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Chapter 6. Rostering Level . Intermediate Rostering 6.2 Intermediate Rostering The basic section of this chapter set the foundation for rostering using a relatively LEVEL simple example. In this section, you will develop rosters for Route based on the 2 Run Guide from the intermediate section of Chapter : Runcutting (shown below). This Run Guide includes eight full-time runs, as shown below. Completed Run Cut - Blocks Rehooked Start End Total Run Block Report Sign Off Plat Report Paid Travel Spread Paid Pay/ Type Work Spread Make-up Overtime # # Time Time Hours Hours Break Hours Penalty Hours Plat Time Place Type Time Place Type Hours 101 Str 1 5:31 5:46 Garage Pull 13:09 A Street 13:34 7:23 0:30 0:10 8:03 8:03 0:00 0:01:30 0:00:00 8:04:30 1.094 102 Str 1 12:44 13:09 A Street 19:53 Garage Pull 20:08 6:44 0:30 0:10 7:24 7:24 0:36 0:00:00 0:00:00 8:00:00 1.188 103 Str 2 5:35 5:50 Garage Pull 12:39 A Street 13:04 6:49 0:30 0:10 7:29 7:29 0:31 0:00:00 0:00:00 8:00:00 1.174 104 Str 2 12:14 12:39 A Street 19:49 Garage Pull 20:04 7:10 0:30 0:10 7:50 7:50 0:10 0:00:00 0:00:00 8:00:00 1.116 105 Str 3 5:46 6:01 Garage Pull 12:09 A Street 12:34 6:08 0:30 0:10 6:48 6:48 1:12 0:00:00 0:00:00 8:00:00 1.304 106 Str 3 11:44 12:09 A Street 19:19 Garage Pull 19:34 7:10 0:30 0:10 7:50 7:50 0:10 0:00:00 0:00:00 8:00:00 1.116 4 5:50 6:05 Garage Pull 10:19 Garage Pull 10:24 107 Spl 7:47 0:50 0:00 8:37 12:44 0:00 0:18:30 1:22:00 10:17:30 1.322 6 14:31 14:46 Garage Pull 18:19 Garage Pull 18:34 5 6:05 6:20 Garage Pull 9:53 Garage Pull 9:58 108 Spl 7:06 0:50 0:00 7:56 12:48 0:04 0:00:00 1:24:00 9:24:00 1.324 7 14:50 15:05 Garage Pull 18:38 Garage Pull 18:53 56:17 4:40 0:00 1:00 61:57 2:43 0:20 2:46 67:46 1.204 Cafeteria-style rosters will be considered first, since these are simpler for the scheduler. In a cafeteria system, the scheduler is only responsible for calculating the number of operators needed and the available days off by day of the week. A discussion of agency-developed ros- ters follows the cafeteria rostering. Cafeteria Rostering--Weekday-only Service The Run Guide for Route , as shown above, has a total of eight daily runs. In this cafeteria rostering example, assume that the route operates only on weekdays and there are no / rosters. The formulas for calculating days off and the number of operators required are shown below, yielding the following result: 6-18

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Level . Intermediate Rostering Chapter 6. Rostering OPERATORS REQUIRED FOR 8-HOUR RUNS Weekly total Day # daily runs # days per week (daily runs * days) Weekdays (M-F) 8 5 40 Saturdays 0 1 0 Sundays 0 1 0 Weekly Total 40 Total Operators (weekly total runs / 5 days of work per operator) 8 DISTRIBUTION OF DAYS OFF total # Operators off each day available operators # daily runs (# operators - # daily runs) Weekdays (M-F) 8 8 0 Saturdays 8 0 8 Sundays 8 0 8 Weekly Total (weekdays * 5 + Saturday + Sunday) 16 Operators have no choice but to take Saturday and Sunday as their days off. The most straightforward operating roster that could result from cafeteria-style selection of work assign- ments would include the same run for each operator Monday through Friday. An example of this weekly roster is shown on the following page, under the assumption that the most senior operators would pick weekly assignments with overtime. Of course, the scheduler cannot pre- dict how the cafeteria roster will look. 6-19

