Optimal decision making for air traffic slot allocation in a Collaborative Decision Making context
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Optimal decision making for air traffic slot allocation in a
Collaborative Decision Making context
UniversitàdegliStudidiTriesteDipar&mentodiIngegneriaeArchite3ura
CorsodiLaureaMagistraleinIngegneriaInforma4ca
Relatore:prof.LorenzoCastelli
Correlatore:prof.SergioRuiz
AcademicYear2015/2016
Laureando:StefanoPacchiega
The problem (1)Air traffic growth in Europe +2.6% per year1
increase in flights delay
large costs for airlines
The busiest airports in Europe in 20141
Stefano Pacchiega 2
Introduction Mathematical models Implementation Results Conclusions
1 SOURCE: Eurostat (2016)
Optimal decision making for air traffic slot allocation in a CDM context
The problem (2) Capacity Constraint Situation (CCS)
CCS is a reduction of the nominal capacity of the airport caused by:
• bad weather (i.e. snow, reduced visibility, thunderstorms, ...); • large volume of aircraft in the airport; • closed runways; • aircraft incidents; • conditions that require increased spacing between aircraft.
Example of different capacity reductions
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Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
The problem (3)Hotspot
During a CCS it can happen that the number of requested resources are larger than the reduced actual capacity.
Example of a hotspot
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Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
This condition would not have happened under normal situation
Solutions
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Introduction Mathematical models Implementation Results Conclusions
1. Scheduling FPFS (First Planned First Served):is considered a fair policy by the Airspace Users (AUs);is not flexible;does not consider the flight delay costs.
Optimal decision making for air traffic slot allocation in a CDM context
Solutions
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Introduction Mathematical models Implementation Results Conclusions
1. Scheduling FPFS (First Planned First Served):is considered a fair policy by the Airspace Users (AUs);is not flexible;does not consider the flight delay costs.
Developed within the framework of the Single European Sky ATM Research
2. User Driven Prioritization Process - Selective Flight Protection: is a fair policy;allows to AUs large flexibility in scheduling;ensures the management of flights delay costs.
Optimal decision making for air traffic slot allocation in a CDM context
UDPP - SFP
The basic Airspace Users SFP prioritization options are:
• the suspension of a flight: to increase the delay of one flight until the end of the hotspot area thus earning Operating Credits (OC).
• the protection of a flight: to reduce to the minimum the delay for a flight using the credits.
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Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
SFP is based on the Ration by Effort (RBE) principle
IMAGES SOURCE: Sergio Ruiz - UDPP Credits concept description
SFP example (1)
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Consider an instance in which 5 flights are involved.
Constant cost per minute of delay for each flight
Introduction Mathematical models Implementation Results Conclusions
Initial flights scheduling
Each flight has a different profit and costs
Every minute of delay increases costs
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There is a section capacity reduction of 50% which generates a hotspot.
Flights are scheduled with the FPFS policy
FPFS scheduling
Introduction Mathematical models Implementation Results Conclusions
SFP example (2)
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FPFS scheduling
Introduction Mathematical models Implementation Results Conclusions
SFP example (2)
80 % of the total delay costs for the sector
There is a section capacity reduction of 50% which generates a hotspot.
Flights are scheduled with the FPFS policy
Optimal decision making for air traffic slot allocation in a CDM context
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The Airspace User decides to suspend flight C
SFP scheduling - flight C suspension
Introduction Mathematical models Implementation Results Conclusions
SFP example (3)
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The Airspace User decides to suspend flight C
SFP scheduling - flight C suspension
Introduction Mathematical models Implementation Results Conclusions
SFP example (3)
The suspension of C reduces flight E delay (and related cost)
Optimal decision making for air traffic slot allocation in a CDM context
Same redistributed delay of FPFS
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The user decides to protect flight E
SFP scheduling - flight E protection
Reduction of the 72% of the delay costs
from 55€ (FPFS policy) to 15€ (SFP mechanism)
Introduction Mathematical models Implementation Results Conclusions
SFP example (4)
Optimal decision making for air traffic slot allocation in a CDM context
Methodology
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Introduzione Modelli matematici Implementazione Risultati ConclusioniIntroduction Mathematical models Implementation Results Conclusions
definition of the problem and the solution proposed by SESAR;
design of two mathematical models (the global optimal solution using the SFP rules and the SFP mechanism);
development of an optimization suite in Mosel Xpress;
development of an agent-based simulator in JAVA;
analysis and processing of the results.
