Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines

This paper proposes an efficient algorithm to solve optimally the bicriteria problem of minimising the weighted sum of makespan and mean flowtime on two identical parallel machines. The proposed algorithm allows the decision-maker to minimise makespan and flowtime simultaneously according to his or her relative preference as reflected through the weights placed on makespan and flowtime. Our computational results show that the proposed algorithm can solve optimally problem instances with a large number of jobs in a reasonably small amount of CPU time.