Article Preview
TopProduction scheduling is viewed as one of the key factors in production and operation management, which manages the limited resources allocation to tasks in the whole production process. Since the first scheduling work appeared in 1954 by Johnson (Johnson, 1954), the researches on this topic have been paid seriously attention in the manufacturing field. In the last six decades, most researchers studied the scheduling problems with the focuses on the time requirement. They considered various objectives, such as makespan, lateness/tardiness and weighted completion time (Tavakkoli-Moghaddam, Khalili, & Naderi, 2009; Laha & Chakraborty, 2010; Ziaee, 2014; Demir & İşleyen, 2014; Pezzella, Morganti, & Ciaschetti, 2008; Karthikeyan, Asokan, & Nickolas, 2014; Li, Pan, & Tasgetiren, 2014; Muthiah & Rajkumar, 2014; Spanos, Ponis, Tatsiopoulos, Christou, & Rokou, 2014; Fu, Chan, Niu, Chung, & Qu, 2019). However, in the real-life production, energy consumption always exists, which can be characterized by the power, process times, and machine states. Mouzon and Yildirim (2008) considered the energy consumption related to the idle power and machine setup power. Fang et al. (2011) established a new mathematical model of the scheduling problem in a flow shop with several factors consisting of peak power load, energy consumption, carbon footprint and makespan. Yi et al. (2012) presents a scheduling model in a job shop with the multi-objective to minimize cycle time and carbon emissions. Liu et al. (2014) considered a bi-objective model aims to optimize the electricity consumption and total weighted tardiness. Moon et al. (2013) dealt with the unrelated parallel machine scheduling problem to improve the production and energy efficiency. Shrouf et al. (2016) considered variable energy prices in a day and built a mathematical model to minimize energy consumption costs of a single machine. Dai et al. (2013) established an energy-efficient scheduling model in a flexible flow shop. A genetic-simulated annealing algorithm is designed to optimize the makespan and energy consumption. Yin et al. (2017) established a new low-carbon mathematical scheduling model for the flexible job shop environment to optimize productivity, energy efficiency and noise reduction. A multi-objective genetic algorithm on the basis of a simplex lattice design was developed to deal with the low-carbon scheduling model effectively. The scheduling problem associated to energy consumption is still in the initial stage of exploration. Therefore, more studies should be carried out and extended to more general manufacturing processes. Flexible job shop scheduling problem (FJSSP) is an extended version of the job shop scheduling problem (JSSP) and more difficult than the latter one. Li and Gao (2016) hybridized the genetic algorithm and tabu search for the FJSP to minimize the makespan. Li et al. (2017) proposed a Variable Neighborhood Migrating Birds Optimization Algorithm for Flexible Job Shop Scheduling. Zhu et al. (2017) presented a modified Bat Algorithm for the Multi-Objective Flexible Job Shop Scheduling Problem. Flexible job shop has a wide application in the manufacturing fields. However, as far as we know, few relevant literatures on the low-carbon scheduling problem exist in the flexible job shop. Therefore, the research work in this paper has some significance to a certain extent.