Intelligent timetabling using a microcomputer

Abstract

The timetabling of classes is a major education management activity, with the complexity of the process being highest for tertiary-level institutions, especially where students and program numbers as well as classroom requirements are growing. The pioneering development of a microcomputer-based timetabler using expert system technology for a Hong Kong tertiary institution with a very dynamic academic environment is described. The knowledge, strategies, and heuristics of a small, centralized group of schedulers were modeled and subsequently represented in a readily available expert system shell which runs on a standard IBM-type microcomputer. The broad feasibility of such expert-level timetablers and more generally the application of this knowledge-based systems approach are discussed.

Academic scheduling is one of the more important and complex management activities in an educational institution. Timetabling staff have the responsibility to create a class schedule which meets the constraints and preferences of lecturers and students while optimizing the use of rooms and associated teaching resources. Traditionally, these individuals have scheduled the classes for an upcoming term or semester manually, by using a trial-and-error approach which may be refined by years of experience or specific training.

These efforts, often limited by available time and resources, have sought to balance different interests while minimizing the number of scheduling conflicts. However, criticism from students, teachers and even other administrators has been common. The timetabling problem is made especially difficult in institutions where there are growing numbers of students, study programmes, classroom requirements and even increasingly diverse attendance modes. The manual timetabling process for larger academic organizations can be described as a time-consuming, tedious and often thankless task. This appears to make it an ideal candidate for the application of information technology.

COMPUTERIZED SCHEDULING

A large number of different scheduling tasks on the factory floor, in the office, and for various transportation modes have been successfully computerized in the last three decades. This has given hope to educators that academic timetabling could benefit in a similar manner. Although the most common assistance has come from graphical interfaces, electronic databases, comprehensive bookkeeping mechanisms and very simple models, Dowsland and Lim[1] report that numerous attempts have been made to computerize the academic timetabling process since the 1960s. The use of simple heuristics in the first group of these computerized schedulers limited their use to all but the smallest schools. Subsequent algorithmic approaches appeared more promising at the design stage, but were only successful in the more static real-life environments, such as those found at the primary level.

French[2] noted that methods such as integer programming and the heuristic approaches of operational research lacked the flexibility for general application in dynamic environments. Most academic timetabling is representative of this class of scheduling problems. The complexity of programmes, resources and the imposed constraints made satisfactory computer-derived timetables unfeasible for many institutions, even with the largest-scale computers of the 1970s.

As information technology has evolved, the attempts at computer-assisted timetabling have continued. Many of the recent ones are noted by Floyd and Ford[3]. The approaches have ranged from the use of simple heuristic rules for calculating the best schedule through the simulation of manual timetabling with a digital computer, graph theory and optimization, heuristic algorithm, assignment models with simple rules as decision criteria to the integer programming in 0-1 variables with Lagrangian relaxation, and the branch and bound methods reported by Tripathy[4].

A solution based on decomposing the timetabling activity into two subproblems, one of scheduling the class time and a second of assigning a classroom for the scheduled time, has been proposed by Ferland and Roy[5]. A mathematical programming approach may then be applied to each of the subproblems. However, the continued predominance of manually-created academic timetables is indicative of the shortcomings associated with these approaches. Even though academic timetabling is a form of predictive rather than reactive scheduling there is little hope of finding polynomial algorithms for larger-sized problems of this class, so optimal or exact solutions are unlikely (Graham[6]). The research of the last decade has focused on finding near-optimal results which satisfy the end-users. This approach is typified by the work of Ozdemiral and Satur[7].

A new opportunity for tackling the timetabling problem is provided by knowledge-based systems (KBS). This fifth-generation information technology is rooted in the artificial intelligence research of the 1950s. As an emerging productivity tool for many business activities, knowledge-based systems have been used to model narrow problem areas and retain specific human expertise in a computerized environment (Fiegenbaum, McCorduck and Nii[8]; Martinsons[9]). Although the fundamental KBS technology has changed little in the past decade, more advanced products, better packaging and declining software costs have also made it increasingly feasible to develop "intelligent" computer applications.

