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

Abstract

a b s t r a c tSustainability 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.

Minimizing energy consumption and makespan in a two-machine flowshop scheduling problem

“…These include applications for instance in printed circuit board (Sabouni and Logendran, 2013), shampoo production (Belaid et al, 2012), and metalworking (Uruk et al, 2013). In this paper, we extend the work of Mansouri et al (2016) by developing a new O(n 2 ) heuristic and multi-objective genetic algorithms (MOGAs) for a sequence-dependent two-machine permutation flowshop scheduling problem to extend applicability of the concept of green scheduling in real life applications. In particular, we examine the effect of hybridizing the MOGA with the constructive heuristics to improve the efficiency and the effectiveness of the search.…”

“…However, the research on including energy consumption with variable speeds is yet to grow. Continuing on a previous work by Mansouri et al (2016) that analyzes the trade-off between minimizing makespan, a measure of service level and minimizing total energy consumption, an indicator of environmental sustainability, we are aiming to address this gap by furthering the modelling of energy consumption explicitly in scheduling and developing heuristic and metaheuristic algorithms to solve this problem.…”

“…To address the computational complexity of the constructive heuristic developed by Mansouri et al (2016), which is an O(n 3 ) algorithm (called CH1 in this paper), we first introduce a novel constructive heuristic (CH2) with the reduced complexity O(n 2 ). Subsequently, we develop regular and hybrid MOGAs (denoted by R-MOGA and H-MOGA, respectively) to further improve the effectiveness and efficiency of search for the Pareto frontier of Problem P. Finally, we introduce an ϵ-constraint method run on CPLEX and random search as two widely used benchmark approaches to assess performance of search heuristics.…”

“…It entails complex decision making and trade-off analysis by the operations managers. As one of the first attempts in this field, Mansouri et al (2016) addressed a bi-criteria two-machine flowshop scheduling problem to minimize total energy consumption and makespan. They showed the conflict between the two objectives and developed an O(n 3 ) heuristic to solve large size problems.…”

Multi-criteria decision making approaches for green supply chains: a review

“…In seven publications assigned to production planning no economic indicators were used. Publications that did not use an economic indicator in production planning, focused on balancing between either energy consumption and total completion time (Mansouri et al 2016;Yildirim and Mouzon 2012;Mouzon et al 2007), energy consumption and tardiness (Liu et al 2014b), carbon emissions and total completion time (Liu et al 2014a), or focused on environmental indicators objectives only in pinch analysis (Geldermann et al 2006(Geldermann et al , 2007. In some publications two economic indicators are used simultaneously, e.g.…”