## 2 Related Literature  
This section presents existing literature on scheduling and OAS problems under energy aspects with their developed solution approaches. First, an overview on scheduling problems incorporating environmental aspects is given. Next, related works on OAS problems are introduced. Before concluding, a focus is made on the resolution techniques. [PERSON] et al. 's [15] review on scheduling problems under energy aspects reveals that this topic has been growing in interest in recent years. Complex shop systems, including job shop and flow shop, represent the majority of the studies, whereas single machine features less than 4% of their corpus. One of the most important points highlighted in this study is that energy efficiency is conceptualized by two approaches. First and foremost, it is done by introducing it as a criterion. Indeed, targeted criteria such as Total Energy Consumption or Costs (TEC) or total carbon emissions have been successfully incorporated into scheduling problems in numerous work [16; 17; 18; 19]. Second, energy efficiency is modeled by dedicated constraints coupled with a classical scheduling objective [20; 21]. For example, in the work of [PERSON] et al. [20], weighted tardiness and completion times are minimized while satisfying a periodic threshold on energy consumption for a single machine. In the literature, different assumptions relative to the energy aspects may be encountered. These assumptions are related to the quantity considered (carbon emissions, energy consumption, power etc. ), the machine characteristics (energy states, speed), the variation of the energy costs during the day or the system involved (single machine or shop systems). Depending on these assumptions, the problem entails particular properties and thus is solved with specific approaches. For single machines, [PERSON] and [PERSON] [5] present an adaptive search metaheuristic to minimize TEC and total tardiness. In their study, they examine the idle, setup and processing energy of the machine in order to efficiently adjust the production and avoid tardy jobs. The neighborhood move developed by the authors inserts setup or idle times between jobs, which can reduce energy costs but can lead to tardiness. [PERSON] et al. [22] consider a TI MILP to minimize TEC under TOU electricity tariffs and develop a greedy insertion heuristic which moves jobs to the off-peak periods. [PERSON] et al. [23] propose a dynamic program for the single machine problem under TOU tariffs considering machine states and investigate the complexity of various energy costs strategies that can induce the problem to be polynomial. As for shop scheduling or parallel machines, other energy aspects are studied. [PERSON] et al. [24] address a speed scaling job shop problem with the objective to minimize both tardiness and TEC. In their work, they monitor machines speed to efficiently modulate the production process. Dedicated local search procedures are designed to cope with the complexity of the problem. In the same vein, [PERSON] et al. [25] consider energy consumption per time unit and idle energy consumption minimizing TEC and makespan. They employ an Evolutionary Algorithm (EA) in their solving approach. In [26], the authors optimize the TEC and the makespan of unrelated parallel machines under time-and-machine-dependent electricity costs. Their solving approach involves an hybrid GA that incorporate an idle-time insertion procedure to cut costs on electricity expenses. Considering CO\({}_{2}\) emissions, [PERSON] and [PERSON] [27] assess common carbon reduction policies on a flow shop. One of their conclusion confirms that optimizing the schedule plays a key role in the reduction of CO\({}_{2}\) emissions rather than changing equipment. In the meantime, they show that the 'cap and trade' approach is a cost-effective policy. In [7], a flowshop under time-dependent electricity tariffs and CO\({}_{2}\) emissions is tackled.