Planning of Outbound Baggage Handling at Airports - … · Technische Universität München Planning of Outbound Baggage Handling at Airports 2 Agenda 1. Introduction 2. Decomposition

Technische Universität München

Planning of Outbound Baggage Handling at Airports

Markus Frey

Supervised by Rainer Kolisch

Christian Artigues

Toulouse, 26.04.2010


Planning of Outbound Baggage Handling at Airports 2

Agenda

1. Introduction

2. Decomposition Procedure

3. Assignment- and Scheduling Problem

4. Computational Study

5. Outlook


The way of the Baggage: Incoming Baggage

3

Check-InBaggage

Transfer Baggage

Central Storage

Incoming Baggage Baggage Handling System Circulations Departing Flights

Decisions:

Flow direction of the baggage

Legend



The way of the Baggage: Baggage Handling System

4

Check-InBaggage

Transfer Baggage

Central Storage


Baggage handling has not started yet

Decisions:


Legend



The way of the Baggage: Baggage Handling System

5

Check-InBaggage

Transfer Baggage

Central Storage


Start of the baggage handlingStart of storage depletion

Assignment to one circulation

Decisions:


Legend



The way of the Baggage: Ending of the Baggage Handling

66

Check-InBaggage

Transfer Baggage

Central Storage


Ending of the baggage handling

Transport of the baggage to the departing airplaneFlow direction

of the baggage

Decisions:

Objective: Minimize the maximal workload over all circulations

Legend



Problem Composition

7

Scheduling Problem:

• Determination of the starttime of the baggage handling on a circulation foreach flight

• Determination of the starttime of the storage depletion for each flight

Assignment Problem:

• Assignment of each flight to a circulation Remark: At one circulation it is possible to handle several flights at the same time

• Assignment of the working stations to each flightRemark: One working station canhandle at most one flight at the same time

Arrival process of baggage Legend

Influences



Sets and Parameters: Circulations

• Set of circulations

• Number of parking places on circulation

• Number of working stations on circulation

• Capacity of of circulation

8Planning of Outbound Baggage Handling at Airports


Circulation: Draft

WS04

WS02WS01

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

WS03

Parking places for bag carts

Parking places for bag carts

Working station

9

Working station



Circulation with and

Time table for the baggage handling on :

Time Flight Container

16:00 – 17:45 F1 8

16:30 – 17:30 F2 8

16:30 – 18:00 F3 4

Planning of Outbound Baggage Handling at Airports 10

Example: Assignment on Circulations

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

WS01 WS02

WS03 WS04

16:00 16:30 17:30 17:45 18:00

F1F2F3

Flight

Time





16:00 – 17:45 F1 8

16:30 – 17:30 F2 8

16:30 – 18:00 F3 4


1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

WS01 WS02

WS03 WS04

16:00 16:30 17:30 17:45 18:00

11

F2F3

F1

Time

Flight






16:00 – 17:45 F1 8

16:30 – 17:30 F2 8

16:30 – 18:00 F3 4


1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

WS01 WS02

WS03 WS04

16:00 16:30 17:30 17:45 18:00

12

F2F3

F1

Flight

Time



13

Agenda

1. Introduction




5. Outlook



14

• Planning horizon

• Set of outgoing flights

• Ending time of the baggage handling of flight

• Working rate on each circulation

• Tranfer rate from the storage to one circulation

• Number of required parking places for flight

Sets and Parameters



15

Decision Variables: Scheduling Problem

For all :

• Starting time of the baggage handling

• Starting time of the storage depletion



Decision Variables: Assignment Problem

16

For all and :

• Numbers of assigned working stations forflight

•



Baggage Arrival Function and Storage Function

For each flight we intorduce the• Baggage Arrival Function

gives the amount of baggage on circulation if the baggage handling and storage depletion of flight i is started at time and , respectivley, by given number of assigned working station

• Storage Function

gives the amount of baggage stored in the storage if the baggage handling and storage depletion of flight i is started at time and , respectivley



Regard flight with , and .. The arrival process of the baggage is given by

Amount of baggage

Example: Baggage Arrival Fuction

18

Data setting:

