Electronic schedule program. The problem of complete automation in creating a school schedule

There are eight main modifications of the program for various educational institutions:
. AVTOR School - for intermediates secondary schools, lyceums and gymnasiums;
. AVTOR College - for colleges, technical schools and vocational schools;
. AVTOR Art College - for schools of art and culture;
. AVTOR High School - for universities (full-time education);
. AVTOR High School Semestric - for universities (correspondence courses);
. AVTOR M High School Semestric - for military universities;
. AVTOR Educational Centers - for training centers, educational programs and educational programs;
. AVTOR High Shool Pro - for universities with several remote academic buildings, taking into account the travel time between them (full-time and part-time forms of study, network version).

History of the creation and development of the system.
. The first version of the AUTOR-2 program (under MS DOS) was developed by RSU researcher Igor Gubenko in April 1993. The program was originally intended for scheduling at a multidisciplinary lyceum at RSU with intensive study of a foreign language, computer science and many special subjects (where classes are divided into 2-4 subgroups and can be combined into streams). Already the first version of the program made it possible to build correct schedules.
. Then the program was tested in several more schools in Rostov-on-Don. The experience of many head teachers and the specifics of the schedules of various schools were taken into account. The program was significantly improved and implemented over 2 years in more than ten schools, lyceums and gymnasiums.
. By 1996, the author managed to develop a unique algorithm for automatically constructing and optimizing schedules, which made it possible to significantly increase the power of the program. In the same year, the first version of AUTOR-2 was released for colleges and for a small university.
. In 1997-98 the author develops and successfully implements the first version of the program for a large university with several academic buildings (RGUE "RINH").
. In 2000, the first WIN version of the AVTOR-2000 program was released for all types of educational institutions.
. In 2001, a version of the program was released with an interface in three languages: Russian, Ukrainian and English.
. In 2001, the first university version for distance learning was put into operation.
. In 2002, a network version of the program for universities appeared with several workstations and a common database of audiences.
. In 2003, AVTOR-2003 was successfully integrated into a single package with the PPP "Plany" (YURGUES), which made it possible to automate the entry of the database into the program and build a complete schedule of this university in 2 hours! In YURGUES (Shakhty) there are 7 educational buildings, two of them are located far away. Previously, the same schedule was compiled manually by two methodologists in 2-3 months.
. In 2004, a version of the AVTOR program was developed for military universities.
. In 2005, a version of AVTOR was released for schools of culture and art, as well as for training centers.

Clients.

Currently, the AVTOR program is successfully used by more than three hundred educational institutions in Russia, Ukraine, Belarus, the Baltic states and Kazakhstan. Among them: Don Real Gymnasium (secondary school No. 62), Classical Lyceum at the Russian State University, secondary school No. 104, No. 38, No. 67, No. 81, No. 52, No. 92, No. 27, No. 46, No. 69, No. 83 (Rostov- on-Don), secondary school No. 297, No. 1117 (Moscow), secondary school No. 315, No. 17, Gymnasium of Oriental Languages ​​(Kiev), secondary school No. 44 (Zaporozhye), Tikhoretsky College of Railway Transport, Beloyarsk Pedagogical College, Rostov Mechanical Engineering College, RGUE "RINH", IUBiP, SKAGS, RGASHM, RGSU (Rostov-on-Don), YURGUES (Shakhty), RGAU named after Timiryazev (Moscow), MU Ministry of Internal Affairs of Russia (Moscow), Irkutsk State University, Institute of Foreign Languages, USPU, USU (Ekaterinburg), SGSEU (Saratov), ​​as well as dozens of other schools, lyceums, gymnasiums, colleges and universities.

Specifications.
The running time of the program depends on the size of the educational institution and the power of the computer. A complete calculation and optimization of the schedule for a medium-sized school with complex initial data (40 classes, 80 teachers, more than 10 part-time teachers; two shifts; shortage of classrooms) takes about 2-3 minutes on a Celeron-2000 computer.

AVTOR allows you to:

build a schedule without "ok"He" in classes (study groups);

optimize in schedule"windows" of teachers;

consider the required range of days/hours for classes, for teachers and for classrooms;

take into account the nature of the work and the wishes of both full-time employees and part-time hourly workers;

optimally place classes in classrooms (auditoriums), taking into account the characteristics of classes, subjects, teachers’ priorities and classroom capacity;

enter call schedule;

installtransition time (transition time)ezda) between academic buildings;

optimize the number of transitions from cabinet to cabinT, and from body to body;

easily connect any classes (study groups) into streams when conducting any classes;

divide classes (study groups) when conducting foreign language classes, physical culture, labor, computer science (and any other subjects) for any number of subgroups (up to ten!);

introduce combined lessons for subgroups (such as “foreign/computer science”) in any subjects;

introduce (in addition to the main subjects) special courses and electives;

optimize the uniformity and labor intensity of the schedule;

easily and quickly enter and adjust source data;

have any number of schedule options;

automatically convert schedules when the database changes;

easy to save in archives, copy and send viaE- mailcomplete databases and schedule options (the volume of the archive of the complete database of secondary school schedules is 10-30K, large university - 50-70K);

quickly make any necessary adjustments to the schedule;

find replacements for temporarily absent teachers;

automatically control the schedule, eliminating any “overlaps” and contradictions;

display schedules in the form of convenient and visual documents: text,Word, HTML, as well as filesdBaseand booksExcel;

post ready-made schedules on the local network and on Internet pages for public access.

Difference from analogues.
A comparative analysis of the work of the AVTOR program and programs from other developers has been repeatedly carried out by specialists from various educational institutions. The research results are published on well-known Internet sites, as well as in reports at conferences and master classes. It was concluded that AVTOR has the most powerful algorithm for automatically creating and optimizing schedules: working 10-20 times faster than its analogues, the program builds better schedules according to many criteria. For example, the number of “windows” in teachers’ schedules is 2-3 times less than when using other programs.
AVTOR is a program with unique capabilities. Main advantages compared to similar CIS programs:
. speed, compactness of system files and the ability to work in verylargeeducational institutions with complex schedules;
. high level automation (accommodates 100% of possible classes);
. high performance:cThe system allows you to create a new schedule during one work session, and then quickly adjust, save, print various schedule options, modifying them if necessary throughout the entire school year;
. powerful automated SCHEDULE EDITOR,whichallows you to easily perform ANY actions with the schedule (adding, deleting, rearranging classes, calculating and optimizing the schedule, changing rooms, replacing teachers, etc.). At the same time, the program clearly and conveniently suggests various options for rearrangements (changes) of the schedule and compares their quality;
. Availability detailed statistics and objective assessment of the quality of any schedule option;
. the ability to support anyone national language(at the client's request).

Adaptation and configuration of the program.
At the request of the customer, AVTOR is modified and customized to suit the conditions of a specific educational institution (taking into account the specifics of the educational process, operating mode, form of documents, etc.).

annotation

This article introduces the reader to a unique, recently appeared, algorithm for compiling school timetable. The results of testing the only program in the world that can not create, but create such a schedule in a fully automatic mode are reported. Based on the results of tens of millions of tests (built school timetables), the myth about the impossibility of drawing up a school timetable without human participation is debunked. Forecasts are made for the further development of this software. The SaaS business model for its use is discussed. To understand the main content of the article, no special mathematical preparation is required, so the article is addressed to a wide range of interested readers.

1. Introduction

Over the past decade, at least a dozen dissertations have been defended in the Russian Federation on topics related to the task of compiling educational schedules. Over the previous decade, the number of defended dissertations was no less. Although dissertations are mainly defended for the title of Candidate of Technical Sciences and the problems of drawing up a class schedule for a higher educational institution are considered, nevertheless, this fact indicates that more and more researchers are paying attention to the problems of drawing up a school timetable. Perhaps this stream of work is associated with the constant progress and universal availability of computing technology. Indeed, truly amazing processes are taking place before our eyes. Just twenty-five years ago, only a large, usually defense, enterprise could afford to purchase such an electronic computer as the EC1066. Such a computer was located in a room of up to several hundred square meters, equipped with a powerful uninterruptible power supply system and a microclimate support system. Such electronic computers were primarily intended to solve unique scientific and technical problems that had an impact on the country’s defense capability. Today many people have homes desks there are personal computers. But just think about it. The RAM of such a personal computer is 125 - 250 times larger compared to the above-mentioned giant. Performance is more than 1000 times faster. And this is not a typo. More than a thousand times.

