A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling.

In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost.