Traveling Baseball Players' Problem in Korea

TL;DR

This paper applies Monte Carlo and simulated annealing methods to optimize the fairness of travel distances in the Korean Baseball League's tournament schedule, prioritizing equitable travel over minimal total distance.

Contribution

It introduces a novel approach to maximize fairness in tournament scheduling by redefining the objective and applying advanced optimization techniques.

Findings

Schedule satisfies all constraints set by the Korean Baseball Organization.

Significant increase in fairness of travel distances among teams.

Method effectively balances fairness with constraint adherence.

Abstract

We study the so-called the traveling tournament problem (TTP), to find an optimal tournament schedule. Differently from the original TTP, in which the total travel distance of all the participants is the objective function to minimize, we instead seek to maximize the fairness of the round robin tournament schedule of the Korean Baseball League. The standard deviation of the travel distances of teams is defined as the energy function, and the Metropolis Monte-Carlo method combined with the simulated annealing technique is applied to find the ground state configuration. The resulting tournament schedule is found to satisfy all the constraint rules set by the Korean Baseball Organization, but with drastically increased fairness in traveling distances.