# Design Model of Flow Lines to Include Switch-Off Policies Reducing Energy Consumption
## 1 Introduction and Motivations
[23] and [PERSON] and [PERSON] [16] studied upstream, downstream, and mixed policies in a single machine, and the extension to a production line, assuming stochastic arrivals, and constant warm-up under to stock control. These models did not consider how the control of the machines may reduce the production performance of the manufacturing system. [PERSON] [24] studied a dynamic and adaptive control strategy to switch-off the machines on a production line under the pull control policy. The policy proposed uses the information of the buffers and the level of customer satisfaction. The results also underlined the potential application of the switch-off policies in production lines under pull control. [PERSON] et al. [25] studied one machine with one buffer with a fuzzy controller that includes the information about the buffer, the machine state and the production rate required, considering the warm-up energy. The controller was tested through simulation experiments and it was observed that a large amount of energy could be saved without affecting the throughput significantly. [PERSON] et al. [26; 27] proposed a method based on a fuzzy controller that includes the information of the upstream, downstream buffer and the status of the machine. They proposed a set of fuzzy rules to take the decision to the switch off/on policy. The simulation experiments show that the proposed approach can be a simple, practical way towards the energy saving operation with accepted throughput loss. [PERSON] et al. [28] proposed a model that controls the machine on-line acquiring data and estimating the risk of the control policy actions. The model has several limitations because it is tested for a specific distribution for the estimation of the parameters and the tests are conducted considering a production line composed of two machines. The discussion of the past works highlights the following issues:  
* The switch-off policies are mainly proposed for a single machine and some works considered a flow line with the introduction of buffers;
* Few works evaluate the reduction of the performance level due to the introduction of the switch-off policy, but only energy consumption;
* Works were proposed to consider the possibility of a switch-off policy and were considered from the design step of the production line. In response to the limits in the literature, this paper proposed a design model that includes the switch-off policy by first asking:  
RQI: what is the impact of the design model proposed on the performance of the production line in terms of energy saving maximizing the production rate? Some previous works show how the switch-off policy causes production loss, then our second research question asks:  
RQ2: can the constraint of a limited reduction loss improve significantly the energy saving of the production line obtaining an adequate trade off? The research proposed concerns about the development of a design model of the flow lines that includes the possibility of the switch-off already in this design step. Then, the switch-off policy is introduced in the flow line designed by the proposed model. The proposed design and switch-off policy is compared to a flow line designed with the classical objectives with the same switch-off policy. Simulation experiments will be used to answers our two research questions. The simulations were conducted by considering different levels of production rates in the design model and different levels of the buffers (upstream and downstream) that control the switch-off policy. The paper is organized as follows. Section 2 described the design model of the flow line, while Section 3 introduces the switch-off policy used. Section 4 introduces the reference context investigated with simulation scenarios, while Section 5 discussed the numerical results. Section 6 provides the conclusions and a future research path.