2 Generations of scheduling software

The first publications on the topic of using computer technology to automate the preparation of class schedules appeared in the early 60s of the previous century, so the task of creating an educational schedule using computer technology has a fairly long history. Over almost 50 years of intensive research, enormous intellectual work has been carried out by thousands of specialists around the world. However, the task of creating educational timetables, both then and now, is still a tough nut to crack. It is not at all surprising that programs for creating a school schedule appeared and improved as computer technology developed. Therefore, let us turn (naturally in a telegraphic style) to very conditional periods of this development. Without going too much into historical research and without risking making a big mistake, the appearance of a computer (electronic computer) is possible by 1945. This emergence (again without risking much error) can be attributed to the need for military computing. One of the first tasks that were solved on the first computers was the task of compiling ballistic tables for artillery and aviation. Not the least role in the needs of the military was played by the task of studying atomic and thermonuclear explosions. Due to the above reasons, the very fact of the existence of a computer and the principles of its operation initially remained classified. It took about ten years to bring information about the “tactical and technical characteristics” of the first computers to a wide range of narrow specialists - mathematicians involved in numerical methods. The result was not long in coming. Since 1955, there has been an explosive growth in such a branch of scientific knowledge as applied mathematics. Hundreds and thousands of practically important problems have become the subject of research by mathematicians using electronic computing technology, which has led to the development of completely new numerical methods for solving these problems. For the reason that the cost of computers was completely incomparable with the economic effect that they could bring for a civilian industrial enterprise, the only users of this technology were the military and a very narrow circle of scientists. In other words, those people who did not know the words - expensive, costs or phrases - economic effect. But time passed. Technologies for the production and design of computer technology have developed at a rapid pace. As a result, the performance of computers grew at an unprecedented pace, and their costs quickly decreased. Prices for computers were steadily moving from astronomical to earthly (albeit still exorbitant). By 1965, the circle of scientists who had access to computer technology for research had grown quite noticeably. To this time (the beginning of the sixties), as noted above, the first publications on the topic of compiling a school schedule on mainframe computers date back to this time. It is quite natural that the work was at first staged in nature, and later theoretical. It took about fifteen years to come up with everything that could easily be thought of in relation to the task of drawing up a school timetable. This period (from 1965 to 1980) evokes sharp mixed feelings. On the one hand, beautiful and original mathematical models of the problem of compiling a school schedule were proposed (vertex coloring of graphs, edge coloring of graphs), and on the other hand, without any doubt, these models should be classified as a very simplified version of the problem. In other words, the problem was not completely solved or even formulated in detail. Moreover, in 1976, a work by Israeli mathematicians appeared where, in their opinion, the fundamental difficulty of solving the problem of drawing up a school timetable was proven. So, by 1980, despite the fact that the productivity of computers was constantly increasing and their cost was constantly decreasing, as a result of which civilian industrial enterprises had already moved into the category of active users of computer technology, our problem still remained not completely solved, and computer technology for the main user - schools, remained unavailable. Perhaps the first generation programs for scheduling classes could be attributed to this period. Due to the above two reasons (the difficulty of solving the problem and the unavailability of computer technology for the end user), interest in automatic scheduling of classes has noticeably weakened (and maybe even died out completely). Higher educational establishments, who use this software, have taken a turn from actually drawing up class schedules to recording and monitoring student progress. Let us emphasize once again that the overwhelming majority of school administrations did not even know about the existence of such programs. However, by this time (naturally abroad) among some “egg-headed” students, a fashion arose for construction kits made from radio components. The era of personal computers has dawned. Fashion turned out to be very sticky and the circle of “eggheads” was steadily expanding. It is very likely that designers from radio components would have remained the lot of a handful of “not normal” if the largest manufacturer of typewriters at that time, and one of the most common computers at that time, the American corporation IBM, around 1985, had not perspicaciously I would not have realized that these designers, if given the shape of a typewriter, could replace these typewriters. And not just replace, but make a super intelligent typewriter out of a typewriter, competing with “lead technologies” in publishing. Of course, at that time, no one, except perhaps the most visionary, could have imagined that designers made from radio components would ever be able to compete with real computing devices. However, the die was cast and mass production of typewriter killers began. It didn’t take long for the production ideas to emerge, first “two in one” (typewriter plus a businessman’s assistant - a spreadsheet), then “three in one” (also plus an accounting program), then “four in one”, and so on and so forth. so on and so forth. Yesterday's students, with the help of a magic wand, began to turn into billionaires, and former designers of radio components began to look more and more like real electronic computers. In technical and business language the respectful abbreviation “PC” was introduced, which meant a personal computer, and already in the early 90s of the 20th century no one doubted that on their desk there was not a toy, but a completely real electronic computer. Opposite trends - the explosive growth in the productivity of former toys, on the one hand, and the rapid drop in their prices, on the other hand, have done their job. In some advanced schools, by today's standards, the leaders' desks now had, by today's standards, huge monitors that screamed like a living reproach: “Fill me with the necessary software.” It’s no wonder that I remembered the seemingly completely forgotten idea of ​​scheduling training sessions. Thousands of lovers of easy money rushed to write programs for schools, guaranteeing complete automation of everything they could get their hands on. This period, perhaps, can be attributed to second-generation programs that automate the process of drawing up school schedules. In the 1990s, the personal computer industry experienced incredible growth. The productivity of personal computers doubled almost every year and every year brought innovative software products. Those working in this field “the soles of their shoes were torn.” But the programs for drawing up school timetables somehow didn’t want to work correctly... Now, of course, it is difficult to say whether or not the manufacturers of programs for drawing up school timetables knew about the legacy that their predecessors left them in the 1965 - 1980s of the last century and about the warning of Israeli mathematicians in 1976 that this problem was difficult to solve, but the fact remains that the administration of educational institutions was slowly writing off the good old typewriters, replacing them with personal computers. The schedule was still, with few exceptions, compiled manually. By the beginning of the 21st century, along with the final dominance of operating systems with a graphical user interface, comes the end of second-generation school scheduling programs that used the pseudo-graphical interface of the outgoing MS-DOS operating system. The personal computer industry has successfully stopped its rapid development and moved to the notorious “stability”. Personal computing technology surpassed the performance level of large computers in the mid-80s of the last century, everything was ready for the development of third-generation programs. And indeed, at the very end of the last century, an incalculable number of manufacturers, including Once again but already, as it seemed to them, at a new technical and technological level they began to develop programs for compiling a school schedule. Against the backdrop of the cessation of noticeable (albeit gradual) growth in the productivity of personal computers and the stabilization of ideas in the field of software, programs developed that could be classified as third-generation programs. The main feature of these programs, it seems to us, is that they could be developed taking into account both errors and original findings of their predecessors. Here we primarily mean the developers of the nineties. With the mathematical results of the sixties, seventies and eighties, the situation is simpler. If you know about them, then you use them; if you don’t know, then you “invent a new wheel.” Another feature is that these programs were developed using a new graphical user interface at that time. There is no doubt that the graphical interface provides the developer with fundamentally greater opportunities compared to the pseudo-graphic (text) one. But at the same time, there is danger in this. If we start comparing the school timetable programs available on the market (in use), we will discover an absolutely amazing variety of ways to generate (enter) the initial data necessary for the calculation, although from a mathematical point of view all programs do (or at least should do) absolutely the same thing. Thus, the quality of school timetable programs began to be significantly influenced by the consistency and convenience of the user interface. Today (2013) it is worth noting that compared to the programs of the nineties, third generation (zero) programs have become quite “wiser”. The developers' optimism has noticeably diminished. No one (or almost no one) is promising complete automation of everything that comes to hand. Many of the projects started at the end of the nineties have now ceased to exist due to their lack of demand. Others continue to develop and improve. Still others have frozen in their development over the past ten years. But as previously noted, it is still too early to talk about a final and irrevocable solution to the problem of drawing up a school schedule.

