A survey of practical applications of examination timetabling algorithms
Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
When is the classroom assignment problem hard?
Operations Research - Supplement
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Computers and Operations Research
Scheduling Classes on a College Campus
Computational Optimization and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Variable neighborhood search for the degree-constrained minimum spanning tree problem
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
A Constraint-Based Approach for Examination Timetabling Using Local Repair Techniques
PATAT '97 Selected papers from the Second International Conference on Practice and Theory of Automated Timetabling II
Examination Timetables and Tabu Search with Longer-Term Memory
PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
Tabu Search Techniques for Examination Timetabling
PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
Variable neighborhood search for the maximum clique
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Polynomial reduction of time-space scheduling to time scheduling
Discrete Applied Mathematics
Heuristics for the variable sized bin-packing problem
Computers and Operations Research
An informed genetic algorithm for the examination timetabling problem
Applied Soft Computing
INFORMS Journal on Computing
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In this paper, we investigate a compound of the exam timetabling problems which consists of assigning a set of independent exams to a certain number of classrooms. We can define the exam timetabling problem as the scheduling of exams to time slots in first stage and at a second stage, the assignment of a set of exams extracted from one time slot to some available classrooms. Even though the formulation of this problem looks simple as it contains only two sets of constraints including only binary variables, we show that it belongs to the class of NP hard problems by reduction from the Numerical Matching with Target Sum problems (NMTS). In order to reduce the size of this problem and make it efficiently solvable either by exact method or heuristic approaches, a theorem is rigorously demonstrated and a reduction procedure inspired from the dominance criterion is developed. The two methods contribute in the search for a feasible solution by reducing the size of the original problem without affecting the feasibility. Since the reduction procedures do not usually assign all exams to classrooms, we propose a Variable Neighbourhood Search (VNS) algorithm in order to obtain a good quality complete solution. The objective of VNS algorithm is to reduce the total classroom capacity assigned to exams. A numerical result concerning the exam of the main session of the first semester of the academic year 2009-2010 of the Faculty of Economics and Management Sciences of Sfax shows the good performance of our approach compared with lower bound defined as the sum of the total capacity of all assigned classrooms and the total size of the remaining exams after reduction.