Efficiency and equity in the multi organization scheduling problem

We consider the multi organization scheduling problem (MOSP) [19]: given N organizations owning, each of them, one set tasks and machines, aim is to compute a schedule which gathers all on such that makespan minimized. A rationality constraint must be fulfilled: no should increase its (the completion time last task) compared case where it schedules own (and only tasks) machines. show cooperation (sharing machines can benefit simultaneously, since they may decrease their makespans by factor N. present an algorithm (1+ϵ)-approximate, while increased at most (1+ϵ). also study extent (or relaxed constraint) increases makespan, (P||Cmax) there constraint. Finally, we introduce new problem, focus equity: return fulfills maximizes has decreased makespan. give optimal for this in particular case, NP-hard hard approximate general case. complete paper efficient heuristic problem.