Single Machine Scheduling Problems With Learning And Forgetting Effects

This paper focuses on single machine scheduling problems with learning and forgetting effects in intermittent batch production, and the objective function is weighted total completion time. We consider three models of the scheduling problem based on the transmission of learning effect among batches, that is, the first model with no learning effect’s transmission among batches; the second one with partial learning effect’s transmission among batches; and the last one with total transmission of learning effect among batches. The main results are maintained as follows:(1) We establish a optimal algorithm with time complexity of O(nlogn) for the model with no learning effect’s transmission among batches.(2) For second model with partial learning effect’s transmission among batches, introducing the0-1variable and regarding batch as a workpiece, then the problem can be converted to the assignment problem, and a polynomial algorithm with complicity of O(nlogn+m3) is derived.(3) Under the situation of total transmission of learning effect among batches, it is proved that the completion time of the workpieces in every batch can be minimized in terms of scheduling law H, and then we analyze two special cases of the same number of the workpiece in each batch and existing control relationship among batches, and obtain their optimal polynomial algorithm.At last,we discussed the deterioration of job in the last chapter.