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

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.