Difference: AirCrewRostering (1 vs. 12)

Revision 122009-07-23 - CameronWalker

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META TOPICPARENT name="SubmitCaseStudy"
<-- Under Construction -->
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FORM FIELD CaseStudyType CaseStudyType DIYCaseStudy
FORM FIELD OperationsResearchTopics OperationsResearchTopics IntegerProgramming
FORM FIELD ApplicationAreas ApplicationAreas Rostering
Changed:
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<
|*FORM FIELD ProblemDescription*|ProblemDescription|*Adapted from a real-world problem*

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using less pilots. |

>
>
|*FORM FIELD ProblemDescription*|ProblemDescription|*Adapted from a real-world problem*

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minimise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using fewer pilots. |

 
FORM FIELD ProblemFormulation ProblemFormulation The formulation...
FORM FIELD ComputationalModel ComputationalModel The computational model...
FORM FIELD Results Results The results...

Revision 112008-05-07 - TWikiAdminUser

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META TOPICPARENT name="SubmitCaseStudy"
<-- Under Construction -->
Line: 92 to 92
 
FORM FIELD Results Results The results...
FORM FIELD Conclusions Conclusions In conclusion...
FORM FIELD ExtraForExperts ExtraForExperts
Changed:
<
<
|*FORM FIELD StudentTasks*|StudentTasks|
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this method. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

|
>
>
|*FORM FIELD StudentTasks*|StudentTasks|
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this problem. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

|
 
META FILEATTACHMENT attachment="flights.jpg" attr="h" comment="" date="1203501646" name="flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" size="44700" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="recurring_flights.jpg" attr="h" comment="" date="1203501673" name="recurring_flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" size="24381" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="airline_demo.xls" attr="" comment="" date="1210165005" name="airline_demo.xls" path="airline_demo.xls" size="17920" stream="airline_demo.xls" tmpFilename="" user="BaseUserMapping_333" version="2"

Revision 102008-05-07 - TWikiAdminUser

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META TOPICPARENT name="SubmitCaseStudy"
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META FORM name="OpsRes.CaseStudyForm"
FORM FIELD Title Title AirCrewRostering
FORM FIELD DateSubmitted DateSubmitted 20 Feb 2008
Line: 94 to 92
 
FORM FIELD Results Results The results...
FORM FIELD Conclusions Conclusions In conclusion...
FORM FIELD ExtraForExperts ExtraForExperts
Changed:
<
<
|*FORM FIELD StudentTasks*|StudentTasks|
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this method. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

|
>
>
|*FORM FIELD StudentTasks*|StudentTasks|
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this method. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

|
 
META FILEATTACHMENT attachment="flights.jpg" attr="h" comment="" date="1203501646" name="flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" size="44700" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="recurring_flights.jpg" attr="h" comment="" date="1203501673" name="recurring_flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" size="24381" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
Changed:
<
<
META FILEATTACHMENT attachment="airline_demo.xls" attr="" comment="" date="1210164051" name="airline_demo.xls" path="airline_demo.xls" size="24064" stream="airline_demo.xls" tmpFilename="" user="BaseUserMapping_333" version="1"
>
>
META FILEATTACHMENT attachment="airline_demo.xls" attr="" comment="" date="1210165005" name="airline_demo.xls" path="airline_demo.xls" size="17920" stream="airline_demo.xls" tmpFilename="" user="BaseUserMapping_333" version="2"

Revision 92008-05-07 - TWikiAdminUser

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META TOPICPARENT name="SubmitCaseStudy"
<-- Under Construction -->
Line: 80 to 80
 
Added:
>
>
 
META FORM name="OpsRes.CaseStudyForm"
FORM FIELD Title Title AirCrewRostering
FORM FIELD DateSubmitted DateSubmitted 20 Feb 2008
FORM FIELD CaseStudyType CaseStudyType DIYCaseStudy
FORM FIELD OperationsResearchTopics OperationsResearchTopics IntegerProgramming
Changed:
<
<
FORM FIELD ApplicationAreas ApplicationAreas
|*FORM FIELD ProblemDescription*|ProblemDescription|*THE AIR CREW ROSTERING PROBLEM*

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain’s home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain’s contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline has started an AMPL model, but given up:

FLIGHT_SCHEDULE.MOD

model;

set TODS; # T(our) O(f) D(uty) set = pilot schedules
set FLYS {TODS} within FLIGHTS;

param Blocks {TODS} integer >= 1;
param Base {TODS} symbolic within BASES;

They have asked you to complete their model file and write a data file and script file to solve their rostering problem.