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Chapter 6. Rostering Level . Intermediate Rostering CAFETERIA ROSTER - Route 97 Roster Weekly Platform No. Sun Mon Tue Wed Thu Fri Sat Hours Hours 101 Off 07 07 07 07 07 Off 10:17 10:17 10:17 10:17 10:17 51:27:30 38:55:00 102 Off 08 08 08 08 08 Off 9:24 9:24 9:24 9:24 9:24 47:00:00 35:30:00 103 Off 01 01 01 01 01 Off 8:04 8:04 8:04 8:04 8:04 40:22:30 36:55:00 104 Off 05 05 05 05 05 Off 8:00 8:00 8:00 8:00 8:00 40:00:00 30:40:00 105 Off 02 02 02 02 02 Off 8:00 8:00 8:00 8:00 8:00 40:00:00 33:40:00 106 Off 03 03 03 03 03 Off 8:00 8:00 8:00 8:00 8:00 40:00:00 34:05:00 107 Off 04 04 04 04 04 Off 8:00 8:00 8:00 8:00 8:00 40:00:00 35:50:00 108 Off 06 06 06 06 06 Off 8:00 8:00 8:00 8:00 8:00 40:00:00 35:50:00 TOTAL WEEKLY HOURS 338:50:00 281:25:00 6-20

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Level . Intermediate Rostering Chapter 6. Rostering Cafeteria Rostering--Weekday and Weekend Service In this example, Route operates seven days a week. Weekend service is the same on Sat- urday and Sunday in this example, and is about % of weekday service. The first step is to determine the available days off and the number of operators needed. The master run list is shown below. MASTER RUN LIST Weekday Runs Saturday Runs Sunday Runs Run # Pay hours Run # Pay hours Run # Pay hours 01 8:04 601 8:00 701 8:00 02 8:00 602 8:00 702 8:00 03 8:00 603 8:00 703 8:00 04 8:00 604 8:30 704 8:30 05 8:00 605 9:51 705 9:51 06 8:00 07 10:17 08 9:24 The total number of operators is determined using the formula for computing operators and days off, as shown below. The addition of weekend service on Route results in a total of operators needed for this example, compared to eight for weekday-only service. When Satur- day and Sunday runs are part of the cafeteria rostering process, drivers also need to pick their days off. Since only five operators are needed for Saturday and Sunday service, and opera- tors are needed in total, there will be five operators "off " on Saturdays and Sundays. Eight operators are required each weekday, so two of the operators can choose to be off on each weekday. The table on the following page summarizes the expected rostering outcomes. This goes back to the approach we have discussed in previous sections--that is, to know the outcome before you work through the details and develop a solution. 6-21

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Chapter 6. Rostering Level . Intermediate Rostering OPERATORS REQUIRED FOR 8-HOUR RUNS WITH WEEKEND SERVICE Weekly total Day # daily runs # days per week (daily runs * days) Weekdays (M-F) 8 5 40 Saturdays 5 1 5 Sundays 5 1 5 Weekly Total 50 Total Operators (weekly total runs / 5 days of work per operator) 10 DISTRIBUTION OF DAYS OFF Total # Operators off each day available operators # daily runs (# operators - # daily runs) Weekdays (M-F) 10 8 2 Saturdays 10 5 5 Sundays 10 5 5 Weekly Total (weekdays * 5 + Saturday + Sunday) 20 What might the cafeteria roster look like for this example? Senior operators often prefer to maximize their pay hours and to have weekends free. The nature of the run (straight vs. split) and run begin and end times are also factors considered by operators. Assume that the first two operators maximize their work hours and pick Saturday and Sunday as their days off, the next two are willing to work one weekend day, and the next two are will- ing to work both weekend days. The cafeteria roster after these six operators pick their work would look like the example on the following page. 6-22

