Minimizing the maximum lateness for scheduling with release times and job rejection

Abstract

We study scheduling problems with release times and rejection costs with the objective function of minimizing the maximum lateness. Our main result is a PTAS for the single machine problem with an upper bound on the rejection costs. This result is extended to parallel, identical machines. The corresponding problem of minimizing the rejection costs with an upper bound on the lateness is also examined. We show how to compute a PTAS for determining an approximation of the Pareto frontier on both objective functions on parallel, identical machines. Moreover, we present an FPTAS with strongly polynomial time for the maximum lateness problem without release times on identical machines when the number of machines is constant. Finally, we extend this FPTAS to the case of unrelated machines.