Constraint programming approach for school timetabling

Abstract

In this paper, the timetabling problem for a typical high school environment was modeled and solved using a constraint programming (CP) approach. In addition, operations research (OR) models and local search techniques were also used in order to assist the CP search process by effectively reducing the solution search space. Relaxed models that can be solved using minimum cost matching algorithms were used in order to calculate problem lower bounds at various instances of the solution process. These bounds were in turn used to prioritize the search options of the CP process. The use of minimum cost matching model in the search process is an economical and efficient mechanism for the creation of effective search strategies and it is a competitive manner of introducing problem domain information in the CP environment. By including in the solution process a sequence of local search steps, the solution quality was further improved. Several large problems were solved and actual computational results for specific problem instances are presented. Scope and purpose There exist various school timetabling problems depending on the environment and the characteristics of the particular school level [1]. In this paper the high school situation in which the teachers teach in several different class sections during the day and the students remain in their classrooms is modeled and solved. The objective function attempts to minimize the idle hours between the daily teaching responsibilities of all the teachers while also attempting to satisfy their requests for early or late shift assignments. The school timetabling problem is combinatorial and there are several strict organizational and sequence-related rules that must be respected. The problem specifications used in this paper, although they closely describe the situation of a typical Greek high school, are quite general and abstract, which makes the findings of this paper applicable to wider set of school timetabling problems. The specifications mainly focus on the fact that each teacher is scheduled to lecture for a given number of hours at a fixed subset of class sections and the requirement that all the class sections must be always in session without any empty periods in their daily schedules. The integration of constraint programming and operations research techniques for the solution of this problem is one of the main contributions of this paper. The solutions obtained fully utilized the data management and organizational capabilities of the constraint programming approach while being assisted in the search path selection process by techniques and algorithms form the operations research pool of knowledge. The additional information provided by the calculation of efficient lower bounds and the subproblem domain definition and solution strategy presented in this paper, further assists the CP process in selecting promising search paths.