Optimization of The Best Line-up in Football using Binary Integer Programming Model

Abstract

This paper aims to find the formation with the best line-up of the Liverpool FC football team in the English Premier League in the 2020/2021 season. Researchers used binary integer programming (BIP) modeling to determine optimum solutions. The data used for this optimization is the rating value of the players recorded in the performance data from the previous matches. The optimum result of this problem is the selection of variables that are valued at 1, namely {𝑥1,𝑥4,𝑥6,𝑥8,𝑥11,𝑥18,𝑥21,𝑥28,𝑥34,𝑥37,dan 𝑥39 } for formations 4-3-3 with a maximum value of 82.47, and variables {𝑥1,𝑥6,𝑥7,𝑥8,𝑥11,𝑥14,𝑥16,𝑥29,𝑥31,𝑥32, dan 𝑥42 } for 4-2-3-1 formations with a maximum value of 80.04. The 4-3-3 formation is more effective because it has a higher maximum rating than the 4-2-3-1 formation. 4-3-3 formation is an attacking formation with a higher intensity of attack and faster than 4-2-3-1 formation that tends to defend moderately.