Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem

Xiechen Zhang, Eric Angel, Feng Chu, Damien Regnault

Abstract: Highlights•Identify the complexity for each criterion in uncertain parallel machine scheduling.•Propose a polynomial-time algorithm to minimize total completion time.•Develop a (1+ϵ)-approximation algorithm for makespan criterion.•The uncertain bi-criteria problem with any number of machines can be 2-approximated.•Provide a FPTAS for the uncertain bi-criteria problem with fixed number of machines.