Sustaining Service in the VLJ Market

1
A Complexity Theory Algorithm for Routing and
Scheduling Very Light Jets (VLJs) Dennis F.X.
Mathaisel Professor, Management Science Babson
College AGIFORS Montreal September 2008
2
Presentation Outline

• Opportunities for decision support
• The aircraft scheduling problem
• Large-scale optimization
• Complexity theory
• Computational experience
• Conclusions

3
Opportunities for Decision Support

• Forecasting demand
• Pricing
• Scheduling
• Aircraft
• Crew
• Maintenance
• Aircraft routing
• Irregular operations
• ATC
• Location Impact on regional airports and
  communities

4
The VLJ Scheduling Problem

• Find a minimum cost schedule and aircraft
  routing to satisfy on-demand origin-destination
  requests for service in real-time.
• Cost is a weighted sum of the disutility to the
  customer of a deviation to the desired time and
  the time to provide the service (e.g.,
  deadheading of aircraft and crew).
• Constraints
• Request time windows
• Co-mingling of passengers
• Number and location of aircraft
• Aircraft capacity
• Crew duty times
• Return to base vs. overnighting
• Desire to choose from alternative flight plans
  relates to the fare
• Similar to the Traveling Salesman Problem
• More complex than any other scheduling problem I
  have tackled!

5
Possible Approaches

• Large-Scale Optimization
• Non-linear
• Integer
• Heuristics
• Complexity Science

6
Large-Scale Optimization

• Non-Linear Objective
• Integer Constraints
• Can use Algebraic Multigrid Solvers (which has
  its roots in solving differential equations) to
  solve large systems of linear equations that
  elegantly subdivide the problem into discrete
  sub-problems that can be solved (within limits)
  simultaneously.
• Computational speed is a problem.

7
DayJet A Large-Scale Optimization User

• Delroy Beach, FL
• Eclipse 500s
• First VLJ Air Taxi Operator
• Founder Ed Iacobucci
• IBM veteran
• Cofounder of Citrix Systems.
• However, any request to add another customer to
  a given day's equation requires its software to
  crunch the entire thing again! Source Flight
  Plan (May 2007)

8
Complexity Science

• Complexity is the science of the twenty-first
• century. Stephen Hawking

9
Complexity Science

• Invented by scientists at Los Alamos National
  Laboratory in the 1980s, complexity science is a
  set of insights drawn from biology, physics, and
  economics.
• At its core is the belief that any seemingly
  complex and utterly random system or phenomenon
  (e.g., natural selection, stock market) emerges
  from the behavior of thousands of individuals -
  The whole is greater than the sum of its parts.
• Behavior is modeled as the right set of coupling
  rules that are represented by individual agents.
• Thus, Complexity Science is the development of
  multiple, interacting, linear and non-linear,
  adaptive agents (coupling rules) that lead to
  the complex phenomena.

10
Complexity Science
Complex Behavior
Dampening Feedback
Amplifying Feedback
Agents
Local Relationships
Agents
Data Info
Data Info
11
Complexity Applied to VLJ Scheduling

• Insertion Algorithm
• Demand, usually FIFO (but not a necessary
  condition), specified by departure and arrival
  time windows.
• Complex rules of insertion (the constraints)
  become the agents (simple local relationships)
  for the demand.
• Agents become coupled into a feasible, but not
  optimal, insertion of demands into a schedule.
• Result is a finite set of feasible insertions.
• Minimize the cost of insertion using a
  non-linear objective function weighted sum of
  the disutility to the customer
• Deviation to the desired times
• Flight time
• Positioning and deadheading of aircraft and crew
• Based on a Dial-A-Ride algorithms by Wilson
  Weisberg (MIT 1976) and J.J. Jaw (MIT 1984).

12
Insertion Algorithm

• For each vehicle j
• Find all possible ways in which customer i can be
  inserted into the schedule for j. If infeasible
  to insert i into j, examine j1, otherwise
• Find the set of insertions of i into j at minimum
  additional cost (COSTj).
• Optimality () condition assign i to j for
  which
• COSTj lt COSTj
  (Minimum cost)
• or
• COSTj COSTj
  (Alternative minimums)

13
Definition of Cost

• COSTj f (customer disutility operating cost
  of insertion)
• Customer disutility
• Current customer
• Previous customers
• x and y are the deviations from desired times
• Disutility believed to increase nonlinearly with
  x and y
• Operating cost f (flight time positioning
  time)

14
Rule Agents

• Request time windows
• Earliest latest pick-up time
• Earliest latest delivery time
• Co-mingling of passengers
• Non-stop vs. thru-stop
• Processing of demands
• Forward earliest pick-up time
• Backward latest delivery time
• Pooling of demands vs. one demand at a time
• Pooling opportunity to select among more than
  one demand for an insertion
• Pre-positioning of aircraft and crews
• Deadheading of aircraft and crews
• Return to base vs. overnighting
• Crew duty day
• Trip time circuity
• Max Trip Time A B Non-Stop Trip Time

15
Insertion Alternatives
16
Computation Results

• Computation time 0.34 seconds
• Inputs
• 480 demands per day
• No restriction on the number of regional airports
  in the tour
• 1 aircraft type
• 23 aircraft at 5 pre-positioned aircraft bases
• Results

17
Sample Schedule Report
18
Conclusions

• Insertion Algorithm
• Yields good alternative solutions for air taxi
  operations
• Computation times lt 1 second for medium-scale
  problems (500 demands, 6 airports)
• Solves the non-stop vs. thru-stop problem
• Aircraft can either return to base or not
• Minimizes deadheading of aircraft
• Future Research
• Trials with other air taxi operators
• Real-time operations vs. long-term schedule
  planning
• Graphical user interface

19
References

• Bonnefoy, P. 2005 Simulating Air Taxi Networks.
  Proceedings of the 2005 Winter Simulation
  Conference. M.I.T.
• Bonnefoy, P., Hansman, J., 2004. Emergence and
  Impact of Secondary Airports in the United
  States. American Institute of Aeronautics and
  Astronautics. ATIO6497. M.I.T.
• Bonnefoy, P., Hansman, J., 2005 (January). Light
  Jets Operating Patterns in the Domestic U.S.
  NASA/FAA Joint University Program. M.I.T.
• Chase, M. D., 2007 (January). Recent
  Developments in the Small Jet Market.
  Transportation Research Board Annual Meeting.
• Chase, M. D., DeLong, Marj. 2006 (December).
  Business Aircraft Production Making history in
  more ways than one. World Aircraft Sales. pp.
  140-141.
• Chase, M. D., DeLong, Marj. 2006 (October). Hot
  or Cold - The Global Aircraft Market Paints a
  Warm Picture. World Aircraft Sales. pp. 140-141.
• Jaw, J.J. 1984. Solving Large-Scale Dial-A-Ride
  Vehicle Routing Scheduling Problems. Ph.D.
  Thesis. M.I.T.
• Lindsay, Greg. Flight Plan. 2007 (May). Fast
  Company. Issue 115, Page 100. Retrieved from
  http//www.fastcompany.com/magazine/115/open_featu
  res-flight-plan.html
• Schofer, Joseph L., Czepiel, Edward J. 2001
  (July). Estimating the Value of Business
  Aviation What Do People Pay to Fly in Private
  Aircraft? 2002 Annual Meeting of the
  Transportation Research Board. Northwestern
  University.
• Wilson, Nigel, H.M., Weissberg, H. 1976.
  Advanced Dial-A-Ride Algorithms Research
  Project. M.I.T.

20
VLJ News

• Adam Aircraft Files Bankruptcy AIN Feb. 19,
  2008On Friday, Adam Aircraft voluntarily filed
  Chapter 7 bankruptcy in the U.S. Bankruptcy Court
  for the District of Colorado, bringing an
  official end to the Englewood, Colo.-based
  start-up aircraft manufacturer after it ceased
  operations on Monday last week. In the filing,
  Adam Aircraft lists more than 200 creditors, 50
  million to 100 million in liabilities and
  between 1 million and 10 million in assets. The
  court has appointed a trustee to liquidate the
  companys assets, which include the type
  certificate for the A500 piston twin, several
  A500s in various stages of production and three
  flying A700 very light jets that Adam was using
  for certification trials. A hearing date had not
  been set at press time. Meanwhile, the major
  business aircraft manufacturers are holding job
  fairs in Denver, seeking to hire the more than
  500 skilled employees Adam Aircraft laid off last
  week.

21
VLJ News

• Theres Still a Glimmer of Hope for ATG Javelin
  AIN Mar. 4, 2008Since suspending the development
  of the Javelin very light jet program in late
  December, the board of directors at Aviation
  Technology Group has continued to engage in
  negotiations with its strategic partner and
  various financial institutions, the company said
  in a statement released late this afternoon.
  ATGs strategic partner is Israel Aerospace
  Industries, with which it was planning to develop
  a military trainer version of the civilian
  two-seat jet. These discussions include
  developing alternatives to continue operations in
  the short term as well as long-term options. Much
  of the focus over the last several weeks has been
  in renegotiating both credit and teaming
  agreementswhich has been accomplished, the
  company added. According to ATG, the boards
  efforts are now focused on negotiations with
  interested parties pursuing a possible sale or a
  majority buyout of ATG. The company said several
  teams are pursuing potential buyers, with the
  best and final offer bids from prospective
  buyers expected to reach ATG within the next
  few weeks. At that point the board will review
  all bids and negotiate with interested parties.

22
VLJ News

• Dayjet May 6, 2008
• Effective this week, we have made the difficult
  decision to scale back DayJets 2008 growth plan.
  Because of this change in strategy, the company
  has reduced its employee base across most areas
  of its business. As I will explain, these changes
  were caused by external economic factors and are
  not a reflection of a weakness in the underlying
  DayJet business model.  
• Response to our "Per-Seat, On-Demand" service
  during this first phase was very consistent with
  our expectations and we answered many nagging
  questions Yes, customers will fly in a small
  jet Yes, customers will embrace the per-seat
  model Yes, customers will pay a premium for
  tangible value Yes, the technology works as
  planned and most importantly, Yes, we can find
  these customers. All in all, we have signed over
  1,500 members, more than 550 of which are active
  travelers, and nearly 200 are frequent flyers.
• Our projections have always indicated a network
  of 30-50 "line" aircraft serving 20-30 fully
  developed DayPort markets was needed to reach
  critical scale. More importantly, this required a
  40M infusion of operating capital in the first
  quarter of 2008. Without the growth capital
  required to open new markets, the company must
  scale back to a size that is consistent with the
  demand of our existing customers and service
  region. This restructuring will not reduce our
  existing service region. It will not impact our
  quality of service to our customers, and most
  importantly, it will not impact our commitment to
  safety, which is the heart of our service. We
  will continue to operate and expand our service
  (albeit at a slower rate) to communities across
  the Southeast in response to customer needs. And
  when the capital markets recover, then we would
  expect to resume the growth forecast in our
  original plan.
• Ed Iacobucci, DayJet President and CEO

23
Citation Mustang