Solving the Viva Presentations Timetabling Problem

G7 - 4

2011 International Conference on Electrical Engineering and Informatics 17-19 July 2011, Bandung, Indonesia

Solving the Viva Presentations Timetabling Problem: A case study at FTSM-UKM Masri Ayob, Ghaith M. Jaradat, Abdul Razak Hamdan, Hafiz Mohd Sarim and Mohd Zakree Ahmad Nazri Data Mining and Optimization Research Group, Centre of Artificial Intelligence Technology, Universiti Kebangsaan Malaysia, Faculty of Information Science and Technology, 43600 UKM Bangi, Selangor, Malaysia [email protected],[email protected],[email protected],[email protected],[email protected]

Abstract— There is a growing need to automatically timetable viva presentations for postgraduate candidates due to the increasing number of students enrolled each year, and hence, requiring additional personnel effort. The automatic timetabling process involves the assignment of the people involved in the viva timetable into a limited number of timeslots and rooms. In order to produce a feasible timetable, we must satisfy some regulations (hard constraints), while attempting to accommodate as much as possible some preferences (soft constraints). In this work, we tackle the problem of scheduling viva presentations for the Masters degree students at FTSM-UKM as a case study. Each presentation must be attended by a chair of the school (or representative), a chair of the viva presentation, a technical committee member, a student (presenter), an internal examiner and supervisor(s). The presentation must be scheduled into a room and timeslot. In this work, we propose a new objective function to model the problem and to evaluate the quality of the timetable (schedule). We also introduce a greedy constructive heuristic to construct a valid timetable that satisfies all of the hard constraints and tries to satisfy the soft constraints as much as possible. The heuristic will assign the committee and students into an empty timetable based on a pre-ordered list of prioritized elements. These elements are ordered based on the largest enrolment: specifically a technical person who has the largest number of students enrolled under his/her supervision and examination will be ordered first in the list and is first to be assigned into the timetable. Results show that the automated timetabling solver can efficiently produce good quality timetable in reasonable time. Keywords— Viva presentation timetabling problem, greedy constructive heuristic.

I. INTRODUCTION Generating timetables for courses or other academic events are one of the most challenging problems in educational institutions [1]. Timetabling problems are difficult tasks that deal with the allocation of limited resources to tasks over time [2]. Wren [3] defined timetabling as: “The allocation, subject to constraints, of given resources to object being placed in

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space time, in such a way as to satisfy, as nearly as possible, a set of desired objectives. “ At the Faculty of Information Science and Technology (FTSM) of Universiti Kebangsaan Malaysia (UKM), the viva presentations timetable is produced manually. Scheduling a timetable for viva presentations for the Masters degree at FTSM is a time consuming process. Nowadays, automated schedulers are usually employed to produce high quality timetables [4]. Furthermore, automation also allows a variety of constraints, which were not possible with the manual scheduling, to be taken into account [4]. Recently, some optimization methods (aka metaheuristics) have been applied to tackle timetabling problems. Examples are: scatter search hyper-heuristic for solving examination timetabling problem [5]; hybrid heuristic with variable neighbourhood descent search [6] and greedy constructive heuristic with local search routines [7, 8] for solving nurse rostering problems; Genetic Algorithm for solving personnel timetabling [9] and for solving a constrained employee scheduling problem [10]. In this work, we focus on the viva presentations timetabling problem for the Masters degree candidates at FTSM-UKM for the year 2011. This work mainly aims at producing an effective and efficient automated scheduler to solve the viva presentations timetabling problem. Hence, we proposed a greedy constructive heuristic to produce a feasible viva presentations timetable, where the process of scheduling elements of a timetable is based on the largest enrolment ordering. In order to measure the quality of timetable, we introduce a new objective function. II. PROBLEM DESCRIPTION Generally, the viva presentations timetabling problem involves assigning a set of people involved in the viva timetable (e.g. students, examiners committee and technical committee) into a limited number of timeslots and rooms in a session, while satisfying some constraints. This is a new timetabling problem. A viva, or viva voce, is an oral examination where postgraduate students are required to present and defend their thesis/research work. In order to produce a feasible timetable, we must satisfy some regulations (hard constraints), while attempting to accommodate as much as possible some preferences (soft

