scheduling and revenue management

April 2012

Guideline on the use of Operations Research in the airline industry

Scheduling and Revenue Management

Nabil Si Hammou, Operations Research Analyst

[email protected]

mailto:[email protected]

As a member of AGIFORS (The Airline Group of the International Federation of Operational Research Societies ) and passionate on the operations research, I have established a summary of practices on the use of optimization methods for Scheduling and Revenue Management in the airline industry.

This summary comes as a result of 6 months of individual research on the optimization methods used by different airlines for Scheduling and Revenue Management. It’s based on various information sources (Air France seminar, AGIFORS symposium, AGIFORS presentations, specialized books in the airline industry, ….).

I would welcome the opportunity to discuss with you the potential for making a significant contribution in optimizing the scheduling and revenue management process. Feel free to call me at 00.212.6.18.98.38.61 or email me at [email protected].

Abstract

2Best practices - Optimization processNabil Si Hammou, April 2012

Nabil Si HammouOptimization [email protected]

Being an Operations Research Analyst, I am particularly interested in the positions:

– Scheduling optimization specialist– Revenue management optimization specialist

Plan

Outline( page 3..6)

Optimization Process Overview ( page 7..10)

Scheduling(page 11..49)

Revenue Management(Page 50..83)

Conclusion : Robustness(page 84)


ContextThe global airline industry consists of over 2000 airlines operating and more

than 23 000 commercial aircraft, providing service to over 3700 airports . The world’s airlines flew more than 29 million scheduled flights and transported over 2.5 billion passengers (IATA, 2010).

Since the economic deregulation of airlines, cost management and productivity improvements has became central goals of airlines with the shift to market competition.

The airline schedule affects almost every operational decision, and on average 75% of the overall costs of an airline are directly related to the schedule. Given an airline schedule, a significant portion of costs and revenues is fixed

The management strategies and practices of airlines were fundamentally changed by increased competition within the industry.

Outline


The main principle of airline management is to match supply and demand for its service in a way which is both efficient and profitable.

Airlines use numerous resources to provide transportation services for their passengers. It’s the planning and efficient management of these resources and sales that determine the survival or demise of an airline.

In practice, the objective of airline management is to maximize operating profit (increase sales and/or decrease costs) by defining the optimal resource scheduling and sale policy:

Context

Sales

Investment cost

Operations cost Benefit

Outline


Airline management systemTo maximize the operating profit, the airline management system takes into

account various factors such as demands in various markets, available resources, airport facilities and regulation for achieving optimal solutions

Airport operating hours

Airport runway length

Airport charges

Maintenance requirement

Facility constraints

Aircraft capacities

Aircraft range limitation

Aircraft costs

Operational costs

Route characteristic

Crew availability

Managerial constraint

Other regulations

Passenger behavior

Competitor schedules

Passenger demand

Aircraft

Airport

Minimum turn time

Demand

connection time

Passenger Yield

Airline DecisionSystem

Outline


Optimization process

Currently, all airlines decompose the overall management problem into subproblems and solve them sequentially: sequential approach

Because of the reduced complexity generated by the decomposition, the sequential approach allows to solve decision problem more easily by using optimization algorithms.



The decomposition is usually structured according on two dimensions:

1.Time horizon ( Strategic, Tactical and Operations)

2. Subject ( Aircraft, Crew, Ground and Sales)

Various decomposition used in the airline industry.

Decomposition


Example of an optimization process used by one of the biggest airlines in Europe

8Best practices - Optimization process

The subproblems which make up the overall airline decision system could be solved sequentially according to the below design.

In some cases, the sequence of these decisions is reversed, in that the identification of a profitable opportunity related to a subproblem might modify the decision related to the previous subproblem ( iterating system).

Decomposition


9

Scope

We focus in this presentation on the following subproblems :


B. Revenue Management:5. Optimization6. Forecasting

A. Scheduling:1. Fleet assignment2. Maintenance routing

3. Crew pairing4. Crew assignment


Scheduling


Fleet assignment

Scheduling


Given the fleet availability and flight schedule, the goal of fleet assignment is to find the best assignment of fleet type to flight legs that maximize the expected profit.

Fleet assignment: Introduction

1.Schedule: set of flight legs with given departure and arrival times.

2. Fleet: aircraft owned by the company (number of aircraft by type).

3.Profit : associated to the assignment of a fleet type to flight leg calculated throughout:

– Cost: fuel….

– Revenue: usually substituted by (-) spill cost (rejected demand)

Input Output

Assignment of fleet type to each flight leg of the schedule with profit maximization (expected revenue – operation cost) or cost minimization including spill cost

Airport B

Airport A

Which aircraft type ?

06h00

07h30 08h30 09h00

10h30

10h100

Scheduling





Fleet assignment: Introduction

Coverage: each flight leg is assigned to exactly one fleet type.

