Multiple-Machine Scheduling with Learning Effects and Cooperative Games

Multiple-machine scheduling problems with position-based learning effects are studied in this paper. There is an initial schedule in this scheduling problem. The optimal schedule minimizes the sum of the weighted completion times; the difference between the initial total weighted completion time and the minimal total weighted completion time is the cost savings. A multiple-machine sequencing game is introduced to allocate the cost savings. The game is balanced if the normal processing times of jobs that are on the same machine are equal and an equal number of jobs are scheduled on each machine initially.