# Design Model of Flow Lines to Include Switch-Off Policies Reducing Energy Consumption
## 1 Introduction and Motivations  
Nowadays, the industrial manufacturers study energy-efficient models because of the costs and environmental impact of energy consumption [1, 2]. The manufacturing activities are characterized by a relevant demand from around 40% with relevant growth expectations between 2018 and 2050 across all cases. Increases in industrial energy use from increasing shipments are partially offset by efficiency gains [3]. Studies by the European Association of the Machine Tool Industries [4, 5] on the discrete part manufacturing discussed the importance and environmental impacts of electrical energy consumption. The main models proposed in the literature, for the design of manufacturing systems, focused primarily on the performance in regards to productivity, quality, and work in process, etc. Recently, the models proposed include the energy efficiency issue, but [PERSON] et al. [6] emphasized how the scheduling models that include energy-saving may reduce the other goals of the manufacturing systems. Then, it is more important to propose a model that reduces energy consumption without reducing the productivity performance of manufacturing companies. The works proposed regarding machining energy consumption [7, 8] identified three main energy shares: start-up operations (computers and fans, coolant pumps, etc. ), runtime operations (tool change, Jog axis, etc.) and material removal operations (machining). The first and second parts are constant and independent of the operation, while the third part is variable and depends on the machining operation. [PERSON] et al. [8, 9, 10] underlined how the constant independent of the operation is the major part of the energy consumed by the machining machines and this trend has grown in past years. The reduction in the energy consumption of these parts can be obtained without studying the effect on the particular machining operation as: roughness, cutting paths, cutting time, etc. Therefore,it is more simply to extend a model that reduces the constant energy to several machining systems and other production systems. A promising approach proposed in the literature to reduce the constant energy consumed by the machining machines is the switch-off policy [11]. Reducing the idle time is a good approach to realize energy-efficient production [12]. One example is the suppliers for small-parts in aircrafts, where the idle periods accounted for \(16\%\) of the total production time, and about \(13\%\) of the total energy consumption could be saved if the idle machines were switched off [13]. Another study by [PERSON] and [PERSON] [14] highlighted how almost \(50\%\) to \(60\%\) of energy consumption could be reduced by turning the standby machines into energy-saving states. The switch-off policies switch off when the machine is in the idle state, which reduces the constant energy consumed during this state. When there are a determined number of parts waiting for the operation, the machine switches on, subject to a warm-up period to be operative. The decision of the switch on is crucial to maintain the productivity level of the production line. Some approaches have been proposed, by [PERSON] and [PERSON] [15; 16], with a significant reduction in energy consumption in a flow lines context. The switch-off models proposed works on a flow line designed following classical objectives that solve the simple assembly line balancing problem [17; 18]. An extensive survey of the flow line production system balancing was discussed in References [19; 20]. Mathematical models to support the decision towards the switch off/on, which works off-line, have been proposed by [PERSON] and [PERSON] [21] and [PERSON] et al. [22]. These models did not handle the uncertainty of the production system and the optimization can lead to high computational complexity when the number of machines is higher; this reduces the potential application in real industrial manufacturing systems. [PERSON] et al.