vers un transport aérien plus écologique et plus économique par virginie lurkin | liege creative,...

Vendredi 21 novembre

Vers un transport aérien plus écologique et plus économique

Virginie LURKIN, HEC-ULg / UER Opérations

Avec le soutien de :

Vers un transport aerien plus ecologique et pluseconomique

V. Lurkin and M. Schyns

QuantOM,HEC Management School,

University of Liege,Belgium

Une rencontre LIEGE CREATIVEInterface Entreprises-Universite

Vendredi 21 novembre, 2014

Outline

1 Motivation

2 Problem summary and assumptions

3 Related literature and contributions

4 Mathematical formulationMain parameters and variablesObjective functionConstraints

5 Implementation and results

6 Conclusion

V. Lurkin and M. Schyns (ULg) Cargo Load Planning November 2014 2 / 38

Outline

1 Motivation





6 Conclusion


Problem Statement

“How to optimally load a set of containers/pallets (ULDs) into a cargoaircraft that has to serve multiple destinations under some safety, structural,

economical, environmental and manoeuvrability constraints?”

! Based on a real-world problem submitted by a professional partner


Context of the Research

Transport of goods by air:

- $6.4 trillion/year

- 10% of world trade volume but ⇠ 35% of world trade value

- Highly significant economic role

Optimizing loading assignment on board is critical:

- Conditions safety

- Positive impact on aerodynamics : less fuel consumption

- Saving time during operations on the ground

) Load planning is still a manual task


Outline

1 Motivation





6 Conclusion


Problem description

A cargo aircraft has to deliver goods at two consecutive airports1

We want to find load plans that:

Minimize consumption during the entire trip

Minimize the loading time at intermediate airport

Satisfy safety, structural, economical, environmental and manoeuvrabilityconstraints

1Generalization could be easily done to more than two destinations


Problem description

Weight and balance (W&B) problem

Sequencing problem


Informal summary

The ACLPPD can be informally summarized as:

min fuel and loading operations costs on the entire trips.t. Customer demand is satisfied (each ULD is loaded)

A position accepts only one ULD

Each ULD fits in an aircraft position

Some positions are overlapping: cannot be used simultaneously

Longitudinal stability is within certified limits (ZFW, TOW, LW)

Lateral stability is within certified limits

Weight per position is below the certified limit

Combined weight load limits are set

Cumulative weight load limits are set

Regulations for hazardous goods are fulfilled

Oversized ULDs are managed

Pickup & Delivery sequences are feasible


Informal summary

The ACLPPD can be informally summarized as:

min fuel and loading operations costs on the entire trips.t. Customer demand is satisfied (each ULD is loaded)

Standard









Regulations for hazardous goods are fulfilled

Advanced


Pickup & Delivery sequences are feasible


Main assumptions

We know beforehand:

The flight plan , i.e. the list of airports to visit and the order of visit

The structure of cargo aircraft

- Contains multiple decks with multiple configurations of positions for each

- A position is a particular aircraft space accommodating exactly one ULD

- For each position, we know* its location within the aircraft* the list of ULDs that fit into that position

- We also know the location of the di↵erent doors of the aircraft

The ULDs to be delivered

- For each ULD, we know (or at least we have a good guess of )* its size, shape and weight (IATA code)* its origin and destination


Outline

1 Motivation





6 Conclusion


Related literature

Not extensive scientific literature but still three main categories of papers:

- How to optimally load freight inside the ULDs?

- How to optimally select the ULDs to be loaded in an aircraft or a fleet

- How to optimally load ULDs in the aircraft?

Studies most closely related to our work:

Limbourg, S., Schyns, M., and Laporte, G. (2011). Automatic Aircraft Cargo LoadPlanning. Journal of the Operational Research Society

Verstichel, J., Vancroonenburg, W., Soufriau, W., Vanden Berghe, G. (2011). Amixed integer programming approach to the aircraft weight and balance problem.Procedia Social and Behavioral Sciences, Vol. 20, pp. 1051-1059.

Mongeau, M. and Bes, C. (2003). Optimization of Aircraft Container Loading, IEEETransactions on Aerospace and Electronic Systems, Vol. 39, pp. 140–150.


