[PPT] - Stakeholder Cooperation for Improved Predictability and Lower Cost PowerPoint Presentation

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Joen Dahlberg, Ta/ana Polishchuk, Valen/n Polishchuk, Chris&ane Schmidt

Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

➡ Significant cost savings for small airports (30-120movements a day)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

➡ Significant cost savings for small airports (30-120movements a day)

To ensure safety: No simultaneous movements at airports controlled from the same

module

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

➡ Significant cost savings for small airports (30-120movements a day)

To ensure safety: No simultaneous movements at airports controlled from the same

module ➡ In extreme case in Sweden: simultaneous movements at all five airports

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

➡ Significant cost savings for small airports (30-120movements a day)

To ensure safety: No simultaneous movements at airports controlled from the same

module ➡ In extreme case in Sweden: simultaneous movements at all five airports ➡ Each airport needs separate RTM

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 2

Remotely operated towers enable control of multiple aerodromes from a single

Remote Tower Module (RTM) in a Remote Tower Center.

In Sweden: two remotely controlled airports in operation, five more studied.
Splits the cost of Air Traffic Services (ATS) provision and staff management

between several airports

Labour accounts for up to 85% of ATS cost

➡ Significant cost savings for small airports (30-120movements a day)

To ensure safety: No simultaneous movements at airports controlled from the same

module ➡ In extreme case in Sweden: simultaneous movements at all five airports ➡ Each airport needs separate RTM ➡ Possibilities to perturb flight schedules? (current flight schedules consider only the single airport, ATCO might have to put a/c on hold anyhow…)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 3

Problem Formulation

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F:

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s) ❖ Fas = 1 if a movement happens at airport a at time slot s

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s) ❖ Fas = 1 if a movement happens at airport a at time slot s ❖ Fas = 0 otherwise

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s) ❖ Fas = 1 if a movement happens at airport a at time slot s ❖ Fas = 0 otherwise

Conflict: two movements during the same slot in different airports (in F: two 1s in

the same column)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s) ❖ Fas = 1 if a movement happens at airport a at time slot s ❖ Fas = 0 otherwise

Conflict: two movements during the same slot in different airports (in F: two 1s in

the same column)

Conflicting airports should never be assigned to the same RTM

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 4

Input: Aircraft movements at each airport from Demand Data Repository (DDR)

hosted by EUROCONTROL

Split the time into 5-min intervals, called slots , and put every flight into its slot

➡ Input matrix F: ❖ Row per airport (a) ❖ Column per each slot (s) ❖ Fas = 1 if a movement happens at airport a at time slot s ❖ Fas = 0 otherwise

Conflict: two movements during the same slot in different airports (in F: two 1s in

the same column)

Conflicting airports should never be assigned to the same RTM

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment
Goal: ”small” shifts to the flight schedules → decreased number of required RTMs

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment
Goal: ”small” shifts to the flight schedules → decreased number of required RTMs
Measure for shift?

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment
Goal: ”small” shifts to the flight schedules → decreased number of required RTMs
Measure for shift?

❖ Maximum slot shift Δ (in minutes; multiple of 5, as we shift only by whole slots)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment
Goal: ”small” shifts to the flight schedules → decreased number of required RTMs
Measure for shift?

❖ Maximum slot shift Δ (in minutes; multiple of 5, as we shift only by whole slots) ❖ Number of shifts S

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 5

Output: Shifted flights and Airport-to-RTM assignment
Goal: ”small” shifts to the flight schedules → decreased number of required RTMs
Measure for shift?

❖ Maximum slot shift Δ (in minutes; multiple of 5, as we shift only by whole slots) ❖ Number of shifts S

MAP = maximum number of airports per module

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM

SLIDE 41

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module

SLIDE 42

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module
At most M modules are used

SLIDE 43

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module
At most M modules are used

Decision problem

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module
At most M modules are used

Decision problem For optimisation problem: Move one constraint in objective function

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 6

Formal problem definition:

Flights Rescheduling and Airport-to-Module Assignment (FRAMA)

Given:

Flight slots in a set of airports (the matrix F)
Maximum allowable shift of a flight
Maximum total number of allowable shifts, S
Maximum number of airports per RTM, MAP
Total number of modules, M

Find: New slots for the flights and an assignment of airports to RTMs such that

At most S flights are moved
Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module
At most M modules are used

Decision problem For optimisation problem: Move one constraint in objective function For us: Minimize number M of used RTMs, while respecting the bounds Δ, S, MAP

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 7

Problem Complexity

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3.

