FORMATION OF AN EFFICIENT FOOTBALL TEAM USING DATA ENVELOPMENT ANALYSIS AND INTEGER LINEAR PROGRAMMING

Abstract

In today’s professional football environment, building a competitive squad while operating under tight financial constraints has become a major challenge for club management. This study presents a two stage mathematical approach for constructing an optimal football team in the English Premier League. In the first stage, Data Envelopment Analysis (DEA), specifically the BCC (Banker–Charnes–Cooper) model, is employed to assess the relative efficiency of individual players viewed as decision making units. Player salaries are treated as inputs, while on field performance indicators such as goals and assists are considered outputs. In the second stage, the efficiency scores obtained from DEA are incorporated into an Integer Linear Programming (ILP) framework. The ILP model selects the “Best Eleven” by maximizing overall team efficiency subject to realistic constraints including positional requirements, budget limitations, and formation rules. The results demonstrate how mathematical optimization techniques can support football clubs in assembling high performing teams while maintaining financial discipline.