Contributions

Our main contributions:

We construct a general model based on international standards

We consider a trip of several legs with P&D at intermediate airports- We take into account operations on the ground

- We adapt the basic constraints of the one-leg problem to the multi-leg trip

We analyze the impact of optimal loading in terms of costs- Economic costs

- Environmental costs

We provide information about the complexity of the problem

We show measures of performance based on real data

We developed an interactive computerized decision aid tool (very flexible)(+ iPad version under development)


Outline

1 Motivation





6 Conclusion


Main parameters and variables

Our model is built on three main sets of parameters:

The set L of legs , i.e. the di↵erent parts of trip separating two successive airports

The set U of ULDs, i.e. the di↵erent pallets and containers to be delivered

- wi is the weight of ULD i (uniformly distributed)

- Subsets of ULDs according to the O&D: U1, U2, U3

- Subsets of ULDs according to the legs: UL1 , UL

2

The set P of positions, i.e. the predefined spaces able to accommodate ULDs

- Subsets of positions according to the sides: PR , PL

Main variables are binary variables

xijk =

⇢1 if ULD i is in position j during the leg k, 8i 2 U, 8j 2 P, 8k 2 L0 otherwise


Outline

1 Motivation





6 Conclusion


Minimizing overcosts

The objective of the ACLPPD is to assign each ULD to one positionwhile minimizing total costs

Minimizing total costs is realized by minimizing:

fuel consumption on each leg and handling operations at intermediateairports

More exactly, we will minimize the overcosts

In the same time, we save money:

- by reducing risk of material damages

- by managing more e↵ectively time of operations on the ground


Minimizing Fuel Consumption

The position of the CG influences the fuel consumption

The optimal location for the CG is the most aft within certified limits

minX

8k2L✏k

With:

✏k = |CGk � OCGk | 8k 2 L

- with OCGk :the requested optimal CG location, CGk : the actual CG (after assignments) and ✏k : the resulting deviation.


Minimizing Loading Time

The loading time depends on the number of ULDs to unload

How many ULDs are unnecessarily unloaded?

- ULDs 2 U3: ULDs from the depot to the second airport

- Doesn’t a priori need to be unloaded at intermediate airport (optimal case)

- But ULDs 2 U3 are unnecessarily unloaded if:

* in the exist path of ULDs 2 U1 that must be unloaded

* in the entry path of ULDs 2 U2 that must be loaded


Multiple doors

An aircraft compartment can have more than one door- # of operations can be minimized by using the most accessible door

Two doors can be used for each position:

- one in the direction of the nose (called ”the nose door”)

- one in the direction of the tail (called ”the tail door”)

For each position, we denote:

- BNj the set of positions between the position j and the“nose”door

- BTj the set of positions between the position j and the“tail” door


Unloading through multiple doors

Determine through which door a ULD is unloaded:

a

N(resp.T )j =

⇢1 if ULD in position j is unloaded through the nose (resp. tail) door

0 otherwise

The values of aNj and a

Tj are determined by:

↵Nj + ↵T

j 1 8j 2 P

↵Nj + ↵T

j � xij1 8j 2 P, 8i 2 U1

↵Nj = 0 8j 2 P | BN

j = ;↵Tj = 0 8j 2 P | BT

j = ;


Minimizing loading time taking into account multiple doors

Number of ULDs 2 U3 unnecessarily unloaded at intermediate airport:

n

N(T )j =

⇢1 if ULD in position j is unnecessarily unloaded through the nose (tail) door

0 otherwise

The values of nNj and n

Tj are determined by:

X

j02BNj

↵Tj0 nT

j |BNj |+ (1� xij1)|BN

j | 8j 2 P, 8i 2 U3

X

j02BTj

↵Nj0 nN

j |BTj |+ (1� xij1)|BT

j | 8j 2 P, 8i 2 U3


Minimizing total overcosts

Minimizing total overcosts : fuel consumption and loading time

MinX

8k2Lc

fk ✏k + c

hX

8j2P(nNj + n

Tj )

where :

cfk is the additional cost (fuel) for a deviation of one inch from the most aft CG

-depends on the type of aircraft, the cost of fuel, the pollution cost ...

ch is the additional cost for the loading time of one ULD

-in terms of wages and fees for the usage of the runway

-depends on the airline, the country, ...


