Optimal student/school/class/teacher/classroom matching to support efficient public school system resource allocation

This paper presents a decision support methodology to help increase public school education efficiency at the municipal/district/metropolitan level in Brazil. An important consideration for efficient use of resources in each school district or metropolitan area is the appropriate matching of the supply of human resources (e.g., teachers of specific subjects) and of infrastructure resources (e.g., school locations, classroom availability) with demand (students requesting enrollment in each grade). This resource matching is a necessary periodic (perhaps annual) district level planning task that precedes individual school operational tasks such as registration, timetabling, and other scheduling. This paper describes a mathematical model and computational tool to optimize the allocation efficiency of public school district resources during the long-term strategic planning stage as well as the shorter-term tactical planning stage preceding each academic year, i.e., the stage bridging strategic planning and operational programming. This problem, namely the simultaneous optimization of demand variables (students) and both infrastructure and human capital supply variables (respectively classroom availability and teacher specializations) in the form of student/school/class/teacher/classroom matchings for a given physical plant, was solved through a mixed integer linear programming formulation that endogenously incorporates those supply variables with student demand variables. The paper presents the conceptual framework, provides the mathematical formulation, and describes the implementation of the resulting decision support computational system. The paper also illustrates the suggested methodology by examining public schooling in Itacoatiara, a municipality on the banks of the Amazon River in a resource-constrained and low-HDI region of Brazil, before a new school was added to the local network in 2019.