Working rate

Storage depletion rate

1

23

45

Time1



Example: Baggage Arrival Function

19

1

2

3

4

5

1

23

45

Value of

Time

Values of Baggage Arrival Functionfor with :

Amount of baggage stored for flight : 1

Data setting:

Working rate

Storage depletion rate

2 3 4 5 6 71



MinMax – Flow Problem (MMFP)

Input: Feasible assignment and schedule of ASP

Objective: Find feasible assignment of working stations to flights such that the maximal workload on each circulation is minimized

Output: Feasible assignment of working stations to flights

Dynamic Assignment Problem (DAP)

Input: Assignment of working stations to flights

Objective: Schedule and assign all flights to circulations such that the maximal workload over all circulations is minimized

Output: Feasible assignment and schedule

Decomposition Procedure

20

Try to reduce the maximal peak by assigning more

working stations to the flights

causing this peak

If there is no feasible solution, there will be no feasible solution at all

If ASP has a feasible solution then the Flow Problem also will be feasible

Observation:



Assignment- and Scheduling Problem

21

Objective function: Minimize the maximal worload over all circulations

subject to

(2) Time window for the start time of the baggage handling

(3) Time window for the start time of the storage depletion



Assignment- and Scheduling Problem

22

(4) Assigns each flight to exact one circulation(5) Restricts the availabel number of parking places on circulation (6) Restricts the availabel number of working stations on circulation(7) Capacity for the storage(8) Definition for the assignment variable



Complexity

Lemma: ASP is NP-complete.

Proof: Reduction of the Generalized Assignment Problem (GAP) in polynomial time to the ASP.



Agenda

24

1. Introduction




5. Outlook



4. MIP-A

We compare the solution of the ASP with the solution of a MIP-Formulationsolving the complete problem. This MIP-Formulation works directely on the arrival process of the baggage giving the amount of baggage arriving foreach flight at time .

Objective function of the Mixed-Integer-Program with Arrival ProcessFunction (MIP-A):

25

Variable gives the amount of baggage of flight i at time arriving circulation



MIP-A

26

Variables:



MIP-A



MIP-A



MIP-A



MIP-A



MIP-A



Data Setting

32

Time horizon 97

# Circulations 15

# Working stations per circulation 6

Working rate 6

Depletion rate 19

Storage capacity 500

Circulation capacity 30

Size of the intervalfor all flights 13



** ASP-Red assumes in the ASP

* MIP-A1 assumes in the MIP-A

Sol. (Gap)

Time

Computational Study


ProgramNumber of Flights

3 5 8 10 20 30 50

MIP-A4 4 5 6 7 (100%) - -

6,30s 16,80s 488,70s 50m >2h - -

MIP-A1*10 10 11 11 18 (100%) - -

28,90s 260,30s 433,30s 37m >2h - -

ASP10 10 11 11 18 22 22

3,90s 5,50s 9,30s 13,20s 31,10s 61,10s 640s

ASP-Red**10 10 11 11 27 27 39

0,82s 1,20s 1,90s 13,10s 23,70s 55,30s 270,80s


Agenda

34

1. Introduction




5. Outlook



Upcoming Research

• Implementing and testing the whole decomposition procedure

• Finding some rules to improve the solution of the heuristic solution

• Developing of a „fast“ solution procedure for the ASP and for the Flow Problem

• Taking stochasticity of the baggage arrival process into account




Markus Frey

Supervised by Rainer Kolisch

Christian Artigues

Toulouse, 26.04.2010


Planning of outbound baggage handling at airports 37

Assumptions

• Baggage arrival process is given for all and

• Equal loading rate on all working stations

• Flight is only served by the assigned working station

• Ending time of the baggage handling is given for all flights


I. Baggage Handling: For each

•

•

Example: Flight with and . If we set we have:

Mixed-Integer Program: Scheduling


15:00 15:30 16:00 16:30 17:00 17:30 18:00 18:30

( 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 ) … …( 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ) … …


