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GABRIEL SANCHEZ-MARTINEZ: So today's topic
is workforce planning.
And we have Professor Nigel Wilson,
who is the father of the Transit Lab here
at MIT and of this course.
He's sort of the master of everything related to transit
and the applications of transit data,
to operations planning and study.
You may remember that we divided the course into themes.
And so we already talked about crew scheduling
in the context of operations planning.
And now we're in the strategy and policy theme.
So this lecture is on looking, again, at proofs and planning,
but from a strategic perspective.
I think that's probably--
NIGEL HM WILSON: That's great.
GABRIEL SANCHEZ-MARTINEZ: --enough of an introduction.
Maybe you can provide--
NIGEL HM WILSON: Yeah.
GABRIEL SANCHEZ-MARTINEZ: --a little more.
NIGEL HM WILSON: Thank you, Gabriel.
It's good to see a fair number of familiar faces
and some new ones I don't know yet.
So I encourage you all to jump in and ask
questions if I'm not making things clear or if you disagree
or whatever.
But I'm delighted to be here with you today.
So the work that I'm going to be discussing
is work that I haven't done recently.
It's about workforce planning.
And it was done with the MBTA.
Principally the results I'll give are for the MBTA
as it existed 20-odd years ago.
But the issues are exactly the same then as they are now.
In fact, I gave a summary of this presentation to Brian
Shortsleeve and some of the other people at the MBTA
a year and a half ago, or so.
And they were thinking about maybe
they really should [AUDIO OUT] --thing something
like this again.
So what I want to discuss the problem in general
of the approach that we've taken to this,
and then look at three different levels of the problem.
One is the strategic level, which
is the long-term view, which fits
in with Gabriel's statement about the theme
of this part of the course being on strategy.
Then the tactical level, which is shorter range.
And then the operational level, which is really short range.
And these are all tightly connected and interrelated,
as I hope I'll be able to explain to you.
OK, so the challenge that we have
in this part of the operations planning
process, if you think of it that way, is we
want to provide good service.
We've got hopefully a decent operating plan
that we've developed and want to make sure
that the service that's delivered is reliable.
That requires decent equipment, decent infrastructure, and also
a workforce that's motivated and there
when you need them, which is pretty much every day.
So the operations plan you've all
been through this at this stage in the course.
So you know what goes into the operations plans.
So what comes out of the operations plan
are a set of schedules, timetables, runs, or duties
for operators to perform.
And that require a certain amount of workforce or--
excuse me for using the term "manpower," but it's sort
of the workforce that we need.
So if you don't have the right level of workforce
available on a particular day or at a particular time
on that day, then you've got a problem potentially.
If you can buy work on an overtime basis,
you can do that and at least not drop any trips.
That's going to cost you money though.
And you may not be able to get the overtime, which
will, again, produce unreliable service through dropped trips.
It may also, if some workers in the workforce
feel that they can rely on overtime, which gives them
a 50% premium rate, then maybe you can take more absence time.
So there's a substitution relationship here
between absence and overtime.
So if you rely more heavily on overtime,
perhaps your absence rate will go up.
That's not an outcome you want.
So you've got to be very careful about that.
Certainly, if you can't buy the overtime
and you don't have enough people on the property
that particular day, that particular time,
then you can drop trips because you don't have anyone
to run the bus or to run the train.
And that's a problem because that
produces worse service reliability, worse customer
satisfaction.
Politically, it's a very negative [AUDIO OUT] as well.
And so workforce planning is actually
a fairly critical piece of getting from the operations
plan to good service on the street or on the rails.
This is sort of a high level view of what
the problem is, as I see it.
So on the left of this chart, you
have the operator availability.
So that means the number of drivers you have
available on a particular day.
That's affected by the number of operators
you had available the previous day.
If you hired people, how many people
are coming on to increase the supply?
What sort of attrition-- what sort of outflow
do you have in your workforce from your previous time, day,
or time period?
What's the absence?
Because those guys aren't going to be there.
Those people aren't going to be there to deliver service.
And of course, you have a roster,
so everyone typically works five days and takes two days off.
And that rotates among the workforce.
So this is the supply side, in terms of the operator.
On the demand side, you have the scheduled service,
which is a result of your operating plan--
what you want to provide.
You have unscheduled service additions.
And you potentially have unscheduled service deletions.
For instance, if there's a school vacation,
you will drop some school trips--
trips which are primarily there on high frequency
routes to provide school service.
And these don't fit naturally into the timetable process
because there's lot of overhead in developing and timetable,
as I'm sure Gabriel has explained to you.
So you'll just take those trips off the table that day.
And those operators are then available to provide
other service that you need and to fill in for absent operators
those days.
So you've got the supply.
You've got the demand.
And so you're down here looking at the availability
versus the supply of drivers.
I'll call them "drivers."
The technical jargon in the industry is "operators."
In a perfect world, you'd have an exact balance
between availability and demand, and you
have no additional cost, and you've got someone
to cover every trip.
That will never happen.
Why?
Because the operator availability is stochastic.
It's uncertain.
You don't know what the absence rate is going to be tomorrow.
With the best will in the world, with the best models
in the world, you don't know whether I'm
going to be feeling well enough to work tomorrow.
So that's a problem.
And for instance, in the MBTA, you
don't know if you going to have a failure on the Red Line.
You're going to have to bus parts of the Red Line
tomorrow at 8 o'clock in the morning, OK.
So all of those uncertainties affect this balance
between the availability and demand.
So you'll never be here.
I mean, statistically, it's virtually
certain you'll never be there.
You're either going to be over here, where the availability is
less than the demand.
In that case, you have additional time costs,
because you're going to have to try and buy operators
to work that overtime.
And perhaps more seriously, you have the risk of dropping trips
if you can't persuade operators that they should
work the overtime that day.
Or you're over here, where the availability
is greater than the demand.
In that case, you have additional personnel costs
who aren't going to be used as productively as you might like.
If they were going to be used productively,
you'd have built them into the operating plan.
So they're probably not going to be used as productively
as your average operator.
So this is sort of one way of looking at the framework.
We can think of, again, three levels of planning here.
At the strategic level, this is typically
looking at a one-year or even longer than one year horizon.
So it's not strategic in terms of infrastructure.
It's strategic in terms of operations.
So that's how many people will we
need in the driver workforce over the next 12 months.
And how do we get a hiring plan that
will give us the right number of people throughout the year?
How do we allocate our vacations?
Do we have a certain vacation liability?
If I'm a 20-year employee of the MBTA in the commons union,
I probably have about five weeks vacation time over the year.
So I get my five weeks.
But the MBTA management decisions
include when to provide the vacation allocation.
So you may have an overall life vacation liability
of 2,000 vacation weeks.
So the question of the strategic level,
how do you allocate those 2,000 weeks of vacation liability
over the course of the year?
And there are good ways of doing that.
