Managing Customer Arrivals in Service Systems with Multiple Identical Servers

We analyze a discrete multi-server model for scheduling customer arrivals under no-shows. The challenge is to assign customers to time slots so that the service system utilizes its resources efficiently and customers experience short waiting times. We provide theoretical and heuristic guidelines for an effective practice of appointment overbooking in order to offset no-shows. Recursive and explicit expressions for the performance measures of interest are derived based on the random evolution of the system’s workload in transient state. We prove discrete convexity properties of the optimization problem that restrict our search to a contained solution space and guarantee that a local search algorithm terminates with a globally optimal schedule. Extensive computational experiments reveal additional properties and patterns that appear in the optimal schedule, and motivate the development of two very well performing and computationally inexpensive heuristic solutions.