Design of Single-Facility Multi-Regime Services under Congestion

V. Blanco, M. Martínez-Antón, J. Puerto

We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design.

Keywords: Conic Optimization, Queuing Theory, Facility Location, Service Design, Discrete Optimization.

GT GELOCA I: Optimization models in facility location and service design.
September 3, 2026  9:00 AM
Aula B

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