3 Are such programs necessary?

Usually, when talking about the benefits (necessity) of using a program for automated scheduling, they indicate such a factor as an order of magnitude reduction in the work costs (time) of the head teacher when drawing up the educational schedule. It is often pointed out that better quality schedules can be obtained using a computer. Although this argument, taking into account what is said below, is not without controversy. In our opinion, we should agree that calculating the schedule using a computer will, in addition to saving time and obtaining a better quality schedule, on the one hand, exclude subjective assessments and personal sympathies of the head teacher in relation to the teacher (part of the teachers), when drawing up the schedule, in including when distributing the teaching load, and on the other hand, it will completely eliminate undeserved accusations against the head teacher from teachers of such subjective assessments and sympathies, since it is obvious that the computer is “a person not interested” (the computer is “to blame” for everything) . Thus, calculating the distribution of teaching load and schedule on a computer can improve the psychological climate in the teaching staff (comply with the principles of fairness and equality), just as the match referee improves the mood of the players of a football team after deciding the right to kick the ball first using a draw. . In 2001, the Chronobus company conducted a survey of almost 1000 Moscow schools on the need to create and implement an automated workplace (a) “Schedule”. The survey results showed that all schools have a sincere desire to use such a program, but no one does it. Moreover, the reason for the unanimous disregard of such automation tools is not the lack of necessary equipment or money, but the quality of the programs offered on the market. The phrase: “If I were offered to increase my salary by one and a half times because I use such a school schedule program, then I would refuse this offer” was not uncommon. In other words, according to the head teachers, school timetable programs are software with a negative cost. Today, twelve years after the above-mentioned survey, potential users of programs for drawing up educational schedules - head teachers of schools - have developed a persistent negative, and often aggressive, attitude towards such programs to an even greater extent and not without thoroughness. Misleading advertising about the imposed “school information space” creates an image of the authors of this space as scammers selling rotten goods. According to head teachers of schools with extensive work experience, practice shows that these programs can only be used as a tool for the initial arrangement of objects with subsequent manual finishing, as well as storing information and printing it out. After the automated distribution of objects (the program, as a rule, arranges from 40 to 70%), it is practically impossible to take into account the hygienic requirements for the lesson schedule, since it is necessary not only to deliver the remaining unarranged objects, but also to significantly change (up to 60%) the automated arrangement of objects according to the principle “just to arrange it.” Experienced masters of their craft recommend that beginners, when creating a lesson schedule, use a dozen or more tips, proven by many years of experience and practice, using, instead of a computer, lesson schedule table layouts made from sheets of cardboard, colored paper, wide transparent tape, glue, pockets and so on. And they are certainly right. Using a computer in regular editor mode (like the familiar text editor) or the use of programs that lead the process of arranging classes into dead-end situations, when not a single lesson can theoretically be added to the schedule grid, can bring nothing but unjustified difficulties, inconvenience and anger. The expectations of the users of such programs (head teachers) are beyond doubt. In their opinion, programs for compiling a school schedule, after entering all the initial data, should, in a fully automatic mode, create a schedule that is superior in quality to a manual schedule. The inadequacy of user expectations and the results obtained from such programs gives rise to an aggressive attitude of users towards these programs and, together with them, towards automation systems “expanding the school’s information space.” It should be noted that the developers of programs for drawing up school timetables during the “ natural selection "were divided into three groups. The first group publicly defends the point of view that the problem of automatically calculating the school schedule cannot be solved in principle. And that’s why they “don’t be stupid” don’t even try to do it. And those who try, in their opinion, are complete ignoramuses. “We do not have a school schedule calculation program, but a school schedule editor. We don’t build a schedule instead of a person, but help a person build his own (manual) schedule,” they proudly declare. The second group of developers declares their goal to be complete automation of the school schedule, but in their advertising materials and user manuals they are diplomatically silent about achieving this goal. “Our program can build a schedule in automatic mode, manual mode and mixed (semi-automatic) mode,” they state without deceiving users. These developers do not focus the attention of potential users on the fact that a horse can drink water from the river, but cannot drink it, and the program can build a schedule automatically, but cannot build it. In our opinion, this is a very balanced and worthy position, which, despite a little cunning, can only inspire respect. Or, at least, it does not cause an aggressive attitude towards developers on the part of users. And finally, the third group of developers. “Enter the initial data, click the calculate button, and in a few minutes you are guaranteed to receive a schedule with the arrangement of all classes without exception. There are no restrictions on the size of the problem. At least 99 classes. At least 216 teachers. At least half part-time. We will divide the class into groups of at least 256 groups. There are any restrictions for teachers and subjects. Each teacher chooses working days and hours that are convenient for him. There are no windows for teachers. Classes in subjects are held only during the hours permitted for these subjects. Strict adherence to parallels. Each subject is assigned difficulty scores. Exact compliance with sanitary standards of the distribution of the total complexity of items over time is guaranteed.” - they say without hesitation. By the way, this simple move is taken by the developers of the most helpless programs in terms of automatic scheduling and, moreover, sloppy in appearance (although there is one that looks very attractive). Microsoft aptly dubbed such programs “food dogs.” It is difficult to say what exactly motivates people who engage in direct and simple deception of consumers. This deception always becomes obvious the first time the school curriculum is entered into the program. According to Russian legislation, in accordance with Art. 179 Civil Code Russian Federation, transactions made under the influence of deception can be declared invalid by the court, while the deceiver returns to the deceived all the money received, compensates the deceived for real damage and, in addition, must also transfer to the state income the same amount that he received from the sale of the program.