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Level . Intermediate Rostering Chapter 6. Rostering CAFETERIA ROSTER - Route 97 (7 days) Roster Platform Make-up Spread W No. Sun Mon Tue Wed Thu Fri Sat Hours Work Hours Time Overtime Time 1001 Off 107 107 107 107 107 Off 10:17 10:17 10:17 10:17 10:17 38:55:00 43:05:00 0:00 3:05:00 13:40 1002 Off 108 108 108 108 108 Off 9:24 9:24 9:24 9:24 9:24 35:30:00 39:40:00 0:20 0:00:00 14:00 1003 Off Off 101 101 101 101 605 8:04 8:04 8:04 8:04 9:51 38:16:00 41:26:00 0:00 1:26:00 0:00 1004 705 105 105 105 105 Off Off 9:51 8:00 8:00 8:00 8:00 33:16:00 36:30:00 4:44 1:14:00 0:00 1005 704 101 Off Off 102 102 604 8:30 8:04 8:00 8:00 8:30 36:31:00 39:31:00 1:12 0:43:00 0:00 1006 Off 103 103 103 103 103 Off 8:00 8:00 8:00 8:00 8:00 34:05:00 37:25:00 2:35 0:00:00 0:00 Remaining days off available would be: DAYS OFF ALLOWED Updated Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 1 1 1 2 1 1 The completed cafeteria roster (shown below) has a weekly total of : hours. This is ap- proximately hours more than the roster for weekday-only service, reflecting the additional hours of work on Saturday and Sunday. Most of this time ( : work hours plus : make-up time) will be paid as straight time. Overtime accounts for : hours and spread for : . This assumes that make-up and overtime is calculated on a daily basis. With overtime and spread paid at time and a half and make-up time paid at the straight rate, the actual pay hours will be: Pay hours including make-up time, overtime, and spread penalty = : + : +( : x . )+( : x . )= : 6-23

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Chapter 6. Rostering Level . Intermediate Rostering Some operators calcu- Tip CAFETERIA ROSTER - Route 97 (7 days) late overtime on a weekly Roster Platform Make-up Spread Weekly Pay basis, while others calculate it on a No. Sun Mon Tue Wed Thu Fri Sat Hours Work Hours Time Overtime Time Hours 1001 Off 107 107 107 107 107 Off daily basis, paying overtime for all 10:17 10:17 10:17 10:17 10:17 38:55:00 43:05:00 0:00 3:05:00 13:40 51:27:30 hours over eight in a given day. To 1002 Off 108 108 108 108 108 Off calculate the cost of your service, 9:24 9:24 9:24 9:24 9:24 35:30:00 39:40:00 0:20 0:00:00 14:00 47:00:00 you will need to understand the 1003 Off Off 101 101 101 101 605 8:04 8:04 8:04 8:04 9:51 38:16:00 41:26:00 0:00 1:26:00 0:00 42:09:00 policies that apply to your system. 1004 705 105 105 105 105 Off Off Calculating pay hours for a system 9:51 8:00 8:00 8:00 8:00 33:16:00 36:30:00 4:44 1:14:00 0:00 41:51:00 that pays overtime daily requires 1005 704 101 Off Off 102 102 604 making a calculation for each day 8:30 8:04 8:00 8:00 8:30 36:31:00 39:31:00 1:12 0:43:00 0:00 41:04:30 1006 Off 103 103 103 103 103 Off of the week, and multiplying that 8:00 8:00 8:00 8:00 8:00 34:05:00 37:25:00 2:35 0:00:00 0:00 40:00:00 day times the number of days that 1007 Off 104 104 104 104 104 Off condition occurs in the year. 8:00 8:00 8:00 8:00 8:00 35:50:00 39:10:00 0:50 0:00:00 0:00 40:00:00 1008 701 106 106 106 Off Off 601 When calculating an- 8:00 8:00 8:00 8:00 8:00 36:30:00 39:30:00 0:30 0:00:00 0:00 40:00:00 Tip 1009 702 Off Off 102 106 106 602 nual costs BE CARE- 8:00 8:00 8:00 8:00 8:00 36:04:00 39:04:00 0:56 0:00:00 0:00 40:00:00 FUL--holidays that occur during the 1010 703 102 102 Off Off 105 603 week often use weekend or special 8:00 8:00 8:00 8:00 8:00 34:36:00 38:03:00 1:57 0:00:00 0:00 40:00:00 schedules. Do not assume that TOTAL 359:33:00 393:24:00 13:04:00 6:28:00 27:40:00 423:32:00 "Monday" service occurs on every Monday during a calendar year. It may be useful at this point to walk through an example of the calculations for a specific ros- ter number. In Roster , the daily platform hours for Run , taken from the Run Guide at the beginning of this section, are multiplied by to convert to weekly hours: : x = : . Total hours are calculated by multiplying the daily total hours from the Run Guide for Run by : : x = : . Make-up time is calculated in the same way, but Roster does not include any make-up time. Overtime was shown in the Run Guide as overtime pay hours (equal to one-half the overtime hours worked); the roster shows actual weekly overtime worked for clarity. Roster includ- ed minutes of daily overtime, which equals : weekly overtime. Spread time was also shown in the Run Guide as spread penalty (equal to one-half of actual spread hours); the roster shows actual weekly spread time for clarity. Run included : of daily spread time, which equals : weekly spread time. 6-24

