33 pages. Paper submitted to Journal of scheduling the 8 September 2009.We consider the problems of scheduling independent jobs, when a subset of jobs has its own objective function to minimize. The performance of this subset of jobs is in competition with the performance of the whole set of jobs and compromise solutions have to be found. Such a problem arises for some practical applications like ball bearing production problems. This new scheduling problem is positioned within the literature and the differences with the problems with competing agents or with interfering job set problems are presented. Classical and regular scheduling objective functions are considered and epsilon-constraint approach and linear combination of criteria approach are used for finding compromise solutions. The study focus on single machine and identical parallel machine environments and for each environment, the complexity of several problems is established and some dynamic programming algorithms are proposed
