12 research outputs found
A flexible mathematical model for the planning and designing of a sporting fixture by considering the assignment of referees
Indexación: Scopus.This paper deals with the problems faced with the designing and planning of a sporting fixture considering correct referee assignments. A non-linear binary program model is proposed to solve the problems, which aims to minimize the sums of the differences that exist between the requirements of each match and the quality of the referee assigned achieving the design of the most adequate referee for each match. The efficiency of the proposed model is proved using some real data obtained from various fixtures for sports such as soccer, volleyball, and basketball. The mathematical model is solved by using CPLEX 12.7.0., which allows the automatic linearization of the problems. The results obtained demonstrate the efficiency of the proposed methodology for tackling problems, as well as its extension to other sporting disciplines, which require a similar type of planning. Similarly, given the robust nature of the proposed model, it is possible to implement other objective functions in accordance with the requirements of each league. © 2019 by the authors; licensee Growing Science, Canada.http://growingscience.com/beta/ijiec/2960-a-flexible-mathematical-model-for-the-planning-and-designing-of-a-sporting-fixture-by-considering-the-assignment-of-referees.htm
Particle Swarm Algorithm for Improved Handling of the Mirrored Traveling Tournament Problem
In this study, we used a particle swarm optimization (PSO) algorithm to address a variation of the non-deterministic polynomial-time NP-hard traveling tournament problem, which determines the optimal schedule for a double round-robin tournament, for an even number of teams, to minimize the number of trips taken. Our proposed algorithm iteratively explored the search space with a swarm of particles to find near-optimal solutions. We also developed three techniques for updating the particle velocity to move towards optimal points, which randomly select and replace row and column parameters to find candidate positions close to an optimal solution. To further optimize the solution, we calculated the particle cost function, an important consideration within the problem conditions, for team revenues, fans, and media. We compared our computation results with two well-known meta-Heuristics: a genetics algorithm utilizing a swapping method and a Greedy Randomized Adaptive Search Procedure Iterated Local Search algorithm heuristic on a set of 20 teams. Ultimately, the PSO algorithm generated solutions that were comparable, and often superior, to the existing well-known solutions. Our results indicate that our proposed algorithm could aid in reducing the overall budget expenditures of international sports league organizations, which could enable significant monetary savings and increase profit margins
Hogyan számszerűsĂthetĹ‘ az ösztönzĂ©skompatibilitás? Esettanulmány a sport világábĂłl
Minden sportbajnoksággal szemben alapvetĹ‘ elvárás a versenyzĹ‘k megfelelĹ‘ ösztönzĂ©se. A csalásbiztosságot az irodalom jellemzĹ‘en bináris fogalomkĂ©nt kezeli, amely akadályozza az ösztönzĂ©skompatibilitás Ă©s más kedvezĹ‘ tulajdonságok közötti átváltás feltárását. A cikk a csalás elleni vĂ©delem sĂ©rĂĽlĂ©sĂ©nek számszerűsĂtĂ©sĂ©re tesz kĂsĂ©rletet a 2022-es labdarĂşgĂł-világbajnokság eurĂłpai selejtezĹ‘jĂ©nek pĂ©ldáján keresztĂĽl. SzimuláciĂłval becsĂĽljĂĽk meg az eredmĂ©nyes manipuláciĂł valĂłszĂnűsĂ©gĂ©t, majd megmutatjuk, hogy a csoportkör sorsolásához adott Ăşjabb korlátozĂł feltĂ©telek segĂtsĂ©gĂ©vel lĂ©nyegĂ©ben megszĂĽntethetĹ‘ a hibás ösztönzĂ©s problĂ©mája. Ajánlásunk egyszerű, könnyen elfogadhatĂł, Ă©s nem növeli a szabályok bonyolultságát. EredmĂ©nyeink rĂ©vĂ©n javĂthatĂł a sportbajnokságok igazságossága
A flexible mathematical model for the planning and designing of a sporting fixture by considering the assignment of referees
This paper deals with the problems faced with the designing and planning of a sporting fixture considering correct referee assignments. A non-linear binary program model is proposed to solve the problems, which aims to minimize the sums of the differences that exist between the requirements of each match and the quality of the referee assigned achieving the design of the most adequate referee for each match. The efficiency of the proposed model is proved using some real data obtained from various fixtures for sports such as soccer, volleyball, and basketball. The mathematical model is solved by using CPLEX 12.7.0., which allows the automatic linearization of the problems. The results obtained demonstrate the efficiency of the proposed methodology for tackling problems, as well as its extension to other sporting disciplines, which require a similar type of planning. Similarly, given the robust nature of the proposed model, it is possible to implement other objective functions in accordance with the requirements of each league
Format and schedule proposals for a FIFA World Cup with 12 four-team groups
