A PTAS for Scheduling on Agreeable Unrelated Parallel Batch Processing Machines with Dynamic Job Arrivals

Abstract

We consider the scheduling problem R _m | r _j ,B | C _max under the assumption of agreement, i.e., $p_{ij_{1}} \geq p_{ij_{2}}$ for some i implies $p_{ij_{1}} \geq p_{ij_{2}}$ for all 1 ≤ i ≤ m, where $p_{ij_{1}}$ and $p_{ij_{2}}$ denote the processing times on machine M _i of jobs J _j1 and J _j2, respectively. For the special case when the number of distinct release times t is constant and all processing times and release times integral, we propose a pseudo-polynomial time algorithm by approach of dynamic programming. Without the integral restriction, an FPTAS is provided. And for the general case with arbitrary t, we establish a PTAS.