Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time

Abstract

We consider bicriteria scheduling problems with identical machines in parallel and two popular but conflicting objectives, namely, the makespan and the total completion time. Assuming no prioritization of the two objectives, we are interested in the simultaneous optimization of the two objectives and approximation algorithms relative to an ideal schedule – which may not exist – that has both objectives at their minimum. For the problem with a given number of machines, we propose a fast (ρ1,ρ2)-approximation algorithm where ρ1 and ρ2 represent approximation ratios with regard to the makespan and the total completion time, respectively. We also analyze the problem’s inapproximability by proposing a lower bound of the approximation ratio, which cannot be improved by any algorithm.