongside a replicable algorithmic specification.