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)?

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s.

SLIDE 58

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s. Any solution to FRAMA with Δ=0 and MAP=3 groups the airports (vertices) into triples, such that there are no conflicts between any of the three airports in a triple, that is, such that there is an edge between any of the three vertices in the triple.

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s. Any solution to FRAMA with Δ=0 and MAP=3 groups the airports (vertices) into triples, such that there are no conflicts between any of the three airports in a triple, that is, such that there is an edge between any of the three vertices in the triple.

SLIDE 60

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s. Any solution to FRAMA with Δ=0 and MAP=3 groups the airports (vertices) into triples, such that there are no conflicts between any of the three airports in a triple, that is, such that there is an edge between any of the three vertices in the triple.

SLIDE 61

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s. Any solution to FRAMA with Δ=0 and MAP=3 groups the airports (vertices) into triples, such that there are no conflicts between any of the three airports in a triple, that is, such that there is an edge between any of the three vertices in the triple. ➡ We would obtain a solution to PIT

SLIDE 62

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 8

Theorem: FRAMA is NP-complete, even if Δ= 0 and MAP=3. Proof: Reduction from Partition into Triangles (PIT)

Graph G = (V,E) (of maximum degree four)
Can V be partitioned into triples V1,V2,…,,V|V|/3, such that each Vi forms a triangle in G

(for each triple of vertices Vi each vertex in Vi is connected to both other vertices in Vi)? Given an instance of PIT (graph G = (V,E) with max degree four) we construct the matrix F, the input of FRAMA:

One airport per vertex → F has |V| rows
Time slot per non-existing edge in G (that is per edge in the G’s complement)

Gc=(V,Ec) complete graph on V → |Ec\E| time slots

For time slot corresponding to ec={v,w}∈ Ec\E we add two 1’s to the time slot column: to

the airports of v and w, all other entries in that column are 0’s. Any solution to FRAMA with Δ=0 and MAP=3 groups the airports (vertices) into triples, such that there are no conflicts between any of the three airports in a triple, that is, such that there is an edge between any of the three vertices in the triple. ➡ We would obtain a solution to PIT Solution to FRAMA with Δ=0 (and, thus, S= 0) and MAP= 3 can be verified in polytime.

SLIDE 63

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module).

SLIDE 64

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

SLIDE 65

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

SLIDE 66

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

No edge, as AP1 and AP2 are in conflict

SLIDE 67

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

No edge, as AP1 and AP2 are in conflict

SLIDE 68

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

No edge, as AP1 and AP2 are in conflict module 1

SLIDE 69

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

No edge, as AP1 and AP2 are in conflict module 1 module 2

SLIDE 70

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 9

Theorem: For Δ= 0 and MAP=2 Minimizing the number of modules is equivalent to finding a maximum matching in the airport conflict graph (vertex for every airport and an edge between two airports if they can be put into the same module). Maximum matching can be found in polynomial time.

No edge, as AP1 and AP2 are in conflict module 1 module 2 module 3

SLIDE 71

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

SLIDE 72

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown.

SLIDE 73

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

SLIDE 74

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts

SLIDE 75

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

SLIDE 76

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module)

SLIDE 77

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule?

SLIDE 78

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

SLIDE 79

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part

SLIDE 80

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot

SLIDE 81

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:

SLIDE 82

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)

SLIDE 83

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)

SLIDE 84

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights

SLIDE 85

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased

SLIDE 86

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased
We can also minimize the total amount of shifted minutes: set the weight
f each edge equal to the length of the shift

SLIDE 87

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased
We can also minimize the total amount of shifted minutes: set the weight
f each edge equal to the length of the shift

Runs in polynomial time, but may find suboptimal solutions to FRAMA (not necessary to remove all the conflicts)

SLIDE 88

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased
We can also minimize the total amount of shifted minutes: set the weight
f each edge equal to the length of the shift

Runs in polynomial time, but may find suboptimal solutions to FRAMA (not necessary to remove all the conflicts) For a small number of airports: enumerate all pairs of airports

SLIDE 89

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased
We can also minimize the total amount of shifted minutes: set the weight
f each edge equal to the length of the shift

