Wikipedia defines para-transit as follows:

"Para-transit is recognized in North America as special transportation services for people with disabilities, often provided as a supplement to fixed-route bus and rail systems by public transit agencies. Para-transit services may vary considerably on the degree of flexibility they provide their customers. At their simplest they may consist of a taxi or small bus that will run along a more or less defined route and then stop to pick up or discharge passengers on request. At the other end of the spectrum—fully demand-responsive transport - the most flexible para-transit systems offer on-demand call-up door-to-door service from any origin to any destination in a service area. In addition to public transit agencies, paratransit services are operated by community groups or not-for-profit organizations, and for-profit private companies or operators."

Because the demand for para-transit services is so highly variable, scheduling the drivers is a challenging task. Most para-transit organizations tend to rely on overtime and a large pool of drivers that can be called into work when needed. I believe there is huge opportunity to schedule the drivers more effectively and reduce the costs. This opportunity comes from two key points. The first point is that historical trip volumes can and should be used to develop a schedule. The second point is that relief coverage is the best way to accommodate both employee absences and deviations from historical average trip volumes. Let's take a closer look at the specific steps involved.

Step #1: Historical Trip Volumes

The first step is to determine the workload distribution throughout the hours of operation. Start by categorizing the trip data into 2 or 3 groups based on the time involved. For example, Category A consists of trips that last 30 minutes or less. Category B consists of trips that last 30 to 60 minutes. Category C consists of trips that last more than 60 minutes.

Then look through the past year's historical data of trips made during every 30 minutes of the hours of operation. So if the first trip of the day begins at 6 a.m., I would calculate the average number of trips in each category between 6:00 a.m. and 6:30 a.m. Then I would do the same for 6:30 a.m. to 7:00 a.m., 7:00 a.m. to 7:30 a.m., and so on. I would put these averages into a summary table.

If you have the data (and the time), you could also determine the maximum number of trips that occurred during each 30-minute period and add this data to the summary table. You also could create separate tables for each region in the service area and for each season of the year.

Step #2: Driver Requirements

The second step is to determine the coverage requirements. The number of drivers needed during each 30-minute period depends on the type of service the organization offers. If the service is door-to-door, you will need one driver for each trip. If the service is limited to fixed routes, you will need fewer drivers per trip. The point is that you will need to translate the trip volumes into driver requirements by time of day. In scheduling jargon, this is called establishing the coverage requirements. Once these figures are made available, a scheduling expert can help with the remaining steps. I say this because the next few steps are the most difficult part of the process.

Step #3:  Schedule Framework

This step will determine the shift lengths, start times, and number of drivers needed on each shift.  This is basically a trial and error process. Here is a simple example:

Time Period       Drivers Needed

0600 to 0700                       5

0700 to  0900                      6

0900 to 1300                       8

1300 to 1500                       7

1500 to 1800                       5

You begin with the first time period of the day (0600 to 0700). 5 drivers are needed on this first shift. You can test the three standard shift lengths: 8-hour, 10-hour and 12-hour shifts according to how well they fit with the afternoon requirements. If we use a 12-hour shift, this will means 5 drivers will be working from 0600 to 1800. This matches the coverage needed from 1500 to 1800, so that would be the best choice. For most organizations, it's never this simple and compromises (e.g., over-staffing for part of the day) are likely to be necessary.

6 drivers are needed during the second period (0700 to 0900). We therefore will need 1 driver on this second shift (since we already have 5 people at work from the first shift of the day). Again we will test the three standard shift lengths for the impact on the afternoon. The best choice would be an 8-hour shift since anything longer would unnecessarily boost the coverage after 3 p.m. when it isn't needed.