And there are bad ways of doing that.
I mean, if you give vacation liability
when people don't want to take vacations,
what's likely to happen?
Your absence rate's going to increase.
So you really want to give vacations when
people want to take vacations.
But you don't want to give them so much vacation
when they want to take vacation that it really
costs you a lot more money.
In that case, maybe taking a higher absence
will be a better way of dealing with that.
So there are really important questions
on how to meet the vacation liability.
And this is the timetable.
We've decided what we need in terms
of finding decent service.
And then, at the strategic level,
I'd also include personnel policies.
So as I think you all know, in many agencies,
including the MBTA, you have a mix
of part-timers and full-timers.
In the MBTA, you have Management Rights Act, which
I'm sure you've heard about.
Maybe Fred'll talk about that next week.
It's a very interesting topic.
And Fred will make a meal of it, I guarantee that.
So the MBTA management was given these rights by the legislature
35 years ago, 36 years ago.
And so they cannot negotiate about not using part-timers.
That's not part of the contract negotiation.
That's a right they've been given legally.
It's been challenged in the courts.
It's been upheld.
And so they will use part-timers.
They've decided to use part-timers in a way
that I think is very unproductive.
They use part-timers as apprentice full-timers.
And so someone suffers through perhaps five years
as a part-timer at the MBTA in order
to reach nirvana of being a full-timer at the MBTA.
Well, that's one way of doing it.
But I'm not sure that's the best way of doing it.
Perhaps what you're doing is, you're
making these part-timers suffer for five years,
if that's how long it takes to get promoted from part-time
to full-timer status.
So they're sort of unhappy for that five years,
because that's not what they want.
And it's pretty miserable working conditions.
They don't get full benefits.
And typically, they work a 6-hour day spread over 13
hours--
so covering the AM peak and the PM peak.
And they're doing nothing between the AM peak and PM
peak.
You hope they're not in bars.
But they're certainly not doing anything
productive with the property.
So that's the way the MBTA decides
to use the management rights they
were given by the legislature.
I don't think that was a good decision.
If you have separate AM part-timers,
might you be able to increase your workforce?
I think so.
You have people-- shop clerks who don't really start work
until after the AM peak who might
be very interested in supplementing their shop clerk
job by having an AM-peak driving job.
And similarly, in the PM peak, you probably
can increase your labor pool with people
who are not interested in a full-time MBTA driver's job,
but they would be interested in just a sort of a guaranteed,
3-hour piece of work every day.
So there are lots of different ways of implementing this.
And I'm pretty sure the MBTA didn't do it optimally.
So that's what I mean by personnel policies.
So all of these are at the strategic level.
At the tactical level, what we're making decisions on
is the time horizon is typically one timetable.
How many timetables does the MBTA have per year?
AUDIENCE: Four.
NIGEL HM WILSON: Yeah, four.
So you're making these decisions,
running up to each timetable--
the start of each timetable period.
And the main decisions are the staff.
And you've sort of got your workforce fixed.
And you're deciding how to allocate them
across depots or garages or rail lines and by days of the week.
Those are the tactical-level decisions you're making.
Those, it turns out, are actually quite important.
If you make poor decisions, then you're
going to be providing less reliable service or more
expensive service than you otherwise would.
And then at the final level, your operational level,
is here we are 4 o'clock on a Thursday.
At 12 o'clock today--
so four hours ago-- the MBTA was deciding
when to ask each extra board operator to show up
for work tomorrow if they didn't have a guaranteed assignment.
OK?
So there are unexpected absences that will occur tomorrow.
You don't know when they're going to occur.
You don't know whether it's going
to be an AM report or a PM report or whatever it is.
And you have to make the decision about when,
if you have five extra board operators that
don't have an assignment, because a known,
in advance absence, when you want them to show up?
And that the daily report times for unassigned, extra staff
is the operational-level decision.
Any questions about this, in terms
of strategic, operational, tactical?
And I'm not talking here about policies that may change--
absenteeism, for instance.
Fred will talk about some of those next week
when he talks about labor relations.
But I'm talking about sort of a narrower piece of this puzzle.
Any questions on this?
Yes, Kenji?
AUDIENCE: [? Someone ?] become the part-time operator--
NIGEL HM WILSON: Yeah.
AUDIENCE: So are they required any license or--
NIGEL HM WILSON: Oh, yes.
A commercial driver's license is required for them.
But again, what I was saying is, you
have choice about both who to recruit into those positions--
do we want an AM part-timer or a split-shift, full-day
part-timer who's going to be unhappy
until they get their full-time position at the MBTA
that they really want.
So yeah, sorry.
The other point I wanted to make is that how
you select those people who will get promoted to full-timer.
So you've decided, through attrition
in the full-time ranks, you want to promote some part-timers.
How do you make that promotion?
Do you promote based strictly on seniority?
In other words, the first one to become a part-timer
becomes the first one to be promoted to a full-timer?
Probably not, because you'd really
like people who are motivated, who have a good absence record,
a good accident record.
So you'd like to use criteria in that promotion, which are more
than just strict seniority.
And the MBTA, again, has been, I would say,
not very effective in using that balance between seniority,
which is an important issue--
you want to avoid favoritism and discrimination in the promotion
process--
with having some elements of performance
in the promotion process, I would argue.
Did I answer your question?
AUDIENCE: Yeah.
NIGEL HM WILSON: Go ahead.
AUDIENCE: I was interested in the topic
because, yeah, we have a similar culture for the station's
time--
NIGEL HM WILSON: Yes.
AUDIENCE: --in Japan.
But for the driver, they require a very strict license--
NIGEL HM WILSON: Right.
AUDIENCE: --which takes a long time to test.
So we don't have any part-time drivers.
NIGEL HM WILSON: Right.
Right, yes.
And there are commercial driver's licenses
required for the MBTA.
A bus driver or train driver has to have a commercial driver's
license.
But it's not as a rigorous and long period of qualification
as it is, I'm sure in JR-East.
That would be my guess, anyway.
Any other comments or questions?
OK.
OK, so let's look at this as three levels of planning.
So strategic level-- we're deciding the workforce size,
vacation allocation over the year,
and hiring patterns over the course of a year.
So by period of the year, the input into this
includes absence hours.
If we know we typically have more absence hours
in the winter because the conditions are miserable--
you don't drive in snow and ice--
and if you have observed higher absence rates,
that's important in making the right decisions
on the strategic level.
Required extra work.
If we know that we are going to be bussing on the Braintree
branch of the Red Line because of reconstruction,
then we'll build that into our workforce planning thing.
So that's an example of required extra work.
And attrition-- we do projections
about the number of full-timers and part-timers
who will be retiring or leaving the productive workforce
over the next year.
On the right-hand side, we have input such as budget,
the service plan, the operations plan, vacation liability--
how much vacation do we have to provide in the next year--
work rules and policies that we want to meet.
