Customized Mass Transit

Customized Mass Transit
© 2019 by Dan Trietsch

Talk prepared for the symposium:
AI and Beyond AI in Industrial Engineering
Eindhoven University of Technology
4 July 2019

Talk prepared for the symposium:
AI and Beyond AI in Industrial Engineering
Eindhoven University of Technology
4 July 2019
My purpose today is to sell the idea that
CMT can still be implemented, and it
requires R&D of the type that academia
can foster. For instance, consider our host
university, TU/e.

Quoting from the first bullet in TU/e’s
entry in the DTL web page, Eindhoven
University of Technology pursues:
Science for society: solving the major
societal issues and boosting prosperity
and welfare by focusing on the Strategic
Areas of Energy, Health and Smart
Mobility (emphasis added).

The second bullet says:
Science for industry: the development of
technological innovation in cooperation
with industry.

The second bullet says:
Science for industry: the development of
technological innovation in cooperation
with industry.
CMT speaks to Smart Mobility and
Energy. It was ready for implementation
a decade ago, but it may not be too late.

Although the talk has been prepared very
recently—it may not even be properly
finished yet—a 1-page 2008 document
serves as the abstract (a 4-page one is
also available). Why, because back then
it was not yet obvious. Although I coined
the term in 2008, the work started in
2006.

CMT has two major parts, a model base
(or “engine”) and an interface. For
research purposes, the interface is
irrelevant; for practical purposes it is
almost the opposite. By this I mean that
the quality of the engine is less visible to
most users than the quality of the
interface, so they don’t know better.
Nonetheless, this talk is biased towards
engine design.

Full disclosure: I don’t know much about
Uber (e.g., I don’t even have their app).
So please take the following few slides
with a pinch of salt: I may be totally
wrong. But clearly both Uber and CMT
aim to provide door-to-door service and
now both aim to utilize as many modes
as possible (“now” here relates to Uber,
CMT always included that).

Uber started circa 2010 and its basic
design success disrupted the taxi
business. I would not have been happy to
be the owner of a taxi licence in a city
Uber entered. Now I think they may
disrupt public transit as well, not
necessarily in a good way. Here is how,
within a summary of the main points.

Summary
• Today, Uber (established in 2010) is
poised to achieve CMT as per the
following ‘equation’:
CMT = UberPool + First- or Last-Mile +
the existing mass transit network +
software.

Summary
• They are also into robotic drivers, a
development that I ignored back then.
• And they are experimenting with
vertical takeoff aircraft. (Anecdotally,
over a decade ago I contemplated a
lighter-than-air solution for the same
purpose. Hybrids are also good.)

Summary
• With CMT capability, and a fleet of
newly acquired robotic vehicles (owned,
leased, or franchised—doesn’t matter),
Uber can start disrupting, and eventually
bankrupting, publicly-owned mass
transit systems. They are likely to hi-
jack the profitable lines and leave the
duds to the tax-payer.

Summary
• That’s bad news for public transit.
• Specifically, it is likely to increase the
disparity between the ‘haves’ and ‘have-
nots’ even further, not only by lifting the
former but also by disenfranchising the
latter (the ones who need the ‘duds’).

Summary
• But CMT should not disenfranchise
anyone: Ideally, it should enhance the
existing network, increase utilization and
frequency of transit vehicles, reduce
congestion, decrease total energy
consumption, and promote efficient
vehicles. Everybody, including staunch car
drivers, can win!

Summary
• But CMT should not disenfranchise
anyone.
• If we want true competition within the
system, the CMT platform—especially if
privately owned—should only coordinate
services, not compete in supplying them.
(That is, Uber is not the ideal way to go.)

Summary
• I believe that CMT can still be
implemented by non-Uber-like players,
such as public transit authorities, who
should want to defend their turf. For
them, the best defence is offence.
• And it’s a huge market, with room for
private enterprise as well.

Summary
• And it’s a huge market, with room for
private enterprise as well.
• If a private enterprise takes on this
challenge, they should have no anti-trust
issues and minimal legal obstructions
because they will only coordinate
(existing and new) legal services.

R&D Opportunities
• The original CMT blueprint involved
differential pricing (DP). Uber has not hi-
jacked DP yet, but—relatively recently—
they pioneered the related dynamic
pricing for transit (DPT), which can be
combined with DP easily. DP leads to
interesting new mathematical models
(deterministic and stochastic).

