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

Abstract

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 $O(n\hspace{0.17em}\text{log}\hspace{0.17em}n)$ 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.