And what I'm showing here is strategic level,
tactical level, and operational level.
And what you'll see is these downward arrows
from strategy to tactics to operations,
and the upward pointing arrows back
up the chain from operations to tactical to strategic.
So let's explain each of these arrows.
The downward arrows represent constraints on your decisions.
So if you've made some strategic-level decisions
on workforce size, that limits what you
can do at the tactical level.
And that's this downward arrow here.
Similarly, you make your tactical-level decisions
at the beginning of a timetable, that
limits what you can do at the operational level.
These are these downward-pointing arrows
between these boxes.
The upward pointing arrows are the relationships
between that you need to know about how
efficiently the operations level is conducted
to make good decisions at the higher levels of the planning
hierarchy.
So for instance, if you know that overtime is virtually
impossible to get from your workforce,
for whatever reason-- they may say,
I'm just not going to cooperate, I'm not going to work,
or that could be bad or good reasons for that--
then you need to know that in order
to make the right decisions at the tactical level.
And similarly, you need to know that to make
the right decisions at the strategic level.
So these are these upward-pointing arrows here.
And the difference in the inputs are just more detail.
So absence hours by garage and by day of week
is important input into the tactical level.
Absence hours by garage and time of day
is important input into the operational level, OK.
And you have work rules and policies
as critical inputs on all these levels.
So this is a slightly different look at these relationships.
And I want to lead you through this a little bit.
So this is our strategic planning box
where we're deciding workforce size.
What goes into this?
The unit costs-- how much does it
cost to provide a platform hour, which
is an hour of driving a bus, by an overtime
employee, a full-time employee, and a part-time employee?
Those are very important, basic cost units
that we need to have.
What's the budget, and what are the work rules?
The work rules are important because they tell us
how easy it will be to do certain things.
And I'll give you an example of that later on.
And of course, you have the scheduled hours,
which comes out of your operations
plan-- the timetable requirements.
So given that you've made a decision on the workforce size
at the strategic level, on a particular day,
you may have an amount of open work.
What do I mean by open work?
It's work that we want to deliver,
but there's no one obvious to provide it.
There's no one.
So we'll try and buy time on an overtime basis.
So we're down here.
And if we're lucky, the overtime--
there'll be someone available who's
willing to work the overtime for increased pay.
The negative side of that is it increases the strain
on that employee who's working more hours than he or she was
expecting to.
That may produce this negative feedback on absence.
And I described it previously as the trade-off
between how much do I have to work to get to a certain target
income level?
Well, that's one way of looking at it.
But the other way of looking at it, which is equally realistic,
is if you're working harder, that puts more stress
and strain on the body.
You're more likely to be absent.
Because there are two ways of looking at it, which both raise
the concern about relying heavily on overtime and what
that will do to absence.
Again, over here, if you can't get the overtime,
you're going to be dropping trips.
So reliability suffers.
Negative effect on service reliability, service quality.
Presumably, that will affect ridership
if it goes on long enough.
And that will affect your operating plan,
because your ridership's down.
And so there's that feedback, as well.
So this is sort of another way of looking at the framework.
Now let's look at the strategic level in terms of the planning
process.
What I've shown here is a month, as was said--
four seasons in the MBTA.
Some agencies have more.
Some have less.
Winter, spring, summer, and fall.
And let's have a hypothetical workforce hiring scenario,
where we hire up at the beginning of each timetable.
We sort of run through the timetable.
And then we hire up for the beginning
of the next timetable.
That's sort of the hypothetical.
That's not unusual.
But it's not a very effective way of doing it.
And what I've tried to explain here is why that is the case.
So the bottom bar in this graph indicates the timetable
requirements.
So typically, the timetable requirements for the operating
plan are pretty similar across winter, spring, and fall,
and they're lower in the summer.
Why is that?
No schools, and people on vacation,
so your demand is generally down,
unless it's a very strong summer tourist place, like Boston.
So that generally means that you can reduce your operating plan
requirements in the summer.
That is a wonderful.
Why?
Because many drivers would like to take vacation in the summer,
OK.
I mean, unless you're a serious outdoor skier, ice skater,
whatever have you in the winter, you probably
don't want to take vacation in the winter
because your children are still in school.
Parents want to go on family vacations
when the weather is decent.
So this cross-hatched area here is the vacation allocation
you've made to fulfill your vacation
liability over the year.
And so what you see here is we're
providing much more vacation in the summer
than we are in the winter, or even
in the spring and the autumn.
Why?
That's because our demand is down,
but the vacation demand is up.
So that's a way of minimizing absenteeism.
Makes our workforce happy, it's a good thing.
So this gives us this profile here about the number
of people we need to cover the work and cover the vacations.
So the only thing we haven't covered is the absence.
And we have to cover the absence as well,
because those people aren't there
to work that particular day.
So typically, if you did this--
you hire up at the beginning of each timetable model
that I talked about--
what you would have is something like this, in terms
of the extra board coverage--
sort of a constant level throughout this,
except at the end.
And the end of the timetable is higher
because people have made changes and routes.
There's retraining.
There's training of new operators.
So actually, your required work is
greatest at the end of the timetable in the last three
or four weeks.
So that's what this jump here is, in terms of required work.
However, look at the supply.
Typically what happens, is you have
attrition over the course of the timetable.
And you have increasing absenteeism
over the course of the timetable.
Why?
Because at the beginning of the timetable,
people have just picked that work.
They sort of want to do it.
The grass is always greener.
They're sort of enthusiastic at the beginning of the timetable.
They get out there, and they realize
it wasn't all it's cracked up to be.
And so when they're not feeling up to it,
they're more likely to be absent perhaps, as time wears along.
And then, towards the end, they've
made their new selection of work for the following timetable.
OK?
So what this suggests is you have a surplus of operators
available at the beginning of the timetable
and a significant deficit of operators
at the end of a timetable.
So you sort of have one day in the middle of a timetable,
which is perfect.
But otherwise, you're off.
You haven't got this good balance between the operators
that you have available and what you need.
So clearly doing workforce hiring every month,
for instance, is one way of dealing with this.
So you can reduce this hump for training new operators
and spread it over the whole period because, in round terms,
training for an operator takes about a month
of on-the-road training.
And so you spread that over the month, over the timetable.
So going to monthly hiring makes a lot of sense.
And again, you avoid these problems
having unassigned cover time.
What that means is you've got people
who are being paid not to be very productive in the garage.
You haven't got very, very good things for them to do.
Because otherwise, you'd have built it
into the operating plan.
And large amounts of overtime and unreliability
at the end of the timetable.
And I don't know what your experience is,
but in my experience, that's exactly what you see.
At the end of a timetable, service goes down the tubes,
because you get this imbalance between higher absence
and higher requirements for running
into the next timetable.
So you want to try and avoid that.
OK.
So let's look at this from a total cost perspective.
This is a very simple sketch.
I'll show you something more realistic in a few minutes.
But this is the conceptual part of this.
So on the x-axis--
and I apologize, this is a typo--
that's number of extraboards.
The extraboard is the cover list--
the people who are there to cover absences or do
extra work that's required not built into the timetable.
These are extraboards or cover lists--
whatever.
And that should be the number of drivers--
"extraboard operators," not "extraboard operations."
And on the y-axis, you have the cost.
So if you have a small number of extraboard operators,
your fringe benefit costs are low.
Your fixed fringe benefit cost will increase
as you increase the number.
But you'll be relying very heavily on overtime.
So you'll be having high direct payment costs because
of the reliance on overtime.
And that gives you an overall high cost solution
beyond some point where you get a good balance
between the costs of overtime and the cost of fixed fringe
benefits.
Then you'll get a sweet spot you'll want to try and operate.
And you want to avoid this, where you've
got so many operators that you've
got a lot of people who don't have a lot of work
to do on many days.
Yes, question?
Comment?
GABRIEL SANCHEZ-MARTINEZ: It's a question.
NIGEL HM WILSON: OK.
GABRIEL SANCHEZ-MARTINEZ: I didn't quite
understand why monthly hiring would reduce the time.
NIGEL HM WILSON: OK.
GABRIEL SANCHEZ-MARTINEZ: Can you explain that?
NIGEL HM WILSON: Yeah, yeah.
Sure.
OK, so-- sorry, yeah.
Thanks, Gabriel, for reminding me.
It will take care of this hump at the end of the timetable.
If there really is an extra requirement
for work at the end of a timetable,
you can hire up for that a month before.
So if you think of this as a sawtooth pattern, OK,
which is what it is-- you've got attrition,
and then you've got a bulk hiring--
if you reduce the periodicity of the saws--
the gaps-- you'll reduce the integrated
imbalance between the requirements and what you need.
So that's, in essence, what's going on here.
Thanks.
Good question.
OK so this is sort of the classic schema for analyzing
this problem, for modeling it.
So here on the x-axis, we have number of scheduled runs.
This is for an organization that sort of looks a lot a lot
like the MBTA.
And this histogram here is the cumulative distribution
for number of absence days in the previous period.
OK.
So now we're running into the summer timetable for the MBTA.
So when the MBTA was doing the analysis on this,
they were saying, well, what level of absence
can we expect this coming summer?
Well, we'll start by looking at last summer.
That's probably a fairly good proxy
for what we can expect this summer.
And so the way they would look at that
is look at the number of absent operators
by day of week over the full range of experiences
from last summer.
So on your best day last summer for the MBTA--
these are hypothetical numbers, but I want to give you
the flavor of this--
you had 16 absences.
16 drivers didn't show up for work, for whatever reason.
On your worst day, you had 60 operators
who didn't show up for work that day.
So it's a tremendous range.
Question?
AUDIENCE: Sorry.
AUDIENCE: Yeah.
AUDIENCE: Can you explain how the chart works a little bit
more?
NIGEL HM WILSON: Yeah.
OK, so yeah.
I'm trying to do a lot in one chance here.
So this, if we look at that, it's
the cumulative distribution of absence days.
So this is the percent of days which have absences less
than this number.
So it's a cumulative distribution,
cumulative density function.
So what we're saying here is that every day
had no more than 60 operators absent.
Every day had at least 16 operators absent.
And this is the historical record
of absences over that period.
Now, the reason I've drawn this line here
is to show you what the extraboard sizing trade off is.
So we're looking at, say, 31 extraboard operators here.
If we have 31 extra board operators and we assume
there's no absence in the extraboard operators--
of course, there will be--
then we will be able to cover all of the absences in area B
without paying any overtime.
But all of the absences on days in area A,
we'll have to pay overtime for, and we'll
have to deal with reliability to drop trips on those days.
So the first point I want to make
is this is a very simple model, but it's very useful.
It provides a lot of insight into how
you make these decisions.
The first point to make is, my god,
that's a lot of variability--
from 16 to 60 operators absent on different days
of the timetable.
So probably some of that is systematic.
So some of them, probably you have maybe a higher absence
on Mondays and Fridays than you have on Tuesdays, Wednesdays,
and Thursdays.
So you probably want to do this analysis
at the day-of-week level, OK.
Maybe you can group Tuesdays, Wednesdays, Thursdays.
Maybe you can group Mondays and Fridays.
But the principles are the same.
So there are different ways of classifying days
to reduce the variance.
But you're basically going to have this sort of trade
off between your [AUDIO OUT] --terministic number
from this cumulative density function,
cumulative distribution.
Is everyone comfortable with this?
Because this is important.
Yeah.
AUDIENCE: I'm just curious about--
so this is a broad spin on public transportation here.
But I'm thinking of like delivery companies might
be very similar.
NIGEL HM WILSON: Yes.
Yeah.
AUDIENCE: [INAUDIBLE] consulted by them for this type of work?
[INAUDIBLE]
NIGEL HM WILSON: I don't personally,
but the problems are very similar.
And the airlines have had very similar problems.
I was on a trip, not too long ago,
where I was delayed at Logan Airport for an hour
because they had an unexpected absence.
Their reserved crew member happened
to live in Nashua, New Hampshire, which
a lot of airline pilots live in because it doesn't
have any taxes in that state.
And they had to drive down, in the peak hour,
to get to the plane.
I was delayed for an hour.
So every industry has the same sort of problem
when it's a transportation industry, where
you don't have a shelf life.
It's not a production process.
It's a service.
And you have to deliver it at that time, in that location.
So there are similar problems.
Again, it's not totally dissimilar from staffing
in hospitals for nurses, for doctors, everything like that.
So there's a whole class of problems here
which are quite similar.
And I'm just presenting the particular variant of this
for the transit industry.
Other questions or comments on this?
Yeah.
AUDIENCE: Is this axis mislabeled here?
Should it [INAUDIBLE] drivers, not scheduled runs?
NIGEL HM WILSON: Sorry.
[CHUCKLES]
No.
No, no-- it could be mislabeled.
What I'm trying to say is, these are
the number of scheduled operators
who are absent on that day.
That's what it really means, OK.
AUDIENCE: Runs for which the scheduled operator--
NIGEL HM WILSON: Yeah.
So the analysis is the sort of full day for a full-timer.
That's sort of the unit.
And you can label the x-axis in different ways.
And this probably isn't the best possible label.
But that's what I'm getting at, OK.
Other questions or comments?
OK, so let's quickly look at the strategic-level model here.
Decision variables-- are what we're
trying to decide is the workforce size for each period.
And typically, as I said, maybe the period
of a month, four weeks.
And vacation allocation for each period and the vacation
allocation will typically be over the course of a timetable.
So what's the average number of vacation weeks
we want to provide in the summer at a particular garage
or across the whole system?
