Referee assignment in the Chilean football league using integer programming and patterns

This article uses integer linear programming to address the referee assignment problem in the First Division of the Chilean professional football league. The proposed approach considers balance in the number of matches each referee must officiate, the frequency of each referee being assigned to a given team, the distance each referee must travel over the course of a season, and the appropriate pairings of referee experience or skill category with the importance of the matches. Two methodologies are studied, one traditional and the other a pattern-based formulation inspired by the home-away patterns for scheduling season match calendars. Both methodologies are tested in real-world and experimental instances, reporting results that improve significantly on the manual assignments. The pattern-based formulation attains major reductions in execution times, solving real instances to optimality in just a few seconds, while the traditional one takes anywhere from several minutes to more than an hour.Fil: Alarcón, Fernando. Universidad de Chile; ChileFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Guajardo, Mario. Norwegian School of Economics; Norueg

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

Cooperative game-theoretic features of cost sharing in location-routing

This article studies several variants of the location-routing problem using a cooperative game-theoretic framework. The authors derive characteristics in terms of subadditivity, convexity, and non-emptiness of the core. Moreover, for some of the game variants, it is shown that for facility opening costs substantially larger than the costs associated with routing, the core is always non-empty. The theoretical results are supported by numerical experiments aimed at illustrating the properties and deriving insights. Among others, it is observed that, while in general it is not possible to guarantee core allocations, in a huge majority of cases the core is non-empty

Programación del Fixture de la Segunda División del Fútbol de Chile mediante Investigación de Operaciones

Presentamos en este trabajo la aplicación de técnicas de Investigación de Operaciones a la programación del fixture de la Segunda División del fútbol de Chile. Este fixture debe cumplir una serie de condiciones solicitadas por la Asociación Nacional de Fútbol Profesional (ANFP), entidad que organiza el torneo. El criterio geográfico es particularmente importante, debido a que la disposición de algunos equipos en lugares extremos del país implica largos desplazamientos, a menudo realizados por vía terrestre. Abordamos el problema mediante un modelo de programación lineal entera que define cuándo y dónde se juega cada partido del torneo, sujeto a que todas las condiciones se cumplen. Para las instancias más difíciles, desarrollamos un modelo adicional también de programación lineal entera que genera patrones de localías y los asigna a los equipos, previo a la ejecución del modelo que define la programación de los partidos. Los fixtures así generados han sido exitosamente utilizados en los cinco torneos de Segunda División que se han disputado entre 2007 y 2010, reemplazando la metodología aleatoria que la ANFP utilizaba anteriormente. Durante este período, el tipo de torneo ha sufrido diversas modificaciones, incluyendo un cuádruple round-robin y un torneo en dos etapas que considera fases regionales y nacionales. Hemos debido entonces adaptar nuestros modelos temporada tras temporada, según el tipo de torneo. Esta aplicación marca un nuevo avance en el uso de Investigación de Operaciones para la gestión del fútbol chileno, que se suma a otros proyectos desarrollados en la misma línea en los últimos años.Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Guajardo, Mario. Norwegian School of Economics and Business Administration; NoruegaFil: Wolf Yadlin, Rodrigo. Universidad de Chile; Chil

Operations research techniques for scheduling chile's second division soccer league

In this paper, we use operations research (OR) techniques to schedule the Second Division of the Chilean professional soccer league. The solution must satisfy a series of conditions requested by league officials. Because the teams generally travel long distances by bus, geographical restrictions are particularly important. We specify the scheduling problem and solve it using an integer linear programming (ILP) model that defines when and where each match is played, subject to constraints. For the most difficult instances, we formulate a second ILP model that generates home-away patterns and assigns them to the teams; we then run the model, which determines the match schedule. Chilean league officials have successfully used the models to schedule all five Second Division tournaments between 2007 and 2010, replacing the random scheduling methodology that they used previously. Since 2007, the two formulations have been adapted to various formats with which the Second Division has experimented; these include a quadruple round robin and a two-phase tournament with zonal and national phases. The application we present is one of a number of such projects that the authors and their colleagues developed over the past few years, and it represents an expansion of the use of OR techniques for managing tasks in Chilean soccer.Fil: Duran, Guillermo Alfredo. Universidad de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Guajardo, Mario. NHH Norwegian School of Economics; NoruegaFil: Wolf Yadlin, Rodrigo. Universidad de Chile; Chil

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

Mathematical models for rescheduling Ecuador's 2020 professional football league season disrupted by COVID-19

