School choice modeling and network optimization in an urban environment

Schools are some of the most critical public facilities that significantly affect peoples' lives at potentially more than one stage, as a student or as a student's parent. They impact the educational quality and the social environment students grow in, playing a pivotal role in shaping students' future. Multiple factors influence students' selection of schools, driven by the utility that different school options provide. These factors include but are not limited to the distance to school, the school's academic performance, ranking, and the student's socioeconomic background. The trade-off between school attributes can affect the school choice of students. Given that schools have hard capacity constraints, the preferred choice of students may not be available, forcing students to attend other schools offering less utility. Integrating prefabricated classrooms into existing schools can help increase their capacities. In this paper, we first develop a multinomial logit model to understand the weight and importance of the different attributes influencing students' choice of schools. We then calculate the probability of allocating students to different schools. Next, we formulate a multi-period optimization problem to maximize the number of students allocated to their preferred school while enabling the possibility to increase the capacity of existing schools through the addition of prefabricated classrooms. We apply the developed models to Sydney's public school network. These models can be an effective tool for strategic planners working on improving the system of schools in a large metropolitan area, particularly those with growing population such as Australia's major cities, including Sydney, which is used as a case study in this paper. This work contributes to the literature on school network development by introducing a novel approach that optimises school network capacity increase to improve the overall utility of all users, using a choice modelling approach.