Runs in polynomial time, but may find suboptimal solutions to FRAMA (not necessary to remove all the conflicts) For a small number of airports: enumerate all pairs of airports completely eliminate all conflicts for the given pairs (matching) with a given Δ > 0

SLIDE 90

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 10

Complexity for Δ> 0 and MAP=2 unknown. Possible heuristic:

First remove all conflicts
Then assign airports to RTMs

➡ Solve rescheduling and assignment problem separately Assignment problem is trivial in the absence of conflicts (the airports are arbitrarily packed into the RTMs, with MAP airports per module) ➡ How to deconflict flight schedule? We can reduce deconfliction problem to matching:

Bipartite graph: all flights in one part and all slots in the other part
Flight f is connected to all slots within distance Δ/5 from its original slot
Edge weight:
0, for edge between flight f and its original slot (black edges)
1, otherwise (gray edges)
Find the minimum-weight matching in the graph that matches all flights
If no such matching exists, Δ must be increased
We can also minimize the total amount of shifted minutes: set the weight
f each edge equal to the length of the shift

Runs in polynomial time, but may find suboptimal solutions to FRAMA (not necessary to remove all the conflicts) For a small number of airports: enumerate all pairs of airports completely eliminate all conflicts for the given pairs (matching) with a given Δ > 0 chose combination with minimum possible number of modules

SLIDE 91

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 11

IP for FRAMA

SLIDE 92

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

SLIDE 93

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 94

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 95

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 96

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 97

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 98

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 99

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 100

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t Each flight ±𝜀 from scheduled time

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

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30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t Each flight ±𝜀 from scheduled time Two a/c at same slot at airports a and b

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 102

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t Each flight ±𝜀 from scheduled time Two a/c at same slot at airports a and b → two airports in conflict

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 103

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t Each flight ±𝜀 from scheduled time Two a/c at same slot at airports a and b → two airports in conflict If ∃ conflict → airports not same module

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 104

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 12

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

Decision variables xam: airport a assigned to module m zm: module m is used yatf: flight f arrives/departs at/from airport a in time slot t wab: conflict between airport a and airport b (some t) A = set of airports M = set of modules T = set of time slots Va= flights at airport a patf = cost to move flight f at airport a to time slot t saf = scheduled time for flight f at airport a i 𝜀 maximum shift distance for scheduled aircraft in terms of time slots: 𝜀 = Δ/ 5.

c1*#modules + c2* sum of shifts Some airport assigned to module m →module m used Each airport assigned to 1 module At most 1 flight arrives/departs at airport time slot t Each flight ±𝜀 from scheduled time Two a/c at same slot at airports a and b → two airports in conflict If ∃ conflict → airports not same module Max MAP airports to each module

min # shifts: patf=1 if t≠saf; patf=0 if t=saf min total amount of shifts: patf=|t-saf|

SLIDE 105

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

SLIDE 106

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint)

SLIDE 107

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2

SLIDE 108

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2 IP computes new slots for flights and assigns airports to RTMs, such that:

SLIDE 109

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2 IP computes new slots for flights and assigns airports to RTMs, such that:

Each flight is moved by at most Δ

SLIDE 110

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2 IP computes new slots for flights and assigns airports to RTMs, such that:

Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM

SLIDE 111

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2 IP computes new slots for flights and assigns airports to RTMs, such that:

Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module

SLIDE 112

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 13

min c1 X

m∈M

zm + c2 X

a∈A

X

t∈T

X

f∈Va

patfyatf (1) s.t. xam 6 zm ∀(a, m) ∈ A × M (2) X

m∈M

xam = 1 ∀a ∈ A (3) X

f∈Va

yatf 6 1 ∀(a, t) ∈ A × T (4)

min(|T |,saf +δ)

X

t=max(1,saf −δ)

yatf = 1 ∀(a, f) ∈ A × Va (5) X

f∈Va

yatf + X

f∈Vb

ybtf6 1 + wab∀(a, b, t) ∈ A × A × T, a < b (6) xam + xbm 6 2 − wab∀(a, b, m) ∈ A × A × M, a < b (7) X

a∈A

xam 6 MAP ∀m ∈ M (8) x, y, w, z binary (9)

IP formulation of FRAMA optimises c1*M + c2*S (could move one in constraint) We choose c1 and c2 such that minimizing the modules is the primary objective: c1>>c2 IP computes new slots for flights and assigns airports to RTMs, such that:

Each flight is moved by at most Δ
No conflicting airports are assigned to the same RTM
At most MAP airports are assigned per module

➡ IP formulation solves FRAMA!