4 A little about the complexity of the problem being solved

It is worth saying a few words about the complexity of solving the problem of creating a school schedule. To qualified users of a personal computer who believe in its omnipotence, it seems that the task of creating a school schedule is almost more difficult than the task of creating, for example, a high-quality video editor or sound editor. However, as mentioned earlier, the number of researchers who have studied this problem in one way or another is difficult to count. Among them are dozens of doctors of technical and physical and mathematical sciences, hundreds of candidates of science, not only technical, but also physical and mathematical, not to mention thousands of ordinary lovers of mathematical puzzles, which certainly includes a large army of students in technical and physical and mathematical fields of study. Among the researchers of the problem of compiling a school schedule, two academicians can be mentioned - V.S. Tanaev and V.S. Mikhalevich, one could also name foreign scientists of world renown. In addition to scientists, outstanding businessmen did not ignore the task of drawing up school schedules. And yet, despite, without exaggeration, the titanic efforts of researchers, there is no need to talk about a complete and comprehensive (or at least satisfactory) solution to the problem of drawing up an educational schedule. To confirm what has been said, we give a quote from a famous Russian mathematician. ... Since the task of creating schedules is well known to everyone from school life, in each course there are one or more students overwhelmed by the idea of ​​​​algorithmizing the creation of a class schedule. Therefore, I have to warn you that this is a very difficult task. ... There is a special science - scheduling theory, which studies and systematizes problems of this kind, as well as various approximate methods for solving them (on precise methods there is almost no hope). A special place among them is occupied by heuristic methods, in which attempts are made to describe the logic and technique of the dispatcher’s actions. ... One interesting observation. But first, let's give one more quote. The four-color hypothesis can rightfully be called the “four-color disease,” since it is similar in many ways to a disease. She in highest degree contagious. Sometimes it proceeds relatively easily, but in some cases it becomes protracted or even threatening. There are no vaccinations against it; However, people with a fairly healthy body after a short outbreak acquire lifelong immunity. A person can get this disease several times, and it is sometimes accompanied by severe pain, but no deaths have been recorded. There is at least one known case of the disease being passed on from father to son, so it may be hereditary. Here, an outstanding American mathematician mocks the ancient problem of coloring a political map in four colors, where countries with a common border should be painted in different colors. It seems that everything he said can be attributed to the task of drawing up a school timetable. So, the author of these lines decided, to the best of his ability, to track the future careers of people who defended their dissertations on the relevant topic. It would seem that “God himself” ordered the newly promoted scientist to turn his scientific achievements into money. That is, somehow bring your brainchild to the market, since almost always after defending a dissertation, some program or part of an automated system for scheduling classes remains. So - no. All cases of dissertation defense on this topic known to the author end in one way - after the defense, the dissertation candidate gives up this task and, as a rule, begins (or continues) a career as a teacher at a university. In other words, he acquires a lifelong, lasting immunity to the task of creating a curriculum. To conclude our general discussion about the complexity of solving the problem of drawing up a school schedule, let us refer to two more opinions. But first, let’s pay attention to who expresses this opinion. It's no secret that some school computer science teachers, in fits of didactic experiments, instruct schoolchildren as “homework” to develop a program for creating a class schedule for their favorite school. Schoolchildren, naturally, roll up their sleeves and enthusiastically take on this task. As a result of this idea, on the Internet you can find numerous discussions and theorizing on this matter from the above-mentioned contingent. What the Pioneers don’t come up with and what opinions they don’t express... No less excitement this topic also causes in people with technical education in attempts to automate the activities of dispatchers at his favorite university. But these opinions, to put it mildly, are not of great interest. Professional mathematicians, specialists in the theory of schedules, speak out about the problem of drawing up an educational schedule extremely rarely. Therefore (or even more so) their opinion on this matter seems very interesting. So. Sotskov Yuri Nazarovich, Doctor of Physics and Mathematics. Sciences, professor, chief researcher at the Joint Institute of Informatics Problems of the National Academy of Sciences of Belarus, Minsk, one of the most prominent specialists in the field of scheduling theory, author of a number of monographs on scheduling theory. In his article, in particular, he writes: ... From a mathematical point of view, the problem of constructing an optimal training schedule is quite complex, since it belongs to the class of so-called NP-hard problems. ... This article shows how coloring the vertices of a graph can be used to construct a training schedule. ... ... The graph vertex coloring problem is NP-hard, and hence its generalization described in Sect. 2 is also an NP-hard problem. ... Further. Lazarev Alexander Alekseevich, Doctor of Physics and Mathematics. Sciences, professor, chief researcher at the Institute of Management Problems named after. V.A. Trapeznikova RAS, Moscow, one of the most prominent specialists in the field of scheduling theory, author of a number of monographs on scheduling theory. In his article, in particular, he writes: ... The educational scheduling problem is a well-known combinatorial optimization problem called “timetabling”. Even finding a feasible schedule is a strong NP-hard problem. Therefore, when solving it, it is necessary to use mathematical methods for solving combinatorial optimization problems. ... In short: - “Drain the water, dry the oars, turn out the lights...”

5 Timetable Software Market

The market for scheduling software, which developed along with the market for any software for personal computers, seems simply unique, or at least surprising, or at worst very strange. So what makes it unique or strange? Have you ever seen an advertisement like this: - “Buy our vacuum cleaner that cannot suck up dust.” Or this: “All the pots that we can offer you are full of holes.” Or this: “Our TV is unique - it never shows anything.” And here is the advertisement: “Buy our program for creating a school schedule, which cannot create it, but can create it,” we had to see as much as we wanted. “Well, buy it, buy it, buy it. Our program can also create a schedule. She will arrange almost all the classes for you, but let’s do the rest ourselves. Getting out of a dead end is so interesting. Well, at least for 15 dollars. It’s not a lot of money, we worked so hard...” So how much does a vacuum cleaner that doesn’t suck up dust, a pan with holes, or a TV that never shows anything cost? Before answering this difficult question, let's try to estimate the number of potential buyers and compare it with the number of schools (head teachers) that have already made their purchase. Demographers have found that about 16% of the population of developed countries are schoolchildren. It is this figure that is used when building new schools in new development areas. Next, we will perform arithmetic calculations using the Russian Federation as an example (our homeland, after all). So, the population is approximately 140 million people. Thus, there are approximately 22 million schoolchildren. There are about 50 thousand schools. This means that the average number of students in a school is 440 people. But this is an average amount. It is known that over the past 60 - 70 years, schools for 1000 - 1400 students were considered standard school projects. Hence the conclusion - there are a huge number of schools with a number of students much less than our average figure - 440 people. Obviously, these are schools in rural areas or in very small cities. Hence, a stronger conclusion is that a huge number of schools do not need programs for scheduling classes in principle. It is, of course, very difficult to estimate the number of schools that do not need such programs in principle. However, if we look carefully at the ceiling we will see a figure there - 70%. From which it follows that 30% of schools have a student population of 500 or more, and for such schools a program that cannot create a school schedule, but can create one, would not hurt. We get the final figure - 15 thousand schools. This is, perhaps, the potential market capacity for the Russian Federation. But what do we have in reality today? The question is not simple. There are no reliable statistics. First of all, one program comes to mind, which was “free of charge” for all schools in the Russian Federation. The development of this program began in 1998, and the end ( latest version) by 2003. In appearance, especially for its time, the program is certainly not bad. Compared to other similar programs, it has a very logical and thoughtful user interface. On our Subjective opinion, better user interface. However, although there is a Create a schedule button, the program is absolutely helpless in terms of automatic (without human intervention) scheduling. It is not able to solve even those simple subtasks that other programs can easily handle. Judging by the reviews on the Internet, almost no one uses this program. So, we will consider it a “radiation background” that does not affect the overall market situation. Let's move on. Let's pose this question. Are there programs on the market that can provide the head teacher with at least some assistance in creating a schedule? For example, many head teachers manually draw up a schedule in two stages. At the first stage, according to their expression: - “They deal with foreigners.” In other words, they create a schedule for teachers and classes when studying a foreign language. The second stage is everything else. At least two programs on the market cope enviably well with this first stage. Here you can plan the timing of elective courses. In this case, from 10 to 40 percent of classes are arranged. So, of course, there are some benefits from using a computer equipped with these programs. Moreover, one of these programs is very aggressively and persistently trying to complete the schedule. In some cases, albeit rare ones, she succeeds. The other, when completing the schedule, is absolutely helpless. So how many people today use software for scheduling classes in the Russian Federation? Some manufacturers of such software publish information about their clients on their websites. True, this information should be treated very carefully. As noted above, some manufacturers, in “fits of marketing,” resort to very simple deception of potential customers. And yet, separating the wheat from the chaff, we get a figure of about 1,500 schools. Which is about 10% of the potential market capacity. Therefore, 90% of potential clients have not yet been converted. Now let's turn our attention to the world market. As follows from previous calculations, quite in a convenient way calculating the number of potential customers is this way. We take the population of the country, discard four zeros, and get the number of potential clients. That's what we'll do. Europe - 500 million people. USA - 300 million people. Canada - 30 million people. Japan - 125 million people. Australia - 20 million people. Other developed countries - 25 million people. Here it is - the “Golden Billion”. We discard four zeros. We get 100 thousand potential clients. Now the question is: “How many schools out of this golden billion use software to create a school schedule?” We apply the same methodology, separating the wheat from the chaff, as for the Russian Federation. We get a figure - about 30 thousand schools. Which is 30% of the market. At the same time, 70% are open to aggressive marketing (hilling). Now all that remains is to convert quantity into quality. That is, multiply the number of potential customers by the price of one software license. In other words, estimate the capacity of the world market in American rubles. But to do this you need to know the price of such a license. I wonder if the reader has ever held in his hands a thick book with something like this title: - “Cost of Software.” But we had to. In fact, the formula is very simple. Software, no matter how complex or large it may be, costs exactly as much as the client (user) pays for it. The clearest example of this is the Windows operating system from Microsoft. Probably few people thought that in terms of the amount of work, talent, knowledge, etc., landing a man on the moon, in comparison with this operating system, is childish pranks. And yet, one hundred and fifty bucks per barrel, and you are a legal user. The only problem is that the number of potential clients - users of the operating system and the program for creating a school schedule - is not comparable, neither in the first nor in the second approximation. Hence the conclusion: - “Despite the fact that some are asking $15 for leaky pots, a program that could really solve most of the problems of head teachers must be expensive.” All that remains is to answer the question: - “What is expensive?” Of course, everyone has their own ideas about “Expensive”. But probably, for a head teacher (or a similar position, if we are talking about the global market), his monthly salary is expensive. That is, from 1000 to 5000 US dollars. This is what we are actually observing, or at least previously observed, in reality. At first, these programs cost exactly that much on the world market. The drop in prices, it seems to us, occurred precisely because it suddenly turned out that a pan with holes was bought for $5,000. And finally, multiplying the quantity by the price, we get the approximate capacity of the global software market for creating a school schedule - from 100 to 500 million US dollars. That is, the market is no less money-intensive than, say, the market for various computer-aided design systems in industry and construction. And by the way, no less science-intensive.

