Sequencing and Cooperation

Abstract

In machine scheduling the first problem is to find a timetable that is optimal with respect to some efficiency criterion. If the jobs come from different clients the solution of the optimization problem is not the end of the story. In addition, we have to decide how the minimal total cost must be distributed among the parties involved. In this note, cost allocation problems will be considered to arise from one-machine scheduling problems with an additive and weakly increasing cost function. We will show that the cooperative games related to these cost allocation problems have a nonempty core. Furthermore, we give a rule that assigns a core element of the associated cost saving game to each scheduling problem of this kind and an initial order of the jobs.