Optimizing extracurricular activities assignment and related logistical deployment cost between collaborating schools

In contemporary urban societies, where both parents are working full-time, a significant number of schoolchildren engage in extra-curricular activities after school. These activities can be organized by the school itself and take place in the school. However, sometimes few schoolchildren are interested in an activity organized by the school, or the schoolchildren's preferences do not match the school's offering at all, while on other occasions the school has limited availability for a popular activity. To expand the number of activities offered to their schoolchildren, some schools form a collaborating network, sharing their extracurricular activities and making them accessible to all schoolchildren. Thus, schoolchildren from any school may attend activities organized by other schools in the network. In this case, however, transport of the children between schools must also be organized. This problem can be framed as a school bus routing problem with some special features. A mixed-integer linear optimization model is proposed for the integrated assignment of extracurricular activities and cost-effective vehicle routing. The objective of the model is to minimize unmet demand for extracurricular activities while taking into account the constraints related to the facilities and transport. This model has been tested on a set of instances to analyze its performance, with the goal of deploying it for the projected levels of demand in a city of about 100,000 inhabitants. The results are compared with the current situation and the clustering of the set of schools.