School location and capacity modification considering the existence of externalities in students school choice

• Model of location and modification of capacity of schools.
• Student’s Choice depends not only on the time and income constraints but also on externalities.
• Using a microeconomic approach, a constrained logit discrete choice model is used.
• Nonlinear optimization model incorporates the student’s behavior.
• A Tabu Search metaheuristic is used for solving a fixed point system of equations.

Geographic and socioeconomic characteristics of rural zones in Chile have made schools located in these areas present inefficiencies such long travel times and multi-degree courses1 that affect the academic performance of their students. In this paper, a model of location and modification of school capacity is presented as an alternative to reduce these inequalities. In Chile a student school choice is a process that depends not only on the time and income constraints but also on the decisions made by other students (segregation). This behavior is modeled using a microeconomic approach; thereby a constrained multinomial logit discrete choice model is derived. By incorporating the student’s school choice in an optimization model, it becomes nonlinear. A Tabu Search metaheuristic is proposed, which unlike other implementations requires solving a fixed point system of equations to evaluate each solution. A computing experience for instances of 10 and 45 zones is developed; in the first the quality of the solution is evaluated compared to the optimum obtained by enumeration and in the second different scenarios are analyzed.