Metro Uses a Simulation-Optimization Approach to Improve Fare-Collection Shift Scheduling

In addition to scheduling trains, drivers, and security personnel, many subway companies worldwide are faced with the challenge of determining the staffing levels and shift schedules required to operate their fare-collection systems. Subway companies typically deal with a highly variable demand for fares, several operational requirements, and increasing service expectations from users. In this paper, we describe a simulation-optimization method for fare-collection shift scheduling in a subway network. We use an integer programming model to generate shift schedules and a discrete-event simulation model to evaluate the corresponding service levels in terms of the average number of users waiting in line over time. If the expected service level at a particular station booth does not meet a predefined service standard, then our method automatically generates an additional constraint on the number of fare collectors at that station booth. The proposed approach iteratively adds this new constraint to the integer programming model until either the current schedule meets the service standard or the problem becomes infeasible. We use the proposed solution approach to solve the fare-collection shift-scheduling problem faced by one of the largest subway companies in Latin America, Metro de Santiago in Chile. The resulting shift schedules show a significant improvement compared with Metro's previous scheduling practice in terms of service levels, operational costs, capacity utilization, and solution times.