We continue this process, sometimes going back to the beginning and changing earlier choices to make the entire framework more efficient, i.e. no understaffing and minimal overstaffing. The framework I would choose is as follows:

Shift Length       Drivers                 Time Covered

12                             5                         0600 to 1800

 8                              1                         0700 to 1500

 4                              2                         0900 to 1300

If part-time drivers are not allowed in an organization, I would choose the following framework:

Shift Length       Drivers                 Time Covered

12                             5                          0600 to 1500

8                               3                          0700 to 1500

Step #4:  Basic Staffing Requirements                                                                                                                                   

Now that we know the shift lengths and coverage requirements, we can determine the number of drivers needed to produce the coverage requirements. The 12-hour shift will require 10 drivers to produce 5 drivers every day of the week. The 10 drivers will all work an average of 42 hours a week. The 8-hour shift will require 2 drivers to produce 1 driver every day of the week. They will average 40 hours a week and there will be 3 days a week in which both drivers must be scheduled to work (to ensure 40-hour work weeks). If you can use part-time drivers, you can avoid the days of overlap. The 4-hour shift will require as many part-time drivers as you want.

Step #5:  Supplemental Staffing Requirements                                                                                                                

In the previous step, we focused on the staff needed just for the coverage requirements. But remember, the coverage is based on the average number of trips, not the peak demand. Also, drivers get sick, take vacation, or change jobs. That means we need some extra staff to allow for this. If we assume a 10% absence rate and another 30% difference between the peak demand and average demand, we need a 40% relief allowance.

In addition to the extra staff needed for relief coverage, some of the shifts will need extra personnel to simplify the schedule design. Here's a summary of the staff needed for each shift:

Shift                      Basic Staff           Relief Staff           Extras                 Total Staff

0600 to 1800               10                            4                        1                             15

0700 to 1500                 2                            1                        0                               3

0900 to 1300                 2                             1                       1                               4

Step #6: Schedule Design

For the 12-hour shift, we will create a 3-crew schedule (5 drivers per crew) that averages 42 hours a week. For the 8-hour shift, we will create a 3-crew schedule (1 driver per crew) that averages 40 hours a week. For the 4-hour shift, we will create a schedule that averages 20 hours a week. We will use the staff on this part-time shift as trainees and reserves for full-time employees that decide to change jobs.

Here is an example of a schedule for the 12-hour shift:

Crew/Week       Sun        Mon      Tue        Wed      Thu        Fri           Sat          Hours

A / Week 1            -            12         12             -            -           12            12             48

B / Week 2          12             -            -            12         12           -               R             36

C / Week 3          R              R          R            R           R            R             -               42

The three crews of 5 employees are assigned to one of the 3 weeks in the cycle. Crew A is assigned to start in week 1, Crew B is assigned to start in week 2 and Crew C is assigned to start in week 3. At the end of each week, the crews move to the next week of the cycle: Crew A moves to week 2, B moves to week 3, and C moves up to week 1. They continue to move through the 3-week cycle. All three crews are working the same 3-week schedule. They are merely in different weeks of the 3-week pattern.

R is a relief shift which means the crew is on-call for the entire 7 days shown. If someone from week 1 or week 2 is scheduled for vacation, an employee on relief will simply work the vacationer's schedule that week. If no one is absent, the employees on relief can be called in for a couple of hours to satisfy a temporary increase in demand. The organization should establish rules on the priorities for relief work and limits on the hours and number of days worked during the 7-day period.

Here is an example of a schedule for the 8-hour shift:

Emp / Week       Sun        Mon      Tue        Wed      Thu        Fri           Sat          Hours

A / Week 1            -               -           8             8           8            8              8               40

B / Week 2            8              8           -             -            R            R             R              40

C / Week 3            R             R          R            R           R            -              -                40

Conclusions

We've demonstrated how assembling historical data on trip volumes can be used as the foundation for scheduling transit drivers. We also illustrated how to build extra capacity into the schedule to cover absences/vacancies and temporary fluctuations in demand. The key point is that schedules for variable workloads are ideally based on actual data rather than gut feelings, intuition, overtime considerations, etc. Using a full-time scheduling person that spends the day on the phone trying to get drivers to come to work is not the most efficient or effective approach when it comes to scheduling para-transit drivers. So if you want to keep service levels high and costs low, see if we can make this new scheduling process work for you.