We'll provide the same number of vacation weeks
for all the bus system in the MBTA.
And there's someone who's covering the vacation--
just is covering the different vacations
every week of the timetable.
So we have to have the same number
throughout the timetable.
OK?
And the optimal hiring level-- so you get the right number
throughout the year.
That's sort of what we're trying to achieve here.
And the objective is to minimize the workforce cost,
which includes the cost of the schedule runs,
the costs of the extraboard-- the people who are there
to cover the absences and the extra work--
and the cost of overtime.
And you'll notice there that I didn't include
costs of reliability or unreliability,
because I'm including that in the constraint.
I could have included in the objective function.
But I'm including it in the constraint,
just because it's a little bit easier
to conceptualize it that way.
And we were doing this work for the MBTA, who
kind of like to think of overtime as a constraint.
Because overtime, as you're probably aware,
gets a lot of attention in the medial, in the press.
You know, "10% of our budget is being
spent on overtime for drivers."
Those are headline sorts of issues.
So the MBTA and transit agency generally
are sensitive to the level of overtime.
That's why I structured this as a constraint,
rather than as a multi-objective function--
[INAUDIBLE] multiple objectives.
Constraints we need to meet-- vacation liability,
overtime service reliability, part-time operator constraint--
sorry.
And any other policy constraints that we want to
can be included in this optimization problem.
And the reliability model that we have is basically this.
So what this is saying is we have open work.
What open work means is we have work we want to do.
We don't have anyone who's going to be willing to do it
without paying overtime.
That's what I mean by open work.
It's work that wasn't a regularly scheduled
employee available to cover.
So overtime is available.
If an operator is available and willing to work time,
you come down here.
And overtime is worked.
That may produce more absence.
May have those negative feedback effects.
But at least you've delivered the service that day.
If there's no operator available or there's
no operator willing to work the overtime, you drop the trips.
And you've got a reliability problem on your hands.
Don't worry about the individual points there.
But this is showing for the bus network on the MBTA,
on the x-axis, the open work.
This is for a particular timetable, system-wide
for the bus, and the number of missed trip hours
that were incurred that day.
So each point here represents a day of operation
on the MBTA bus system.
And so this particular day, you had close to 300 hours
of open work.
And you dropped close to 150 hours of service.
And if you do an OLS regression on this,
this was the best fit we got.
So that means for every 100 hours of open work
at the time we did this analysis that you wanted to get,
you were only able to get 72.
And you wound up dropping 28 hours of service.
That is pretty tough.
That's actually really quite bad.
By comparison purposes, I've done other work
in Montreal, Ottawa, and Toronto,
which are pretty good, more or less, east coast properties.
In Canada, they're never more than 10%.
So there's something not being done very efficiently
in the way the MBTA covers their overtime.
And I think part of this is probably
over-reliance on seniority, again, and probably not
doing enough advance planning.
And what do I mean by relying too heavily on seniority?
How many phone calls do you make to the most senior operator who
might be available before you say, he or she isn't
going to do this work, and you go
to the next person on the list?
And how much advance planning do you
do to make sure that you've got a set of operators who
are really going to be available if you have a need for them
at 9 o'clock tomorrow morning?
Those are the things that you could do to try and reduce
this 28% missed trips to 5% or 10% missed trips, which
would be a much better situation for everyone concerned.
So this is the MBTA case study again.
Bear in mind that this was basically mid 1990s.
So it's 20 years ago.
But also, believe me, nothing much
has changed in this regard at the MBTA.
I'm not saying nothing's changed in the MBTA
in any regard over the last 20 years.
But certainly in this regard, nothing much has changed.
And I think there are still some of the same problems
that I'll talk about here still in existence, which
is sad for me to admit because, obviously, I
was trying to help them--
didn't succeed.
So at that point, the part-time workforce
was sized to about 40% of the full-time workforce.
That's a little bit lower now, I believe.
There's a large variability in required work hours.
So what do I mean by that?
The mean daily absence and extra work
required-- this is apart from the timetable.
So this is shuttling service when
you get a line down for signaling problem
or disabled train or whatever it is, or fatality on the tracks.
The mean daily absence and extra work
for the whole MBTA bus system was
1,250 hours on a daily basis.
And the standard deviation of that was 290 hours.
AUDIENCE: What percent of that is total hours?
NIGEL HM WILSON: It's coming up.
I'm getting into it in a few minutes.
But round figure's 10%.
AUDIENCE: Wow.
NIGEL HM WILSON: It's pretty high.
That's not just absence.
It doesn't include extra work.
OK?
AUDIENCE: But it does include sick leave, as well?
NIGEL HM WILSON: Yes.
AUDIENCE: OK.
NIGEL HM WILSON: Yes.
AUDIENCE: Any kind of absence.
NIGEL HM WILSON: Yes.
Any sort of absence, exactly.
So it's not in any sense absenteeism.
It's the amount of extra work you
have to do beyond what's the scheduled work,
the scheduled operating plan.
But anyway, it's quite large, and it's very variable.
So it is highly stochastic.
Now, these figures were from 1996.
And so the numbers will have changed significantly
over the last 20 years.
But the relative ratio of the numbers
in the different columns and cells
has not changed significantly in the last 20 years.
So what this is saying--
what we're showing here is the driver cost per platform hour.
And so this includes the wage rate
and benefits-- fixed and variable fringe benefits.
So an hour of overtime worked by a driver at that time
was around $30 an hour.
So sorry, the first row is the wage rate.
The second row is the full cost.
So the difference here is the benefits that are included,
and the productivity changes between overtime, part-time,
and full-timers.
So for overtime, you get a very small benefit load
because most of the benefits are covered through their base job,
OK.
So the marginal cost of overtime work
in terms of the benefit load is quite small,
in the order of less than 10%--
or just about 10% of this.
Whereas for part-timers and full-timers,
full-timers get somewhat greater benefits.
So it's a significant increment.
So if you just scan across here, this
gives you the straight, direct comparison
between the cost of an hour of work produced on an overtime
basis by a full-timer or by a part-timer.
And in round terms, you say, well,
if it's 40% part-timer, 60% full-timer, as the mix
of workforce, versus $32.72 for an overtime, it's a wash.
It's basically the same.
OK.
So strictly in terms of cost, it doesn't really matter.
It matters a lot if you have far too many people.
But it doesn't matter too much in terms of the cost
if you have about the right number
or slightly less than that number.
If you have a lot less than that number,
the short-run financial costs won't change,
but you'll have reliability problems
because you won't be able to get the overtime.
However, what we really should be looking at
is the marginal cost of the last person on the cover list.
That's where we're making the marginal decision about
whether we want to increase the cover list by 1
or decrease it by 1 or hold it where it is.
So if the last person on the cover list
is being used 50% of the time, then you're
making a trade off between $32.72 for an overtime hour
versus $69.56 for the marginal person on the cover list.