constraints). As an example of hard constraints: we cannot assign the same examiner to more than one presentation or rooms at the same timeslot. An example of soft constraint is the preference of a technical person to be assigned into the same room throughout the whole session(s), which means consecutive assignments. We formulate the problem as follows: A set of N events (consists of a student, supervisors and an examiner, where N=89 in our case study); a set of M technical committee members (where M=18); a set of C Chair of school (where C=2); and a set of P chair of the viva presentation (where P=16) need to be scheduled into 5 working days for the whole session of 3 rooms (R) and 6 timeslots each day, where T=30 timeslots. Each day includes two sessions (morning and evening), each session has 3 timeslots. Students/technical committee members are divided into two groups corresponding to two schools, namely the School of Computer Science (PPSK) and the School of Information Technology (PPTM), where PPSK holds 68 students with 9 technical committee, whilst PPTM holds 21 students with 9 technical committee. There are two types of constraints: hard and soft. In order to produce a feasible timetable, all hard constraints must be satisfied, whereas the violation of the soft constraints must be minimized in order to produce a good quality timetable. Each violation of soft constraints will incur a penalty cost, where lower penalty values indicate good quality solution. A feasible timetable is one in which all people involved in the timetable have been assigned to timeslots and rooms, and all hard constraints are satisfied. The hard constraints for this problem are: H1: No presentation is scheduled into the timetable more than once; H2: No chair of the viva presentation or chair of school or technical committee member or examiner attends more than one presentation at the same time; H3: For each presentation; examiner, technical committee member, supervisor and chair of viva must be independent from each other (different personnel); H4: No chair of school or technical committee member of a certain school attends a presentation of another school; H5: Only a technical committee member is allowed to represent the chair of school. Then, we measure the quality of timetable (i.e. the objective function) by penalising equally each violation of the following soft constraint (i.e. penalty cost=1 for each violation). The soft constraints for the problem are: S1: A chair of the viva presentation should be assigned to the same room for the whole session (consecutive three assignments); S2: A technical committee should be assigned to the same room for the whole session (consecutive three assignments); S3: If an examiner or supervisor has to attend many viva presentations, he should have consecutive assignments

(and in the same room if it happen in the same session); S4: A chair of the viva presentation or chair of School or technical committee should not attend other presentation while her student is having a viva presentation at the same time; The value of the objective function of a timetable is simply calculated as the summation of the soft constraints violations. The hard constraints must be satisfied. Table I shows an example of a feasible viva presentations timetable (partial timetable). The presented timetable in Table I is a small part of the complete timetable, showing only the assignments for half a day. TABLE I AN EXAMPLE OF FEASIBLE VIVA PRESENTATIONS TIMETABLE

Student: Examiners: Chair of viva: Chair of school: Supervisor: Tech. committee: Student: Examiners: Chair of viva: Chair of school: Supervisor: Tech. committee: Student: Examiners: Chair of viva: Chair of school: Supervisor: Tech. committee:

DAY 1 – Morning Session (9:00-12:00) Room 1 Room 2 Room 3 P49106 P45086 P50135 SZ SMA NMA ARH AA SAN SA RS SS RH JS ZMY ZMY DSS SS P50202 P50082 P53698 AP NO MA ARH AA KO OAP RS AZ RH SAN SA ZMY DSS AZ P54421 P50164 P47969 MM MA SA ARH AA AMZ SA RS ZMA MJA NO AAB ZMY DSS ZMA