Successful KBS developments have been widely reported in the manufacturing industry (see Kusiak and Chen[10]). They include job-shop scheduling (Smith, Fox and Ow[11]), robot world and action modelling (Elleby and Grant[12]), resource scheduling under constraint, employee timetable scheduling (Chow and Hui[13]) and semiconductor wafer production scheduling (Savell et al.[14]). Most of these applications have taken a reformulative rather than an algorithmic approach, whereby the problem is proactively reformulated until a satisfactory solution becomes easier to find, perhaps by relaxing some constraints.

In education, this new technology has been successfully applied to teaching (Ruyle[15]), library services and administration functions like enrolment management (Dienbach[16]). However, previous efforts at intelligent academic timetabling are typified by the work of Monfroglio[17], which requires specialist knowledge, sophisticated programming and expensive hardware. The recent commercial emergence of ready-to-use KBS applications as well as cost-effective development "shells" led us to consider this technology for scheduling classes.

Academic timetabling is deemed suitable for KBS development since there is a business need for this activity and the application of conventional information technology has proved relatively ineffective in this area. With campus-wide computer systems becoming increasingly common (Brindley[18]) and cost-effective microcomputer hardware gaining an omnipresent status in the administrative world of the 1990s, it is both technically and economically feasible to implement a computer-based academic timetabler.

After a preliminary investigation found no off-the-shelf academic timetabling software products, we examined the feasibility of quickly developing such an application using a commercially available development tool. We determined that it was both realistic and cost-justified to build an intelligent timetabler using a KBS shell as the software development tool and a standard microcomputer as both the development and implementation hardware. A successful product could demonstrate the general applicability of simple KBS technology to the academic timetabling domain and reinforce the view that the knowledge-based approach should be considered for a wide variety of management activities.

THE CLASS TIMETABLING PROBLEM

Academic timetabling represents the allocation of scarce time and room resources for study programmes subject to the constraints and preferences of lecturers and students. After a preliminary analysis of the problem domain and some discussions with the current scheduling staff and educational administrators, the two-step approach described by Ferland and Roy[5] was chosen for our development. First a class is scheduled for a specific time and then an appropriate room is found. If no room is available, the time of the class is changed and the room search repeated.

Our prototype development environment was the City Polytechnic of Hong Kong (CPHK). It is a research and teaching university (in all but name) near the geographic centre of the British territory. In 1990, this tertiary institution had a total of 76 different study programmes (from the higher diploma to the doctorate level) with durations varying from one to six years. The 209 classes in each week of class ranged in size from 17 to 204 students. Both the study programme and class numbers are planned to increase by more than 10 per cent per year through the first half of the 1990s. Furthermore, four different modes of attendance were identified: full-time, sandwich, part-time evening as well as part-time day and evening.

Taught subjects typically have three contact hours per week: a single two hour lecture and a one hour tutorial. However, for some subjects, the tutorials are substituted or complemented with laboratory sessions. In rarer cases, three-hour seminars or two-hour laboratories and a single hour lecture are desired. Each class is divided into small groups of ten or 20 students to attend the tutorials or laboratories.

Full-time students take up to six subjects per term and have one afternoon per week dedicated for sports. In addition, some have an additional afternoon of off-campus training. In contrast, part-time students take three subjects per term and should have classes on no more than three evenings. Students of part-time day and evening study programmes should have lessons scheduled for one full day and two evenings each week.

There are about 600 full-time faculty and an equal number of part-time lecturers. Each full-time academic must be allocated one research day, free from teaching, and should have at most two evenings of teaching. The 124 rooms available for the 1991-2 academic year varied in size from 10 seats to 300 seats. However, only 17 of these classrooms can cater for more than 80 students. In 1991-2, these rooms were utilized at more than 98.5 per cent of capacity for Monday to Friday evening teaching and about 85 per cent of capacity for the corresponding day-time teaching. Furthermore, selected rooms may be set aside for some special purposes and hence not be allocated for teaching. There are also special rooms such as video studios, language laboratories, satellite computer areas and drawing offices to be scheduled.

Time scarcity is a particular concern for the part-time evening study programmes. Students should come for lessons on only three evenings per week. However, there are only three teaching hours in each evening. The three subjects require nine hours of teaching. This need to have all the available times of the students scheduled is the tightest constraint on the student side. Since a single lecturer frequently handles the two-hour lecture and multiple tutorials for a subject, it is simply not possible to dedicate a single evening for all the classes of one subject.