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Definitions (1)
Example of a slot
A slot is the right to use a physical (and scarce) resource for a specific period of time.
The capacity is the amount of the slots available in a period of time.
Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
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Definitions (2)Indexes
Operating Index (OI) represents the severity of a hotspot:
The number of credits required to protect a flight is:
The maximum number of flights which an AU can protect with each suspension (MFP) is :
Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
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Cost of delay (1)• depends on many factors • is difficult to know exactly
Average care costs per delayed passenger1
1 SOURCE: Cook, Tanner, Jovanovic, Lawes, The cost of delay to air transport in Europe - quantification and management, 2009
Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
Costs of delayhard cost: fuel, crew, compensation, care, …
soft cost: dissatisfaction, passengers perception, ….{
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Parabola of costs per minute of delay (Base scenario)2
2 it is assumed that on average for each flight there are 150 passengers; further delays over 240 minutes are not considered.
Interpolating the data via MATHEMATICA software, the following cost curve for a flights delay2 will be obtained:
Introduction Mathematical models Implementation Results Conclusions
Cost of delay (2)
Total passenger costs of delay per minute in three different scenarios (Low, Base and High cost scenario)1
1 SOURCE: Cook, Tanner, Jovanovic, Lawes, The cost of delay to air transport in Europe - quantification and management, 2009
Optimal decision making for air traffic slot allocation in a CDM context
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UDPP - SFP
Introduction Mathematical models Implementation Results Conclusions
Consider a sector in which f1, f2, ..., fn flights want to use s1, s2, ..., sm resources (slots).
Each flight f1, f2, ..., fn is characterized by: • the scheduled arrival time; • the actual time to use the slot according
to the FPFS policy; • the different cost for the first minute of
delay (CMD).
Each slot s1, s2, ..., sm has: • the duration (or size); • the start time.
The binary decisional variable is x(i,j)
Optimal decision making for air traffic slot allocation in a CDM context
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SFP - SUSHSingle User Single Hotspot
Introduction Mathematical models Implementation Results Conclusions
The unique user can choose in the sector which flights to suspend and protect in order to find the best solution for reducing delay costs.
Best global / social solution using the SFP rules.
The Objective Function minimizes the flights delay costs for all the sector
where d(i,j) = delay for flight i in slot j
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SFP - SUSHConstraints
c1. Each flight must have one and only one slot allocated:
c2. Each slot cannot be allocated to more than a single flight:
c3. Each flight is normal [n] or protected [p] or suspended [s]:
c4. The delay of each flight, except for the suspended ones, must be between 0 minutes and the FPFS scheduling delay;
c5. The suspended flights are scheduled in the last position of the hotspot;
c6. The protected flights will be scheduled in their best possible position.
Introduction Mathematical models Implementation Results Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
SFP - MUSHMultiple Users Single Hotspot
Each airline tries to minimize the delay costs for its flights using SFP mechanism ignoring other companies tactical interests.
The Objective Function minimizes the flights delay costs for the specific user
where d(i,j) = delay for flight i in slot j
There is a new binary vector that represents which is the set of flights that the user can manage in the sector:
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
How can the Network Manager combine the various MUSH solutions?
SFP - MUSHInterpolation (1)
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
How can the Network Manager combine the various MUSH solutions?