OK, so what a critical issue is, in terms of any of you guys
doing analysis for transit agency,
be it JR-East or the MBTA or whatever it is, in this area,
you really want to look at what the distribution of the costs
are of the cover list.
And a good proxy for that is who's
picking the work on the cover list.
If it's the most senior operators who
are picking the work on the cover list,
that means that's pretty easy work.
If the senior operators are not picking the cover list
and it's being left to the junior people on the seniority
list, that means the senior operators want to avoid it
because it's difficult work.
So that's a sort of very simple shortcut--
do we have an oversized cover list or an undersized cover
list?
Look at who's picking that work on the cover list.
Is it very senior operators or not?
Any questions on this?
AUDIENCE: So cover lists-- are those people who come in,
and they're sort of waiting to go on a [INAUDIBLE]??
NIGEL HM WILSON: Yeah.
Yeah.
AUDIENCE: They're not people who are sitting at home,
waiting for a phone call.
NIGEL HM WILSON: No, no, no.
They're in the garage--
maybe playing cards in the garage.
But they're in the garage, and they're available.
AUDIENCE: OK.
NIGEL HM WILSON: OK.
OK, so I'm not going to go through the model.
Again, I'm happy to give you the papers and theses on this.
One of these theses was done by Haris Koutsopoulos, who
many of you know quite well.
He's a senior faculty member at Northeastern.
Another of the theses was done by Yoram Shiftan,
who was entertaining me in Israel just three days ago.
So there's some very good work that's been done on this.
But the model that came out of this--
I'm going to go show you some results
and talk about what they mean.
What this is showing is, under different scenarios,
the number of full-time operators,
the number of part-time operators that produce
the optimal solution, the overtime as a percent
of the full cost--
the full cost, $96.4 million in this case, per year.
Sorry, that's the regular cost, regular time cost.
It's the overtime cost.
You add them up, and you get the total cost--
$97.8 here.
And this is adding different constraints.
So the base case, without any constraints beyond vacation
or liability-- the things that we've already talked about--
are that the cost of the MBTA bus drivers should be--
these are 1996 dollars again-- but $98 million.
And the reliability, given 1.5% of the time
has to be worked on overtime, and given
the way they manage their overtime, which is not
very good, not very well, they'll
be dropping about 0.4% of the trips--
4 trips out of every 1,000.
That was their existing level of unreliability
in terms of dropping service.
So that's the base case numbers.
You could then add different constraints.
If you add a constant hiring constraint, which
means that we hire the same number of operators every month
over the course of the year and we
don't allow it to vary from month to month,
what does that do?
It makes it easier for the human resources folks.
It makes it easier for the training people,
because they know what their load is going
to be throughout the year.
And in fact, you can incorporate that single constraint
with zero impact on the budget or reliability.
So the solution is exactly the same.
We've just juggled vacation liability
between different periods.
OK?
If we wanted to have a constant vacation as a policy
in the organization, we add that as a constraint--
so the same month vacation throughout the year--
then that would result in about an almost $2 million
increase in the total cost of the MBTA bus drivers.
We'd have less overtime.
And so our reliability would improve
to dropping 2 trips out of every 1,000,
rather than 4 trips out of every 1,000.
And if we included in them both the constant hiring
and vacation, which I don't think you'd want to,
but this is just to show what you
can do with this sort of model, then
that would increase the budget by an additional $1.5 million
a year.
And because you'd be relying less on overtime,
you'd be having even more reliable service.
So it gives the MBTA managers a sense of the trade offs here,
but between the size of the workforce optimally structured
over the course of the year and reliability and overtime.
One different set of results here.
This is showing, OK, so what happens
if we change the level of the overtime constraint?
So the base case here is 1.5% time as a constraint.
If we just eliminated the overtime constraint completely
and said, just choose the amount of overtime
that gives you the minimal cost solution,
then your overtime costs would be close to $12 million a year.
And that would enable you to save about $1.3 million
per year on the overall budget, because
of the relative costs of overtime versus regular work.
However, your reliability would go to hell in a hand basket.
And you'd be dropping 3 trips out of every 100--
3 hours of service out of every 100.
And probably, this is much better
than it would really be if you did that.
Because this is not a linear function, OK.
You're going to have more and more trouble
covering those trips and getting people
to agree to work overtime if there's so much overtime being
asked of the workforce.
So this is a gross underestimate.
But if you looked at 5%, which is still pretty high,
then you'd save, in theory, about $800,000 a year--
less than $1 million a year.
And your reliability would decrease significantly
from dropping 4 trips out of every 1,000
to dropping 120 trips out of every 1,000--
no, 12-- from 4 to 12.
And then if you tighten the overtime constraint
for whatever reason, then this is what it would cost you.
It would cost you about half a million dollars a year.
And again, you get some improvement in reliability.
So these are the sort of uses of the model that you
can use to inform management decisions about how you
structure your hiring process and training process
and extraboard size.
OK.
That's all I want to say on the strategic level.
Any questions?
Yes.
AUDIENCE: Do you have a sense of how difficult it is
or how costly it is to hire additional, new drivers?
NIGEL HM WILSON: Yes.
Yes.
So there is a training period.
The MBTA, since Fred was Secretary,
has had a lottery process for selection of new employees.
And every agency, including the MBTA,
has a pretty rigorous testing procedure
you have to go through to get to the point of being hired.
You then go through training, the criminal records
check, all sorts of checks before the training begins.
And then the training--
I'm trying to remember, I don't have it on top of a head--
I think that the total training is
in the order of six weeks, which includes
getting your commercial driver's licenses,
as we talked about earlier.
So you've got a certain amount of advance planning in here.
You can't decide today, I want to have more people
on the driver workforce tomorrow.
It's not going to work.
So that's why you need to have a strategic view of this.
Yes?
AUDIENCE: Does this model capture the behavioral feedback
loop?
NIGEL HM WILSON: It does not.
So that was separate work.
And we did look at that.
But it's not in the results I presented.
Though, as I said, Yoram Shiftan looked
at feedback effect between if you provide more overtime,
what does that do to absence?
And what he found was, it's variable.
For some operators, there is a feedback effect.
But it's not as strong as you might expect, OK.
So the MBTA management, for instance,
was pretty convinced this was really a serious issue.
It wasn't, in our analysis.
But there is a feedback effect.
It's not reflected in here.
Yeah, Scott.
AUDIENCE: Earlier, you said you look
at the seniority of the extraboards that are taking
work from the cover list.
NIGEL HM WILSON: Yes.
AUDIENCE: And you said it's approximately
more than the work that's desirable, right?
NIGEL HM WILSON: Yes.
AUDIENCE: The more senior person takes the work
from the [INAUDIBLE]?
NIGEL HM WILSON: Yes, yes.
AUDIENCE: And I didn't quite get the implication there
for the amount of work, [INAUDIBLE]..
