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A Branchandcut Procedure for the Udine Course Timetabling Problem
 PROCEEDINGS OF THE 7TH PATAT CONFERENCE
, 2008
"... This paper describes a branchandcut procedure for an extension of the bounded colouring problem, generally known as curriculumbased university course timetabling. In particular, we focus on Udine Course Timetabling [di Gaspero and Schaerf, J. Math. Model. Algorithms 5:1], which has been used in ..."
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This paper describes a branchandcut procedure for an extension of the bounded colouring problem, generally known as curriculumbased university course timetabling. In particular, we focus on Udine Course Timetabling [di Gaspero and Schaerf, J. Math. Model. Algorithms 5:1], which has been used in Track 3 of the 2007 International Timetabling Competition. First, we present an alternative integer programming formulation for this problem, which uses a lower than usual number of variables and a mildlyincreased number of constraints (exponential in the number of periods per day). Second, we present the corresponding branchandcut procedure, where constraints from enumeration of event/freeperiod patterns, necessary to reach optimality, are added only when they are violated. We also describe further problemspecific cuts from bounds implied by the soft constraints, cuts from patterns given by days of instruction and free days, and all related separation routines. We also discuss applicability of standard cuts from graph colouring and weighted matching. The results of our preliminary experimentation with an implementation using ILOG Concert and CPLEX 10 are provided. Within 15 minutes, it is possible to find provably optimal solutions to two instances (comp01 and comp11) and good lower bounds for several other instances.
Decomposition, Reformulation, and Diving in University Course Timetabling
"... In many reallife optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of ..."
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In many reallife optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective/valuerestricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality.
The teaching space allocation problem with splitting
 Proceedings of the Sixth International Conference on the Practice and Theory of Automated Timetabling (PATAT
, 2006
"... Abstract. A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will ..."
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Cited by 8 (5 self)
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Abstract. A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will need to be broken up, or ‘split’, into multiple sections. A lecture might be too large to fit into any one room. Another common example is that of seminars or tutorials. Although hundreds of students may be enrolled on a course, it is often subdivided into particular types and sizes of events dependent on the pedagogic requirements of that particular course. Typically, decisions as to how to split courses need to be made within the context of limited space requirements. Institutions do not have an unlimited number of teaching rooms, and need to effectively use those that they do have. The efficiency of space usage is usually measured by the overall ‘utilisation ’ which is basically the fraction of the available seathours that are actually used. A multiobjective optimisation problem naturally arises; with a tradeoff between satisfying preferences on splitting, a desire to increase utilisation, and also to satisfy other constraints such as those based on event location and timetabling conflicts. In this paper, we explore such tradeoffs. The explorations themselves are based on a local search method that attempts to optimise the space utilisation by means of a ‘dynamic splitting ’ strategy. The local moves are designed to improve utilisation and satisfy the other constraints, but are also allowed to split, and unsplit, courses so as to simultaneously meet the splitting objectives. 1
A supernodal formulation of vertex colouring with applications in course timetabling
, 2009
"... For many problems in Scheduling and Timetabling the choice of an mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using ..."
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Cited by 6 (2 self)
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For many problems in Scheduling and Timetabling the choice of an mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using “supernodes”. In the definition of George and McIntyre [SIAM J. Numer. Anal. 15 (1978), no. 1, 90–112], “supernode” is a complete subgraph, where each two vertices have the same neighbourhood outside of the subgraph. Seen another way, the algorithm for obtaining the best possible partition of an arbitrary graph into supernodes, which we give and show to be polynomialtime, makes it possible to use any formulation of vertex multicolouring to encode vertex colouring. The power of this approach is shown on the benchmark problem of Udine Course Timetabling. Results from empirical tests on DIMACS colouring instances, in addition to instances from other timetabling applications, are also provided and discussed.
Threshold Effects in the Teaching Space Allocation Problem with Splitting
, 2008
"... Universities aim for good “Space Management ” so as to use the teaching space efficiently. Part of this task is to assign rooms and timeslots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require s ..."
