Multi-Objective Multi-Criteria Approach to Cost-Effective Sport Teaming with Consideration of Player's Social Network

Vicki Lam Su Qi

Abstract

In any sports discipline, the selection of players within a finite budget is a complex task. Many factors condition the selection process ranging from the regulations of the sport to financial constraints. Moreover, many tend to overlook the importance of considering interpersonal relationships among team members. In reality, a team's success also depends on how the members collaborate, communicate and work together effectively. To tackle this factor, the paper briefly describes the social network between players using basic network structures such as edges, k-stars, and triangles. Therefore, the weight that measures the strength of social ties between players will be included in the model. The task of selecting a team of basketball players can be viewed as a multi-objective optimisation and Multi-Criteria Decision-Making (MCDM) problem. This paper proposes multi-objective Binary Integer Programming (BIP), multi-objective Mixed-Integer Quadratic Programming (MIQP) and Analytic Hierarchy Process (AHP) to optimise the players’ cost, value, and weights. There will be three models to account for different objective functions and criteria. After which, an efficient frontier analysis will be adopted to showcase the trade-off relationship between the key attributes. These models are illustrated using a set of 200 National Basketball Association (NBA) players with their respective salary and performance indicator. Insights generated by the presented framework and directions for future work are discussed. The efficient frontier for the cost-effective multi-objective model suggests that the non-dominated alternatives lie on the left side of the curve. The ultimate team choice is dependent on the general manager’s preference trade-off. Following that, the AHP model accounting for four criteria has managed to screen the pool of players and reduce the parameter from 200 to 50 players. Using the data for the top 50 players, a multi-objective MIQP model was constructed and efficient frontiers for the multi-objective MIQP model which considers players’ social networks were constructed for different ranges of budgets. The efficient frontier for low budget features four non-dominated alternatives while the medium and high budget has seven and nine non-dominated alternatives respectively. It is to note that the methodology is generic and can be easily extended to other sports disciplines which require optimal team formation such as cricket and American football..