R&D Opportunities
• DP minimizes the total flowtime cost of
the vehicle and the passengers on it. For a
particular vehicle/pax combo, that leads
to the weighted flowtime TSP (Fw-TSP).
• The Fw-TSP is the first step. It generalizes
to the more relevant problem of the Fw-
Vehicle Routing Problem (Fw-VRP).

The Relevance of Fw-TSP
A simple bus example “project” where the
number of passengers joining the bus at
each station differs can serve to motivate
that. Here, however, the sequence is known
in advance. In the more interesting problem
the sequence is part of the challenge. Of
course the challenge is even bigger for Fw-
VRP.

A Stochastic Gantt Chart
A
B
C
D
E
Project
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
100%
100%
100%
100%
100%
100%

R&D Opportunities
• Both problems can benefit by prelimi-
nary deterministic analysis, but that’s
only a first step. (Literature search is not
my strength, but I suspect that even the
simpler Fw-TSP it has not yet been
solved. By contrast, for engineering
purposes, the TSP is solved.)

R&D Opportunities
• When we consider the stochastic
version, one may think that because
flowtime is a linear operator, if we just
use mean travel times, the deterministic
solution suffices.

R&D Opportunities
• On average, that is true. But that’s not
what we need! To make this point, time
permitting, later I’ll talk a bit about the
only published model that I know of: the
Safe TSP.

R&D Opportunities
• Another important subject is network
design for optimal CMT coverage.
• Vehicle sizing also comes to mind: not
all of them should work all day; less
efficient or larger vehicles should only
be employed during rush hour. It’s a
stochastic balance issue.

R&D Opportunities
• There are plenty of other R&D
opportunities there, but I can’t even
begin to cover them all and I am sure I
failed to think of many.

R&D Opportunities
• Finally, almost needless to say, AI plays
a major part here (although I am not
really an AI expert). Specifically, at the
heart of the engine we have a major
need for big-data, and one assumes key
parameters will be adjusted on an
ongoing basis.

The Safe-TSP
Now to the solved model. It’s by
Mazmanyan and Trietsch and covers the
normal and lognormal cases, although the
latter is not analytically ‘kosher,’ it’s an
excellent approximation nonetheless. We
start with a presentation of all possible
tours in terms of mean and variance:

34
But first…
• Here is a glimpse into the structure of the
solution set of a stochastic TSP with
independent stochastic times ()
• And with dependencies ()

35
0
500
1000
1500
2000
2500
3000
0 100 200 300 400 500 600
Series1
Figure 4

36
By safe scheduling we imply models minimizing
d + γ E(T)
where d is a due date - which we treat as a decision
- and γ > 1 is a weighing factor used to balance the
objective of minimizing d with the objective of
minimizing the expected tardiness, E(T).
(If γ ≤ 1 then d = 0 is optimal.)
Brief definition of safe scheduling

37
Alternatively, safe scheduling may involve
minimizing d subject to a service level constraint of
the form
Pr{C ≤ d} ≥ SL0
where C is the completion time and SL0 is a target
service level. We can represent both these
objectives as linear functions of the mean and the
standard deviation of the relevant distribution.
In the former, the standard deviation always has a
positive coefficient.

38
In the latter, for symmetric distributions with
SL0 < 50%, large standard deviations are desired so
the coefficient is negative. We refer to these
coefficients as prices, because they give the price
of the standard deviation in mean terms.

39
In contrast to safe scheduling, a stochastic
counterpart (of a deterministic model) seeks to
optimize by expectation the objective function of a
deterministic scheduling model. But deterministic
scheduling models do not consider safety time.
(One caveat: it is possible to show in some
instances that minimizing d + γE(T) can be
obtained by the stochastic counterpart of the
deterministic early/tardy problem.)
What is NOT Safe Scheduling?

Customized Mass Transit (CMT)
The fact that the case with related parameters has
a steeper right-bottom profile indicates that using
the deterministic counterpart is an excellent
heuristic, BUT we must still provide safety time
buffers.

The following observation (from Baker and
Trietsch 2009) about dense and loose schedules is
also relevant (and reinforces the validity of using
the deterministic counterpart solution as the basis
of the stochastic schedule).

Dominance Relationships (Figure 11.5)
D+J+B
L+J+B D+J
L+J
L
D
Legend:
D=dense schedule
L=loose schedule
J=Jensen correction
B=buffer

For more details on the solved case, see:
Mazmanyan, L. and D. Trietsch (2014).
Stochastic traveling salesperson and shortest
route models with safety time, International
Journal of Planning and Scheduling 2(1), 53-76.
http://faculty.tuck.dartmouth.edu/images/uploads/
faculty/principles-sequencing-
scheduling/StochasticTSP.pdf

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