Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model is p(j) = a(j) + alpha t and of the second model is p(j) = a + alpha(j)t The objective is to minimize the makespan. We present O(nlogn) time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.