# Design Model of Flow Lines to Include Switch-Off Policies Reducing Energy Consumption
## 4 Reference Context and Simulation Scenarios  
Using the mathematical model described in Section 2, four production lines with 10 stations and 20 tasks to complete have been designed. The flow line only produces one product type. The operation processing times and the precedence constraints are described in Table 1 and have been obtained from the simple assembly line balancing problem dataset (SALBP) according to Reference [29]. The basic assumptions for the line design are the following:  
Figure 3: Machine states. * The stations can perform every possible operation assigned by the design model;
* The precedence constraints are fixed;
* No machine failure has been considered;
* The operations processing times are deterministic and are the same for each station. Figure 4 shows the precedence graph. In the precedence graph, each task is represented as a node, and each direct precedence constraint is illustrated as an arrow that links node i and k if the i-th operation must precede the k-th operation. For example, in Figure 4, operation 6 must be executed before operation 10. Four flow lines are obtained in order to get respectively:  
1. Minimization of total idle time for each cycle with minimum Cycle Time (MinTTd);
2. Maximization of distance between stations with a 2.5% increment of minimum Cycle Time (2.5% loss production rate, MaxD_2.5%);
3. Maximization of distance between stations with a 5% increment of minimum Cycle Time (5% loss production rate, MaxD_5%);
4. Maximization of distance between stations with a 10% increment of minimum Cycle Time (10% loss production rate, MaxD_10%). The solution of the mathematical model, considering the previous constrains, gives the following flow line designs (Table 2); moreover, the station processing times and the station idle times have been reported in Table 2.  
The first production line is considered to be the benchmark of the other production lines, because it gives a balanced production line with 10 stations and the minimum cycle time. A discrete event simulation, implemented in Arena, has been used to evaluate the performances of the four flow line designs and to analyze the application of switch off policies in unbalanced production lines. Figure 4: Precedence graph. Each model has been simulated by considering machines in the \"always on\" (AO) state and the UPD switch off policy. The basic assumptions of the AO model are:  
* Each station has a buffer;
* The buffer capacity is fixed, and equal to \(K\);
* The buffer of the first station is always full, that is the raw material is always available;
* The power absorbed in each state is equal for all machines. In addition, for the models with switch off policies, the following conditions apply:  
* Each station is controlled by a switch off policy;
* The control policy parameters (\(N^{U}_{\mathit{on}}\), \(N^{D}_{\mathit{off}}\), \(N^{D}_{\mathit{on}}\)) are the same for stations from 2 to 9;
* The first station has only DP policy;
* The last station has only UP policy. As described by [PERSON] and [PERSON] [15], the production line machines can be in the following states:  
* Working state: the machine is processing a piece and absorbs the power \(P_{w}\);
* Idle state: the machine is ready to work a part, and absorbs the power \(P_{i}\);
* Out-of-service (Inactive) state: the machine is not ready to process a part. In this state the machine absorbs the minimum amount of power \(P_{\mathit{off}}\);
* Warmup state: the machine changes its state from Out-of-service in idle or working state, consuming the power \(P_{wu}\) for the time to complete the warmup \(t_{wu}\). According to [23], the power required by a generic machine in each state is:  
* \(P_{w}=12\) kW;
* \(P_{i}=5.35\) kW;
* \(P_{\mathit{off}}=0.52\) kW;
* \(P_{wu}=6\) kW for \(t_{wu}=20\) s.  
To determine the best switch off control parameters, a full factorial design has been developed.