After the expansion of the FIFA World Cup from 32 to 48 teams starting from the 2026 edition, the initial proposal was to split the 48 national teams into 16 groups of three. Among other drawbacks, this proposal provides potential for collusion. Recently, after widespread criticism, FIFA officials signaled the possibility to re-discuss that proposal, pointing to a tournament with 12 groups of four teams. If this new proposal prevails, relevant questions arise about tournament design and schedule. In this paper, we propose tournament formats for a World Cup with 12 groups of four teams, considering a number of criteria, such as non-collusion, symmetry in rest days, no dead rubbers, and a tournament length of about one month. At the same time, our proposals attempt to adhere to the traditional format, with some nuances either in the group stage or in the knockout stage
An instance data repository for the round-robin sports timetabling problem
The sports timetabling problem is a combinatorial optimization problem that consists of creating a timetable that defines against whom, when and where teams play games. This is a complex matter, since real-life sports timetabling applications are typically highly constrained. The vast amount and variety of constraints and the lack of generally accepted benchmark problem instances make that timetable algorithms proposed in the literature are often tested on just one or two specific seasons of the competition under consideration. This is problematic since only a few algorithmic insights are gained. To mitigate this issue, this article provides a problem instance repository containing over 40 different types of instances covering artificial and real-life problem instances. The construction of such a repository is not trivial, since there are dozens of constraints that need to be expressed in a standardized format. For this, our repository relies on RobinX, an XML-supported classification framework. The resulting repository provides a (non-exhaustive) overview of most real-life sports timetabling applications published over the last five decades. For every problem, a short description highlights the most distinguishing characteristics of the problem. The repository is publicly available and will be continuously updated as new instances or better solutions become available
Fair draws for group rounds in sport tournaments
We propose two draw systems for the group round of sport tournaments where there are some geographical and/or seeding restrictions. One of the systems, related to the equal-sum partition problem, is "perfect, " since it yields perfectly balanced groups. The other system, which uses the classical scheme of extracting teams from pots, is heuristic and gives results where the groups have very similar scores. We apply our results to Federation Internationale de Football Association (FIFA) Soccer World Cups and show that our proposals are much better than the FIFA system and also outperform other recently developed systems
A paradox of tournament seeding
A mathematical model of seeding is analysed for sports tournaments where the
qualification is based on round-robin contests. The conditions of
strategyproofness are found to be quite restrictive: if each team takes its own
coefficient (a measure of its past performance), only one or all of them should
qualify from every round-robin contest. Thus the standard draw system creates
incentives for tanking in order to be assigned to a stronger pot as each team
prefers to qualify with teams having a lower coefficient. Major soccer
competitions are shown to suffer from this weakness. Strategyproofness can be
guaranteed by giving to each team the highest coefficient of all teams that are
ranked lower in its round-robin contest. The proposal is illustrated by the
2020/21 UEFA Champions League.Comment: 23 pages, 3 table
Scheduling the South American Qualifiers to the 2018 FIFA World Cup by integer programming
Every four years, the 10 national teams members of the South American Football Confederation (CONMEBOL) compete for one of the South American slots in the final phase of the FIFA World Cup. The qualifying competition consists of a double round robin tournament. The matches are scheduled in 9 closely spaced pairs known as double rounds. Every team plays twice in each double round. The tournament is spread over 2 years, so the double rounds are months apart. After using the same mirrored schedule for about twenty years, and persistent complaints from its members, CONMEBOL decided to change the schedule for the 2018 World Cup. Supported by one of CONMEBOL's members, we used integer programmming to construct schedules that overcome the main drawbacks of the previous approach. After exploring many design criteria, we proposed a candidate schedule based on a French scheme. The main feature of the proposed schedule is that every team plays once at home and once away on each double round, a departure from traditional symmetric (mirrored) schemes. This proposal was unanimously approved by CONMEBOL members and is currently being used in the qualifier tournament for the 2018 FIFA World Cup in Russia.Fil: Duran, Guillermo Alfredo. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Guajardo, Mario. NHH Norwegian School of Economics; NoruegaFil: SaurĂ©, Denis. Universidad de Chile; Chil