From the Table I, we can see that there are no hard constraints violations. This means, this timetable is feasible (number of hard constraint violations = 0), whilst the number of soft constraint violations occurred in this timetable is equal to 4 violations. This is calculated as follows (summation of all penalties): a) Room 3: Violation of S1 (3 different chair of viva were assigned into this room for the same session). Penalty=1; b) Room 3: Violation of S2 (3 different technical committees were assigned into this room for the same session). Penalty=1; c) Room 3 (2nd timeslot) and room 2 (3rd timeslot): Violation of S3 (the examiner ‘MA’ was assigned into different room for consecutive timeslot). Penalty=1; d) Room 1 (1st timeslot) and room 3 (1st timeslot): Violation of S4 (a technical committee ‘ZMY’ was assigned as a technical committee in room 1 while his student having viva presentation at the same timeslot in room 3). Penalty=1. III. CONSTRUCTIVE HEURISTIC In this work, we use the Greedy Constructive Heuristic based on the Largest enrolment degree first heuristic ordering

(descending ordering) to construct a viva presentations timetable. In which technical committee or chairs of viva or examiners or supervisors who have larger number of students enrolment (under his supervision or examination) involve in viva presentation have higher priority to be scheduled first into the timetable. That is, we scheduled the most difficult personnel (to be scheduled) first. Fig. 1 shows the pseudo code of our greedy constructive heuristic. The greedy constructive heuristic starts with an empty timetable. Given for lists (Step1), L1A and L1B (sorted list of viva presentation which include students, supervisors and internal examiner for PPSK or PPTM students, accordingly), L2 (a sorted list of technical committee) and L3 (a list of viva chair), we begin (Step2) by sequentially assign all the viva presentation into conflict free timeslots and rooms. That is, this assignment is considered feasible/valid only when there is no conflict among personnel involved in the schedule (examiners and supervisors) and all the viva presentations are scheduled. In order to have better quality timetable, we try as much as possible to assign viva presentations of the same school into consecutive timeslots in the same session (by trying not to mix presentations between different schools in the same room at the same session). L1A and L1B are sorted based on the personnel (examiners/supervisors) that have larger number of student enrolment (under his supervision or examination) in descending order. That is, the presentation which has examiners or supervisors who need to attend many viva presentations will have higher priority to be scheduled first. Since L1A and L1B is sorted based on personnel that have larger number of student enrolment (in descending order), this may produce a good quality timetable because, those personnel who need to involve in many viva presentations will have better assignment (that will affect the quality of timetable). Whereas, those who have few assignments (only need to attend a few viva presentations or perhaps just one), their assignment is not crucial in that it will not really affect the quality of timetable. Next (Step 3), we will assign a conflict free technical committee member, together with a conflict free chair of viva and chair of school, starting from the first session and room. A conflict free technical committee member and chair of viva that has smaller counter values (i.e. techCount or chairCount, accordingly) will be randomly selected to be scheduled first. We use two counters (techCount and chairCount) to keep track the number of assignment for each personnel in order to give fair assignment as much as possible. During this step, we will try to assign the whole timeslots for each session and room to only one conflict free technical committee, one conflict free chair of viva and one chair of school. That is, we try to maintain the same personnel in the same room for all timeslots in the same session (minimize personnel moving between room).

Step1: Initialize candidate lists L1A,L1B,L2,L3; Step2: For i:= 1 to N Select a presentation from L1, presentation*; Sequentially assign presentation* into a conflict free timeslot and room; Remove presentation* from L1; End For Rectify and verify hard violations (H1); Step3: For j:= 1 to M //for each viva session Step3.1: For v:= 1 to P //for each room Step3.2: Radomly select a conflict free technical committee (that has the least number of assignment, techCount and largest number of enrolment) from L2; Step3.3: If there is no conflict free technical committee skip to Step 3.5 Step3.4: Assign technical* and chair of school into the vth room in the jth session; Increase techCount accordingly; Step3.5: Randomly select a conflict free chair of viva (that has the least number of assignment, chairCount) from L3 (chairViva*); Step3.6: If there is no conflict free chair of viva, skip to Step 3.2. Step3.7: Assign chairViva* into the vth room in the jth session. Increase chairCount accordingly; End For End For Step4: While there exist viva presentation that has not complete (no technical committee and/or chair of school and/or chair of viva): Assign conflict free personnel(technical committee and/or chair of school and/or chair of viva, accordingly) by selecting those who has less assignment. If there is no conflict personnel, return an infeasible timetable. Increase techCount or chairCount, accordingly; End While; Step5: Rectify and verify hard constraint violations (H2, H3, H4 and H5); Step6: Calculate the quality of timetable. Return a complete feasible/infeasible viva presentations timetable;