6 “Ancient Egyptian” algorithm for solving the problem

In the spring of 2012, an archaeologist turned to some programmers he knew with a strange request. According to him, while deciphering ancient Egyptian manuscripts, he came across a description of an algorithm for compiling a school schedule. The authorship of the algorithm was attributed to an Egyptian priestess named Anush. Actually, his request was to check on a modern computer whether this algorithm is really capable of creating a school schedule. At first his friends laughed at him. But after carefully reading the strange records, we still decided to check them. So, let's begin to describe the idea of ​​​​this algorithm, in fact, to a brief summary of the translation of an ancient manuscript. Let us first say that the very terminology of this algorithm and the organization of the ancient Egyptian school are of separate historical interest, but since this article is not intended for historians, we will present the algorithm in modern terminology familiar to people living today. The main difference between the ancient Egyptian algorithm (hereinafter we will omit the word ancient Egyptian) from modern approaches lies in the fact that the problem is divided into parts, or more precisely, into a number of sequentially solved problems, with each solved problem at the previous step being a constraint for the problem to be solved at the next step. In modern terminology, the method of decomposition of the problem being solved is used. It should be noted that each individual problem that is solved sequentially during the algorithm is not NP-hard (unsolvable). This allows you to use sequential solution a series of easily solved problems, solve the entire problem of creating a school schedule entirely. On the first step you should choose the operating mode of the educational institution, namely, decide how many days a week the school will work (5 or 6) and decide on the number of lessons held per school day (7 or 6, respectively). You also need to set the number of classes of students in the school. Next, you need to put restrictions on those hours during which lessons are not held. These are the last hours of each school day. For junior grades (in our terminology, this is starting from the 5th grade) there are more such prohibitions, for middle grades there are fewer, and for the oldest (11th grade) these prohibitions are completely absent. What matches our sanitary standards. The table of prohibitions for conducting lessons, which will be used throughout the entire algorithm, is remembered. On the second step a schedule for part-time workers is being built. It turned out that ancient Egyptian educational institutions did not disdain part-time work. The main feature of this task is that part-time workers are allowed to declare in an ultimatum form the days on which they will work. In addition, some part-time workers are allowed to refuse work on the first lesson of all working days when they work. Apparently these part-time workers were women and they could not come to school early. The problem is solved using an algorithm for prescribed coloring of the vertices of an ordinary graph. You can get acquainted with this mathematical model in detail using the already mentioned article or with the help of numerous other journal articles, for example, [,], as well as by getting acquainted with books [,]. Next, for each lesson (class, teacher, time), using an algorithm for solving the assignment problem, a room for conducting this lesson is selected. The algorithm for solving the assignment problem is described in many modern textbooks; in particular, you can get acquainted with it in the book. The end of the second step is the operation of combining a table of prohibitions on conducting lessons, built in accordance with sanitary restrictions and the resulting schedule for part-time workers. Thus, we obtain a new table of prohibitions on conducting lessons, which will be one of the restrictions for the next step of the algorithm. Third step consists of solving the problem of conducting classes of students' choice (in our terminology, elective courses). The peculiarity of this task is that a certain number of classes, at a certain school hour, are combined into streams, and then at that hour they disperse to their elective courses. The construction of the schedule will consist in the fact that each stream will be assigned a time at which elective courses will be held, but teachers will be appointed after the entire schedule has been finalized. That is, at this step, teachers are not assigned to conduct elective courses. When constructing the schedule, the rule is observed - for any stream in one academic day, no more than one academic hour can be assigned to conduct an elective course. In addition, another rule is observed - elective courses cannot be scheduled for more than one stream at any given time. This rule (restriction) seems quite reasonable, since when conducting elective courses, the need for premises for conducting classes increases sharply. It was introduced precisely for the purpose of preventing a situation when several threads need to a large number of free premises. At this stage, premises for conducting elective courses, as well as teachers, are not selected; they will be selected together with teachers after constructing the entire schedule. The algorithm for solving the problem of conducting elective courses is the algorithm for prescribed coloring of the vertices of an ordinary graph, which we pointed out when describing the previous step. The new table of prohibitions on conducting lessons is built in exactly the same way as in the previous step. The resulting schedule is combined with the prohibition table. On the fourth step algorithm to build a schedule for lessons in learning a foreign language. A special feature of this task is that the class can be divided into groups. Teachers cannot declare as an ultimatum what days they will work. However, for teachers with light workloads, one or two days off are guaranteed and will be given to them. Just like in the second step of the algorithm, some teachers teaching a foreign language may require them to be released from lessons in the first hour of the working day when they work. The problem of scheduling teachers/classes for studying a foreign language, just like in the second and third steps, is solved using an algorithm for prescribed coloring of the vertices of an ordinary graph. In the same way as in the second step, using an algorithm for assigning each lesson, or rather, each group of students and their teacher, a room is selected for its conduct. Ending fourth step, as well as the second and third, is the operation of combining the table of prohibitions on conducting lessons with the resulting schedule. So we get new option this table, which we will use in the sixth step. After completing the 4th step of the algorithm, depending on the school curriculum, usually from 15% to 40% of the entire teaching load provided for by this plan is assigned. On the fifth step the load determined by the curriculum is calculated for premises that are in short supply for the school. Such premises, as a rule, are gyms, workshops for conducting labor lessons (technology), rooms equipped with computers for conducting computer science lessons. This calculation is carried out with the goal of maximum possible load (minimum “downtime”) of such premises. On the sixth step a schedule is built for all remaining subjects except those taught in scarce premises. Teachers do not have the opportunity to declare an ultimatum about which days they will work, but for those teachers whose workload is low, one or two days off are guaranteed, and for some teachers there is the opportunity to refuse to work during the first lesson. This problem is solved using a prescribed edge coloring algorithm for a bipartite multigraph. You can get acquainted with the idea of ​​​​this algorithm from a book or from journal articles [, , , ,]. The constructed schedule consists of fours - class, teacher, subject, time. At the same step, all fours, using an algorithm for solving the assignment problem, are matched with the premises where these classes (fours) will be held. After completing this step, the entire schedule is filled, with the exception of classes held in scarce premises. However, the remaining “holes” in the schedule are the schedule for conducting classes in scarce premises. Thus, we can consider that at this sixth step, in a sense, two schedules are simultaneously constructed - for regular teachers/classes and for scarce premises/classes. On the seventh step classes are divided into groups according to subjects that will be held in scarce premises. As a rule, in subjects such as physical education, labor (technology), and computer science, classes are divided into groups. If the set of teachers for whom the schedule was built in the previous step intersects with the set of teachers conducting classes in scarce premises, then a table is formed for the prohibited working hours of teachers, which is the intersection of these sets. Using an algorithm for solving the assignment problem, teachers are selected for each group. The last step is the eighth. At this step, all previously obtained schedules are combined, that is, the final schedule is formed. To carry out this step, no algorithms are required, simple arithmetic operations are sufficient. After receiving the final schedule, each teacher can decide for himself when it is convenient for him to conduct elective courses. Time for them was reserved at step 3 of the algorithm. And if this teacher can recruit a group of students, then he will independently put his elective course on the schedule, along with the premises selected by him. The general rule for all previously described steps, except for the fifth, is the rule - each class cannot have more than one lesson in any subject on one day. In addition, the general rule for teachers is that each teacher can teach several subjects, including one class.