In addition to the above constraints, certain involvement of individual lecturers in, and allocation of rooms for, non-teaching activities must be considered when formulating the timetable. Finally, the institution's current staged transition from a trimester (three terms of ten weeks) to a semester (two terms of 15 weeks) system required that both term lengths be scheduled for the 1991-2 and 1992-3 academic years. Thus the timetabling problem at this Hong Kong university offered a seemingly severe test for the flexibility and utility of any timetabling approach.

BECOMING FAMILIAR WITH THE DOMAIN

Weitzel and Kerschberg[19] have reported the successful use of a KBS development methodology whereby the developers gain initial familiarity with the domain experts, with other potential users and the work environment. Our knowledge engineering team, consisting of three faculty members, with varying levels of previous KBS experience, and a recent computer engineering graduate, began by spending considerable time with the institution's schedulers. We felt it was important to acquire the expertise on-site, so that the nuances of the current scheduling process could be documented and evaluated before modelling them in an intelligent application.

Administrative difficulties are compounded in Hong Kong because of communication problems in the work environment, where the use of a non-native language (English) is required. The linguistic backgrounds of the enduser community, native Cantonese speakers with varying levels of English, must be taken into account, since the value of the end product for the Hong Kong context would be largely dependent on its ease of understanding and use. Due to the interpretation and occasional translation of information related to constraint and preference inputs, and more importantly the sheer volume of different study programmes and classes that must be timetabled, the manual approach currently requires over 12 person-months to create the schedules for one calendar year of study.

Academic timetabling was demonstrated to be suitable for development and implementation with a microcomputer-based artificial intelligence tool based on the domain selection framework proposed by Martinsons[20]. The problem has a medium level of complexity and was important to the organization. The domain consists of specific knowledge familiar to human schedulers, who were available during the development; though there was a high likelihood of a successful system by applying KBS technology, conventional algorithmic approaches had proved to be relatively unsatisfactory.

Our knowledge acquisition resembled a simplified version of the approach subsequently reported by Motta, Rajan and Eisenstadt[21]. The team began by eliciting details about the scheduling process from the three administrative staff who are responsible for creating the class timetables. The aims at this stage were to understand the process and its general concepts, and to document the flow of data which supports this activity. A series of short interviews with the timetabling staff and a review of various documents were followed by intensive content analysis. Sifting through and synthesizing the data led to the formulation of a preliminary model of the domain after about four weeks of part-time work. This model was primarily documented in charts showing the sources, uses and details of various data.

An additional two months were needed to refine and validate this model. The timetabling staff were observed as they scheduled the classes for an upcoming term using magnetic tapes on a series of large whiteboards. A large number of discussions during the manual timetabling process and several subsequent focused interviews helped the developers to understand the finer details of the academic timetabling process at this institution. Finally, several simple scenarios were developed to consider the more subjective aspects of the timetabling task. This led to the production of a detailed knowledge model ready for coding in an appropriate software tool.

SELECTING A SHELL

The existing hardware in Hong Kong education institutions is a mixture of minicomputers and microcomputers. However, to maximize the utility and minimize the delivery cost of this application, the use of a readily-available microcomputer was favoured. The flexibility, representation mechanisms and interface capabilities available with such hardware in the early 1990s were deemed sufficient for our academic timetabling problem. This represents marked progress from the 1970s, when such a problem could not be addressed by large computers using more conventional information systems approaches.

An IBM-compatible PC-AT with a 80386 processor, 1 MB RAM and a 30 MB hard disk was chosen as the benchmark computer, since such a machine is commonly accessible to tertiary education administrators in Hong Kong. This choice of hardware led to a consideration of appropriate software for development. Simplifying the project's technical and programming aspects in this way enabled the rapid development of an application prototype. The nature of the user group and their environment made ease of use, after-purchase support, flexibility for future applications enhancement and cost-effectiveness important software selection criteria.

Based on an evaluation of PC-based expert system tools by Gevarter[22], a decision was made to use a commercially available expert system shell. By now we had more precisely defined our goal-driven expectations for the application and noted that scheduling is a forward chaining assignment problem with constraint relaxation. Whereas jobs are assigned to machines in a manufacturing plant, our problem requires class assignment to specific rooms at specific times. The assessment of numerous PC-based expert system shells reported by Freedman[23] and a survey of local availability for different products and corresponding after-sales support, led us to select Personal Consultant PlusTM as our development tool. It was readily available in the local market and both extensive documentation and telephone service support were included with the product.

