assigning judges to competitions of several rounds using tabu search

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  • e, judges have to be selected to evaluate the performance of the competitors and to identify a winner.ered when assigning judges to the competitions. These requirements include the ofcial rules of theand thny ruleis difc

    e assigCanadd to ot

    rience, and the set of new judges participating for the rst time. Note that all lead judges are experienced but the converse is false. Inaddition, 6 different elds of expertise for the judges are considered, and each judge indicates at least one of these expertises. Also, alljudges are uent in English, but only some of them are also uent in French. Finally, each judge indicates the rounds for which he isavailable.

    Following the round-robin tournament, the best teams move to the nals in the second part of the competition.

    Corresponding author. Tel.: +1 514 343 5687; fax: +1 514 343 5834.

    European Journal of Operational Research 210 (2011) 694705

    Contents lists available at ScienceDirect

    European Journal of Operational ResearchE-mail addresses: (A. Lamghari), (J.A. Ferland).Every year, the John Molson School of Business organizes the John Molson International Case Competition involving 30 teams of busi-ness students coming from top international universities. This set of teams is partitioned into 5 groups, each including 6 teams. The rstpart of the competition consists of a round-robin tournament including 5 rounds where each team competes against each of the other 5teams of its group. Thus, each round includes 15 individual competitions, giving a total of 75 individual competitions that take place overthe rst part of the competition.

    In each round, all teams have the same specied business case to analyze, to evaluate, and to propose solutions for it. After a 3 hoursperiod to prepare their presentation, each team of an individual competition makes an oral presentation in front of a panel of judges. Priorto the competition, teams specify the language (English or French) that they will use during their presentations.

    More than 200 university professors and/or senior business executives representing various rms are usually available for judgingthe presentations. According to their past experience and other considerations, the judges are divided into 3 sets: the set of leadjudges having the skills to chair the jury in a given individual competition, the set of experienced judges having previous judging expe-Whenever competitions take placSeveral requirements must be considcompetition that cannot be violated,most of the competitions involve masuming task for the staff involved. Thgenerating the assignments.

    In this paper, we analyze the judgat Concordia University in Montreal (should nevertheless be easily adapte0377-2217/$ - see front matter 2010 Elsevier B.V. Adoi:10.1016/j.ejor.2010.10.034e objectives of the organizing committee that should be satised as much as possible. Becauses and several objectives, manually generating the assignments is often a difcult and time-con-ulty motivates the interest of the scientic community in developing automated procedures for

    nment problem for the John Molson International Case Competition that takes place every yeara) for more than 25 years. Even if the solution approach is introduced for this specic context, ither contexts by making proper minor adjustments to deal with slightly different specic rules.Innovative Applications of O.R.

    Assigning judges to competitions of several rounds using Tabu search

    Amina Lamghari a, Jacques A. Ferland b,aCOSMO Stochastic Mine Planning Laboratory, McGill University, Department of Mining and Materials Engineering, FDA Building,3450 University Street, Montreal, Quebec, Canada H3A 2A7bDpartement dInformatique et de Recherche Oprationnelle, Universit de Montral, C.P. 6128, Succursale Centre-Ville, Montral, Qubec, Canada H3C 3J7

    a r t i c l e i n f o

    Article history:Received 21 January 2010Accepted 27 October 2010Available online 9 November 2010

    Keywords:Tabu searchSchedulingAssignment

    a b s t r a c t

    The judge assignment problem consists in nding an assignment satisfying the competition rules (hardconstraints) and meeting, as much as possible, the competition organizers objectives (soft constraints).In this paper, various specic real-world constraints found in organizing academic competitions are han-dled. We tackle the corresponding problem with a metaheuristic approach based on Tabu search. Thenumerical results indicate that very good solutions can be generated in reasonable computational times.

    2010 Elsevier B.V. All rights reserved.

    1. Introduction

    journal homepage: www.elsevier .com/locate /e jorll rights reserved.

