Efthymios Housos

An integer programming formulation for a case study in university timetabling

A novel 0–1 integer programming formulation of the university timetabling problem is presented. The model provides constraints for a great number of operational rules and requirements found in most academic institutions. Treated as an optimization problem, the objective is to minimize a linear cost function. With this objective, it is possible to consider the satisfaction of expressed preferences regarding teaching periods or days of the week or even classrooms for specified courses. Moreover, with suitable definition of the cost coefficients in the objective function it is possible to reduce the solution space and make the problem tractable. The model is solvable by existing software tools with IP solvers, even for large departments. The case of a five-year Engineering Department with a large number of courses and teachers is presented along with its solution as resulted from the presented IP formulation. � 2003 Elsevier B.V. All rights reserved.

Hybrid optimization techniques for the workshift and rest assignment of nursing personnel

In this paper, a detailed model and an efficient solution methodology for the monthly workshift and rest assignment of hospital nursing personnel is presented. A model that satisfies the rules of a typical hospital environment based both on published research data and on local hospital requirements is designed. A hybrid methodology that utilizes the strengths of operations research and artificial intelligence was used for the solution of the problem. In particular, an approximate integer linear programming (ILP) model is firstly solved and its solution is further improved using local search techniques. Finally, a tabu search strategy that uses as its neighborhood the solution space that the local heuristics define is presented. The use of heuristics is required because one of the main user requirements involving the user preference for specific workstretch patterns is not, for efficiency reasons, explicitly modeled in the ILP. In addition, for comparison and evaluation purposes the CLP based ILOG solver is also used to solve the same problem. The inferior computational results obtained with the ILOG solver do verify the speed and efficiency of the hybrid solution approach suggested in this paper. Extensive computational results are presented together with a detailed discussion on the quality, the computational efficiency and the operational acceptability of the solutions.

Crew Pairing Optimization

Next to fuel costs, crew costs are the largest direct operating cost of airlines. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is usually considered as two problems: the crew pairing problem and the crew assignment (rostering) problem. These problems are solved sequentially. In this paper we focus on the pairing problem. The aim of the paper is twofold. First, we give an overview of the crew pairing problem and synthesize the optimization methods that have been published previously. Second, we present the Carmen pairing construction system which is in operation at most major European airlines. Our purpose is to identify the particular properties of the Carmen system that have made this system the preferred decision support system for crew pairing optimization in Europe.

Constraint programming approach for school timetabling

Abstract In this paper, the timetabling problem for a typical high school environment was modeled and solved using a constraint programming (CP) approach. In addition, operations research (OR) models and local search techniques were also used in order to assist the CP search process by effectively reducing the solution search space. Relaxed models that can be solved using minimum cost matching algorithms were used in order to calculate problem lower bounds at various instances of the solution process. These bounds were in turn used to prioritize the search options of the CP process. The use of minimum cost matching model in the search process is an economical and efficient mechanism for the creation of effective search strategies and it is a competitive manner of introducing problem domain information in the CP environment. By including in the solution process a sequence of local search steps, the solution quality was further improved. Several large problems were solved and actual computational results for specific problem instances are presented. Scope and purpose There exist various school timetabling problems depending on the environment and the characteristics of the particular school level [1] . In this paper the high school situation in which the teachers teach in several different class sections during the day and the students remain in their classrooms is modeled and solved. The objective function attempts to minimize the idle hours between the daily teaching responsibilities of all the teachers while also attempting to satisfy their requests for early or late shift assignments. The school timetabling problem is combinatorial and there are several strict organizational and sequence-related rules that must be respected. The problem specifications used in this paper, although they closely describe the situation of a typical Greek high school, are quite general and abstract, which makes the findings of this paper applicable to wider set of school timetabling problems. The specifications mainly focus on the fact that each teacher is scheduled to lecture for a given number of hours at a fixed subset of class sections and the requirement that all the class sections must be always in session without any empty periods in their daily schedules. The integration of constraint programming and operations research techniques for the solution of this problem is one of the main contributions of this paper. The solutions obtained fully utilized the data management and organizational capabilities of the constraint programming approach while being assisted in the search path selection process by techniques and algorithms form the operations research pool of knowledge. The additional information provided by the calculation of efficient lower bounds and the subproblem domain definition and solution strategy presented in this paper, further assists the CP process in selecting promising search paths.

