A Nash bargaining model for flow shop scheduling problem under uncertainty: a case study from tire manufacturing in Iran

Production scheduling has a considerable impact on productivity and resource assignment. In many situations, every job has an owner, which is called an agent. Since the agents are independent and selfish, it is possible that they have not any incentive to cooperate. Scheduling games help us to understand interactions between the agents. In this study, we consider a real firm with a flow shop manufacturing system that receives various orders from different agents so that each order belongs to a unique agent and includes some jobs. We propose a Nash bargaining model to find a compromise solution among agents. We suppose the utilities of the agents in disagreement point are non-deterministic. Therefore, to overcome this problem, we used linear programming with interval coefficients in order to find the best and the worst Nash bargaining solution. To find a compromised solution, we propose an improved genetic algorithm and compare it with other meta-heuristic algorithms. The comparisons indicate that the proposed algorithm has a good potential to evaluation of Nash bargaining problem in hybrid flow shop environment. Based on the results to reach an agreement between agents, it is required to create a trade-off between usage rates of fastest machines at each stage especially in bottleneck stages and total processing time of orders. The results indicate that the Nash bargaining solution is suitable to solve real-life agent-based production scheduling with the consideration of interactions among the agents when disagreement points are under uncertainty.