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Level . Intermediate Rostering Chapter 6. Rostering The formula for weekly pay hours is: Work Make-up Weekly + + (Overtime x . ) + (Spread time x . ) = pay hours time hours Weekly pay hours For Roster = : + + ( : x . ) + ( : x . ) = : : Combining daily runs with Tip significant overtime with daily runs under eight hours can in- The pay-to-platform ratio is one of the most useful means of evaluating rosters. In this exam- crease efficiency when overtime and ple, the pay-to-platform ratio is: guarantees are calculated weekly. Pay to platform = : / : = . 6-25

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Chapter 6. Rostering Level . Intermediate Rostering Agency-developed Rostering--Weekday and Weekend Service With agency-developed rostering, the agency "pre-packages" the runs into weekly rosters. The operators then pick from the agency-developed list of weekly rosters. A number of factors influence how packages (Lines of Work) are developed for the weekly ros- ters. In cases where overtime and make-up time are calculated on a weekly and not daily basis, there is the opportunity to combine daily runs with greater than eight hours pay time with daily runs paying less than eight hours to reduce or eliminate weekly overtime and make-up time. In the basic rostering section, the agency-developed roster reduced the pay-to-platform ratio from . for the cafeteria roster to . . As shown earlier on the Master Run list, there are two long runs on weekdays and two on weekends. Several weekday runs (notably runs , , and ) require at least minutes of make-up time daily. The objective of developing weekly rosters is to combine these runs into weekly work assignments that minimize overtime and make-up time. Ideally, work assign- ments will be as close to hours per week as possible. A common approach to developing agency rosters is to adjust assignments with the most overtime or make-up time first, and then address remaining assignments. Rosters and have the most weekly overtime, while Rosters , , , and have the most make-up time. In the example on the following page, switches in assignments are highlighted in bold. The first switch is between Rosters and : the Wednesday through Friday runs have been exchanged to reduce overtime on Roster and make-up time on Roster . Next, the Saturday runs have been switched between Rosters and . The Tuesday runs on Rosters and have been exchanged. Finally, Run on Thursday, which had been switched from Roster to Roster , has been exchanged again with Run from Ros- ter . What is the end result of this agency-developed roster? See below--weekly overtime has been eliminated, and weekly make-up time has been reduced from : to : . Pay hours are now calculated as: Pay hours including make-up time, overtime, and spread penalty = : + : +( : x . )+( : x . )= : Pay to platform = : / : = . 6-26

