Optimal decision making for air traffic slot allocation in a Collaborative Decision Making context

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

33Stefano PacchiegaStefano Pacchiega 3



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




This condition would not have happened under normal situation

Solutions



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.


Solutions



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.


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.




SFP is based on the Ration by Effort (RBE) principle

IMAGES SOURCE: Sergio Ruiz - UDPP Credits concept description

SFP example (1)


Consider an instance in which 5 flights are involved.

Constant cost per minute of delay for each flight


Initial flights scheduling

Each flight has a different profit and costs

Every minute of delay increases costs



There is a section capacity reduction of 50% which generates a hotspot.

Flights are scheduled with the FPFS policy

FPFS scheduling


SFP example (2)



FPFS scheduling


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



The Airspace User decides to suspend flight C

SFP scheduling - flight C suspension


SFP example (3)



The Airspace User decides to suspend flight C

SFP scheduling - flight C suspension


SFP example (3)

The suspension of C reduces flight E delay (and related cost)


Same redistributed delay of FPFS


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)


SFP example (4)


Methodology


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.



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.




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 :




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



Costs of delayhard cost: fuel, crew, compensation, care, …

soft cost: dissatisfaction, passengers perception, ….{


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:


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



UDPP - SFP


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)



SFP - SUSHSingle User Single Hotspot


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



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.





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:




How can the Network Manager combine the various MUSH solutions?

SFP - MUSHInterpolation (1)





After suspension of A1 and A2

Example of hole due suspensions


1. Unify the AUs MUSH prioritizations;The unite process can lead to the creation of holes in sequence.






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






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




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




Implementation (2)Simulator

…

create fileOK

FPFS & SUSHresultMUSHresult

UNION (MUSH)result

resultIterative Conditional MUSH

save resultsOK

}Simulation

Random costs and

airlines




Results


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.



Conclusions


saves on average the 24% of delay costs

centralized decision making

the AUs should share sensitive data

global optimal solution

no local optimal solution


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



Conclusions


Iteration MUSH


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



Conclusions


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.



Conclusions


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.



Conclusions


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

3535Stefano PacchiegaStefano Pacchiega 30Optimal decision making for air traffic slot allocation in a CDM context

Thank you for the attention

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Optimal decision making for air traffic slot allocation in a Collaborative Decision Making context

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