The year 2020 saw the world turned upside down by the coronavirus pandemic. Countless human activities were suspended or cancelled as the virus spread across the globe. In this paper, we show how the regular season matches of Ecuador’s professional football league were rescheduled due to the disruption caused by the pandemic. As with many others, this league had to reschedule its remaining games to fit within in a much shorter period of time than originally planned. To address this problem, we developed two mathematical models that designed new match calendars. The first one, a round assignment model, rescheduled the various rounds in the season still to be played while the second one, a day assignment model, took the solutions of the first model as input to assign the matches within each round to specific days. The implementation of our models secured a well-balanced number of days off before each match across all of the teams. Also, it enabled the league to conclude a full season without cancelling any matches or changing the schedule format, unlike what occurred in many other leagues, and won the approval of all stakeholders including league officials, players, team coaches, the TV broadcaster and fans

Design of a HACCP Plan for Vacuum-Packed Beef Cuts

Objective: To elaborate a HACCP plan, for the process of vacuum-packed cuts of meat, in a federal inspection type trail (TIF) located in the East of the State of Mexico, in order to improve its hygiene and safety conditions. Design / Methodology / approach: The research has a mixed approach that consists of two phases, a field phase where the HACCP methodology was applied in terms of reviewing the activities carried out in the company, the second phase is a cabinet where they were analyzed the hazards identified during the first phase, in order to determine if the hazard found is significant for the safety of the food, to finally conclude whether or not it is a critical control point (CCP). Results: A PCC (Critical Control Point) was identified, in the metal detection phase, the identified hazards were: the passage of metal chips from the transfer rails, pieces of knives or saws and pieces of needles coming from previous steps in the process. Study limitations / implications: Bibliographic documentation on meat cut case studies as well as the management of their CCPs is limited. Findings / Conclusions: The PCC1 Metal Detection is a control measure carried out by the company, however when analyzing it, an opportunity for improvement in the current operation was evidenced, so the adaptation of formats for records that allowed monitoring was also proposed. and verify the control of the PCC.Objective: To elaborate a Hazard Analysis and Critical Control Points (HACCP) plan for the process of vacuum-packed beef cuts, in a Federal Inspection Type (FIT) meat processor located in eastern Estado de México, with the aim of improving its conditions of hygiene and innocuousness. Design/Methodology/Approximation: The activities performed in the business were revised applying the HACCP methodology and the dangers identified were analyzed, to determine whether the danger found was significant for the innocuousness of the food, finally concluding if it represented, or not, a critical control point (CCP). Results: A CCP was identified in the phase of metal detection, the dangers identified were the passing of metal      shards from the transport rails, pieces of knives or saws, and pieces of needles from prior steps in the process. Study limitations/implications: Documentation about case studies of beef cuts, as well as about management of their CCP is limited. Findings/Conclusions: The CCP1 Metal Detection is a control measure that the business performs; however, under analysis, there was evidence of an opportunity to improve the current operation, which is why the adaptation of registry formats that could allow monitoring and controlling the CCP was proposed

Identification of viral infections in the prostate and evaluation of their association with cancer

<p>Abstract</p> <p>Background</p> <p>Several viruses with known oncogenic potential infect prostate tissue, among these are the polyomaviruses BKV, JCV, and SV40; human papillomaviruses (HPVs), and human cytomegalovirus (HCMV) infections. Recently, the Xenotropic Murine Leukemia Virus-related gammaretrovirus (XMRV) was identified in prostate tissue with a high prevalence observed in prostate cancer (PC) patients homozygous for the glutamine variant of the RNASEL protein (462Q/Q). Association studies with the R462Q allele and non-XMRV viruses have not been reported. We assessed associations between prostate cancer, prostate viral infections, and the RNASEL 462Q allele in Mexican cancer patients and controls.</p> <p>Methods</p> <p>130 subjects (55 prostate cancer cases and 75 controls) were enrolled in the study. DNA and RNA isolated from prostate tissues were screened for the presence of viral genomes. Genotyping of the RNASEL R462Q variant was performed by Taqman method.</p> <p>Results</p> <p>R/R, R/Q, and Q/Q frequencies for R462Q were 0.62, 0.38, and 0.0 for PC cases and 0.69, 0.24, and 0.07 for controls, respectively. HPV sequences were detected in 11 (20.0%) cases and 4 (5.3%) controls. XMRV and HCMV infections were detected in one and six control samples, respectively. The risk of PC was significantly increased (Odds Ratio = 3.98; 95% CI: 1.17-13.56, p = 0.027) by infection of the prostatic tissue with HPV. BKV, JCV, and SV40 sequences were not detected in any of the tissue samples examined.</p> <p>Conclusions</p> <p>We report a positive association between PC and HPV infection. The 462Q/Q RNASEL genotype was not represented in our PC cases; thus, its interaction with prostate viral infections and cancer could not be evaluated.</p