Coordinating paths and schedules of groups visiting multiple capacitated locations

We study a situation where a large number of people visit a popular venue (e.g., an art gallery, a mall, a theme park, or an exhibition) where points of interest are located (e.g., paintings, shops, attractions, or pavilions). Visitors have a maximum amount of time available for the overall experience. The points of interest have a limiting capacity and, whenever the turnout of visitors exceeds such capacity, queues and service disruptions occur. Given the maximum time available along with the time spent queuing, a selection of the points of interest may become necessary. Visitors usually act as autonomous decision-makers and do not take into account their interaction with other visitors. This leads to remarkable inefficiencies that could be, to a certain extent, overcome through a coordination of the paths and schedules of the different visitors. The resulting optimization problem is modeled as a Mixed-Integer Linear Program (MILP), where the goal is to minimize a weighted combination of the points of interest not selected and the time spent queuing. Computational results show the benefits that can be achieved by using the model proposed as a tool to support decision-making.