NIGEL HM WILSON: OK.
So yeah.
So if the most senior operators--
who can pick anything-- are picking the extraboard,
that means you don't have to work
very hard in the extraboard.
The extraboard is probably too large.
OK.
That's the simple proxy.
Similarly, if the most senior operators
are picking certain duties in a garage in terms
of the types of shifts and the days they work,
that's a good proxy for what's easy, what's not so easy.
That's not to say senior operators aren't
highly motivated.
They are.
But they also have their own self-interest at heart.
They don't necessarily want to be on a dangerous, difficult
route to operate.
Now, the problem here, which Fred will get into I
think next week, in terms of the way the US transit
industry operates-- there are lots of problems.
But one of the problems in terms of the way the US transit
industry operates, compared with European industry,
is they rely very heavily on seniority.
So what does that mean?
It means the least capable drivers, who
are the people who are new in the job
and haven't got a lot of experience,
have the most difficult assignments.
That's almost certainly not optimal.
So it means you have very poor drivers,
in terms of not their capability,
but where they are on the learning curve,
driving very difficult routes.
And the European approach to this
is typically to have a rotating roster, OK.
And again, in the US transit industry,
one of the main benefits of more seniority
for a particular individual is you get to pick your work,
and you get to pick your vacation time.
So if you get to 10 years at the MBTA,
perhaps you never have to work weekends unless you
particularly want it, which you often won't.
Whereas in most European systems,
you're assigned to a roster that rotates.
So you will all go through the same experience
over the course of two months.
I don't know how JR-East does it, Kenji.
AUDIENCE: Similar to Europe.
NIGEL HM WILSON: Similar to Europe.
That's really the dominant model elsewhere
that I'm familiar with.
There are trade offs in this.
So one of the trade offs is that if you
use that as your main motivation for keeping people
on the workforce--
you want to keep your good operators working,
you don't have to replace them--
you can either pay a wage rate incentive
for longevity, which is more common in other agencies
around the world.
But it's not very common in the US.
And so you progress from the entry level wage in the MBTA
to the top level in about two years.
OK, and that's not unusual in the US transit industry.
And so because that is such a minimal incentive
to hang around for 20 years, you want
to provide other incentives.
And so seniority, picking your work, picking your vacation,
is the way the US transit industry has followed this.
Gabriel, you were going to make a comment.
GABRIEL SANCHEZ-MARTINEZ: It's a half-comment, half-question.
NIGEL HM WILSON: Yeah.
GABRIEL SANCHEZ-MARTINEZ: But when
we discussed crew scheduling, we briefly
touched on rostering and differences
between North American and European practices.
NIGEL HM WILSON: Yes.
GABRIEL SANCHEZ-MARTINEZ: And well, part of that
was that in European practice, rostering is done sometimes
with some help of alarm or helping
them to make the different rosters as even as possible.
NIGEL HM WILSON: Right.
GABRIEL SANCHEZ-MARTINEZ: And that
is slightly different from picking them.
NIGEL HM WILSON: Yes.
GABRIEL SANCHEZ-MARTINEZ: Right, so in North American,
these rosters are formed by people,
but then they assemble the rosters from crew schedules.
Is that correct?
NIGEL HM WILSON: Well, the roster,
as I'm describing the roster, is the rotation, if any,
of the work that's done among individuals
over the course of a period, maybe a timetable or two
months.
If you have a rotating roster, that
means everyone in this group goes
through the same set of driving responsibilities
over the course of a two-month period or a timetable.
In the US transit industry case, you don't have any rotation.
You don't even have a roster.
So you're there, you do the same trip every day
if you show up for work.
If you don't show up for work, you don't do the duty.
So it's a trade off.
Personally-- maybe it's my European roots--
I kind of tend to prefer a European approach to this
than the US approach to this.
OK.
Let me quickly jump into the tactical level.
So here, we're going into the summer timetable
the MBTA in about a month's time.
And so we'll be deciding.
We know how many drivers we have on the property.
What we're deciding now is when to assign
the work on a daily basis and how many operators
to provide to Lynn versus Quincy versus Arborway versus Cabot--
the different depots in the system.
And again, so we're allocating the extra staff,
these floaters, by garage and by day of week.
And so we want to know the absence level
on a more detailed basis here.
We have basically the same sort of issues and concerns,
just at a more detailed level of analysis.
And we can either use a heuristic or optimization
for this.
And heuristics actually give you a very good solution
because it's much simpler.
This is real data from the MBTA, again, from 20 years ago.
So I'm not saying it's exactly the same today.
But I would bet it's not that different from now
from what it was then.
So this is a single MBTA garage.
This is the Cabot garage, which is one of the biggest MBTA bus
garages.
And for that garage, this shows the mean number
of open hours of work on a daily basis over a timetable.
So on Mondays, 259 hours was the mean number
of hours you had to cover because you
didn't have someone available.
Standard deviation of that was 36.
So that's quite variable.
Tuesday and Wednesday is lower in terms of absences--
also quite variable.
Thursday and particularly Friday is much higher and also
even more variable.
So following our analysis principles,
the cumulative density function, then you
would expect to want to allocate your workforce,
your spare workforce, reflecting the level of absence.
But no.
The MBTA was allocating their extraboard exactly equally
across all weekdays--
20 extraboard operators on Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday--
Wednesday, Thursday, Friday, lower levels
on Saturday and Sunday, but the same percentage, independent
of the observed level of difference in absence
or extra work required on those days.
The model showed that if you optimally reallocated
the same level of resources, basically the same level down
here in terms of operator days, you
provide more cover on Fridays, on Mondays,
and weekends, and less coverage on Tuesdays, Wednesdays,
and Thursdays, reflecting the absence patterns.
That's optimizing the daily level for a particular garage.
And at that point, they weren't using part-timers.
They were using part-timers, but the part-timers
were not on the extraboard and not being used in quite
the same way that they are now.
And what you get out of this is the expected overtime
hours over the whole timetable, recognizing
the variability on a particular day
is the expected level of overtime
hours over the whole week is 140 hours versus 99 hours.
So you're saving about 25% to 30% of your overtime costs,
just by reallocating your existing workforce more
effectively across days of the week.
This is not rocket science.
This is actually pretty easy to do.
I mean, you can get these absence figures quite easily
and implement them.
So the tactical level findings are significant variation,
absence, and required extra work by garage and by day of week.
So what would you expect by garage,
in terms of absence rates?
You might expect-- and you'd be right--
that the most difficult garages would have the highest absence
rates.
Those are tough conditions.
So if you look at Cabot, those are very tough routes.
And so when you do a system-wide pick that
allows the operators to select the garage they work at,
so the most senior operators will avoid Cabot.
So it's the most junior operators
that wind up at Cabot on the most difficult routes.
Not a great surprise your absence rate is higher at Cabot
than it is at Lynn or Quincy--
nice, comfortable suburban garages.