Within this software, the developers created and coded a series of IF-THEN rules to mimic the human schedulers. This "knowledge base" was then linked to the dBase III PlusTM database management package. The latter software gathers the requirements and constraints of the timetables and stores the results, enabling the entire application to run on the microcomputer.

TAKING AN INTELLIGENT APPROACH

Our timetabling application sought to enable the creation of a schedule for an upcoming semester or trimester which would optimize the use of time and room resources, and maximize the satisfaction, or conversely minimize the dissatisfaction of all the people involved and affected. To achieve these goals, the timetabling activity was broadly classified into five tasks:

(1) information collection;

(2) time selection;

(3) room selection;

(4) conflict relief; and

(5) record updating and housekeeping.

The basic information, summarized in Table I, forms the starting point for the timetabling process at the City Polytechnic of Hong Kong. In addition, the human scheduler should know the constraints and preferences associated with individual study programmes, subjects, lecturers and even certain rooms.

Scheduling study programmes requires an iteration of four activities--time selection, room selection, conflict relief, and database updating and house-keeping--for each subject. Time selection involves finding the more suitable time slot for a lecture or a tutorial. At this institution, a total of 49 time slots (from 9 a.m. to 6 p.m. on Mondays to Fridays and 9 a.m. to 1 p.m. on Saturdays) are available for full-time classes, while part-time student programmes usually have 19 available slots (from 6.30 p.m. to 9.30 p.m., Monday to Friday as well as 9 a.m. to 1 p.m. on Saturdays). Clearly, both the students and the lecturer involved must be available at the allocated time. Thus this selection is subject to student's and lecturer's constraints. The goal is to optimize the combined preferences of the lecturer and the student, thereby finding the best time for the class.

The reservation of a large lecture room for public presentations, the requirement to free each room for cleaning once a week (requiring about one half hour for the larger rooms), the need for teaching staff who are part of the same faculty committee to have mutually available meeting times and the need to provide full-time students with at least one free hour for lunch between noon and 3 p.m. each day are important constraints. Preferences are more numerous and proved difficult to fully incorporate into the application.

For example, a part-time day and evening study programme may prefer the daytime lessons to be on a certain weekday. A subject may have a teaching pattern deviating from the two-hour lecture, one hour tutorial weekly format. In some cases, it may have different patterns on alternate weeks. Lecturers are asked to input their preferred weekday for research and preferred time in the day for teaching as well as their various committee and community commitments.

The collection of this information and the entry of all lecturer and student data, together with their constraints and preferences, is the first timetabling stage. Preferences incorporated into this application include: favouring the same or an adjacent room for consecutive classes; favouring adjacent time slots up to a maximum of 4 consecutive hours to avoid excessive scattering of classes (unless otherwise indicated by a particular lecturer or for a specific student group); and favouring the early evening (6.30 p.m. rather than 7.30 or 8.30 p.m.) for part-time classes.

A classroom must be found after the lesson time slot has been decided. This should be just large enough for the class while minimizing the distance travelled by students and lecturers. Once a particular room is scheduled for use, it should be utilized for as much time as possible. If there is not suitable time for a lesson or all rooms at the desired time are occupied, the conflict must be resolved. This may be done by moving a previously scheduled lesson to some other time or swapping it with another lesson in order to a) free the lecturer's time, b) free the student's time, or c) free a room. Sometimes constraint relaxation will be required. In order to schedule some lessons, the student's sports afternoon or the faculty member's research day will have to be changed.

Each class is considered to be scheduled only after an appropriate time and room are found. At this point, the lecturer and student timetables are updated. When all the subjects of a study programme are scheduled, the process continues for the next programme. New study programme and subject information are retrieved within the housekeeping and database updating activities.

Constraints and preferences are considered using a priority scheme, with each time slot in the faculty member's and student's respective timetables receiving a priority value. This is done according to the extent it satisfies the constraints and preferences of the faculty member or the student due to its status and environment. Consistent with the objective of minimizing staff and student dissatisfaction with the timetable, a time slot which violates one constraint will be assigned the lowest possible priority value. Undesirable time slots will have low priority values while favourable times will receive a high priority value. Thus classes are more likely to be allocated to the latter.