Outline

1 Motivation





6 Conclusion


Standard Constraints

s.t. Customer demand is satisfied (each ULD is loaded)




















X

j2Pxijk = 1 8i 2 UL

k , 8k 2 L












X

i2ULk

xijk 1 8j 2 P, 8k 2 L












xijk = 0 8i 2 U, 8j 2 P, 8k 2 L | Ui does not fit in Pj












xijk + xi0j0k 1 8i , i 0 2 ULk , 8j 2 P, 8j 0 2 Ej , 8k 2 L












minCGk CGk maxCGk 8k 2 L












� D X

i2ULk

wi (X

j2PRxijk �

X

j2PLxijk) D 8k 2 L












wixijk Wj 8i 2 ULk , 8j 2 P, 8k 2 L












X

i2ULk

X

j2P|Pj\Oda 6=;

xijkodija Od

a 8d 2 D, 8a 2 Od , 8k 2 L












X

i2ULk

X

j2P|Pj\Sa

c=1 Fc 6=;

aX

l=1

xijk fijl Fa 8a 2 F, 8k 2 L

X

i2ULk

X

j2P|Pj\Sa

c=1 Tc 6=;

aX

l=1

xijk tijl Ta 8a 2 F, 8k 2 L


Advanced Constraints

s.t. Regulations for hazardous goods are fulfilled


-Categories of ULDs

P&Delivery

-Correct unloading sequence

-No exchange of positions inside the aircraft

-Feasible loading sequence

-Inaccessibility of some doors

-Domino e↵ect





-Categories of ULDs

P&Delivery





-Domino e↵ect

xijk + xi0j0k 1 8i , i 0, j , j 0 | ejj0 sii0 ; 8i , i 0 2 ULk , 8j , j 0 2 P, 8k 2 L





-Categories of ULDs

P&Delivery





-Domino e↵ect

xijk X

8j02Aj

xti j0k 8i 2 ULk , 8j 2 P, 8k 2 L





-Categories of ULDs

P&Delivery-Correct unloading sequence




-Domino e↵ect





-Categories of ULDs

P&Delivery





-Domino e↵ect

xijk = 0 8i /2 ULk , 8j 2 P





-Categories of ULDs

P&Delivery





-Domino e↵ect

X

j02BNj

↵Tj0 (1� ↵N

j )|BNj | 8j 2 P

X

j02BTj

↵Nj0 (1� ↵T

j )|BTj | 8j 2 P





-Categories of ULDs

P&Delivery





-Domino e↵ect

xij1 � xij2 (nNj + nTj ) 8i 2 U3

xij2 � xij1 (nNj + nTj ) 8i 2 U3





-Categories of ULDs

P&Delivery





-Domino e↵ect

X

i02U3

X

j02BNj

(xi0j01 � nTj0 � nNj0 ) �Nj |BN

j | 8j 2 P





-Categories of ULDs

P&Delivery





-Domino e↵ect

X

i02U3

X

j02BTj

(xi0j01 � nTj0 � nNj0 ) �Tj |BT

j | 8j 2 P





-Categories of ULDs

P&Delivery





-Domino e↵ect

�Tj + �N

j � 1 (1� xij2) 8j 2 P, 8i 2 U2

�Nj = 1 8j 2 P | BN = ;

�Tj = 1 8j 2 P | BT = ;





-Categories of ULDs

P&Delivery





-Domino e↵ect

xijk (1� ↵Nj ) 8i 2 UL

k | Ui doesn’t pass through the nose door, 8j 2 P, 8k 2 L

xijk (1� ↵Tj ) 8i 2 UL

k | Ui doesn’t pass through the tail door, 8j 2 P, 8k 2 L





-Categories of ULDs

P&Delivery





-Domino e↵ect

xij01 � 1 + nTj nTj0 8i 2 U3, 8j 2 P, 8j 0 2 BTj

xij01 � 1 + nNj nNj0 8i 2 U3, 8j 2 P, 8j 0 2 BNj


Outline

1 Motivation



4 Mathematical formulation


6 Conclusion


Environment

Model implemented in Java using IBM ILOG CPLEX 12.4 library

Tested on a set of real-world instances provided by TNT Airways

- TNT Airways, a wholly owned subsidiary of TNT Express

- TNT Express, one of the leading delivery integrators in Europe

- Head o�ce in Liege, Belgium

Graphical interface in order to visualize the loading plans

Important:

The loadmaster has the freedom to modify the solution proposed and can visualizethe impacts of modifications


The case of a Boeing 777

Historical intercontinental flight

The flight plan:

- First leg: ⇡ 2740 nautical miles

- Second leg: ⇡ 3200 nautical miles

The Boeing 777:

- One of the most used freighters

- 4 compartments, one door/compartment

- Main deck: 13 larger positions overlapping 26 smaller ones + 1 central

- Lower deck: 10 larger positions overlapping 32 smaller ones + 16 central



The list of ULDs (loaded at full capacity):

Set Origin Destination # ULDsU1 Liege DES1 19U3 Liege DES2 24 (1 large one)U2 DES1 DES2 9

UL1 Leg 1 (Liege-DES1) 43 (1 large one)

UL2 Leg 2 (DES1-DES2) 33 (1 large one)

Computed optimal CG: 39.3% and 38.3% (security margin: reduced by 1%)

c

h is fixed at 40 USD

c

fk is fixed at 100 USD

- 10% MAC shift of the CG ! % of 2% of fuel consumption

- One USD per fuel liter



Optimal solution found by our software:

- All constraints are satisfied



Feasibility envelopes:

Quality of the solution found:

Load Master Our solution%MAC ZFW (leg1) 24.4 38.3 2

%MAC ZFW (leg2) 31.1 37.3 3

# unloadings at DES1 43 19# loadings at DES1 33 9# ULDs 2 U3 unloaded at DES1 24 0Computation Time 20 minutes 16 hours

- The objective function is almost zero: no overcosts !

- High Computation time (NP-hard) BUT...

2✏1 w 03✏2 w 0V. Lurkin and M. Schyns (ULg) Cargo Load Planning November 2014 32 / 38


Time limit of 10 minutes:

Load Master Our solution With time limit%MAC ZFW (leg1) 24.4 38.3 38.2%MAC ZFW (leg2) 31.1 37.3 37.2# unloadings at DES1 43 19 22# loadings at DES1 33 9 12# ULDs 2 U3 unloaded at DES1 24 0 3Computation Time 20 minutes 16 hours 10 minutes

- Wasting time on optimality

- So high computation time remains the exception



Potential savings

Load Master Our solution With time limit%MAC ZFW (leg1) 24.4 38.3 38.2%MAC ZFW (leg2) 31.1 37.3 37.2# unloadings at DES1 43 19 22# loadings at DES1 33 9 12# ULDs 2 U3 unloaded at DES1 24 0 3Computation Time 20 minutes 16 hours 10 minutes

Fuel saving: 2010 USD

Operations saving: 840 USD (3 operations instead of 24)

=) Total saving for this flight: 2850 USD

Flight operated 3 times a week, every week in both direction

=) 650 000 USD/year


Additional cases

Hundreds of other real-world cases solved

Results for eight configurations (computation time limit of 10 minutes)

P&D Pickup DeliveryA B C D E F G H

|U1| 22 20 0 0 0 24 18 19|U3| 15 21 23 22 14 14 23 23|U2| 14 10 14 20 22 0 0 0Status O O O O O O O F✏ %MAC 0 0 0 0 0 0 0 0# unloadings 0 0 0 0 0 0 0 8Comput. time 1’15” 6’58” 2’04” 5’15” 54” 3’26” 5’58” 10’

All other simulations lead to similar results

Potential saving in all cases

Cases with hazardous goods and/or nose door provide similar results


Outline

1 Motivation



4 Mathematical formulation


6 Conclusion


Conclusion

- The ACLPPD, a crucial problem encountered every day by airlines

- We are the first to consider trips made of several legs with P&D operations

- We have proposed a new mixed integer linear model. Our model:

- is based on international standards ! valid for most of the commercialoperators

- integrates, and adapts to the multi-leg context, a large set of real constraints

- takes care of the loading/unloading sequences when P&D arises

- considers aircraft with several doors

- We showed that the problem is NP-hard

- We have proposed an original approach with a focus on the costs: fuelconsumption and handling operations costs

- We have tested our on real data and we conducted hundreds of experiments

- We have developed a flexible decision aid tool: based on the loadmaster’sexperience, the solution proposed can be adapted


Conclusion

Possible to find quickly optimal or near-optimal solutions

Substantial savings with respect to current typical practices:

- direct savings: fuel and operations costs

- indirect savings: less material damages, time saved for some last minutedecisions with added value,...


Contact me

My email address : [email protected]

QuantOM website : http://www.quantom.hec.ulg.ac.be

THANK YOU for your attention !


vers un transport aérien plus écologique et plus économique par virginie lurkin | liege creative,...

Technology