An integrated queueing simulation and multi-objective optimization framework for business operations management
Abstract
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.