Fleet availability : it limits the assigned aircraft of each fleet type to the number available.

Balance: the total numbers of aircraft of each type arriving and departing each airport are equal.

Additional restriction: technical restriction ( some aircrafts can’t cover some flight legs…), ….

Constraint

Scheduling


For modeling the fleet assignment problem, we represent at first the flight schedule as time space network in order to facilitate the mathematical modeling of constraints.

Fleet assignment: Time-space network

Airport A

Airport B

Airport C

Schedule cycle time(week, day..)

Time-space network

: Flight arc: represents a flight leg with departure and arrival location

: Arc’s origin node: represents a flight leg departure time

: Arc’s destination node: represents a flight leg arrival time including turn time.

: Ground arc: represents aircraft on the ground during the period spanned by the times associated with the arc’s end nodes

: Count time : a point in time used specifically to count the number of aircraft needed to cover the aircraft rotations in a solution

Scheduling


Fleet assignment: Modeling

Input

Scheduling

F : set of flight legs to be operated

K: set of fleet types

Mk number of aircraft available of type k.

Lk: the set of flight legs could be covered by the fleet type k.

Nk : set of nodes (departure , arrival) could be served by the fleet type k

Gk : set of ground arc could be covered by the fleet type k.

O(k,n): set of flight legs Lk and originating by the node n

I(k,n): the set of legs Lk and terminating at the node n

N+: set of ground arc originating from node n Nk ( n- ground arc terminating at n Nk)

CL(k) : the set of flight legs Nk and cross the count time.

CG(k): the set of ground arc Gk and cross the count time

Cik operating cost minus revenue of flying leg f with fleet type

k

Decision variables

fik

:1 if flight leg i is assigned to fleet type k,

0 otherwise.

yak : number of aircraft of type k on the

ground arc a


Fleet assignment: Modeling

kk

a

kki

k

kCLi

ki

kCGa

ka

k

nkIi

ki

kn

nkOi

ki

kn

Kk

ki

Kk Fi

ki

ki

GaKky

NiKkf

KkMfy

NnKkfyfy

Fif

tosubject

fC

0

1;0

;

;

;1

min

)()(

),(),(

Minimizing costs ( operation & spill)

Coverage constraint

Balance constraint

Fleet availability constraint

Variable definition

Model

* Additional restriction constraints are expressed throughout parameter definition

Scheduling


Fleet assignment: Solving methods

Solving Methods

Exact Methods Approximate Methods

Brunch and Bound

Column Generation &Brunch and

Bound

Meta-heuristic ( genetic

algorithm…)

Specific heuristic

Absolute optimum

Implementing time

Solution time

flexibility

Scheduling

18

Fleet assignment: Solving methodsAirline companies and solution vendors use all methods presented in the previous

diagram. However , exact methods tends to dominate the use of solving methods for the fleet assignment.

There is no rule that confirm that airline can get ( or not) a solution by using branch and bound in reasonable time given the size of the model. However, based on results of some airlines , we may guess that in case of 2.000 of flight legs and 10 fleet type, the use of branch and bound method is sufficient to solve the fleet assignment problem in reasonable time.

Besides, the biggest airlines use column generation method combined with branch and bound methods to solve the fleet assignment problem although the size problem complexity.

Scheduling


Fleet assignment: IT DevelopmentBecause of the size problem complexity, the program is usually developed with C++.

The branch and bound method is already available as library provided by commercial solver software ( Cplex, Xpress,...) and other open source(GLPK).

The program is mainly made up of three parts : loading data, optimization algorithm, and report the fleet assignment.

Solver

Creating a Master model

Loading data Optimization Algorithm Report results

Call solver library for solving RMP (brunch and bound method)

Get the optimal solution of RMP

Initialization Reduced Master

Problem RMP

CMP <=0

NoIntroduction to the best new

column

Optima solution found

1

Restriction

Flight schedule

Fleet availability

Column generation diagram

Display the fleet

assignment

Scheduling

20

2 3

Fleet assignment optimization, which has been applied widely in practice, is attributed with generating solutions that lead to significant improvements in operating profit:

- USAir indicates annual savings of $15 million attributable to the use of a fleet assignment optimizer.

- Fleet Assignment solution at American Airlines have led to a 1.4% improvement in operating margins.

Fleet assignment: Impact

Scheduling


Some airlines add other constraints to the fleet assignment model such as time window that assumes departure time are not fixed and there is time window during which flight may depart.

Other companies integrate further parameters such as passenger spill decision in order to better estimate the spill costs ( Extended Fleet Assignment Problems)

In these above cases, the column generation method will be more useful to solve the fleet assignment problem

Fleet assignment: Improvements / Future

Scheduling


Maintenance routing

Scheduling


Maintenance routing: IntroductionGiven the fleet assignment solution, the objective of maintenance routing is to

identify the sequence of flight legs to be covered by the same aircraft within each fleet that satisfy operational and physical constraint.