7 Algorithm testing

As can be seen from the previous section, there is nothing difficult to understand in the operation of the algorithm for constructing a school schedule. One after another, individual easily solvable (non-NP-hard) problems are solved, interconnected, until they are all exhausted. Nevertheless, there was no basis to assert with confidence that each of these problems could be solved. In the absence of any theoretical justification for the algorithm, it was possible to test its performance only experimentally, especially since this was precisely the task posed by the archaeological scientist who stumbled upon the ancient manuscript and translated it. It is quite natural that the first thought that came to the programmers’ minds was to create a regular application for the Windows operating system. But what is a regular win application? Once activated (launched for execution), it waits for events from the user, for example, input of initial data. How can this initial data be obtained and later entered into the program? Thank God, or rather the USA, now a more or less self-respecting school has opened its website on the Internet and the first thing that appears on this site, not counting photographs from various festive events, is the school curriculum. All that remains is to copy it and enter it into the program as initial data for calculating the schedule. Question. How much time do you need for this? The practice of using school schedule programs currently offered on the market has shown that entering a curriculum along with the formation of a table for distributing the teaching load requires from 8 to 10 hours, painstaking work, to put it mildly. Let's assume that this curriculum has been introduced, and the teaching load distribution table has been formed, and lo and behold... the schedule has been built. What does this mean? Absolutely nothing. There is no guarantee that the next task will be solved. Now, if the schedule had not been built, then this would say a lot, namely, that the algorithm does not solve the problem. In other words, a regular win application is, in a sense, practically untestable. How to be? Again, thank God, or rather glory to Microsoft, modern versions of the Windows operating system support the so-called console application mode. By the way, for some young people this is a complete revelation; they have never seen black windows with lines of text running inside these windows. Indeed, this is the style of mainframe computers from the distant past and long gone from the scene - MS-DOS. But these windows have one advantage. They can hang on the computer screen, making the necessary calculations, without any human intervention, for a day, a month, and... I can’t say how long. This is exactly what was required to test the algorithm. The further course of reasoning was as follows. Writing a source data generator (roughly speaking, a curriculum for a typical school and a teaching load distribution table) will of course take some time, but once written it will allow you to get an unlimited number of test tasks to test the algorithm; it will only be enough after solving the next one tasks to transfer control to this generator to build a new (next) task. It will be possible to obtain statistically reliable data on the quality of the tested algorithm. For example, 80 percent of problems are solved, but 20 are not, or vice versa. You just need to make the number of tasks to be solved large enough. This is exactly what had to be done - a console application, this was the way out of this situation. As they say, a fairy tale is told quickly, but things are not done quickly. Coming up with a source data generator that adequately reflects all practical situations, even in a typical school, turned out to be not such an easy task. But one day crazy dreams came true..., sooner or later..., no matter how much the string is tied... The source data generator is finished, the ancient Egyptian algorithm is programmed, “all errors are corrected”, traps for errors are set, checks of the calculation results are installed. At the beginning, the program offered a small number of classes for scheduling - from 9 to 14 (small school). Solutions popped out like from a machine gun. With an increase in the number of classes - from 15 to 21 (secondary school), decisions were fired quickly, but no longer like from a machine gun... rather like from a pistol. Further. Here it is... a large school, up to four classes in parallel, the total number of classes from 22 to 28. The brakes were clearly on... The process began to resemble a lazy duck waddling from foot to foot. But one thing was pleasing - the line: “The number of unsolved problems =” constantly showed zero. It became clear. To obtain statistically reliable data confirming the possibility of solving any reasonable problem in a fully automatic mode, one computer is not enough. Small arithmetic calculations showed that in order to operate with numbers of six or more digits about the number of solved problems, at least a dozen computers are required. And for a dozen computers (you can estimate the amount of heat generated from these computers and the constant noise emitted from the fans) a separate room is required. But nothing, you can’t stop us... A dozen, not a dozen, but seven four-core computers were soon put into operation. As a result, after a year of “violent actions” of the ancient Egyptian algorithm in relation to the venerable quad-core seven, and after tens of millions of solved problems, we can say with confidence: - “Any, without exception, reasonable, correctly specified task for calculating the school schedule, can be solved without human intervention in a fully automatic mode.” Wherein, total time calculation of 1000 problems is approximately the following: for a group of problems from 9 to 14 classes = 20 minutes, for a group of problems from 15 to 21 classes = 40 minutes, for a group of problems from 22 to 28 classes the calculation time is from 6 to 8 hours, i.e. . for this group, on average, about half a minute per task. Thus, more than a year-long experiment to verify (test) the algorithm for compiling a school schedule in a fully automatic mode, without human participation, for which tens of millions of test tasks were solved, was successfully completed. For almost all test tasks (initial data), a schedule was completely constructed that satisfied all restrictions.

8 Logical model of future software

After completing the annual testing of the school schedule algorithm, the question arose: “What next?” First of all, what is striking is that a console application cannot convince anyone that the problem of creating a school schedule is really being solved... except perhaps the programmer who wrote this application. Even a low-performing fifth-grader can create a black window with lines like: “Number of solved problems = 12547564” appearing there from time to time. Thus, a normal person simply will not believe such a program, so to speak, and he will do the right thing. It’s impossible to do without a full-fledged win-application. But first, it wouldn’t be a bad idea to decide on the goals of creating such an application. At least two such targets are in sight. This is the creation of full-fledged software with all the ensuing consequences, and the creation of an application demonstrating the operation of the algorithm, which is better or worse able to convince a person that he is not being deceived. And it’s clear to everyone that in terms of labor intensity, these two projects are simply not comparable. It is quite natural that the decision was made to take the easy path. Good: - “What is required from such a win-demonstration application?” First, you can even ask another question: “What should it be?” Firstly. Immediately removed headache about a convenient, understandable, practical and beautiful user interface. For such a demo, a very primitive interface is quite enough. The only important thing is that the user sees the initial data that is offered to the program for calculation (generated naturally at random) and the results of this calculation. At least theoretically, the user will have the opportunity to check the consistency of the source data and the result obtained using the program. Is such a test difficult?... The answer is unequivocal: “Yes, it’s not easy...”. Especially if you know how many traps and checks are contained in the console application for constant verification of the results obtained, as well as the size of the code of these checks and traps. Are there other methods of persuasion?... Perhaps, transferring to everyone interested... the source code of the program. But, for example, this is not accepted at Microsoft. Secondly. The problem of the help file, user manual, and other bells and whistles absolutely necessary for full-fledged software is removed. That's what they did. More than twenty buttons were stuck on the main form of the application, of which only one is active at each stage of the calculation, not counting buttons like - About the program, Start a new task, Close me. When you click on this button, a window appears with a Data Generation button. You click Data Generation, and the generated data appears in a window on a white background. We close the window. The button that was just pressed goes out (no longer active), the next one to be pressed becomes active. Click. The following window opens. And there is a button Create a schedule. Click on Build schedule, the constructed schedule appears. Anyone can check whether the schedule is built correctly or not. And so on until all steps of the algorithm have been completed. And then you can click on the big Start a new task button. And so on in a circle. Or click the Close me button. At first glance it may seem: “This whole demonstration program is a monkey’s work.” But that's not true. For at least three reasons. Firstly. During the development of the demonstration, a rather important task of developing the future architecture of full-fledged software was solved. Namely. It was necessary to severely separate the “brains” from the “torso”. To put it more clearly, separate the schedule calculation algorithm code from the source data generator code and user interface code. The entire code of the schedule calculation algorithm is concentrated in a dynamically linked library, thus, the user interface, as a client, can submit tasks to the dynamic library, which acts as a server, to build various schedules compiled on various steps algorithm. This will allow in the future, without touching the code of the schedule calculation algorithm, to conduct experiments with various options interface until the complete and final satisfaction of users. Secondly. Despite its primitiveness, the demo user interface is a logical model of the future convenient, understandable, practical and beautiful user interface. For example, it implements the ability to return to the previous step of the algorithm, and this ability, in turn, influenced the structure of the program data. In addition, the demo interface supports such a feature of the algorithm as moving from step to step in a strict sequence, which ensures the integrity of the data and its protection from incorrect changes. Third. Again, we repeat, despite its primitiveness, the existing user interface is suitable for analysis mathematical model practical situations that arise when drawing up the school schedule adopted in this program. Such an analysis or examination could be carried out by specialists who are well acquainted with the topic, for example, head teachers with sufficient work experience who teach mathematics at school. To understand the details of the calculation, of course, their qualifications are not enough (and no one would have such a desire), but due to the general mathematical culture they have acquired, they can discern obvious omissions in the formulation of the problem much better than any professional mathematician who is familiar with the work of the school only by hearsay or various publications. “So what next?” And then the development of full-fledged software in accordance with all the laws and rules of software engineering, which now, in complexity, does not exceed conventional software for ERP systems. Just don’t ask: - “How long will this take and what is the labor intensity of developing such software?...”. And especially don’t ask: - “How much will such a development cost?...”.