  • The teams schedules are established by the organizing committee. In this paper, we are interested in generating the judge assignmentsfor the rst part of the competition. These assignments should fulll specic rules which are divided into 2 categories:

    Hard rules or constraints that must be satised: Since all the individual competitions of a specic round take place simultaneously, an available judge can be assigned to at most one

    individual competition of the round. 3 or 5 judges must be assigned to each individual competition. At least one of the judges belongs to the set of lead judges. At least one of the judges, different from the lead judge, belongs to the set of experienced judges. A judge cannot be assigned to an individual competition involving a team coming from a University where he received his degree or

    where he is a faculty member. A judge cannot be assigned to an individual competition involving a team which he does not wish to evaluate. If a team in an individual competition is presenting in French, then the judges assigned to this individual competition must also be

    uent in French.Soft rules or constraints (or objectives) to be satised as much as possible: Balance constraints: in each individual competition, the number of experienced judges assigned should be equal to the number of new

    judges. Afliation constraints: if several judges assigned to an individual competition are coming from rms, then they should come from

    different ones. Diversity constraints: the expertises of the judges assigned to an individual competition should cover as many of the 6 elds of exper-

    tise as possible. Coupling constraints: two judges should not be assigned together more than once during all rounds. Sequence constraints: during the different rounds, a judge should not be assigned to different individual competitions involving the

    same team. Number constraints: the number of individual competitions having 5 judges assigned should be maximized.

    In previous works (Lamghari and Ferland, 2005, 2007, 2010), we consider a simplied version of the problem and propose heuristictechniques and metaheuristic methods related to Tabu search (Glover and Laguna, 1998; Hansen, 1986) to solve it. In the simplied ver-sion, the following assumptions are made:

    There are only two sets of judges: the set of lead judges and the set of other judges. Therefore, the fourth hard constraint and the balanceconstraints are not considered.

    The judges preferences are not taken into account when assigning them to individual competitions, and thus the sixth hard constraint isnot considered.

    We assume that the competition language is English, hence the last hard constraint is not taken into account. All judges are university professors. Accordingly, afliation constraints need not to be considered. Each judge has only one expertise. The diversity constraints are thus reduced to the requirement that the expertises of the judgesassigned should be as different as possible.

    We were solving the problem involving only one round, and thus coupling and sequence constraints are not considered.

    The metaheuristic methods in Lamghari and Ferland (2010) have proved very efcient for the simplied version of the problem involv-ing one round. Thus, it is worthwhile examining their efciency for the more difcult problem involving several rounds and including morerealistic constraints. Furthermore, to solve the problem associated with several rounds, we consider two different alternatives. The rst oneis a global approach dealing simultaneously with the different rounds. It is obtained by a straightforward extension of the Tabu searchmethod in Lamghari and Ferland (2010). In the second alternative, we develop a decomposition approach separating the problem into aseries of sub-problems, each associated with one round. The sub-problems are considered sequentially and the solution of each sub-prob-lem is improved by xing the solutions of the other sub-problems to their current values.

    We provide numerical results allowing to evaluate and compare the performance of the proposed solution approaches. These resultsindicate that the decomposition approach generates better solutions requiring smaller solution time.

    Several papers appeared in the literature reporting the study of the judge assignment problem in the context of sport competitions. Theassignment rules and the objectives differ with the specic contexts. For instance, some constraints are related to the number of judgesrequired, to their level of experience, and to the sequence of assignments of a given judge. The objective function might be to minimizethe total traveled distance of the judges, or to balance their workload, or to minimize a weighted sum of violations of the soft constraints,for instance. These applications induce difcult combinatorial optimization problems usually solved with heuristic or metaheuristic meth-ods. A three-phase approach based on a constructive heuristic, a repair heuristic, and an iterated local search improvement heuristic wasproposed by Duarte et al. (2006, 2007b).