View metadata,Downloaded citation and from similar orbit.dtu.dk papers on:at core.ac.uk Dec 20, 2017 brought to you by CORE provided by Online Research Database In Technology Solving Multiple Timetabling Problems at Danish High Schools Kristiansen, Simon; Stidsen, Thomas Jacob Riis; Herold, Michael B. Publication date: 2014 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA): Kristiansen, S., Stidsen, T. R., & Herold, M. B. (2014). Solving Multiple Timetabling Problems at Danish High Schools. Department of Management Engineering, Technical University of Denmark. 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Ph.D. thesis Solving Multiple Timetabling Problems at Danish High Schools Simon Kristiansen November 28, 2013 Dansk titel: Løsning af flere planlægningsproblemer p˚ade danske gymnasier Type: Ph.D.-afhandling Forfatter: Simon Kristiansen ISBN-nr: Division of Management Science Department of Management Engineering Technical University of Denmark Produktionstorvet, Building 426, DK-2800 Kgs. Lyngby, Denmark Phone: +45 45 25 48 00, Fax: +45 45 25 48 05 [email protected] MaCom A/S Vesterbrogade 48, 1. DK-1620 Kbh V., Denmark Phone: +45 33 79 79 00 November, 2013 Abstract Planning problems at educational institutions are often time-consuming and complex tasks. Ed- ucational planning problems are studied using operational research techniques, which have been used with success and resulting in great improvements on the field. Educational planning prob- lems are often divided into four main categories; University Course Timetabling, High School Timetabling, Examination Timetabling and Student Sectioning. This Ph.D. thesis addresses some of the planning problems the high schools are struggling with annually, and it is partitioned into three research directions; High School Timetabling, Student Sectioning and the Meeting Planning Problem. The underlying work of this thesis is carried out as an Industrial Ph.D. project in co-operation with the Danish software company MaCom A/S, which delivers administrative software solutions for high schools in Denmark. Research in High School Timetabling has mainly been concentrated on local problems until recently. By the creation of an XML-format, XHSTT, and applicable wide ranging benchmark instances, it is been possible to solve the more generalized High School Timetabling problem. The first part of this thesis presents two approaches for the High School Timetabling problem of XH- STT; a heuristic method and an exact method. The heuristic method presented is an Adaptive large Neighborhood Search (ALNS) and was submitted as a contribution to the Third Interna- tional Timetabling Competition in 2011. The algorithm was one of the finalists, and it achieved a third place. For the exact method a Mixed Integer Programming (MIP) model has been devel- oped, and a two stage method has been used to solve it in a state-of-the-art MIP solver. Using the exact method has made it possible to generate lower bounds for several instances and to prove optimality of a few. In the second part two different Student Sectioning problems at Danish high schools have been presented with three papers. Firstly the Elective Course Planning problem has been presented, which is the problem of assigning 2nd and 3rd year students to elective courses given their re- quests. The problem has been solved using Dantzig-Wolfe decomposition in a Branch-and-Bound framework. The method applied shows that a previously applied method performs poorly and is insufficient. A more comprehensive model has been created, containing the lacking constraints, using the more appropriate name; Elective Course Student Sectioning. The problem is solved us- ing ALNS and solutions are proven to be close to optimum. The algorithm has been implemented and made available for the majority of the high schools in Denmark. The second Student Sectioning problem presented is the sectioning of each first year student to a cohort, based on his/hers study line request, and two elective courses based on the requests for these. The High School Student Sectioning problem has been modeled as a bipartite network model and solved using two solution methods, a direct and a sequential method. The results show that by using a sequential method it is possible to gain much better results. I The last part of the thesis is concerned the Meeting Planning Problem and presented