Green parallel machines scheduling problem: A bi-objective model and a heuristic algorithm to obtain Pareto frontier

Sustainability consciousness in manufacturing has become an interesting topic for many researchers in recent years. There is also more concern in many companies about reducing energy consumption in manufacturing. Improving environmental health and safety, production cost saving, access to governmental incentives such as grants and tax credits and also improving the brand image are the most important reasons which is leading many companies to an environmental-friendly production planning. For example, one of the most applicable scheduling problems deals with planning jobs on numbers of parallel machines. In such an application, different machines have different technologies and different speed and power of energy consumption in manufacturing similar jobs. This article introduced a mathematical formulation which models the green parallel machines scheduling problem with total energy consumption and total completion time as objectives. Due to high computational complexity of the proposed model, a heuristic algorithm is developed to obtain the exact Pareto frontier of these two objectives with a polynomial complexity. Numerical experiments are presented to show the efficiency and speed of the proposed algorithm compared to solving the model using the optimisation software directly.