The dissertation solves the actual scientific and applied problem of forming timetable matrices based on a permanent approach with the use of special additive-disjunctive forms, which allows for improving the processes of automating time-consuming tasks of forming timetables, in particular timetables of higher education institutions, taking into account several additional criteria.
The object of the study is the process of drawing up an optimal schedule of classes using a permanent approach.
The subject of the study is the models, methods, and means of information technology for making an optimal schedule of classes using a permanent approach.
The work includes an analysis of known approaches, methods, information technologies, and tools for solving calendar planning problems.
The main result of the work is the development of many new methods and algorithms based on the properties of specially modified permanent matrices of schedules. A permanent approach to solving the problems of generating combinatorial objects in scheduling systems was proposed for the first time. The basis of this approach is the procedure of decomposing the modified permanent by row with memorization of the identifiers of the matrix elements, which allows you to choose convenient data structures and carry out the instant direct recording of individual component objects that are generated.
Since the algorithms proposed in the paper are new, as is the permanent approach itself, significant attention is paid to the complexity of the corresponding algorithms and tasks.
Since the result of the schedule of the modified permanent is all possible systems of different representatives of sets formed by the columns of the schedules matrices, the problem arises – how to generate based on such systems of different representatives (SRP) all possible configurations of schedules that satisfy the necessary criteria. To solve this problem, a special calculation of additive–disjunctive forms (ADF) is proposed for the first time in the work: the definition of ADF is introduced, the main properties are described, the application of ADF in the permanent decomposition procedure is proposed, which allows generating all admissible variants of schedules in the process of decomposition of a modified permanent incidence matrix. Based on the appropriate approach, appropriate algorithmic solutions are proposed, which are implemented in the appropriate software.
The permanent approach proposed in the work and several technical solutions, in particular, based on ADF, have a universal character and can be used to solve a wide range of problems in the theory of schedules.
In today's conditions, the problem of the widest possible participation of all stakeholders in the processes of implementing educational programs of higher education institutions, the widest possible consideration of their interests, is extremely important. In the work, this problem is considered in the context of taking into account the interests of stakeholders in the process of forming the schedule of classes in a higher education institution. A heuristic approach to the problem of automated preparation of the class schedule is proposed, within which the interests of a wide range of stakeholders are taken into account as much as possible. The corresponding approach was tested when drawing up the class schedule of the Rivne State Humanitarian University. An appropriate software package and some original solutions are proposed, including a specific data encoding system, optimized from the point of view of the memory of the data structure, and basic algorithms using bitwise operations are implemented. The proposed information system is of practical importance and can be used in the processes of generating admissible matrixes of schedules.
The main scientific results of the dissertation were published in 13 works, in particular: one article in periodical scientific publications of other countries that are members of the Organization for Economic Cooperation and Development and/or the European Union; seven articles in scientific and professional periodicals of Ukraine; four publications in the materials of international and Ukrainian scientific, scientific and technical conferences. Of them, three works are included in the international scientometric database Scopus, one work is included in the international scientometric database Web of Science, and one work is included in the international scientometric database Index Copernicus.
Keywords: information technology, permanent, decomposition, decomposition matrix, additive–disjunctive form, algebraic structure.
