Search results for: timetabling

Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem (UETP)

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Authors: Nur Aidya Hanum Aizam, Vikneswary Uvaraja

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The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming model to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describe about creating a general model which solve different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling

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Authors: Nurul Liyana Abdul Aziz, Nur Aidya Hanum Aizam

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Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.

Keywords: university course timetabling problem, integer programming, preferences, constraints

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Authors: Huazhen Lin, Ruihua Xu, Zhibin Jiang

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In this real-world case, timetabling the LRT network as a whole is rather challenging for the operator: they are supposed to create a timetable to avoid various route conflicts manually while satisfying a given interval and the number of rolling stocks, but the outcome is not satisfying. Therefore, the operator adopts a computerised timetabling tool, the Train Plan Maker (TPM), to cope with this problem. However, with various constraints in the dual-line network, it is still difficult to find an adequate pairing of turnback time, interval and rolling stocks’ number, which requires extra manual intervention. Aiming at current problems, a one-off model for timetabling is presented in this paper to simplify the procedure of timetabling. Before the timetabling procedure starts, this paper presents how the dual-line system with a ring and several branches is turned into a simpler structure. Then, a non-linear programming model is presented in two stages. In the first stage, the model sets a series of constraints aiming to calculate a proper timing for coordinating two lines by adjusting the turnback time at termini. Then, based on the result of the first stage, the model introduces a series of inequality constraints to avoid various route conflicts. With this model, an analysis is conducted to reveal the relation between the ratio of trains in different directions and the possible minimum interval, observing that the more imbalance the ratio is, the less possible to provide frequent service under such strict constraints.

Keywords: light rail transit (LRT), non-linear programming, railway timetabling, timetable coordination

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Authors: Gianpaolo Ghiani, Emanuela Guerriero, Emanuele Manni, Alessandro Romano

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In this article, we deal with a variant of the classical course timetabling problem that has a practical application in many areas of education. In particular, in this paper we are interested in high schools remedial courses. The purpose of such courses is to provide under-prepared students with the skills necessary to succeed in their studies. In particular, a student might be under prepared in an entire course, or only in a part of it. The limited availability of funds, as well as the limited amount of time and teachers at disposal, often requires schools to choose which courses and/or which teaching units to activate. Thus, schools need to model the training offer and the related timetabling, with the goal of ensuring the highest possible teaching quality, by meeting the above-mentioned financial, time and resources constraints. Moreover, there are some prerequisites between the teaching units that must be satisfied. We first present a Mixed-Integer Programming (MIP) model to solve this problem to optimality. However, the presence of many peculiar constraints contributes inevitably in increasing the complexity of the mathematical model. Thus, solving it through a general purpose solver may be performed for small instances only, while solving real-life-sized instances of such model requires specific techniques or heuristic approaches. For this purpose, we also propose a heuristic approach, in which we make use of a fast constructive procedure to obtain a feasible solution. To assess our exact and heuristic approaches we perform extensive computational results on both real-life instances (obtained from a high school in Lecce, Italy) and randomly generated instances. Our tests show that the MIP model is never solved to optimality, with an average optimality gap of 57%. On the other hand, the heuristic algorithm is much faster (in about the 50% of the considered instances it converges in approximately half of the time limit) and in many cases allows achieving an improvement on the objective function value obtained by the MIP model. Such an improvement ranges between 18% and 66%.