I. Baggage Handling



Determination of the start time of the baggage handling

Setting of the on/off variable for the baggage handling


II. Storage: Start Time of the storage depletion



Number of pieces of baggage in the storage

Determination of the starttime of the storage depletion


II. Storage: Setting of the on/off variable for storage depletion



Determine the ending time of the storage depletion

Setting of the on/off variable for the storage depletion



II. Storage: Storage capacity



Mixed-Integer Program: Assignment Problem


Assignment of each flight to onecircutlation

Assignment of eacht flight to the required working stations

Capacity of the parking spaceson a circulation


Number of baggage piecesarriving on circulation at time

Utilization of circulation at time relative to circulation capacity

Working rate

Objective: Equal workload over all circulations


Objective Function

Objective function minimize the maximum relative amount of baggage on the circulations d at each time

Scheduling Problem Assignment Problem



Agenda

1. Introduction

2. Mixed-Integer Program


4. Outlook


Test Instance


Time horizon 80

Number of flights 4

Circulation 1

Circulation capacity 55

Working stations 4

Working rate 5 pb / t

Storage capacity 100

Number of variales 5.562

Number of restrictions 15.895

Legendpb piece of baggage


Heruistic of Terminal 2 of Munich Airport

Scheduling Problem:• Start of the baggage handling after a rule of thumb• for all • Release as many baggage as possible (We set )

Assignment Problem:System of rules for the assignment of flights to circulation and to working stations

Maximal workload on the circulation: 58Objective function value: 1,05



Solution of the MIP


Instance Heuristic MIP 1 MIP 2 MIP 3 MIP 4

Variables

x x x

x x x

Assignment Problem x x x

Objective functionvalue 1,05 0,98 0,87 0,62 0,42

Improvement in comp. to the heurstic - 6,90% 17,24% 41,38% 60,34%

Legendx Solution method of the heuristic Optimized with the MIP


Computing Time


2sd test instance Real instance

Time horizon 80 288 (5 min. int.)

Number of flights 8 ca. 350

Circulations 2 22

Working stations per circulation 4 ca. 4

Storage capacity 100 4.000

Number of variales 17.514 ca. 4.885.552

Number of restrictions 51.000 ca. 14.064.086

Computing times of up to 2 hours are possible!

Efficient solution mehtods required!


Agenda

1. Introduction

2. Mixed-Integer Program


4. Outlook



Upcoming Research

Reformulation of the Problem


Capacity restrictionsover all flights

Scheduling and Assignment restrictions for each flight

Decomposition of the problem in subproblems in combination with dynamic programming techniques

Flights in the morning have only little influence on flights in the evening



Next Steps

• Elaboration of the decomposition of the problem

• Usage of column generation techniqus with branch & price and dynamicprogramming techniques

• Test with real data of terminal 2 of Munich Airport



Planning of outbound baggage handling at airports

Markus FreySupervised by Rainer Kolisch

Technische Universität MünchenLehrstuhl für Technische Dienstleistungen und Operations Management

Prof. Dr. Rainer Kolisch

Project Management and Scheduling, Tours26.04.2010


Erwarteter Ankunftsprozess von Gepäck aus Check-In und Transferflügen in der GFA von Flug LH 428 (5 Minuten Intervall; )


Ankunftsprozess von Gepäck

Ankunftsprozess

0

2

4

6

8

10

12

14

16

18

20

07:00

07:15

07:30

07:45

08:00

08:15

08:30

08:45

09:00

09:15

09:30

09:45

10:00

10:15

10:30

10:45

11:00

11:15

11:30

11:45

Zeit

Gep

äckm

enge

Ankunftsprozess



Baggage Types

At an airport, we got two kinds of baggage types:

• Check–In Baggage: Baggage, which is given offat an Check-In counter

• Transfer Baggage: Baggage, which istransferred from incoming flights to outgoing flights



Baggage Handling System (BHS)



Circulation



Control System for the Baggage Handling

CI

Direction of the baggage

Storage

Circulations

Storage

1. Start of the Baggage Handling of flight at time ?

a. No: Transfer of the incoming baggage to the storage

b. Yes: Transfer of the incoming baggage to the assigned circulation, set i. Decision at which

time storage depletion for flight starts

Objective: Equally workload over all circulations

1i

i



Zeitfenster



Im Folgenden betrachten wir die Zuweisung der Flüge zu den Rundläufen und Entnahmestellen sowie die Zuweisung zu den Stellplätzen