Yeah.
AUDIENCE: How do you define a difficult route?
What constitutes [INAUDIBLE]?
NIGEL HM WILSON: Oh, OK.
So there can be any number of things--
very heavy traffic, danger of accidents, danger of assault,
crime, danger of altercations among customers,
passengers on the bus, altercations with the driver.
So a number of things like that.
And so I'm not saying all the routes in the Lynn garage
are great routes.
But compared with operating in the inner city, which
is where the Cabot routes typically serve,
there is a difference.
And certainly in Quincy, there will be a big difference
as well.
Yes?
AUDIENCE: So the workforce would have differing levels
of information about which route or which garage would
be more difficult [INAUDIBLE]?
NIGEL HM WILSON: By word of mouth.
It's not a sort of a conscious campaign.
The idea is basically, you say, hey,
we've got a seniority system.
So you'll get to know other operators of different depots,
word of mouth.
And you'll select, based on what's available
when it gets to you of your place in your seniority list,
where you want to work.
And often, it's based on where you live.
You don't want to have to commute from Lynn to Quincy
every day to do your work.
So it's a question of proximity to where you live
and the ease, the comfort level you'll have on the routes
and the conditions that you'll be operating on.
OK?
And the policy of the MBTA at this point
was to provide the same level of cover at every garage.
Why?
Their argument that they articulated to me--
and obviously, I discussed this with them extensively--
they would not dispute the fact that Cabot has a higher level
of absence than Quincy or Lynn.
They accept that.
That's not in dispute.
But their argument would be, you're
rewarding the manager of Cabot by giving
them more manpower if you recognize the existing absence
level.
So they're concerned about this feedback loop.
If you have more absence, you get more manpower.
To me, that's a completely backwards way
of thinking about this.
You need to have incentives for the managers
to do a good job, hopefully.
But you shouldn't let that be the motivation
for making bad decisions about how
you use your resources, which is basically
what's happening here.
And they were arguing the same thing in terms of day of week,
as well.
So they were really fighting that, that concept.
And I wasn't successful in persuading them
that they should really separate out the management
incentives from the efficiency of the decisions they're
making.
OK.
All right.
The final level--
I've got a few minutes left--
is the operational level.
So again, we've gone from the one-year planning horizon
to the timetable planning horizon for three or four
months, now down to the daily level.
OK.
So the objective here is pretty much the same thing.
We're trying to minimize the weighted sum of overtime
and missed trips.
Oh, I'm sorry.
I'm still at the operational level here.
Yeah, no this is right, sorry.
So what we want to do here is decide the report times
for any unassigned, extra staff for the next day.
So as I said, at 12 o'clock today,
if there were five operators who had not
been assigned work for tomorrow at Cabot, then the MBTA
manager--
desk superintendent or whoever you want to call him or her--
at Cabot will be posting the report times
for those five people tomorrow.
You don't know what the absence is going to be.
You didn't have any known in advance
absence to give them work to cover.
But you want them to be available
so that when you do get the absences, which
you don't know about, they will be in a good position
to cover them.
And so this gets into the most detailed level of this.
So it's not just a question of having
the right number of drivers available on a particular day.
It's a question of having the right number
of available drivers at every time of that day.
That's the problem we're dealing with here.
So again, much more uncertainty about how
the absence is at 9 o'clock AM versus 5 o'clock PM.
And what this is showing is this glorious concept.
It used to be called "slop overtime."
The MBTA didn't like the term "slop overtime,"
so it's now "excess overtime."
So you have regular overtime, which is just,
you didn't have enough personnel on the payroll.
And so you had to buy overtime if you were
going to deliver the service.
Excess overtime is where, in theory you have enough people
to cover the needs, but they're not available
when you want them to be, because you couldn't make
perfect decisions about when they should show up to make
sure they're productive.
So here, I'm showing, here, this is
time of day from 5:00 AM to 1:00 AM the next morning.
This shows the open run profile, OK, like that.
Sorry, this is the open run profile like this.
And this is the available cover profile, based on your report
time decisions, like this.
And so what this shows is that you have these periods
here and here and here, where you
had more operators available than you had work to cover.
And so that means that there were other periods of the day
here and here and here, where you
didn't have enough operators.
You had the right number on the whole day,
you just didn't have them at the right time in the day.
And it's not just you made bad decisions,
it's that this is stochastic.
You can't make perfect decisions.
So you've got to expect there's going
to be some excess overtime built in here.
And this is the excess overtime curve.
And I will wrap this up in four minutes, I promise.
I may not go through everything.
But I'll cover most of what we want.
So this, on the x-axis, is the available cover
minus the required cover.
So again, if it's a perfect balance,
excess cover minus required cover
is 0 because you had a perfect fit.
But what that gives you is the greatest number
of excess overtime hours.
Because unless you made every decision perfectly,
you're going to have excess overtime hours.
If you go way out here, you had far more people
available than you needed.
So you shouldn't have any access overtime,
even if you make lousy decisions.
You put them out any time, they'll be covered.
And you put them out-- if you have
far fewer people available than you require,
you'll be out here.
And you shouldn't have any access overtime either,
because you don't have to be very
good to make decisions which will have these people be fully
employed.
OK.
So it's when you have this exact balance,
you have to make every decision perfectly
to avoid excess overtime.
And you're never going to do that.
OK, so I've got some results here,
which you can go through on your own.
And I don't think I need to cover this specifically.
But let me get to the conclusion on this.
The analysis we did on this level of the model
shows, because of the natural peaking in work requirements,
that you have much more service in the peak
than in the middle of the day, the base,
it doesn't matter that absence rates are actually
higher in the peak than they are in the middle of the day.
Because your decisions are driven
by the same underlying dynamic.
And so you just can make good report time decisions,
based on the average absence rate on that day at that depot.
So you don't have to go into super detailed analysis, which
is good news.
And in fact, you can wind up with having
a ranked list of report times that the desk manager at Cabot
can just work off that list for tomorrow,
based on the number of unassigned cover
operators you have.
And it will always give you a good solution, as opposed
to the desk manager making decisions de novo, every day.
This is a very simple decision support tool that can help.
So the operational level findings--
significant improvements are possible,
can reduce the overtime and missed trips,
and a single set of report times can be used across all weekdays
and seasons for each garage.
Separate ranked report times for Saturdays and Sundays,
and constant absence rates can be assumed
by hour of day and day of week.
Those are the main conclusions.
OK, sorry I raced towards the end.
But I'm available.
I am retiring, as Gabriel well knows,
at the end of the summer.
This is probably my last lecture as a non-retired MIT faculty
member.
It's been fun doing it with you.
And I'm around.
And I will be around after the end of the summer as well.
Just I won't be being paid by MIT.
So if anyone wants to discuss any of this
or go through any of the background topics,
please feel free to come see me.
OK?
Thanks very much.
[APPLAUSE]