Bi-objective green scheduling in uniform parallel machine environments

Green and sustainability issues are being considered extensively in industry and in the literature. Most of the green-related effects in the manufacturing sector can be modeled by the costs associated with the production machines due to their resource consumption and/or pollutant emission, as a part of the operation cost. Accordingly, taking into account the machine processing costs alongside the other production criteria is one of the main approaches to consider green issues in the production management problems. In the same way, scheduling as one of the major operational problems in the factories can benefit this point of view to involve sustainability aspects. In this paper, the aforementioned modeling approach is taken one more time to establish a formulation for a green scheduling problem in uniform parallel machine environments. Here, it is assumed that the machines have different processing cost rates, i.e. they are different with regard to sustainability. The considered problem objectives are the total green cost and the makespan which are minimized simultaneously with the aim of earning Pareto optimal solutions. To this end, the epsilon-constraint method is first used to convert the problem into single objective problems. Then an existing heuristic is improved to solve these problems and estimate the Pareto solutions that show the trade-offs between the green cost objective and the ordinary time objective. Moreover, having a rigorous analyze in a theorem, some useful upper bounds for the gap of the green cost of the heuristic solution from optimality is derived. Finally, conducting numerical experiments at the end of the paper, the superiority of the improved heuristic to the previous one and its effectiveness in approximating the Pareto optimal solutions is demonstrated. (C) 2019 Elsevier Ltd. All rights reserved.