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Level . Intermediate Rostering Chapter 6. Rostering AGENCY-DEVELOPED ROSTER - Route 97 (7 days) Roster Platform Straight Make-up Spread Weekly Pay No. Sun Mon Tue Wed Thu Fri Sat Hours Time Time Overtime Time Hours 1001 Off 07 07 03 03 03 Off 10:17 10:17 8:00 8:00 8:00 36:01:00 39:41:00 0:19 0:00:00 5:28 42:44:00 1002 Off 08 08 08 08 08 Off 9:24 9:24 9:24 9:24 9:24 35:30:00 39:40:00 0:20 0:00:00 14:00 47:00:00 1003 Off Off 05 01 01 01 603 8:00 8:04 8:04 8:04 8:00 35:47:00 38:58:00 1:02 0:00:00 0:00 40:00:00 1004 705 05 01 05 07 Off Off 9:51 8:00 8:04 8:00 10:17 36:10:00 39:02:00 0:58 0:00:00 2:44 41:22:00 1005 704 01 Off Off 02 02 604 8:30 8:04 8:00 8:00 8:30 36:31:00 39:31:00 0:29 0:00:00 0:00 40:00:00 1006 Off 03 03 07 05 07 Off 8:00 8:00 10:17 8:00 10:17 35:20:00 39:01:00 0:59 0:00:00 5:28 42:44:00 1007 Off 04 04 04 04 04 Off 8:00 8:00 8:00 8:00 8:00 35:50:00 39:10:00 0:50 0:00:00 0:00 40:00:00 1008 701 06 06 06 Off Off 601 8:00 8:00 8:00 8:00 8:00 36:30:00 39:30:00 0:30 0:00:00 0:00 40:00:00 1009 702 Off Off 02 06 06 602 8:00 8:00 8:00 8:00 8:00 36:04:00 39:04:00 0:56 0:00:00 0:00 40:00:00 1010 703 02 02 Off Off 05 605 8:00 8:00 8:00 8:00 9:51 35:50:00 38:51:00 1:09 0:00:00 0:00 40:00:00 TOTAL WEEKLY HOURS 359:33:00 392:28:00 7:32:00 0:00:00 27:40:00 413:50:00 Weekly pay hours have been reduced from : to : . The agency-developed roster has reduced the pay-to-platform ratio from . to . . Typically, agency-developed rosters are more efficient because of the ability to package long and short runs in a weekly roster. The reduction in pay-to-platform ratio was slight in this example only because the original roster was very efficient. Another key benefit is the ability to package a greater proportion of attractive Lines of Work. The outcome can be that the less senior employees are not just operating the undesirable runs or workweeks, and have an overall better working life. This has the potential to translate into lower staff turnover among the less senior employees, which is an issue for many transit sys- tems. One other consideration is that early and late runs should generally not be mixed in a given roster. The reasons for this are both fatigue-related (obvious if moving from a late finish to an early start), and also because, as a general rule, operators prefer low variance in the start and/or end times of their working days. The agency may have rules governing time off between 6-27

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Chapter 6. Rostering Level . Intermediate Rostering shifts, but even without such rules it is not a good idea to have an operator pull in late in the evening and pull out early the following morning. A roster with early runs and a late run on the last work day would be acceptable under time-off rules, but operators generally do not find this desirable. A comparison of the cafeteria and agency rostering results is shown below. COMPARISON CHART FOR CAFETERIA VS. AGENCY ROSTERING Cafeteria Agency Total hours for all weekly rosters 423:32:00 423:32:00 @ Straight time without make-up 393:24:00 392:28:00 @ Make-up hours 13:04:00 7:32:00 @ Overtime hours 6:28:00 0:00:00 @ Spread hours 27:40:00 27:40:00 Pay hours 423:32:00 413:50:00 Number of operators required 10 10 Total platform hours 359:33:00 359:33:00 Pay-to-platform ratio 1.178 1.151 Day Off Patterns Quality of working weeks is also an important consideration when developing rosters. This applies particularly to how day off patterns are developed and rest times are ensured (above minimum requirements). The scheduler should be able to predict the day off patterns before developing the rosters. For any fixed set of input runs (i.e., the weekday, Saturday & Sunday runs to be rostered) there will be an `optimum' set of day off patterns. Some of the consider- ations of day off patterns will include: Whether days off must be consecutive (particularly applies to four-day workweeks where two consecutive plus one other day may be acceptable) Which combinations of days are preferred. For example, is a Thursday/Friday combina- tion preferable to a Friday/Saturday combination (probably not)? Whether having an entire weekend off is an important consideration. If so more Thurs- day/Friday and Monday/Tuesday combinations will be preferred over Friday/Saturday and Sunday/Monday combinations, which will in turn allow more Saturday/Sunday weekend day off combinations to be created. The following graphics illustrate day off patterns for two options. Option requires consecutive days off. Option allows this to be traded off against additional full weekends off. The patterns that result are shown below: 6-28