The sequence of flight legs has to ensure that the aircraft is able to receive the required maintenance checks at the right time and at the right base.

Hub1

Hub2Hub3

Maintenance base

Maintenance base

Maintenance baseAirport

4

Airport 5

Airport 6

Airport 7

Airport 9

Airport 8

Airport 10

Airport 11

4 types of aircraft maintenance are required. The most frequent check is required every 30 hours ( 2- 3 days). This check can be performed overnight or during downtime during the flight day.

Scheduling


Flight schedule with fleet assignment: set of flight legs with given departure and arrival times and fleet type assigned.

Input

Output

For each fleet type, the best aircraft rotations that allows the aircrafts to undergo periodic maintenance checks and satisfy other physical and operational constraints.

Routing generation

Routing evaluation

Solving optimization model

1

2

3

Maintenance routing: Introduction

Scheduling


1.Flight coverage: each flight leg must be covered by only one aircraft.

2.Fleet availability: number of aircraft by fleet type must not exceed the number available

3.Feasible routing: The routing must incorporate the turn-around time. turn-around time is the minimum time needed for an aircraft from the time it lands until it is ready to depart again

4.Regular return (overnight) to the maintenance station has to be insured for each routing in order to provide the maintenance opportunity at least once in 3 days.

5.Optional constraints:

1.favor closed cycle: when an aircraft starts from a city, and at the end of the routing cycle, ends up at that same city to start another cycle.

2.Favor succession of flights with the same custom status ( Schengen to Schengen ..)

Constraints

Maintenance routing: Introduction

Scheduling


Maintenance routing (1): Routing generationAt first, airlines should define its routing cycle. Many airlines set the routing cycle

to 2 or 3 days.

We begin by generating all possible valid aircraft routings that satisfy physical and operational constraints routing:

– The routing must incorporate the turn-around time. turn-around time is the minimum time needed for an aircraft from the time it lands until it is ready to depart again.

– the routing must include at least one overnight stay at maintenance base in order to provide the first type of maintenance check.

LAX JFK JFK ORD ORD JFK JFK IAD IAD JFK JFK LAX

05h00 13h30 15h05 16h05 17h10 18h10 6h20 7h20 14h25 15h25 17h00 21h30

BOS JFK JFK ATL ATL JFK JFK ATL ATL JFK JFK BOS

06h15 07h45 09h00 12h00 13h10 15h40 09h10 12h00 13h10 15h40 17h00 18h30

Routing 1

Routing 2

Overnight day 1

Overnight day2

JFK

JFK

LAX

BOS

Day 1 Day 2

Scheduling


Creating all one day routing

Building routing by attaching one day routing

Examination of constraint satisfaction

Establishing a list of potential routing candidate

Maintenance routing (1): Routing generationAutomated systems are used extensively to generate and filter all these

routes for the airlines in a relatively short time.

An overview of a methodology has been implanted for generating the rotations:

1

2

3

4

Scheduling


This generation could be enhanced by using constraint programming techniques

Maintenance routing (2): Routing evaluationThe ultimate goal of the maintenance routing is to select the best flight legs

sequences that contribute in the maximization of the airline profit.

In practice, airlines evaluate routings by various ways according to the structure adopted for the objective function of maintenance routing model :

Scheduling

Objective function

Minimizing pseudo-cost

Maximizing through values

Maximizing maintenance opportunities


Maintenance routing (3): Optimization modelAfter generating feasible routings that satisfy maintenance requirement, we

should select from this list the optimal routings that satisfy the coverage flight constraint and the fleet availability limit.

Optional constraint are usually taken into account in the objective function in order to penalize some routings and/or favorite others.

The decision problem consists to chose routings from the long list of routing built that :

- Satisfy constraints of coverage flight and fleet availability

- Minimize cost (or Maximizing through values ..)

Scheduling


Maintenance routing (3): Optimization model

Input

R: set of feasible routings

L: set of flight legs

N: number of aircrafts ( associated to the fleet type that is subject of the maintenance routing)

Cr: cost of routing r

&l,j: 1 if leg l is in routing r, 0 otherwise

Scheduling

Decision variables

1. Xr :1 if routing r is chosen. 0 otherwise


RrX

NX

LlX

tosubject

XC

r

Rrr

rRr

rl

rr

1,0

1*

*min

,

Minimizing costs

Coverage constraint

Fleet availability constraint

Variables definition

Model

* Maintenance requirement and feasibility routing constraint are satisfied by routing construction


Scheduling


Solving Methods


Branch and Bound

Column Generation &Branch and

Bound


algorithm…)

Specific heuristic

The backbone of comparison analysis regarding exact and approximate method for the fleet assignment remains useful for the maintenance routing .