The airline is also curious if they can reduce the cost of their roster by using less pilots. As a second deliverable, they have asked you to investigate this option. |

>
>
FORM FIELD ApplicationAreas ApplicationAreas Rostering
|*FORM FIELD ProblemDescription*|ProblemDescription|*Adapted from a real-world problem*

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using less pilots. |

 
FORM FIELD ProblemFormulation ProblemFormulation The formulation...
FORM FIELD ComputationalModel ComputationalModel The computational model...
FORM FIELD Results Results The results...
FORM FIELD Conclusions Conclusions In conclusion...
FORM FIELD ExtraForExperts ExtraForExperts
Changed:
<
<
|*FORM FIELD StudentTasks*|StudentTasks|*STUDENT TASKS*

1. Add a ??? LINK ?? columnwise formulation for finding a pilot roster flight_schedule.mod.

What to hand in Your completed flight_schedule.mod file.

2. Design a system/process for generating all possible Tours of Duty (TODs). Generate the TODs to create flight_schedule.dat.

What to hand in A brief (less than 1 page) description of your system/process. Your flight_schedule.dat file.

3. Solve The Air Crew Rostering Problem. Be sure to investigate the possibility of less pilots.

What to hand in A management summary of your solution.

Extra for Experts' Tasks

1. The airline had hired another AMPL consultant to generate TODs automatically. She had almost finished before going on parental leave. She has left a multitude of files in a zip archive:

??? LINK ??? flights.zip

All the files are complete except flight_schedule.run (there is an incomplete version in the archive). Complete flight_schedule.run and run generating_flights.run to solve The Air Crew Rostering Problem.

What to hand in Your completed flight_schedule.run file. A comment on whether your solution from generating_flights.run agrees with your solution where you generated the TODs yourself.

|
>
>
|*FORM FIELD StudentTasks*|StudentTasks|
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this method. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

|
 
META FILEATTACHMENT attachment="flights.jpg" attr="h" comment="" date="1203501646" name="flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" size="44700" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="recurring_flights.jpg" attr="h" comment="" date="1203501673" name="recurring_flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" size="24381" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
Added:
>
>
META FILEATTACHMENT attachment="airline_demo.xls" attr="" comment="" date="1210164051" name="airline_demo.xls" path="airline_demo.xls" size="24064" stream="airline_demo.xls" tmpFilename="" user="BaseUserMapping_333" version="1"

Revision 82008-05-07 - TWikiAdminUser

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META TOPICPARENT name="SubmitCaseStudy"
<-- Under Construction -->
Line: 84 to 84
 
FORM FIELD Title Title AirCrewRostering
FORM FIELD DateSubmitted DateSubmitted 20 Feb 2008
FORM FIELD CaseStudyType CaseStudyType DIYCaseStudy
Changed:
<
<
FORM FIELD OperationsResearchTopics OperationsResearchTopics
>
>
FORM FIELD OperationsResearchTopics OperationsResearchTopics IntegerProgramming
 
FORM FIELD ApplicationAreas ApplicationAreas
|*FORM FIELD ProblemDescription*|ProblemDescription|*THE AIR CREW ROSTERING PROBLEM*

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain’s home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain’s contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline has started an AMPL model, but given up:

FLIGHT_SCHEDULE.MOD

model;

set TODS; # T(our) O(f) D(uty) set = pilot schedules
set FLYS {TODS} within FLIGHTS;

param Blocks {TODS} integer >= 1;
param Base {TODS} symbolic within BASES;

They have asked you to complete their model file and write a data file and script file to solve their rostering problem.

The airline is also curious if they can reduce the cost of their roster by using less pilots. As a second deliverable, they have asked you to investigate this option. |

FORM FIELD ProblemFormulation ProblemFormulation The formulation...
Line: 93 to 93
 
FORM FIELD Conclusions Conclusions In conclusion...
FORM FIELD ExtraForExperts ExtraForExperts
|*FORM FIELD StudentTasks*|StudentTasks|*STUDENT TASKS*

1. Add a ??? LINK ?? columnwise formulation for finding a pilot roster flight_schedule.mod.

What to hand in Your completed flight_schedule.mod file.