Keywords: heuristic, MIP model, remedial course, school, timetabling

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Authors: Marcel Schneider, Nils Nießen

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Microscopic simulation programs enable the description of the two processes of railway operation and the previous timetabling. Occupation conflicts are often solved based on defined train priorities on both process levels. These conflict resolutions produce knock-on delays for the involved trains. The sum of knock-on delays is commonly used to evaluate the quality of railway operations. It is either compared to an acceptable level-of-service or the delays are evaluated economically by linearly monetary functions. It is impossible to properly evaluate dispatching decisions without a well-founded objective function. This paper presents a new approach for evaluation of dispatching decisions. It uses models of choice of transport and considers the behaviour of the end-costumers. These models evaluate the knock-on delays in more detail than linearly monetary functions and consider other competing modes of transport. The new approach pursues the coupling of a microscopic model of railway operation with the macroscopic model of choice of transport. First it will be implemented for the railway operations process, but it can also be used for timetabling. The evaluation considers the possibility to change over to other transport modes by the end-costumers. The new approach first looks at the rail-mounted and road transport, but it can also be extended to air transport. The split of the end-costumers is described by the modal-split. The reactions by the end-costumers have an effect on the revenues of the railway undertakings. Various travel purposes has different pavement reserves and tolerances towards delays. Longer journey times affect besides revenue changes also additional costs. The costs depend either on time or track and arise from circulation of workers and vehicles. Only the variable values are summarised in the contribution margin, which is the base for the monetary evaluation of the delays. The contribution margin is calculated for different resolution decisions of the same conflict. The conflict resolution is improved until the monetary loss becomes minimised. The iterative process therefore determines an optimum conflict resolution by observing the change of the contribution margin. Furthermore, a monetary value of each dispatching decision can also be determined.

Keywords: choice of transport, knock-on delays, monetary evaluation, railway operations

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Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: Yuzhen Hu, Sirui Wang

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As a training base for intellectual talents, universities have a large number of students. Teaching is a primary activity in universities, and during the teaching process, a large number of people gather both inside and outside the teaching buildings, posing a strong risk of close contact. The class schedule is the fundamental basis for teaching activities in universities and plays a crucial role in the management of teaching order. Different class schedules can lead to varying degrees of indoor gatherings and trajectories of class attendees. In recent years, highly contagious diseases have frequently occurred worldwide, and how to reduce the risk of infection has always been a hot issue related to public safety. "Reducing gatherings" is one of the core measures in epidemic prevention and control, and it can be controlled through scientific scheduling in specific environments. Therefore, the scientific prevention and control goal can be achieved by considering the reduction of the risk of excessive gathering of people during the course schedule arrangement. Firstly, we address the issue of personnel gathering in various pathways on campus, with the goal of minimizing congestion and maximizing teaching effectiveness, establishing a nonlinear mathematical model. Next, we design an improved genetic algorithm, incorporating real-time evacuation operations based on tracking search and multidimensional positive gradient cross-mutation operations, considering the characteristics of outdoor crowd evacuation. Finally, we apply undergraduate course data from a university in Harbin to conduct a case study. It compares and analyzes the effects of algorithm improvement and optimization of gathering situations and explores the impact of path blocking on the degree of gathering of individuals on other pathways.

Keywords: the university timetabling problem, risk prevention, genetic algorithm, risk control

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Authors: Nahid Parween Anwar, Sadia Muzaffar Bhutta, Takbir Ali

