Open Shop Scheduling Games
📝 Original Paper Info
- Title: Open shop scheduling games- ArXiv ID: 1907.12909
- Date: 2019-07-31
- Authors: Ata Atay, Pedro Calleja, Sergio Soteras
📝 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.💡 Summary & Analysis
This paper explores the application of game theory to tackle open shop scheduling problems where each job has a unit execution time and aims at minimizing the sum of completion times. The authors propose to treat each job as a player in a cooperative transferable utility (TU) game, allowing for a strategic analysis of how different job sequences can optimize overall efficiency. By assigning cost savings to coalitions based on permissible rearrangements of jobs' operations, they demonstrate that their approach yields balanced outcomes, ensuring fair and efficient scheduling.The core of this research lies in its innovative use of cooperative games to model the interactions between tasks in a complex scheduling environment. The authors show how a game-theoretic framework can not only identify optimal job sequences but also ensure that all participating entities benefit from the resulting schedule. This approach opens new avenues for optimizing resource allocation and time management, particularly in industries where multiple jobs need to be processed simultaneously.