2. Design a system/process for generating all possible Tours of Duty (TODs). Generate the TODs to create flight_schedule.dat.

What to hand in A brief (less than 1 page) description of your system/process. Your flight_schedule.dat file.

3. Solve The Air Crew Rostering Problem. Be sure to investigate the possibility of less pilots.

What to hand in A management summary of your solution.

Extra for Experts' Tasks

1. The airline had hired another AMPL consultant to generate TODs automatically. She had almost finished before going on parental leave. She has left a multitude of files in a zip archive:

??? LINK ??? flights.zip

All the files are complete except flight_schedule.run (there is an incomplete version in the archive). Complete flight_schedule.run and run generating_flights.run to solve The Air Crew Rostering Problem.

What to hand in Your completed flight_schedule.run file. A comment on whether your solution from generating_flights.run agrees with your solution where you generated the TODs yourself.

|
Changed:
<
<
META FILEATTACHMENT attachment="flights.jpg" attr="" comment="" date="1203501646" name="flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" size="44700" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="recurring_flights.jpg" attr="" comment="" date="1203501673" name="recurring_flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" size="24381" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
>
>
META FILEATTACHMENT attachment="flights.jpg" attr="h" comment="" date="1203501646" name="flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" size="44700" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\flights.jpg" tmpFilename="" user="LaurenJackson" version="1"
META FILEATTACHMENT attachment="recurring_flights.jpg" attr="h" comment="" date="1203501673" name="recurring_flights.jpg" path="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" size="24381" stream="C:\Users\Lauren Jackson\Documents\Desktop\Desktop stuff\Twiki\Twiki images\AirCrewRostering\recurring_flights.jpg" tmpFilename="" user="LaurenJackson" version="1"

Revision 72008-04-02 - TWikiAdminUser

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Revision 62008-03-01 - TWikiAdminUser

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Operations Research Topics: IntegerProgramming

Application Areas: Rostering

Contents

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<
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>
 

Problem Description

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minimise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using fewer pilots.

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Problem Formulation

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The formulation...
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The formulation...
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Computational Model

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The computational model...
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Results

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The results...
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Conclusions

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In conclusion...
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<--
  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this problem. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

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Revision 52008-03-01 - TWikiAdminUser

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META TOPICPARENT name="SubmitCaseStudy"
<-- Under Construction -->
Line: 26 to 26
 

Operations Research Topics: IntegerProgramming

Application Areas: Rostering

Contents

Changed:
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<

>
>
 

Problem Description

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minimise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using fewer pilots.

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Problem Formulation

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Problem Formulation

 
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The formulation...
 
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Computational Model

 
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Results

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Conclusions

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Student Tasks

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  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this problem. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

>
>
 
Changed:
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<
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META FORM name="OpsRes.CaseStudyForm"
FORM FIELD Title Title AirCrewRostering
FORM FIELD DateSubmitted DateSubmitted 20 Feb 2008
Added:
>
>
FORM FIELD CaseStudyType CaseStudyType DIYCaseStudy
 
FORM FIELD OperationsResearchTopics OperationsResearchTopics
FORM FIELD ApplicationAreas ApplicationAreas
|*FORM FIELD ProblemDescription*|ProblemDescription|*THE AIR CREW ROSTERING PROBLEM*

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain’s home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain’s contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline has started an AMPL model, but given up:

FLIGHT_SCHEDULE.MOD

model;

set TODS; # T(our) O(f) D(uty) set = pilot schedules
set FLYS {TODS} within FLIGHTS;

param Blocks {TODS} integer >= 1;
param Base {TODS} symbolic within BASES;

They have asked you to complete their model file and write a data file and script file to solve their rostering problem.

The airline is also curious if they can reduce the cost of their roster by using less pilots. As a second deliverable, they have asked you to investigate this option. |

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Case Study: AirCrewRostering

Submitted: 20 Feb 2008

Operations Research Topics: IntegerProgramming

Application Areas: Rostering

Contents

Problem Description

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain's home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain's contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline wants to know what shifts the captains should fly to minimise the cost of covering the flights.

