# Design Model of Flow Lines to Include Switch-Off Policies Reducing Energy Consumption
## 5 Numerical Results  
As shown in the following figure (Figure 7), an increment of the cycle idle time for each station has been achieved by choosing the maximization of the distance between stations as the objective function, instead of the minimization of idle time. The maximum increment of \(TT_{d}\) has been obtained in the case where the cycle time has been increased by 10%. Figure 6: Simulation process and performances evaluation. Figure 7: Increment of idle time for each cycle. The discrete event simulation results, as compared to the model MinTTd, are shown in Figure 8. The results in the figure only consider the effects of the unbalanced line on the idle time, so the simulations have been made by considering machines with an always on control policy. It can be noticed that the higher the idle time, the lower the throughput. Indeed, by increasing the distance, stations are in the idle state for longer than in a balanced flow line. Increased cycle time allows for mathematical optimization, which aims to maximize the distance between station process times and to have greater freedom in assigning operations to the machines. The 10% increase in cycle time (MaxD_10%) results in a flow line where the idle time has grown by 159%, but productivity has decreased by only 9%. However, the increase in downtime leads to more energy consumption in a non-productive state. In order to reduce energy consumption, switch-off policies should be in place. The UDP policy achieves a significant reduction in energy consumption in non-productive states. In Figure 9, the energy consumption in unproductive states (Idle, Out-of-service, Warmup) of the four lines (MinTTd, MaxD_2.5%, MaxD_5%, MaxD_10%) are compared to a case with machines that are always on and those applying switch off policies. In all the cases analyzed, adopting a shutdown policy allows for a significant reduction in energy consumption in non-productive states, ranging from 86% to 89%. For these reasons, switch-off policies in unbalanced flow lines are necessary and achieve a reduction in unproductive state energy consumption. If the machines are in always on states, the unbalancing flow line leads to a reduction in throughput and energy consumption due to more time being spent in the idle state. Staying for a long time in the idle state is detrimental, since in this state, the machine is ready to work and then absorbs power without producing. The switch-off policies warrant energy saving due to the lower energy consumption during warmup. Designing an unbalanced flow line and controlling the machines state with a switch-off policy can lead to a reduction in total energy consumption, not only in unproductive states. Figure 10 shows the increment of energy consumption for an unbalanced flow line design with switch-off policies, compared to an always on balanced flow line. For this reason, designing a flow line to achieve a high unbalance under cycle time constraints, and applying a machine shutdown policy, leads to a reduction in total energy consumption. Figure 8: Results with always on policy. Figure 11 shows the total time that stations hold in the inactive state and the number of warmups. Like the number of pieces in the buffer, the number of times that machines switch on depends on the position of the bottleneck. Machines turn on fewer times when using model MaxD_5% than model Max_2.5%, even if the total inactive time is longer, because the last station is the bottleneck. It can be seen that, if the bottleneck is among the first machines on the line, it can lead to a reduction of the work in process and storage costs. However, this leads to more switch-ons and higher energy consumption during warmup. Figure 10: Total energy reduction. Figure 9: Reduction of energy consumption in unproductive states using switch-off policies. Figure 12 reports the switch-off mean times. It can be noticed that the model MaxD_5% gives the maximum value of the mean inactive time. Thus, this configuration leads to a high inactive time for each switch off.