After suspension of A1 and A2
Example of hole due suspensions
SFP - MUSHInterpolation (1)
1. Unify the AUs MUSH prioritizations;The unite process can lead to the creation of holes in sequence.
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
SFP - MUSHInterpolation (1)
How can the Network Manager combine the various MUSH solutions?
1. Unify the AUs MUSH prioritizations;
2. Conditional MUSH solutions (1 step): each AU waits for the scheduling proposed by a competitor and then decides the strategy to be carried out.
High number of combinations: O(n2) 1
The unite process can lead to the creation of holes in sequence.
After suspension of A1 and A2
Example of hole due suspensions
1 n is the number of airlines considered
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
SFP - MUSHInterpolation (2)
How can the Network Manager combine the various MUSH solutions?
3. Iterative conditional MUSH solutions
Complexity of iterative conditional solution - three airlines
The idea of a market: every AU can handle its flights schedules in
response to other competitors choices.
1 n is the number of airlines considered, h the iterations
High number of combinations: O(nh) 1
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Introduction Mathematical models Implementation Results Conclusions
Implementation (1)
Implementation of the optimization mathematical model in FICO Xpress Optimizer
Linearization of the mathematical models
Development of an agent based simulator
Monte Carlo simulations
Results in Excel spreadsheet for future
analysis
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
Implementation (2)Simulator
…
create fileOK
FPFS & SUSHresultMUSHresult
UNION (MUSH)result
resultIterative Conditional MUSH
save resultsOK
}Simulation
Random costs and
airlines
Optimal decision making for air traffic slot allocation in a CDM context
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Introduction Mathematical models Implementation Results Conclusions
Results
Optimal decision making for air traffic slot allocation in a CDM context
2 In the simulator the union mechanism is managed with upper bound U and lower bound L
Summary of the distribution (on average) between the two airlines of the delay cost in all the considered mechanisms 2
1 The term equitable means here that all individual users do not receive the same amount of benefits relative to their effort.
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Introduction Mathematical models Implementation Results Conclusions
Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
saves on average the 24% of delay costs
centralized decision making
the AUs should share sensitive data
global optimal solution
no local optimal solution
saves on average the 8% of delay costs
decentralized decision making
no sensitive data sharing
no global optimal solution
local optimal solution
SUSH versus MUSH
Selective Flight ProtectionSingle User Single Hotspot
Selective Flight ProtectionMultiple User Single Hotspot
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Introduction Mathematical models Implementation Results Conclusions
Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
Iteration MUSH
saves on average the 15% of delay costs
equitable solution
at every step the improvement decreases and the running time for
finding a solution increases exponentially.
Interpolation MUSH
Union & FPFS(FPFS policy in case of hole)
saves on average the 9%-13% of delay costs
holes in 1% of the cases
equitable solution
Union & MUSH(MUSH mechanism in case of hole)
saves on average the 10.5%-13% of delay costs
holes in 1% of the cases
not equitable solution in hole case
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Introduction Mathematical models Implementation Results Conclusions
Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
Achievements
The linear mathematical model of SFP - SUSH;
The linear mathematical model of SFP - MUSH;
The suite in Xpress Mosel of FPFS, SUSH and MUSH;
The agent-based simulator in JAVA;
Results analysis and reduction costs conclusions.
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Introduction Mathematical models Implementation Results Conclusions
Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
Limitations
The instances of the simulator are characterized by:
• only two different Airspace Users; • a limited constant number of flights (15); • a slot size constant quantity of 2 minutes; • a non realistic cost structure; • a not realistic traffic.
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Introduction Mathematical models Implementation Results Conclusions
Conclusions
Optimal decision making for air traffic slot allocation in a CDM context
Future work
Find new functional ways to interpolate the various MUSH results
Demonstrate the validity of SFP via testing with real data
Improve the simulator (model & view part)
Design the mathematical model of Enhanced Selective Flight Protection (ESFP)
Design the mathematical model of a sale and purchase market of minutes of delay in the case of CCS
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Thank you for the attention
StefanoPacchiegastefano.pacchiega@gmail.com
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