For example, a subject may be taught to full-time students by a lecturer who prefers to do research on Fridays, has committee meetings on Tuesday and Thursday afternoons and teaches Tuesday and Wednesday evenings. These students may have a Thursday sports afternoon and already have classes scheduled on Monday and Wednesday mornings. The highest priority among mutually available times for the lecturer may be Monday afternoon, while the students might prefer a Tuesday morning class. However, a compromise, avoiding the less favoured time slots of both the lecturer and the students, and mutually undesirable times like Monday mornings, may allocate the class to a Wednesday afternoon.

This knowledge base has a high degree of dynamic flexibility, enabling the rapid addition, alteration and deletion of both lecturer and student constraints and preferences. In addition, while the general nature of constraints is specified in the knowledge base, the constraints and preferences for scheduling a specific term or semester, together with the courses, student groups and faculty are captured from appropriate databases or solicited from the user. This addresses the realities of organizational environments, such as the one at the City Polytechnic of Hong Kong, where there is course and staff turnover, and both the faculty and particular student groups have preferences which may change over time.

DEVELOPING THE APPLICATION

The use of a microcomputer-based KBS shell released us from the technical details of implementation, allowing efforts to be concentrated on the details of the timetabling domain. This reinforces the support for using KBS shells expressed by Vedder[24]. A working prototype was completed after only seven months of part-time work. Although the development version of the Personal Consultant Plus shell was used in this process, the delivered product does not require the complete Texas Instrument product. The consultation support utilities, along with the knowledge base, are sufficient. The software for a single run-time implementation would be about US $200.

Our development emphasized the creation of very simple menu-driven user interfaces, suitable for individuals with non-native English language skills. Because of unique local circumstances considerable testing, using a formative approach with the three timetabling experts, was carried out to ensure that ambiguities and discrepancies between British and North American English in the user interfaces were eradicated. The knowledge model coded in the initial prototype was tested by taking a typical data input subset for CPHK's timetabling process.

Class schedules for three courses were constructed on the assumption that only three rooms of different sizes were available. This successful test was followed by the complete scheduling of a term's classes in parallel with the traditional method. Two vastly different schedules were produced, primarily because of different (but in both cases valid) heuristics in assigning small classes to particular times and rooms. Unfortunately, seven courses with very stringent constraints failed to be scheduled by the system and had to be manually rearranged.

The human schedulers assessed the timetable produced by the computer application as generally satisfactory, noting that less than three dozen minor adjustments (taking less than one hour of their time) were needed to make the computer-generated schedule acceptable. Subsequent changes to the knowledge base are expected to reduce the number of required future changes. With the general constraints appearing as part of the knowledge base and many specific constraints and priorities being applied in timetabling each term, an increased level of satisfaction is expected among both the faculty and the students.

THE PRODUCT

The prototype application consists of a knowledge-based system (the shell with a coded knowledge base) and various databases, augmented by dBase programs and procedures written in the symbolic language Scheme.

The academic timetabling process is controlled and executed by the KBS and the databases. To broaden the potential user group for this application, Dbase III Plus was used not only for developing the database structure, but also for application programs outside the KBS shell.

The information collected in the various databases is supplemented by about two dozen selections from an almost equal number of menus at the beginning of the session. The software application is then able to select the best time for a lesson, relieve any conflicts, produce decision trails, and make conclusions for the whole application when necessary. To choose a suitable time slot, the time slots for both the relevant faculty member and the student group are prioritized by the system, in accordance with constraints and preferences which have been previously specified.

The two time priorities are then combined to get the highest priority time slot. In case of a conflict, sequential attempts are made to reschedule (a) a previously scheduled lesson of the lecturer, (b) a previously scheduled lesson of the student, or (c) some other study programme, so as to free a time slot or a room. If none of these actions resolve the conflict, the user is prompted to relax one or more of the constraints. This process is depicted in Figure 1. (Figure 1 omitted)

The sub-tasks involved in academic timetabling have been previously reported by Martinsons[25]. Our knowledge base has a corresponding rule set for:

* information gathering through the database interface;

* prioritizing lecturer's days;

* prioritizing lecturer's time slots;

* prioritizing student's days;

* prioritizing student's time slots;

* combining lecturer's and student's time priorities;

* time selection;

* room selection;

* conflict relief;

* database updating and housekeeping; and

* steering the processing steps of the whole system (see Figure 2). (Figure 2 omitted)

A total of 11 database files is used to store information related to:

(1) the study programmes;

(2) subjects;

(3) staff;

(4) students; and

(5) rooms.

