# Research on Low-Carbon-Emission Scheduling of Workshop under Uncertainty
## 1 Introduction  
Increasing carbon emissions play a crucial role in global warming, especially in industrial fields. Industries produce 35% of carbon emissions in China, which hurts the environment [1; 2]. Carbon emissions are not eco-friendly, and the associated repercussions are global warming, severe meteorological deviations, and serious environmental pollution [3]. With the development of people's ecological awareness, low carbon emissions and energy efficiency in the manufacturing industry have been receiving much attention [4]. The workshop scheduling optimization method effectively reduces carbon emissions and relieves environmental pressure [5]. Various scheduling strategies result in varying levels of carbon emissions, and reasonable scheduling methods are essential to complex flexible shop-floors. To increase enterprise profitability and control carbon emissions in the manufacturing sector, it is critical to implement a low-carbon-emission scheduling optimization method for workshops. Manufacturing enterprises must carry out high-efficiency, low-carbon-emission, and low-cost manufacturing to enhance their competitiveness. The scheduling optimization model is constructed to optimize the manufacturing workshop. [PERSON] and [PERSON] [6] applied the non-dominated sorting genetic algorithm (NSGA) to design a non-compact flow shop scheduling plan. They successfully solved the multi-objective optimization problem considering process connection, which carries profound theoretical and practical significance for enterprises, e.g., improving the scheduling of non-compact flow shops, the production efficiency, and the response to market situations. [PERSON] [7] proposed the improved NSGA-II to minimize the makespan, total energy consumption, and total costs of the flexible job shop cell scheduling problem to achieve flexible manufacturing. [PERSON] et al. [8] established the many-objective job shop intelligent scheduling model with complex constraints. Theyproposed an improved intelligent decision optimization algorithm named NSGA-III-APEV based on NSGA-III, which can ensure that the decision-maker obtains a more suitable production scheduling scheme. Various uncertainties in the production process can disturb the production system and affect the scheduling plan, so many studies are focused on workshop robustness to improve resistance to disturbances. [PERSON] et al. [9] proposed a genetic algorithm for robust hybrid flow shop scheduling to evaluate the quality of the robustness when faced with uncertainty. [PERSON] et al. [10] introduced a robustness framework for the stochastic hybrid flow shop problem under uncertainty to find a robust solution that can resist changes in input data. [PERSON] et al. [11] constructed the multi-objective stochastic flexible job shop scheduling problem model, considering three objectives: makespan, maximal machine workload, and robustness to uncertainties. Considering various uncertainties in the actual manufacturing process, [PERSON] et al. [12] proposed a flexible job shop scheduling problem with machine breakdown, with the objectives of maximum completion time and robustness. Meanwhile, there is more and more research on low-carbon scheduling problems. [PERSON] et al. [13] designed a multi-objective NEH algorithm and a modified multi-objective iterated greedy algorithm to solve a permutation flow shop model to minimize the carbon emissions and makespan. [PERSON] and [PERSON] [14] studied the problem of distributed low-carbon parallel machines. [PERSON] and [PERSON] [15] constructed a two-stage re-entrant hybrid-flow-shop bi-level scheduling model and used the NSGA-III algorithm to lower carbon emissions and energy costs. [PERSON] and [PERSON] [16] proposed that green manufacturing has become a hot topic globally, and they designed a customer-oriented method to support multi-task green scheduling in cloud manufacturing, intending to minimize the total energy consumption during scheduling.