A systematic two phase approach for the nurse rostering problem

Nurse rostering is an NP-hard combinatorial problem which makes it extremely difficult to efficiently solve real life problems due to their size and complexity. Usually real problem instances have complicated work rules related to safety and quality of service issues in addition to rules about quality of life of the personnel. For the aforementioned reasons computer supported scheduling and rescheduling for the particular problem is indispensable. The specifications of the problem addressed were defined by the First International Nurse Rostering Competition (INRC2010) sponsored by the leading conference in the Automated Timetabling domain, PATAT-2010. Since the competition imposed quality and time constraint requirements, the problem instances were partitioned into sub-problems of manageable computational size and were then solved sequentially using Integer Mathematical Programming. A two phase strategy was implemented where in the first phase the workload for each nurse and for each day of the week was decided while in the second phase the specific daily shifts were assigned. In addition, local optimization techniques for searching across combinations of nurses’ partial schedules were also applied. This sequence is repeated several times depending on the available computational time. The results of our approach and the submitted software produced excellent solutions for both the known and the hidden problem instances, which in respect gave our team the first position in all tracks of the INRC-2010 competition.

An improved multi-staged algorithmic process for the solution of the examination timetabling problem

The efficient creation of examination timetables is a recurring and important problem for universities worldwide. Good timetables typically are characterized by balanced distances between consecutive exams for all students. In this contribution an approach for the examination timetabling problem as defined in the second International Timetabling Competition (http://www.cs.qub.ac.uk/itc2007/) is presented. The solution approach is managed on the top level by GRASP (Greedy Randomized Adaptive Search Procedure) and it involves several optimization algorithms, heuristics and metaheuristics. A construction phase is executed first producing a relatively high quality feasible solution and an improvement phase follows that further ameliorates the produced timetable. Each phase consists of stages that are consumed in a circular fashion. The procedure produces feasible solutions for each dataset provided under the runtime limit imposed by the rules of the ITC07 competition. Results are presented and analyzed.

Combined bus and driver scheduling

The daily bus and driver scheduling, for all bus companies that operate a non-fixed daily schedule of legs, is a difficult combinatorial problem that must be solved every afternoon. The work of the next day is changing on a daily basis either due to different load requirements on the standard routes or due to additional services and trips that the busses need to perform and the bus companies do wait until late afternoon before solving the scheduling problem. In addition, there exist hard customer requirements on the time required for the solution of the problem. This paper firstly presents a quick heuristic scheduling procedure named QS for the solution of the problem. QS has worked very well in the production environment of several bus companies of Greece. The main algorithms used by QS are minimum cost matching, set partitioning and shortest path. In addition, a column generation procedure named CGQS that uses an LP-solver and the QS process as its integer solution finder is presented. CGQS starts from the solution point of a single QS run and then performs several iterations in which LP problems are solved and new promising shifts are created using the LP dual solution.

A column generation approach for the timetabling problem of Greek high schools

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.

School timetabling for quality student and teacher schedules

The school timetabling problem, although less complicated than its counterpart for the university, still provides a ground for interesting and innovative approaches that promise solutions of high quality. In this work, a Shift Assignment Problem is solved first and work shifts are assigned to teachers. In the sequel, the actual Timetabling Problem is solved while the optimal shift assignments that resulted from the previous problem help in defining the values for the cost coefficients in the objective function. Both problems are modelled using Integer Programming and by this combined approach we succeed in modelling all operational and practical rules that the Hellenic secondary educational system imposes. The resulting timetables are conflict free, complete, fully compact and well balanced for the students. They also handle simultaneous, collaborative and parallel teaching as well as blocks of consecutive lectures for certain courses. In addition, they are highly compact for the teachers, satisfy the teachers’ preferences at a high degree, and assign core courses towards the beginning of each day.

Rule handling in the day-to-day resource management problem: an object-oriented approach

The day-to-day resource management problem is caused by a set of unexpected events which disturb the planned daily activities and thus change the long-term optimal schedule. The solution to this problem presupposes that all the regulations for the handling of resources in the particular application domain have been satisfied. In this paper, a new approach to handling the rules in the resource management problem is presented. An object-oriented application specific language that allows the flexible expression of the rules, as well as the corresponding rule handling subsystem are presented. The design of the whole system is based on a generic meta-model derived from the object-oriented paradigm. This makes the system applicable to a wide range of problem domains such as repairs management, airline and other transportation scheduling, school scheduling, etc. The system has been developed and tested as a subsystem of the DAYSY system, a day-to-day resource management system for the airline domain.