###### Abstract  
This research focuses on an Order Acceptance Scheduling (OAS) problem on a single machine under time-of-use (TOU) tariffs and taxed carbon emissions periods with the objective to maximize total profit minus tardiness penalties and environmental costs. Due to the NP-hardness of the considered problem especially in presence of sequence-dependent setup-times, two fix-and-relax (FR) heuristics based on different time-indexed (TI) formulations are proposed. A metaheuristic based on the Dynamic Island Model (DIM) framework is also employed to tackle this optimization problem. These approached methods show promising results both in terms of solution quality and solving time compared to state-of-the-art exact solving approaches. single machine scheduling; order acceptance; green scheduling time-indexed; fix-and-relax 4.0.11.11.11.11.1.11.1.11.1.11.1.1.11.1.11.1.1.1.11.1.  
energy aspects into planning and scheduling, besides replacing obsolete equipment, is one of the most cost-effective ways to attain sustainability objectives [5] such as reducing GHG emissions and energy consumption. However, a trade-off between reducing energy consumption and productivity is always noticeable [6]. Nevertheless, energy sobriety is beneficial for both economic and environmental reasons. First, energy cost is a shortfall for heavy energy-using industry as the energy supplies are becoming expensive. For this purpose, smart grid technologies have already been deployed. In this context, energy providers have designed preferential tariffs rate such as time-of-use (TOU), real-time or critical peak pricing. TOU rates incite manufacturers to shift their production to cheaper off-peak hours instead of on-peak hours. Second, depending on the energy mix used (e.g., coal or gas based), reducing energy consumption or costs is a direct way to reduce GHG emissions [7]. Early industry focused on mass production with high volumes of few products. Yet, this past decade, major changes in industry have been occurring [8]. Product variety and demand for tailor-made products force manufacturers to make a compromise between their available production capacity, their production organization and their sales volume. This global trend appears in a plethora of manufacturing sectors from textiles to the food industry. Indeed, this can be observed in real manufacturing settings, such as printing processes in packaging companies [9], service delivery including food or critical equipment maintenance companies facing time windows, high demands with limited resources deployment [10; 11]. Order acceptance scheduling (OAS) is an abstraction to model this particular trend. In this vein, this paper investigates a single machine OAS problem with release date and sequence-dependent setup times under TOU tariffs and taxed carbon emissions. In this problem, the company has to decide which order to produce, among \(n\), and establish a schedule accordingly. Each order is available within a specific time window. Moreover, a setup operation is performed between orders, and its duration depends on the previous order sequenced. The objective is to maximize the total revenue of orders minus tardiness penalties while meeting clients deadlines and green manufacturing considerations. The latter has an impact on the orders selection and their schedule. [PERSON] et al. [12] are the first to introduce this problem while proposing a disjunctive Mixed Integer Linear Program (MILP). [PERSON] et al. [13] consider an arc-time-indexed (ATI) MILP to cope with the high complexity of this NP-hard problem and successfully solve some large instances. However, these approaches are limited by design and thus require the use of heuristics. For this purpose, this paper analyses two time-indexed (TI) formulations and two Fix-and-Relax (FR) heuristics applied to the provided formulations. Moreover, an island-based genetic algorithm (GA) first proposed by [PERSON] et al. [14] is developed. The contributions of this paper are threefold. First, we refine mathematical models on this problem.