They serve as the repositories for the input information as well as the timetable output. The five functions built with dBase III Plus application programs perform the following functions:

(1) assist in the input of required information;

(2) help search the room database for the best room at a specified time, aiming to meet basic size and location requirements, striving for high utilization and avoiding the creation of small idle-time gaps;

(3) update faculty and student databases once a lesson is scheduled;

(4) retrieve relevant information for the next lesson to be scheduled; and

(5) print out the full schedule.

Significantly, the intelligent approach has reduced the total duration for timetabling an upcoming school term by about one third, while the dedicated time of the human expert is slashed to about 10 per cent of that needed with the manual approach. The schedulers are now able to focus on gathering and verifying the information from the different academic faculties and coping with last-minute changes to various input data, rather than manually timetabling each class. This should improve the quality of the process and increase the satisfaction of timetabling "customers".

TOWARDS A GENERAL-PURPOSE INTELLIGENT TIMETABLER

Since the rationale behind timetabling is similar across different schools, an intelligent timetabler is expected to be suitable for a large number of academic institutions. Many education organizations worldwide are experiencing institutional growth amid organizational constraints. The intelligent timetabling approach is designed to schedule classes in a way which surmounts as many constraints and fulfils as many preferences as possible. In order to use this product for scheduling classes at a different university or other schools of higher education, the information gathering part and the internal data structure would need to be reviewed. However, the flexibility which is inherent in this design should reduce the extent of needed changes.

The intelligent timetabler can accept a variety of constraints and preferences from different schools with various teaching patterns and attendance modes. The accepted information can be converted to a standard internal form understandable by the knowledge-based system regardless of the school. The growth in education is especially strong in developing countries, where English is seldom the first language for administrative staff at tertiary institutions. Thus an intelligent academic timetabler with this breadth of applicability is believed to be of significant interest and considerable potential benefit.

THE BOTTOM LINE

The development of an intelligent timetabler was found to be a cost-effective, if not an imperative proposition for the City Polytechnic of Hong Kong. As an NP-complete activity, the application of conventional algorithmic or integer programming approaches to academic timetabling in a dynamic environment was found to be infeasible. Our approach using knowledge-based systems technology to model the expertise of human schedulers has been shown to e not only feasible, but also satisfactory in enabling the rapid development of a viable academic timetabler. Although this application was developed for timetabling at a particular institution, the easy modification of the general constraints in the knowledge base and the use of other constraints and preferences recorded in a database enable it to be used for timetabling in universities and even secondary schools around the world.

As the focus for information technology shifts from merely automating routine tasks and high volumes of data to formalizing and disseminating organizational knowledge, the application of knowledge-based systems can be expected to increase. This new-generation technology is already being used as a tool to enhance productivity and leverage scarce expertise for a wide variety of both private and public sector management activities. It is hoped that this article will stimulate education managers to consider the potential use of knowledge-based information technology for academic timetabling and other business processes.

REFERENCES

1. Dowsland, W. and Lim, S., "Computer-aided School Timetabling, Part I", Computer Education, November 1982, pp. 22-3.

2. French, S., Sequencing and Scheduling: An Introduction to the Mathematics of the Job Shop, Wiley, New York, NY, 1982.

3. Floyd, S.A. and Ford, D.R., "Knowledge-based Dynamic Scheduling and Decision Support", International Journal of Computer Applications in Technology, Vol. 4 No. 3, 1991, pp. 166-74.

4. Tripathy, A., "School Timetabling--A Case in Large Binary Integer Linear Programming", Management Science, Vol. 30 No. 12, 1984, pp. 1473-89.

5. Ferland, J. and Roy, S., "Timetabling Problem for University as Assignment of Activities to Resources", Computers Operation Research, Vol. 12, 1985, pp. 20718.