Note:

L1A is a sorted list of viva presentation for PPSK; L1B is a sorted list of viva presentation for PPTM; L2 is a sorted list of technical committee; L3 is a list of viva chair; N is a number of viva presentations to be scheduled; M is a number of viva sessions; P is a number of rooms used for the viva; Fig. 1 A pseudo code of our greedy constructive heuristic

However, if there still exists viva presentations that have incomplete assignments (e.g. no technical committee and/or chair of school and/or chair of viva), we will select and assign a conflict free personnel (e.g. technical committee and/or chair of school and/or chair of viva, accordingly) by randomly selecting those who have fewer assignment first (Step 4). If

there is no a conflict free personnel, the algorithm will terminate with infeasible timetable. Step4 is performed only when we fail to find conflict free personnel to be allocated to whole timeslots for each session and room. Once completed, the algorithm will verify and rectify the timetable to check for any violation of hard constraints. We also calculate the quality of timetable. If there is any violation of hard constraint that cannot be fixed, we will end with an infeasible timetable. Otherwise, the algorithm returns a feasible timetable.

quality of the generated timetable. There is no specific tool to measure the quality of timetable. Thus, this work helps the decision maker (administrator) to decide which timetable is the best among the generated table. In short, the automated scheduling saves the time and effort of the administrator involved in the scheduling process. V. CONCLUSIONS We have introduced a new timetabling problem (viva presentations) and a greedy constructive heuristic. Our heuristic constructs a viva timetable based on the largest enrolment ordering. In order to evaluate the quality of timetable, we also introduced an objective function that penalises each violation of soft constraints. Our heuristic managed to produce a feasible timetable within few seconds. In our future work, we will investigate the capability of improvement heuristics for further enhancement of the quality of the timetable.

IV. EXPERIMENTS AND RESULTS In this work, we tested our constructive heuristic on the data of Masters degree viva presentations at the FTSM-UKM as a case study for the year 2011. We ran our constructive heuristic 20 times on Intel Pentium Core2 Duo 2.16 GHz processor, 2GB RAM, and implemented in Java NetBeans IDE v 6.9. Our heuristic is able to produce 17 feasible timetables out of 20 runs. Table II shows the results of 20 runs. ACKNOWLEDGMENT In this experiment, the best obtained solution has penalty=16 (that is, it violated 16 soft constraints). Smaller penalty value The authors wish to thank Ministry of Higher Education indicates higher quality solutions. The computational time (Malaysia) for supporting this work under the Fundamental taken in producing a timetable was a few seconds for each run Research Grant Scheme (FRGS) no. (UKM- TT - 02 – FRGS (i.e. 2.24 seconds in average). 0121 – 2009) and the Faculty of Information Science and Technology. TABLE II COMPUTATIONAL READINGS OF OUR GREEDY CONSTRUCTIVE HEURISTIC

Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Avg. Std. Best Worst

Quality of timetable 20 21 38 17 22 19 29 16 32 34 24 18 23 25 36 20 18 16 24 21 23.65 6.714 16 38

Feasibility of timetable Yes Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No -

Time (sec.) 1.6 2.0 2.0 2.0 2.4 1.6 2.6 2.5 1.1 1.6 1.4 3.6 1.7 2.3 2.1 4.3 4.0 1.4 3.1 1.4 2.24 -

In contrast to the manual scheduling process, this timetable has been produced in a matter of seconds by our greedy constructive heuristic. Whereas, the human scheduler usually takes several days (depending on the size of data, i.e. how many viva presentations that need to be scheduled) to construct the timetable. Therefore, due to human ability and time constraint, she usually produce only one timetable for each exercise. Indeed, she do not has any idea about the

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