Wir definieren für alle , und

• die binären Entscheidungsvariablen ––

• die binäre Hilfsvariable––

Zuweisungsproblem – Rundläufe und Entnahmestellen



Zuweisungsproblem - Rundläufe und Entnahmestellen

und werden im Preprocessing ermittelt. Es gilt:

Aus Rundlaufannahme folgt für alle :

mit



Zuweisungsproblem - Stellplätze

Wir definieren für alle , und

• ganzzahlige Entscheidungsvariable–



Speicher

Es sei die Menge an Gepäckstücken, welche im Zeitintervall pro Flug aus dem Speicher zu den Rundläufen befördert werden kann



Speicher

Wir definieren für alle und die beiden Mengen:

• d = Menge aller Flüge , für die zum Zeitpunkt Gepäck in den Speicher abgelegt werden kann

• d = Menge aller Flüge , die zum Zeitpunkt bereits bearbeitet werden können

Wir definieren für und die binären Hilfsvariablen

•

•



Speicher

Es sei die Kapazität des Speichers



Gemischt – Ganzzahliges Programm

Modellierung des Multi-Mode RCPSP als Gemischt – Ganzzahliges Programm (MIP), um die Startzeiten für die Flugbearbeitung und den Speicherabzug sowie die Zuweisung zu den Rundläufen, Entnahmestellen und Stellplätzen zu erhalten. Ziel dabei ist es, eine gleichmäßige Auslastung aller Rundläufe zu erhlaten


Ressourcen- und Aktivitätstypen


• Kumulative Ressourcen– Speicher mit Kapazität – Bandkapazität der einzelnen Rundläufe

• Auffüllende Aktivitäten– Start des Ankunftsprozesses – Speicherabzug

• Verzehrende Aktivitäten– Verladung der Gepäckstücke in die Boxen

(Beachte: Verladungsrate an den Rundläufen hängt vom Zuordnungsproblem ab)– Speicherabzug

Beachte: Startzeit der Aktivtäten sowie die Verwendung der vorhandenen Ressourcen hängen von den Ankunftsprozessen der Gepäckstücke ab!

LiteraturNeumann, K., Schwindt, C. and Zimmermann, J. (2003). Project Scheduling with Time Windows and Scarce Resources, 2nd Ed., Springer.


Optimaler Start der Flugbehandlung zum ZeitpunktSpeichermenge

Beispiel: Startzeitpunkte für Flugbearbeitung


Ankunftsprozess am Rundlauf

12

3

4

5

Gepäckmenge

Zeit

Die maximale Rundlaufauslastung liegt bei 2 Gepäckstücken pro Zeiteinheit


Lösungsidee

Dies ergibt folgende Problemstruktur:


Masterproblem

Subprobleme


Eine Betrachtung des Problems ergibt eine Diagonalstruktur, was auf eine Dekomposition des Problems (Spaltengenerierung) als Lösungsstrategie deuten lässt:

Für alle Flüge gilt:

• Flugbearbeitungsrestriktion• Speicherrestriktion II• Zuweisungsproblem IV

Über alle Flüge gilt:

• Speicherrestriktion III• Zuweisungsrestriktion V

Lösungsidee



Computational Study

Workload on the circulation if we additionally optimize the start of the baggage handling time


Reduction of the workload of 33 % in comparison to the used heuristic


Parameters of the Heuristic

Start time of the baggage handlingAssignment to the working stations

Assignment to the working stations

Optimizedvariables

Delay of the storagedepletion with

Delay of the storage depletion with

Delay of the storage depletion with

Start time of the baggage handling

Start time of the baggage handlingAssignment to theworking stations

Objective functionvalue 0,98 0,87 0,42

Improvement to the herustic 6,90% 17,24% 60,34%

Solution of the MIP



Computational Study

Workload on the circulation if we finally optimize the assignment to the working stations


Reduction of the workload of 45 % in comparison to the used heuristic

Computing time: 7,78 sec.

Conclusion: All proposed control elements optimize the workload on the circulations

Documents

Planning of Outbound Baggage Handling at Airports - … · Technische Universität München Planning of Outbound Baggage Handling at Airports 2 Agenda 1. Introduction 2. Decomposition