with two papers. The Consultation Timetabling Problem is one of the minor, but still time-consuming, planning problems at the Danish high schools. Two types of consultations are presented; the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Prob- lem (SCTP). One mathematical model containing both consultation types has been created and solved using an ALNS approach. The received solutions are close to optimum. Based on the Consultation Timetabling Problem, a Generalized Meeting Planning Problem (GMPP) has been developed. Column generation with a Branch-and-Price (B&P) algorithm has been applied as solution method for the GMPP, and it has been tested on the PCTP and SCTP problem instances. The results prove that the B&P algorithm is an efficient method for solving the GMPP, and that the ALSN method performs better than anticipated. The thesis has been aiming at solving the planning problems to optimality, or near optimality, and opening up research within the area of educational timetabling. It gives a thorough introduc- tions to the domain of educational planning problems and presents several solution methods for High School Timetabling, Student Sectioning and the Meeting Planning Problem. From an industrial point of view, this thesis has been able to formulate different high school planning problems as mathematical models and solve them using operational research techniques. Two of the models and the suggested solution methods have resulted in implementations in an actual decision support software, and are hence available for the majority of the high schools in Denmark. These implementations can improve the solution process in terms of time and quality. II Resum´e (Summary in Danish) Planlægningsproblemer for uddannelsesinstitutioner er ofte b˚adetidskrævende og komplekse. Ud- dannelsesrelaterede skemalægningsproblemer er et forskningsomr˚ade indenfor operationsanalyse, hvor teknikker er blevet anvendt med succes og har resulteret i store forbedringer indenfor omr˚adet. Planlægningsproblemer indenfor undervisningssektoren er ofte opdelt i fire hovedomr˚ader;Univer- sitets skemalægning, gymnasial skemalægning, eksamensplanlægning og elevfordeling. Denne ph.d. afhandling adresserer nogle af de planlægningsproblemer som gymnasierne kæmper med, og er opdelt i tre omr˚ader;første del omfatter skemalægningen p˚agymnasier, anden del har fokus p˚aholdpakning af eleverne og den sidste del omhandler mødeplanlægningsproblemer. Det underliggende arbejde af denne afhandling er udført som et ErhvervsPhD-projekt i sam- arbejde med den danske software-virksomhed MaCom A/S, der leverer administrative softwa- reløsninger til gymnasierne i Danmark. Forskning af gymnasial skemalægning har hovedsageligt været koncentreret om enkelte lokale gymnasier. Med oprettelsen af et XML-format, XHSTT, med dertilhørende omfattende benchmar- king datasæt, er der blevet skabt en mere generaliseret problemstilling. Denne afhandling præsen- terer to forskellige løsningsmetoder for XHSTT skemalægningsproblemet; en heuristisk metode og en eksakt metode. Adaptive Large Neighborhood Search (ALNS) er anvendt til den heuristiske metode og var et bidrag til den tredje internationale skemalægningskonkurrence. Algoritmen var blandt finalisterne og opn˚aedeat f˚aen tredjeplads. Til den eksakte metode er der anvendt heltalsprogrammering til at lave en matematisk model til problemet og en to-trins løsningsmetode er anvendt i et avanceret løsningsværktøj. Ved brug af den eksakte metode har det været muligt at generere nogle grænseværdier for flere af problemerne, og bevise optimalitet i nogle enkelte tilfælde. I den anden del af afhandlingen er to forskellige holdpakningsproblemer p˚ade danske gymna- sier præsenteret i tre artikler. Først er holdpakningsproblemet for 2. og 3. ˚arselever præsenteret. Problemet best˚ari at tildele eleverne til valgfagsklasser baseret p˚aderes respektive ønsker. Pro- blemet er blevet løst ved brug af Dantzig-Wolfe dekomponering i en Branch-and-Price (B&P) konstruktion. Resultaterne viser at en tidligere anvendt metode performer d˚arligt og generelt er utilstrækkelig. En mere omfattende matematisk model er oprettet og løst ved brug af ALNS og løsningerne har vist at være tæt p˚ade optimale. Det andet holdpakningproblem er første˚arsholdpakning,hvor de nye studerende skal tildeles en stamklasse baseret p˚aderes retningslinjer og to valgfagsklasser,