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Level . Intermediate Rostering Chapter 6. Rostering Combination Option 1 Option 2 Saturday/Sunday 4 5 Sunday/Monday 1 Monday/Tuesday 1 2 Tuesday/Wednesday 1 Wednesday/Thursday 1 1 Thursday/Friday 1 1 Friday/Saturday 1 Wednesday/Friday (Split Days) 1 As the table shows, revising day off combinations can achieve an additional entire weekend off (increases from four to five) with the same set of input runs. However, this outcome requires a split days off combination, which may or may not be permissible under your labor rules. If split days off are not allowed, this would not be a valid option; however the example is provided to illustrate the concept of alternative approaches to days off patterns. Days off can be easily displayed as a basic roster, without the daily hours or numbers. This al- lows a more simple visualization of the roster pattern. In developing a roster it may be best to develop this blank pattern first, and then simply "fill in the blanks" to complete the roster. 6-29

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Chapter 6. Rostering Level . Intermediate Rostering Days Off Pattern - Option 1 Roster Sun Mon Tue Wed Thur Fri Sat 1 Off Off 2 Off Off 3 Off Off 4 Off Off 5 Off Off 6 Off Off 7 Off Off 8 Off Off 9 Off Off 10 Off Off Days Off Pattern - Option 2 Roster Sun Mon Tue Wed Thur Fri Sat 1 Off Off 2 Off Off 3 Off Off 4 Off Off 5 Off Off 6 Off Off 7 Off Off 8 Off Off 9 Off Off 10 Off Off 6-30

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Level . Intermediate Rostering Chapter 6. Rostering Agency-developed Rosters with Part-time Operators Part-time operators are allowed at many transit agencies, often with restrictions on the maxi- mum number of hours allowed per week or the number or percentage of part-timers. The examples in this section did not involve part-time operators because the runcut did not pro- duce any runs shorter than : . If your runcut results in runs of six hours or less, these can be combined into a weekly part-time roster ( hours per week is a typical upper limit for part- time operators). Alternately, short and long runs might be mixed as in the preceding example to produce a more efficient roster. The naming of which runs are part time and which are full time can be reconsidered as part of the rostering process, again depending upon what the labor agreement allows. This is dis- cussed in greater detail in the advanced section. Agency-developed Four-day and Five-day Rosters The development of four-day rosters is a viable option for many agencies. The ability to con- vert overtime to straight time is a primary advantage of four-day rosters (especially if overtime is paid on a daily basis), and is usually present if there are runs close to hours in length. The example in this section includes one weekday run longer than : , another weekday run : in length, and a Saturday and Sunday run : in length. Since each weekday run is operated five days a week, these runs could have formed three four-day rosters. The remaining runs could then form seven five-day rosters and one part-time roster consisting of three days' work. However, the ability to mix and match runs in rosters would be limited if the longer runs are reserved for four-day rosters. A significant portion of any cost savings from the use of four-day rosters may be offset by the added cost of hiring and training additional operators and paying additional fringe benefits. The iterative nature of runcutting and rostering may result in a different runcut that would be conducive to four-day rosters without increasing the need for added operators. For many op- erators, a four-day roster is a welcome option because it provides an additional day off during the week. In short the number of operators required to operate four -hour runs over a workweek is usu- ally the same as required to operate five eight-hour runs. While the -hour runs result in fewer runs at the runcut stage, the additional days off required for the four-day workweek result in the same number of total operators. In simple terms the % saving in runs (eight hours to hours) is offset by the equivalent additional days off required ( % or one in four) by four-day workweeks. 6-31

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Chapter 6. Rostering Level . Intermediate Rostering LEVEL End of Intermediate Rostering. 2 The Advanced Section of Rostering continues on the next page. To jump to Rail Scheduling, go to page - . 6-32