9 Problems with the business model

As previously estimated, the global market for school schedule software, in a fully automatic mode, ranges from 100 million to 500 million US dollars. However, this market, as venture investors say, still needs to be “raised.” And here, at least two problems emerge quite clearly. One problem is: - “Expensive”. We have already stopped there. And another, in our opinion more serious, is: - “The reputation of such software.” To use a metaphor, the reputation of such software is reminiscent of a dirty, heavily manured and smoking garbage dump, like after the battle on the Kulikovo Field. Moreover, the smoke is so acrid that you want to close your eyes and stop breathing. As mentioned earlier, when talking to potential clients of school scheduling software, the conversation can easily turn to swear words. “We’re fed up... with our automation, the school’s information space and electronic diaries, let us work in peace...” What can be done to change the reputation of such software and the attitude of head teachers towards it from hostile to at least neutral? About positive image We don't stutter yet. About ten years ago, it was still possible to say that computers in the offices of head teachers were for furniture, as an indispensable accessory of scholarship and progressiveness. That in the best case, a computer is used instead of a typewriter (although, as noted earlier, it was precisely this circumstance that contributed to such a rapid flourishing of the personal computer industry). Currently the situation has changed. Many have already tried... We have just discussed the results of such tests. All that remains is to start all over again. Namely. From the business model of distributing such programs. Even without looking very closely, you can see that this business model has remained virtually unchanged over the past 15 years. Find the program website, download the demo version, issue an invoice for payment... Everything seems to be clear with the invoice for payment. It’s also impossible to do without the program’s website. But what about demo versions? But with demo versions everything is different. Option one. Our demo version is no different from the working version of the program, but you cannot save the entered data, and you cannot print the results obtained. And so, everything works. Is it possible to use such a demo version to evaluate all the advantages and disadvantages of the program? As noted earlier, to enter all the initial data, no matter how squeaky the advertisement is about an hour, maximum one and a half, it actually requires a minimum of 8 - 10 hours of continuous and painstaking (boring as hell) work. A normal person, and even more so a user starting to work with a program for the first time, when he needs to simultaneously learn how to work with the program and accurately, without errors, enter a mountain of initial data, will not be able to do this in one go. It takes at least two, or even three days (times). Now imagine the beginner’s fear that the power will definitely go out or something will reboot. Well... a normal person would not have the desire to use such a demo version. So, either decide to buy a “pig in a poke”, knowing about the “marketing fits” of some developers, or, as most often happens, press the Del key with bitterness for wasted time. To be fair, it should be noted that the same developers came up with another option. We made a “breaker” for our program. An unsuspecting, good-natured user, having previously turned off his conscience with a small key, downloads an illegal copy (demo + hack). It installs, breaks, and... everything works... As they say, use it to your health... True, after about half a year, the program will announce to you that it is going into demo mode, and to save your data, please be so kind. .., contact the developer for an invoice... Looking from the outside at such tricks, this option seems, after all, more honest. Although, of course, the user is trying to deceive the manufacturer, the manufacturer is deceiving the user..., by the way, promising him that in a few minutes after entering all the initial data he will receive a ready-made schedule. It is safe to say that the vast majority of users will never know that their data was exposed to a real threat. Having spent 15 - 20 hours working with the program and convinced of its uselessness, shouting: - “All programs, like men, are like that...” potential buyers angrily delete this program from their computer. And after an hour or an hour and a half, having calmed down, having caught their breath, they say to themselves: “How smart I am... after all, I’m smart for not paying money for this..., my mother told me, “Don’t take a pig in a poke.” Option two. Our demo version is no different from the working version, there is only one limitation, the maximum number of classes is five. And so, everything works. As a result, such a statement appears on the forum. “I saw your program, if I may say so. And he introduced that, nothing at all - four classes. And she told me: “I can’t make a schedule.” You can stick it in your... Damn speculators.” Here we are faced with a case where the developers found adventures on their “... (head)”. Those who think that creating a schedule for a school with four classes is much easier than, for example, with twenty, are deeply mistaken. It is for this reason that when testing the “Ancient Egyptian” scheduling algorithm, it was decided that when generating test data, for the minimum number of classes, choose the number nine. This is sometimes explained by the impossibility of automatically compiling a table for the distribution of teaching load. Simply put, distribute the load between a tiny number of classes and, accordingly, a tiny number of teachers. Apparently, such tricks can only be performed by a very experienced hand (or eye, if you like) of a person. Option three. OK then. Use our program. But, two weeks. And in two weeks it’s all over. “We’ll turn off the water...” Is it possible to master the program in two weeks and evaluate all its advantages and disadvantages? Let's put our hand on our hearts: “Perhaps it’s possible...”. But on one condition. You need to stop doing everything else. And the head teacher’s favorite word is: “Busy.” “Oh, busy. I’m so busy that I don’t even have time to breathe.” Will the head teacher drop everything in the world for two weeks and immerse himself in a timetable program for this period? As scientists say: “It’s hard to say...”. In short, everything is bad... And so bad, and so inconvenient... Where to look for a way out? Maybe rent?

10 Business model for SaaS software use

Initially, the entire computer industry used a rental business model - the first computers cost a lot of money and their computing power was rented out to customers. With the advent of the Internet, the old business model was revived, but on a fundamentally different technological basis. SaaS(English) software as a service - software as a service) - a business model for selling and using software in which the supplier develops a web application and independently manages it, providing the customer with access to the software via the Internet.

The main difference between SaaS and the old model is that previously customers accessed computers directly, rather than using global networks. Since the SaaS model is focused on providing services via the Internet, its development is directly related to the development global network. The first companies offering software as a service appeared in Western countries in 1997 - 1999, and the acronym SaaS came into widespread use in 2001. It seems that in our “difficult case”, this business model is the most optimal, and maybe even the only acceptable one. It will save potential clients from risking a relatively large amount of money when paying for a software product from a group of products with an almost hopelessly damaged reputation. Using a rental business model, the customer can calmly and gradually become convinced that the product being offered is what he really needs, and that his expectations from using the product coincide with what he actually receives. We previously spoke in some detail about the expectations of head teachers from this type of program.

11 Instead of a conclusion

Sometimes, some people ask sarcastically: “Do you have a business plan?...” Yes. And at the same time, very simple. “Consistently solve emerging problems as they arise...” As a last resort, you can use the SaaS model (business plan - upon request). If anyone needs it, it will be possible to plan everything in detail and not a single accountant will find fault!