The airline is also curious if they can reduce the cost of their roster by using fewer pilots.

Return to top

Problem Formulation

The formulation...

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Computational Model

The computational model...

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Results

The results...

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Conclusions

In conclusion...

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Student Tasks

  1. Write a columnwise formulation to solve the Airline Rostering Problem. Generate feasible shifts for your formulation using any method you choose, be sure that your method generates all possible shifts. The spreadsheet airline_demo.xls shows some of the possible shifts. Solve the Airline Rostering Problem and write a management summary.

    Hint Using depth-first search or power sets in AMPL is difficult for this problem. Using a different programming language to generate the shifts, or generating them by hand using a carefully thought out method may be easier.

    What to hand in Your model file. A description of your shift generation method. Your management summary.

Return to top

META FORM name="OpsRes.CaseStudyForm"
FORM FIELD Title Title AirCrewRostering
FORM FIELD DateSubmitted DateSubmitted 20 Feb 2008
FORM FIELD OperationsResearchTopics OperationsResearchTopics
FORM FIELD ApplicationAreas ApplicationAreas
|*FORM FIELD ProblemDescription*|ProblemDescription|*THE AIR CREW ROSTERING PROBLEM*

Adapted from a real-world problem

An airline is trying to roster captains for 6 flights. The flight schedules are:

flights.jpg

Only one captain is required for each sector, but a captain may be a passenger on a flight (this is called paxing). In addition to the six flights above the following flights are available for paxing and operate every 2 hours:

recurring_flights.jpg

The following rules for shifts must be observed:

  • Shifts start and finish at a captain’s home base;
  • The earliest start time is on Day 1 (0001 hours) and the latest finish time is on Day 6 (2359 hours);
  • Shifts are composed of blocks of work. Each block must be no more than 13 hours;
  • Captains must have at least 12 hours break between blocks. The exception is when a block consists only of paxing flights, then a 9 hour break is all that is needed;
  • There must be a 30 min break between sector changes.

There are 6 captains available for work, 2 based in Auckland (AKL), 1 based in Christchurch (CHCH) and 3 based in Singapore (SNG). Each captain is paid $1000 for each block of work (even if it is only a 45 min pax). Each captain’s contract guarantees he/she will be paid for 3 blocks of work even if they perform less.

The airline has started an AMPL model, but given up:

FLIGHT_SCHEDULE.MOD

model;

set TODS; # T(our) O(f) D(uty) set = pilot schedules
set FLYS {TODS} within FLIGHTS;

param Blocks {TODS} integer >= 1;
param Base {TODS} symbolic within BASES;

They have asked you to complete their model file and write a data file and script file to solve their rostering problem.

The airline is also curious if they can reduce the cost of their roster by using less pilots. As a second deliverable, they have asked you to investigate this option. |

FORM FIELD ProblemFormulation ProblemFormulation The formulation...
FORM FIELD ComputationalModel ComputationalModel The computational model...
FORM FIELD Results Results The results...
FORM FIELD Conclusions Conclusions In conclusion...
FORM FIELD ExtraForExperts ExtraForExperts
|*FORM FIELD StudentTasks*|StudentTasks|*STUDENT TASKS*

1. Add a ??? LINK ?? columnwise formulation for finding a pilot roster flight_schedule.mod.

What to hand in Your completed flight_schedule.mod file.

2. Design a system/process for generating all possible Tours of Duty (TODs). Generate the TODs to create flight_schedule.dat.

What to hand in A brief (less than 1 page) description of your system/process. Your flight_schedule.dat file.

3. Solve The Air Crew Rostering Problem. Be sure to investigate the possibility of less pilots.

What to hand in A management summary of your solution.

Extra for Experts' Tasks

1. The airline had hired another AMPL consultant to generate TODs automatically. She had almost finished before going on parental leave. She has left a multitude of files in a zip archive:

??? LINK ??? flights.zip

All the files are complete except flight_schedule.run (there is an incomplete version in the archive). Complete flight_schedule.run and run generating_flights.run to solve The Air Crew Rostering Problem.

What to hand in Your completed flight_schedule.run file. A comment on whether your solution from generating_flights.run agrees with your solution where you generated the TODs yourself.

|
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