Scheduling Players in Team Competitions: Theory and Computational Results

SYNOPTIC ABSTRACT

Consider two teams, each with n players, that must match up players to compete in n events. In each event, a given player either wins or loses (with known probabilities) thereby earning his team 1 or 0 points, respectively. The team with the larger point total wins the match. We formulate the problem of maximizing the probability of winning for a team that has perfect information on the opposing team's assignment of players to events. We propose surrogate objective functions that one may use in lieu of the probability of winning to make the problem computationally tractable and we provide algorithms based on fractional programming to maximize these surrogate objectives.

Key Words and Phrases:

• Operations Research in Sports
• Assignment Problem
• Fractional Programming
• Nonlinear Optimization