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Cited by 4 (3 self)
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Universities aim for good “Space Management ” so as to use the teaching space efficiently. Part of this task is to assign rooms and timeslots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require splitting into multiple events. For example, lectures can be too large to fit in one room or good teaching practice requires that seminars/tutorials are taught in small groups. Then, space management involves decisions on splitting as well as the assignments to rooms and timeslots. These decisions must be made whilst satisfying the pedagogic requirements of the institution and constraints on space resources. The efficiency of such management can be measured by the “utilisation”: the percentage of available seathours actually used. In many institutions, the observed utilisation is unacceptably low, and this provides our underlying motivation: to study the factors that affect teaching space utilisation, with the goal of improving it. We give a brief introduction to our work in this area, and then introduce a specific model for splitting. We present experimental results that show threshold phenomena and associated easyhardeasy patterns of computational difficulty. We discuss why such behaviour is of importance for space management. Contact Author. 1 1
Improving the RoomSize Profiles of University Teaching Space
, 2007
"... The utilisation of University teaching space is notoriously low: rooms are often unused, or only half full. We expect that one of the reasons for this is overall mismatch the sizes of rooms and the sizes events. For example, there might be an excess of large rooms. Good space planning should match t ..."
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Cited by 3 (2 self)
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The utilisation of University teaching space is notoriously low: rooms are often unused, or only half full. We expect that one of the reasons for this is overall mismatch the sizes of rooms and the sizes events. For example, there might be an excess of large rooms. Good space planning should match the set of rooms to the set of events whilst taking account of the pedagogic requirements of the institution. We give methods to visualise and demonstrate the mismatch between the event and roomsize profiles. We then provide methods to generate better room profiles. In particular, a method to produce robust room profiles. The method is based on scenariobased ideas of stochastic programming. We give evidence that such robust room profiles allow the reliable achievement of higher levels of utilisation. 1
Recent Work on Planning and Management of University Teaching Space
"... Universities have to invest considerable financial and human resources in the provision of space for teaching activities such as lectures, seminars, tutorials and workshops. Naturally, they would like such investments to be made wisely and efficiently. However, there is considerable evidence that in ..."
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Universities have to invest considerable financial and human resources in the provision of space for teaching activities such as lectures, seminars, tutorials and workshops. Naturally, they would like such investments to be made wisely and efficiently. However, there is considerable evidence that in many Universities the resulting space is considerably underused. In a report by the Higher Education Funding Council for England (HEFCE), roughly speaking, it was found that often space was only used half the time, and then only half filled [9]. At least on the face of it this seems like an inefficient use of resources; it is natural to expect or hope that better planning for the space capacity would improve this. However, a fundamental problem has been that there was no real foundation for deciding whether or not such usage levels are in fact an inevitable result of meeting the timetabling and teaching resources, or alternatively, to provide methods to improve the situation. In this abstract we briefly overview our work towards remedying this situation. Here, we cannot hope to cover all work in the topic; instead the aim is to discuss our various strands of research and how they are woven together. The space planning process needs to decide upon what space resources need to be provided
Clustering Within Timetabling Conflict Graphs
"... A key concept in timetabling problems is that of the conflict graph with edges representing pairs of events that are not allowed to occur at the same time. Usually, the only information presented about such graphs is their density. However, intuitively, it seems likely that such graphs are structure ..."
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A key concept in timetabling problems is that of the conflict graph with edges representing pairs of events that are not allowed to occur at the same time. Usually, the only information presented about such graphs is their density. However, intuitively, it seems likely that such graphs are structured, and likely to have some clustering. In analysing the structure of social networks or of the worldwide web it is common to use various measures. Amongst these is the “clustering coefficient”. We propose using this coefficient to analyse timetabling conflict graphs, and give results showing that on some common benchmarks the graphs are indeed clustered by this measure. 1