Integrated Operational Decisions for Configuration, Staffing, and Workforce Routing in Two-Stage Multi-Location Service Systems

Service systems often face time-varying demands, requiring effective workforce allocation to manage queue lengths and wait times. This paper addresses workforce management in a two-stage, multi-location server system with shared, movable staff, and location-specific demand patterns. Each stage operates under multiple configurations (e.g., number of servers), each with distinct staffing needs. We develop a mixed-integer programming model to optimize dynamic configurations, minimizing workforce requirements while meeting QoS targets (e.g., maximum wait time) and operational constraints. Our approach integrates a distribution-free queue-length prediction method and leverages valid inequalities to improve solution times. We also introduce a rolling-horizon scheme to approximate optimal solutions efficiently and warm start the exact model. Through a case study of passenger screening in a multi-terminal U.S. airport, we demonstrate the strategic value of proactive workforce management in handling fluctuating demand peaks, integrating staffing, scheduling, and workforce routing decisions to enhance system performance.