Bibliography

Baltak S.V., Sotskov Yu.N. Construction of a training schedule based on coloring the vertices of the graph // Informatics, 2006, No. 3, p. 58 - 69. Borodin O.V. Colorings and topological representations of graphs // Discrete analysis and operations research. 1996, Vol. 3, No. 4, p. 3 - 27. Borodin O.V. Generalization of Kotzig's theorem and prescribed coloring of edges of planar graphs // Mathematical Notes. 1990, Volume 48, Issue 6, p. 22 - 28. Vizing V.G. Coloring of graph vertices under majority restrictions on the colors used // Discrete Analysis and Operations Research. 2009, Vol. 16, No. 4, p. 21 - 30. Vizing V.G. On connected coloring of graphs in prescribed colors // Discrete Analysis and Operations Research. 1999, Series 1, Volume 6, No. 4, p. 36 - 43. Gafarov E.R., Lazarev A.A. Mathematical methods of optimization when drawing up an educational schedule // New information Technology in education. Collection scientific works. - M.: 1C-Publishing, 2013, Part 2, p. 51 - 55. Gary M., Johnson D. Computers and hard-to-solve problems. - M.: Mir, 1982. - 416 p. Distel R. Graph theory: Trans. from English - Novosibirsk: Publishing House of the Institute of Mathematics, 2002. - 336 p. Emelichev V.A., Melnikov A.I., Sarvanov V.I., Tyshkevich R.I. Lectures on graph theory. - M.: Science. Ch. ed. physics and mathematics lit., 1990. - 384 p. Ichbana D., Knepper S. Bill Gates and the creation of Microsoft. - Rostov-on-Don: Phoenix Publishing House, 1997. - 352 p. Karpov D.V. Dynamic regular colorings of graph vertices. // Notes of scientific seminars of POMI. 2010, Volume 381, p. 47 - 77. Magomedov A.M., Magomedov T.A. Interval regular edge 5-coloring of a bipartite graph on one part // Applied discrete mathematics. 2011. No. 3(13), p. 85 - 91. Papadimitrou H., Steiglitz K. Combinatorial optimization. Algorithms and complexity. Per. from English - M.: Mir, 1985. - 512 p. Romanovsky I.V. Discrete analysis. A textbook for students specializing in applied mathematics and computer science. - 2nd edition, revised. - St. Petersburg: Nevsky Dialect, 2000. - 240 p. Swami M., Thulasiraman K. Graphs, networks and algorithms: Trans. from English - M.: Mir, 1984. - 455 p. Smirnov V.V. Pererburg schools and school buildings. History of school construction in St. Petersburg - Petrograd - Leningrad 1703 - 2003. - St. Petersburg: Publishing house "Russian-Baltic Information Center "BLITS"", 2003. - 144 p. Stetsenko O.P. On one type of coloring of graph edges in prescribed colors // Discrete Mathematics. 1997. Volume 9, issue 4, 92 - 93. Urnov V.A. Schedule - the most popular workstation in education // Informatics and education. 2001, No. 4, p. 47 - 52. Harari F. Graph theory. - M.: Mir, 1973. - 302 p. Even S., Itai A., Shamir A. On the complexity of timetable and multicommodity flow problems // SIAM J: Comput. Vol. 5, No. 4, December 1976, 691-703

Links:

Therefore, the entire floor where such a computer was located was covered with a fine metal mesh in order to exclude the possibility of “electronic spying” on the part of the sworn enemies of the Soviet regime. The very task of drawing up an educational schedule (without the help of computer technology) is apparently at least three hundred years old. Cases have been recorded when head teachers - in general, cultured and well-mannered people, having heard the phrase: - “A program for drawing up a school schedule,” immediately switched to swear words. Here we will not dwell on the theory of NP-hard problems, since a discussion of this issue would take the reader far away from the topic that interests us, and would also be clearly premature and superficial. The interested reader can be recommended to turn to perhaps the most cited publication on this topic in our country. To fully understand this article, NP-hard problems can be understood as practically unsolvable problems, although this is not an entirely accurate “translation”. This refers to Russian-language publications, of which there are not so many in comparison with English-language ones. Most likely, their number does not exceed the total contribution of the Russian Federation in the field high technology, which is estimated to be between 0.4 - 0.6% (from zero point four percent to zero point six percent) of the global total. True, there are an order of magnitude fewer physical and mathematical sciences. Vyacheslav Sergeevich Tanaev (1940 - 2002) - Belarusian mathematician, director of the Cybernetics Research Institute of the National Academy of Sciences of the Republic of Belarus, Doctor of Physical and Mathematical Sciences (1978), professor (1980), full member of the National Academy of Sciences of Belarus (2000). Area of ​​scientific interests: operations research, scheduling theory, optimization methods. Mikhalevich Vladimir Sergeevich (1930 - 1994) - Ukrainian mathematician and cyberneticist, academician of the Academy of Sciences of Ukraine, academician of the Russian Academy of Sciences (1991; academician of the USSR Academy of Sciences since 1984). Works on the theory of optimal statistical solutions, system analysis, theoretical and economic cybernetics. USSR State Prize (1981). However, transferring the source data generator code and the code for checking the correctness of the compiled schedule is quite possible, since this code does not represent any commercial value. In honor of the ancient Egyptian priestess Anush, the program, in the Russian manner, was named Annushka.

And even... maybe... But what! an empty dream.
There's no way this will happen.
Fate is envious and evil!
Oh, why am I not tobacco!... A.S. Pushkin

File translated from T E X by T T H, version 4.03.
On 27 Jul 2013, 00:53.

Download it to your phone so you don’t forget anything and won’t be late for anything.

Android

Timetable

A beautiful and intuitive application for managing school life. You can enter your schedule, homework, exams, and even vacations. The application can synchronize with all your Android devices, and during classes it will go into silent mode.

School diary

In this electronic diary you can keep a schedule, indicating the name and telephone number of the teacher, as well as the location of the lesson. To make sure you don’t forget anything, the application has widgets for your phone’s home screen. It is also possible to take notes on subjects and grade them. But perhaps the most pleasant feature is crossing off completed homework.

LightSchool

Allows you not only to maintain a schedule and record homework, but also to track the time before the start or end of the lesson. A special feature is the presence of theoretical materials. If you suddenly forgot how to find the sine of an angle, you can look it up directly in the application.

Sign up

Not very colorful, but multifunctional application. You can create a schedule in it and export it to the calendar on your device. You can view your class schedule for a week or several at once and display a widget with reminders on your home screen. During a lesson, the application automatically turns on silent mode, and you can set due dates for homework.

Schedule - school planner

The essence of the application: one user publishes his school schedule so that his classmates can then find a ready-made class schedule. Comfortable! It's a pity that not many people use the service yet. But there is a widget and a QR code scanner.

iOS

iSchool

Allows you to create a beautiful multi-colored schedule indicating the rooms where classes will be held. It’s convenient to write down tasks: you can simply take a photo of the board or dictate by voice. And one more super useful function: you can enter grades in subjects and calculate your average score. The application supports Russian language, synchronization with iCloud works.

iStudiez pro

Allows you to create a schedule with repeating lessons. Each subject can be assigned its own color - this will make it easier to navigate the schedule in the future. You can add holidays and weekends to your calendar, and also save useful information about classmates and teachers.

Class Timetable

Rainbow Planner for Students. The standard set of functions includes a schedule with reminders and a list of homework. But there is also interesting feature: The application works not only on iPhone and iPad, but on Apple Watch. It’s convenient if, in addition to studying, there is also sport sections and you have to be on time everywhere.

Grade Hound

Calendar for schoolchildren and students with the ability to mark subjects by color and assign grades to subjects. The highlight: time graphs that show how much time you'll spend on a particular subject. Minus: does not support Russian language.

Class Schedule – Timetable

Another helper for students who lack organization. You can create a study schedule with repeating or alternating weeks, share it with friends, and write down homework assignments. Thanks to the convenient widget, you don't even need to unlock your device to quickly check your schedule.

Foxford timetable

The class-by-class schedule of classes in the Foxford Home School and external studies is on the website in the section “ Educational process».

Select your class and click "More details". You will see what day of the week and what time this or that lesson takes place and you will be able to enter the schedule into your electronic planner.

Also, at the beginning of the school year, students receive schedules in the form of convenient pdf tables.

All homework is stored in the student’s Personal Account. You just need to select a course and lesson number.

The dashboard will remind you of new and already completed tasks. From there you can proceed to completing the task in one click.

Well, if a student forgets about some lesson or homework, he will be immediately reminded of it. More reliable than any application! :)