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Mentoring is a structured activity which is designed to facilitate engagement between mentor and mentee to enhance mentee’s professional capability as an effective teacher. Both mentor and mentee are important elements of the ‘mentoring equation’ and play important roles in nourishing this dynamic, collaborative and reciprocal relationship. Cluster-Based Mentoring Programme (CBMP) provides an indigenous example of a project which focused on development of primary school teachers in selected clusters with a particular focus on their classroom practice. A study was designed to examine the efficacy of CBMP as part of Strengthening Teacher Education in Pakistan (STEP) project. This paper presents results of one of the components of this study. As part of the larger study, a cross-sectional survey was employed to explore nature and patterns of mentoring process from mentees’ perspectives in the selected districts of Sindh and Balochistan. This paper focuses on the results of the study related to the question: What are mentees’ perceptions of their mentors’ support for enhancing their classroom practice during mentoring process? Data were collected from mentees (n=1148) using a 5-point scale -‘Mentoring for Effective Primary Teaching’ (MEPT). MEPT focuses on seven factors of mentoring: personal attributes, pedagogical knowledge, modelling, feedback, system requirement, development and use of material, and gender equality. Data were analysed using SPSS 20. Mentees perceptions of mentoring practice of their mentors were summarized using mean and standard deviation. Results showed that mean scale scores on mentees’ perceptions of their mentors’ practices fell between 3.58 (system requirement) and 4.55 (personal attributes). Mentees’ perceives personal attribute of the mentor as the most significant factor (M=4.55) towards streamlining mentoring process by building good relationship between mentor and mentees. Furthermore, mentees have shared positive views about their mentors efforts towards promoting gender impartiality (M=4.54) during workshop and follow up visit. Contrary to this, mentees felt that more could have been done by their mentors in sharing knowledge about system requirement (e.g. school policies, national curriculum). Furthermore, some of the aspects in high scoring factors were highlighted by the mentees as areas for further improvement (e.g. assistance in timetabling, written feedback, encouragement to develop learning corners). Mentees’ perceptions of their mentors’ practices may assist in determining mentoring needs. The results may prove useful for the professional development programme for the mentors and mentees for specific mentoring programme in order to enhance practices in primary classrooms in Pakistan. Results would contribute into the body of much-needed knowledge from developing context.

Keywords: cluster-based mentoring programme, mentoring for effective primary teaching (MEPT), professional development, survey

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Authors: Anum Rafiq

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Adolescence is a vulnerable period for youth across the world. It is a period of new learning with opportunities to understand and develop perspectives on health and well-being. With youth beginning to engage in intimate relationships at an earlier age in the 21st century, concentrating on the learning opportunity they have in school is paramount. The nature of what has been deemed important to teach in schools has changed throughout history, and the focus has shifted from home/family skills to teaching youth how to be competitive in the job market. Amidst this emphasis, opportunities for them exist to learn about building healthy intimate relationships, one of the foundational elements of most people’s lives. Using an Institutional Ethnography (IE), the lived experiences of youth in how they understand intimate relationships and how their learning experience is organized through the high school Health and Physical Education (H&PE) course is explored. An empirical inquiry into how the actual work of teachers and youth are socially organized by a biomedical, employment-related, and efficiency-based discourse is provided. Through thirty-two qualitative interviews with teachers and youth, a control of ruling relations such as institutional accountability circuits, performance reports, and timetabling over the experience of teachers and youth is found. One of the facets of the institutional accountability circuit is through the social organization of teaching and learning about healthy intimate relationships being framed through a biomedical discourse. In addition, the role of a hyper-focus on performance and evaluation is found as paramount in situating healthy intimacy discussions as inferior to neoliberally charged productivity measures such as employment skills. Lastly, due to the nature of institutional policies such as regulatory guidelines, teachers are largely influenced to avoid diving into discussions deemed risky or taboo by society, such as healthy intimacy in adolescence. The findings show how texts such as the H&PE curriculum, the Ontario College of Teachers (OCT) guidelines, Ministry of Education Performance Reports, and the timetable organize the day-to-day activities of teachers and students and reproduce different disjunctures for youth. This disjuncture includes some of their experiences being subordinated, difficulty relating to curriculum, and an experience of healthy living discussions being skimmed over across sites. The findings detail that the experience of youth in learning about healthy intimate relationships is not akin to the espoused vision outlined in policy documents such as the H&PE (2015) curriculum policy. These findings have implications for policymakers, activists, and school administration alike, which call for an investigation into who is in power when it comes to youth’s learning needs, as a pivotal period where youth can be equipped with life-changing knowledge is largely underutilized. A restructuring of existing institutional practices that allow for the social and institutional flexibility required to broach the topic of healthy intimacy in a comprehensive manner is required.

Keywords: health policy, intimate relationships, youth, education, ruling relations, sexual education, violence prevention

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