# Open shop scheduling games

## TL;DR

This paper applies game theory to open shop scheduling with unit times, modeling jobs as players and analyzing cost savings through cooperative game concepts, including core allocations and balancedness.

## Contribution

It introduces a cooperative game framework for open shop scheduling, demonstrating balancedness and exploring the effects of relaxing admissible rearrangements.

## Key findings

- The associated cooperative games are balanced.
- Core allocations can be constructed for these games.
- Relaxing admissible rearrangements affects the balancedness property.

## Abstract

This paper takes a game theoretical approach to open shop scheduling problems with unit execution times to minimize the sum of completion times. By supposing an initial schedule and associating each job (consisting in a number of operations) to a different player, we can construct a cooperative TU-game associated with any open shop scheduling problem. We assign to each coalition the maximal cost savings it can obtain through admissible rearrangements of jobs' operations. By providing a core allocation, we show that the associated games are balanced. Finally, we relax the definition of admissible rearrangements for a coalition to study to what extend balancedness still holds.