SLIDE 113

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 14

Experimental Study

SLIDE 114

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

SLIDE 115

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

SLIDE 116

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

Airport 1 (AP1): Small airport with low traffic, few scheduled flights per hour, non-

regular helicopter traffic, sometimes special testing activities.

Airport 2 (AP2): Low to medium-sized airport, multiple scheduled flights per hour,

regular special traffic flights (usually open 24/7, with exceptions).

Airport 3 (AP3): Small regional airport with regular scheduled flights (usually open

24/7, with exceptions)

Airport 4 (AP4): Small airport with significant seasonal variations.
Airport 5 (AP5): Small airport with low scheduled traffic, non-regular helicopter

flights.

SLIDE 117

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

Airport 1 (AP1): Small airport with low traffic, few scheduled flights per hour, non-

regular helicopter traffic, sometimes special testing activities.

Airport 2 (AP2): Low to medium-sized airport, multiple scheduled flights per hour,

regular special traffic flights (usually open 24/7, with exceptions).

Airport 3 (AP3): Small regional airport with regular scheduled flights (usually open

24/7, with exceptions)

Airport 4 (AP4): Small airport with significant seasonal variations.
Airport 5 (AP5): Small airport with low scheduled traffic, non-regular helicopter

flights. We use traffic data from October 19, 2016—the day with highest traffic in 2016

SLIDE 118

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

Airport 1 (AP1): Small airport with low traffic, few scheduled flights per hour, non-

regular helicopter traffic, sometimes special testing activities.

Airport 2 (AP2): Low to medium-sized airport, multiple scheduled flights per hour,

regular special traffic flights (usually open 24/7, with exceptions).

Airport 3 (AP3): Small regional airport with regular scheduled flights (usually open

24/7, with exceptions)

Airport 4 (AP4): Small airport with significant seasonal variations.
Airport 5 (AP5): Small airport with low scheduled traffic, non-regular helicopter

flights. We use traffic data from October 19, 2016—the day with highest traffic in 2016 286 flight movements were scheduled on this day for the five airports

SLIDE 119

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

Airport 1 (AP1): Small airport with low traffic, few scheduled flights per hour, non-

regular helicopter traffic, sometimes special testing activities.

Airport 2 (AP2): Low to medium-sized airport, multiple scheduled flights per hour,

regular special traffic flights (usually open 24/7, with exceptions).

Airport 3 (AP3): Small regional airport with regular scheduled flights (usually open

24/7, with exceptions)

Airport 4 (AP4): Small airport with significant seasonal variations.
Airport 5 (AP5): Small airport with low scheduled traffic, non-regular helicopter

flights. We use traffic data from October 19, 2016—the day with highest traffic in 2016 286 flight movements were scheduled on this day for the five airports For first set of experiments: without self-conflicts → 233 movements

SLIDE 120

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 15

Additional airports considered for remote operation in Sweden:

Airport 1 (AP1): Small airport with low traffic, few scheduled flights per hour, non-

regular helicopter traffic, sometimes special testing activities.

Airport 2 (AP2): Low to medium-sized airport, multiple scheduled flights per hour,

regular special traffic flights (usually open 24/7, with exceptions).

Airport 3 (AP3): Small regional airport with regular scheduled flights (usually open

24/7, with exceptions)

Airport 4 (AP4): Small airport with significant seasonal variations.
Airport 5 (AP5): Small airport with low scheduled traffic, non-regular helicopter

flights. We use traffic data from October 19, 2016—the day with highest traffic in 2016 286 flight movements were scheduled on this day for the five airports For first set of experiments: without self-conflicts → 233 movements One optimization problem for each pair (Δ, MAP)

SLIDE 121

17

#shifts max shift (in minutes)

SLIDE 126

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

Original Traffic

17

20

SLIDE 138

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

21

Duplicate each of the original flight movements Shift randomly by plus/minus one hour Shift again, randomly, by plus/minus 15 minutes If two flight movements end up in the same slot, one of the movements is deleted “2x” data created from all data of the year 2016 ➡ shifted duplicates of flights from October 18, 2016 and October 20, 2016 may now happen on October 19, 2016 ➡ Not exactly twice the number of movements

