Open and closed blocks
                                        | 
                                                         Note: The combination of e-mobility and open line blocks is methodologically problematic because in this case, it is not possible to check whether the vehicle can be charged sufficiently to provide the intended services by the time it is used the next day. We therefore recommend forming only closed blocks for e-mobility.  | 
                                                
Independent of the selected calendar type, open and closed blocks can be generated. Open blocks start on the first day of the line blocking time period (or later) and end by the latest on the last day. For closed blocks, the last day is again followed by the first day of the line blocking time period, so that each end of a sequence of line block items is connected with a start. This ring closure is analog to timetable-based public transport assignment and is used to include the costs for creating the initial situation into the model. The creation of closed blocks assures that the created line block schedule "in perpetuo" can be traversed. The following example with an extremely unsymmetrical timetable makes this clear.
                                            
                                        
Illustration 192: Unsymmetrical timetable with trips beyond 24 hours
If open blocks are created in this example, then one vehicle is sufficient, because the trip from A Village to X City plus the empty trip in the opposing direction will require 66 minutes and the departure of this cycle in A village is every 2 hours. The vehicle can therefore reach the starting point before the start of the next trip.
When creating closed blocks however, two vehicles are required. The reason for this lies in the last trip, which is scheduled for 26:05 and thus still belongs to the previous day. Only one hour lies between the departure of this vehicle journey and the subsequent first trip on next day, so that the vehicle cannot return to the starting point in the meantime. When creating open blocks, this transition to the following day is not regarded, which may result in underestimating the vehicle demand.
Apart from the pure vehicle demand, the open block solution of course has one empty trip less. If costs are evaluated for empty trips, this solution also simulates a less expensive situation. In each case it has to be decided, whether the empty trip which is required to form the ring closure has to be included in the model or not.
| 
                                                         Note: Open blocks can be created if the model represents the planning situation for a certain single day or period. If the line blocking time period however, represents a longer cycle which is to be repeated (for example a default day), closed blocks should be created, to correctly determine the costs for restoring the initial state in the model.  | 
                                                
| 
                                                         Block no.  | 
                                                    
                                                         Block version code  | 
                                                    
                                                         Number of block days  | 
                                                    
                                                         Block closed  | 
                                                    
                                                         Mean operating time  | 
                                                    
                                                         Mean operating kilometers  | 
                                                
| 
                                                         1  | 
                                                    
                                                         OpenBlocks  | 
                                                    
                                                         1  | 
                                                    
                                                         0  | 
                                                    
                                                         12h 51min  | 
                                                    
                                                         616  | 
                                                
| 
                                                         2  | 
                                                    
                                                         Self-ContainedBlocks  | 
                                                    
                                                         2  | 
                                                    
                                                         1  | 
                                                    
                                                         6h 36min  | 
                                                    
                                                         321  | 
                                                
| 
                                                         Block no.  | 
                                                    
                                                         Index  | 
                                                    
                                                         Blocking day  | 
                                                    
                                                         Block item type  | 
                                                    
                                                         Line name  | 
                                                    
                                                         Vehicle journey no.  | 
                                                    
                                                         Start time  | 
                                                    
                                                         From StopPointName  | 
                                                    
                                                         End time  | 
                                                    
                                                         To StopPointName  | 
                                                
| 
                                                         1  | 
                                                    
                                                         1  | 
                                                    
                                                         1  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         16  | 
                                                    
                                                         03:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         03:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         1  | 
                                                    
                                                         2  | 
                                                    
                                                         1  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         3.50  | 
                                                    
                                                         X-City  | 
                                                    
                                                         04:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         1  | 
                                                    
                                                         3  | 
                                                    
                                                         1  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         04:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         05:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         1  | 
                                                    
                                                         4  | 
                                                    
                                                         1  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         18  | 
                                                    
                                                         05:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         05:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         1  | 
                                                    
                                                         5  | 
                                                    
                                                         1  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         5:50:00 AM  | 
                                                    
                                                         X-City  | 
                                                    
                                                         06:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         1  | 
                                                    
                                                         6  | 
                                                    
                                                         1  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         06:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         07:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                
| 
                                                         1  | 
                                                    
                                                         31  | 
                                                    
                                                         1  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         36  | 
                                                    
                                                         23:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         23:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         1  | 
                                                    
                                                         32  | 
                                                    
                                                         1  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         23:50:00  | 
                                                    
                                                         X-City  | 
                                                    
                                                         00:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         1  | 
                                                    
                                                         33  | 
                                                    
                                                         1  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         00:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         02:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         1  | 
                                                    
                                                         34  | 
                                                    
                                                         1  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         37  | 
                                                    
                                                         02:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         02:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         2  | 
                                                    
                                                         1  | 
                                                    
                                                         1  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         
  | 
                                                    
                                                         00:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         02:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         2  | 
                                                    
                                                         1  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         37  | 
                                                    
                                                         02:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         02:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         2  | 
                                                    
                                                         3  | 
                                                    
                                                         1  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         02:50:00  | 
                                                    
                                                         X-City  | 
                                                    
                                                         03:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         4  | 
                                                    
                                                         1  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         03:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         00:00:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         5  | 
                                                    
                                                         2  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         00:00:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         03:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         6  | 
                                                    
                                                         2  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         16  | 
                                                    
                                                         03:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         03:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         2  | 
                                                    
                                                         7  | 
                                                    
                                                         2  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         3.50  | 
                                                    
                                                         X-City  | 
                                                    
                                                         04:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         8  | 
                                                    
                                                         2  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         04:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         05:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         9  | 
                                                    
                                                         2  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         18  | 
                                                    
                                                         05:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         05:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         2  | 
                                                    
                                                         10  | 
                                                    
                                                         2  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         05:50:00  | 
                                                    
                                                         X-City  | 
                                                    
                                                         06:11:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         2  | 
                                                    
                                                         11  | 
                                                    
                                                         2  | 
                                                    
                                                         Layover  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         06:11:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         07:05:00  | 
                                                    
                                                         A-Village  | 
                                                
| 
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                    
                                                         ...  | 
                                                
| 
                                                         2  | 
                                                    
                                                         36  | 
                                                    
                                                         2  | 
                                                    
                                                         Vehicle journey  | 
                                                    
                                                         BUS1  | 
                                                    
                                                         36  | 
                                                    
                                                         23:05:00  | 
                                                    
                                                         A-Village  | 
                                                    
                                                         23:50:00  | 
                                                    
                                                         X-City  | 
                                                
| 
                                                         2  | 
                                                    
                                                         37  | 
                                                    
                                                         2  | 
                                                    
                                                         Empty trip  | 
                                                    
                                                         
  | 
                                                    
                                                         0  | 
                                                    
                                                         23:50:00  | 
                                                    
                                                         X-City  | 
                                                    
                                                         00:11:00  | 
                                                    
                                                         A-Village  | 
                                                
Table 217: Block items of both blocks in the example – Block items in the recurring rhythm were omitted for a better overview. Block 1 is open, block 2 is closed.