6. Graham, R., "The Combinatorial Mathematics of Scheduling", Scientific American, No. 238, 1978, pp. 124-32.

7. Ozdemiral, N.E. and Satur, A., "Design of a Decision Support System for Detailed Scheduling", Information & Management, Vol. 12, 1987, pp. 47-56.

8. Fiegenbaum, E., McCorduck, P. and Nii, H.P, The Rise of the Expert Company, Random House, New York, NY, 1989.

9. Martinsons, M.G., "Modelling Organizational Decision Making Using Artificial Intelligence", Distinguished Speaker Seminar, University of Western Australia, November, Perth, 1990.

10. Kusiak, A. and Chen, M., "Expert Systems for Planning and Scheduling Manufacturing Systems", European Journal of operational Research, Vol. 34, 1988, pp. 113-30.

11. Smith, S., Fox, M. and Ow, P., "Constructing and Maintaining Detailed Production Plans: Investigations into the Development of Knowledge-based Factory Scheduling Systems", AI Magazine, September 1986, pp. 45-61.

12. Elleby, P. and Grant, T., "Knowledge-based Scheduling", Computer-Assisted Decision Making, Vol. 3, 1986, pp. 175-86.

13. Chow, K.P. and Hui, C.K., "Knowledge-based Approach to Scheduling Problems", Hong Kong Computer Journal, Vol. 4 No. 2, 1988, pp. 16-23.

14. Savell, D., Ashbourne, S., Clark, J., Chong, K.C. and Azurnendi, J.D., "Scheduling Semiconductor Wafer Production: An Expert System Implementation", IEEE Expert, Vol. 4 No. 3, 1988, pp. 9-15.

15. Ruyle, K.E., "Artificial Intelligence in Education" in Opinion Papers, EDRS, Texas, 1988.

16. Diffenbach, J., "Expert Systems Could B e a Valuable Tool for Enrollment Management", Cause/Effect, Vol. 11 No. 2, 1987, pp. 22-6.

17. Monfroglio, A., "Timetabling through a Deductive Database: A Case Study", Data & Knowledge Engineering, Vol. 3, 1988, pp. 1-27.

18. Brindley, L.J., "The Electronic Campus: Aston University", Higher Education Management, Vol. 2, 1990, pp. 334-42.

19. Weitzel, J.R. and Kerschberg, L., "A System Development Methodology for Knowledge-based Systems", IEEE Transactions on Systems, Man and Cybernetics, Vol. 19 No. 3, 1989, pp. 598-605.

20. Martinsons, M.G., "A Domain Selection and Evaluation Framework for Introducing Knowledge-based Systems in Smaller Businesses", Journal of Information Systems, Vol. 1, 1991, pp. 207-15.

21. Motta, E., Rajan, T. and Eisenstadt, M., "Knowledge Acquisition as a Process of Model Refinement", Knowledge Acquisition, Vol. 2 No. 1, 1990, pp. 21-49.

22. Gevarter, W.B., "The Nature and Evaluation of Commercial Expert System Building Tools", IEEE Computer, May 1987, pp. 24-41.

23. Freedman, R., "27 Product Wrap-up: Evaluating Shells", AI Expert, September 1987, p. 74.

24. Vedder, R., "PC-based Expert System Shells: Some Desirable and Less Desirable Characteristics", Expert Systems, Vol. 6 No. 1, 1989, pp. 28-42.

25. Martinsons, M.G., "Knowledge-based Scheduling: Development Using a Shell", special presentation at the Australian AI '90 conference (Management programme), November, Perth, 1990.

*T TABLE 1. BASIC INFORMATION FOR STARTING THE TIMETABLING PROCESS

CLASSROOMS

* Designated name

* Size

* Proximity to other rooms

STUDY PROGRAMMES

* Name

* Description

* Constituent subjects

* Modes of attendance

SUBJECTS

* Names

* Descriptions

* Teaching pattern

* Number of students

LECTURERS

* Number of lectures

* Types of lectures

* Number of tutorials

* Types of tutorials

* Number of laboratories

Maris G. Martinsons is Senior Lecturer, Business and Management, City Polytechnic of Hong Kong and Fellow, Poon Kam Kai Institute of Management, University of Hong Kong. Kong Cheong Kwan is a Systems Analyst, Mass Transit Railway Corporation, Hong Kong.