October 19: data set has 416 flight movements (after deleting double movements in

time slots) out of 575 flight movements (all of the movements from 2016 that the duplication and shifting process produces)

SLIDE 152

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

Increased Traffic Volume

22

SLIDE 153

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

Increased Traffic Volume

22

For MAP=2 we get the optimum of 3RTMs for 𝜀=1 33 shifts ⬌ 7 shifts for original traffic

SLIDE 154

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

Increased Traffic Volume

22

For MAP=2 we get the optimum of 3RTMs for 𝜀=1 33 shifts ⬌ 7 shifts for original traffic

Same tradeoffs: more shifts — larger shifts (more minutes) — more APs/module

SLIDE 155

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 23

Conclusion/Future Work

SLIDE 156

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Conclusion Future Work

SLIDE 157

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):

Conclusion Future Work

SLIDE 158

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots

Conclusion Future Work

SLIDE 159

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC

Conclusion Future Work

SLIDE 160

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity

Conclusion Future Work

SLIDE 161

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches

Conclusion Future Work

SLIDE 162

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

Conclusion Future Work

SLIDE 163

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach

Conclusion Future Work

SLIDE 164

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module

Conclusion Future Work

SLIDE 165

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules

Conclusion Future Work

SLIDE 166

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs

Conclusion Future Work

SLIDE 167

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary

Conclusion Future Work

SLIDE 168

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

Conclusion Future Work

SLIDE 169

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations

Conclusion Future Work

SLIDE 170

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures

Conclusion Future Work

SLIDE 171

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures ➡ Possibly: consider uncertainty

Conclusion Future Work

SLIDE 172

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures ➡ Possibly: consider uncertainty

Computational complexity of FRAMA with Δ > 0 and even MAP=2 is open

Conclusion Future Work

SLIDE 173

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures ➡ Possibly: consider uncertainty

Computational complexity of FRAMA with Δ > 0 and even MAP=2 is open
Currently we do not care which airlines affected by shift (possibly all to a single airline)

Conclusion Future Work

SLIDE 174

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures ➡ Possibly: consider uncertainty

Computational complexity of FRAMA with Δ > 0 and even MAP=2 is open
Currently we do not care which airlines affected by shift (possibly all to a single airline)

➡ Take equity into account (2 airlines, airline A operating 150 flights, airline B operating 75; reassign slot for 60 flights→ aim for 40 new slots for airline A, 20 new slots for airline B)

Conclusion Future Work

SLIDE 175

30.11.2017 SID 2017 - Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services 24

Optimization problem for remote towers (FRAMA):
Shifts flights to other, nearby, slots
To minimize the total number of modules in the RTC
Discussed computational complexity
Presented different solution approaches
Experiments for IP for five Swedish airports

➡ Show applicability of our approach ➡ Tradeoffs: more shifts — larger shifts (more minutes) — more APs/module ➡ Minor shifts (few minutes) can significantly reduce necessary number of modules ➡ Cooperation between airlines, airport owners and ANSPs may help in reduction of RTC

peration costs
Our conflict definition may be too conservative/precautionary
They cannot be discarded, and will influence staff planning

➡ Continues discussion with operations ➡ Possibly: distinguish arrival/departures ➡ Possibly: consider uncertainty

Computational complexity of FRAMA with Δ > 0 and even MAP=2 is open
Currently we do not care which airlines affected by shift (possibly all to a single airline)

➡ Take equity into account (2 airlines, airline A operating 150 flights, airline B operating 75; reassign slot for 60 flights→ aim for 40 new slots for airline A, 20 new slots for airline B)

Stakeholder Cooperation for Improved Predictability and Lower Cost Remote Services

Problem Formulation

Problem Complexity

IP for FRAMA

Experimental Study

Original Traffic

Original Traffic

Original Traffic

Original Traffic

Original Traffic

Original Traffic

Original Traffic

All 286 movements

All 286 movements

All 286 movements

All 286 movements

All 286 movements

All 286 movements

All 286 movements

All 286 movements

All 286 movements

Computation times: Solve in two steps

Computation times: Solve in two steps

Computation times: Solve in two steps

Computation times: Solve in two steps

Computation times: Solve in two steps

Computation times: Solve in two steps

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Increased Traffic Volume

Conclusion/Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work

Conclusion Future Work Thank you.