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

Time Relaxed Round Robin Tournament and the NBA Scheduling Problem

This dissertation study was inspired by the National Basketball Association regular reason scheduling problem. NBA uses the time-relaxed round robin tournament format, which has drawn less research attention compared to the other scheduling formats. Besides NBA, the National Hockey League and many amateur leagues use the time-relaxed round robin tournament as well. This dissertation study is the first ever to examine the properties of general time-relaxed round robin tournaments. Single round, double round and multiple round time-relaxed round robin tournaments are defined. The integer programming and constraint programming models for those tournaments scheduling are developed and presented. Because of the complexity of this problem, several decomposition methods are presented as well. Traveling distance is an important factor in the tournament scheduling. Traveling tournament problem defined in the time constrained conditions has been well studied. This dissertation defines the novel problem of time-relaxed traveling tournament problem. Three algorithms has been developed and compared to address this problem. In addition, this dissertation study presents all major constraints for the NBA regular season scheduling. These constraints are grouped into three categories: structural, external and fairness. Both integer programming and constraint programming are used to model these constraints and the computation studies are presente