Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

Sustainability considerations in manufacturing scheduling, which is traditionally influenced by service oriented performance metrics, have rarely been adopted in the literature. This paper aims to address this gap by incorporating energy consumption as an explicit criterion in shop floor scheduling. Leveraging the variable speed of machining operations leading to different energy consumption levels, we explore the potential for energy saving in manufacturing. We analyze the trade-off between minimizing makespan, a measure of service level and total energy consumption, an indicator for environmental sustainability of a two-machine sequence dependent permutation flowshop. We develop a mixed integer linear multi-objective optimization model to find the Pareto frontier comprised of makespan and total energy consumption. To cope with combinatorial complexity, we also develop a constructive heuristic for fast trade-off analysis between makespan and energy consumption. We define lower bounds for the two objectives under some non-restrictive conditions and compare the performance of the constructive heuristic with CPLEX through design of experiments. The lower bounds that we develop are valid under realistic assumptions since they are conditional on speed factors. The Pareto frontier includes solutions ranging from expedited, energy intensive schedules to prolonged, energy efficient schedules. It can serve as a visual aid for production and sales planners to consider energy consumption explicitly in making quick decisions while negotiating with customers on due dates. We provide managerial insights by analyzing the areas along the Pareto frontier where energy saving can be justified at the expense of reduced service level and vice versa.