A great amount of energy is wasted in industry by machines that remain idle due to underutilisation. A way to avoid wasting energy and thus reducing the carbon print of an industrial plant is to consider minimisation of energy consumption objective while making scheduling decisions. To minimise energy consumption, the decision maker has to decide the timing and length of turn off/turn on operation (a setup) and also provide a sequence of jobs that minimises the scheduling objective, assuming that all jobs are not available at the same time. In this paper, a framework to solve a multiobjective optimisation problem that minimises total energy consumption and total tardiness is proposed. Since total tardiness problem with release dates is an NP-hard problem, a new greedy randomised multiobjective adaptive search metaheuristic is utilised to obtain an approximate pareto front (i.e. an approximate set of non-dominated solutions). Analytical Hierarchy Process is utilised to determine the ‘best’ alternative among the solutions on the pareto front. The proposed framework is illustrated on a case study. It is shown that a wide variety of dispersed solutions can be obtained via the proposed framework, and as total tardiness decreases, total energy consumption increases.