However, some airlines have expressed that the use of column generation for routing maintenance remains still a challenge because of non convergence issue.

Other airlines have implemented other approximate methods for solving the maintenance routing (formulated as asymmetric traveling salesman problem with side constraints ) by using Lagrangian relaxation and heuristics


Scheduling


The maintenance routing problem as presented, is based on the flight schedule and the fleet availability. In reality , the flight schedule could be changed at the last minute because of disruptions.

The robustness of the maintenance routing solution becomes an essential criteria in order to keep the scheduling process feasible.

In addition to profit maximization, airlines could take into account robustness criteria (proxy) in different ways to define the best routings


Scheduling


Crew scheduling:

Scheduling

a. Crew pairing b. Crew assignment


Crew scheduling: Introduction

After the flight schedule is developed and fleet are assigned to cover all the flight legs in the schedule, crew work schedules are started with the help of optimization techniques.

Crew scheduling involves the process of identifying sequences of flight legs and assigning both the cockpit ) and cabin crews to these sequences.

Cockpit crews: charged with flying the aircraft

Cabin crews: responsible for in-flight passenger safety and service.

Tim

e

Scheduling

36


One fleet type

Authorized for

Different fleet type

Able to work on

VS

The crew scheduling problem is solved separately for thecockpit crew and cabin crew

fleet typeCockpit crew size depends on

Number of passengers

on board

Cabin crew size depends on

VS

Scheduling trends to be Individual for cabin crew and per team for cockpit crew

Cockpit

Cockpit

Cabin

Cabin

Scheduling



Because of the complex structure of work-rules and crew costs, the crew scheduling problem is typically solved in a two-step process:

Crew pairing: the objective is to minimize the crew costs associated with covering all flight legs in the flight schedule,

Crew assignment: The objective is mainly to assemble pairings into schedules that maximize the satisfaction levels of crews.

Crew Pairing

Crew Assignment

Generation of mini-schedules, called pairings typically spanning 1–5 days

Assembling pairings into longer crew schedules typically spanning about 30 days and assign it to

crew members

Scheduling


Crew pairing: Introduction

A crew pairing is composed of a sequence of flight legs, with the flight legs comprising a set of daily work activities, called duty, separated by overnight rest periods.

The sequence of flight legs starts and ends at the same crew base(city in which the crew actually lives). The sequence may typically span from 1 to 5 days.

The objective of crew pairing is to find a set of pairings that covers all flights which:

- satisfies various constraints such as union, government, and contractual regulations.

- minimizes the total crew cost.

Scheduling


Crew pairing: Constraints

JFK ATL ATL JFK JFK MIA MIA JFK JFK BOS BOS JFK

12h00 13h10 15h40 16h10 19h10 9h10 12h10 12h30 14h00 15h00 16hh309h30

Overnight Rest

Sign In :08h00

Sign out :19h25 Sign In :

08h10Sign out :

16h40

Duty Period 1Duty Period 2

Constraints

C.1 Flights in a pairing must be sequential in time and space;

C.2 The elapsed time between the arrival of a flight leg and the departure of the subsequent flight leg in the pairing is bounded by a maximums and a minimums threshold:

a-connection time

b-rest time

C.3 Each duty should not exceed a maximum hours of flight time.

C.4 The maximum number of hours worked in a day.

C.5 The maximum time the crew may be away from their home base

C.6 Pairings starts and ends at crew base

C1

C2.a

C2.b

C3

C4 C5.Time Away From Base

C6 C6

Feasibility

C.7 Flight covering

C.8 Fleet restriction for cockpit crew

others

Scheduling

40

Crew pairing: Costs

The crew costs structure can vary widely by airline, with significant differences existing between airlines in different countries or regions.

Duty cost= Max of

Total flying time cost

Total duty time cost

Minimum guaranteed per day

Scheduling

Time away from base cost

Pairing cost

Minimum guaranteed pairing pay Sum of duty cost

Maximum of

Example of a pairing cost structure in Europe

41Nabil Si Hammou, April 2012

Crew pairing: Optimization model

All possible feasible pairings are generated based on rules and regulations.

Select the best pairings that cover all the flight and minimize the total crew costs

Generators are normally equipped with filters to identify and select good potential pairings

Pairing generation

Pairing optimization

Scheduling


Crew pairing: Optimization model

Decision variables

1. Xp :1 if pairing p is chosen. 0 otherwise

Input

F = Set of flights

P = set of feasible pairings

K = set of crew home-base cities

al,j: 1 if flight i is covered by pairing j, 0 otherwise

cj: crew cost in pairing j

* For the cockpit crew pairing, the problem is solved by fleet family ( driving license)

Scheduling


Crew pairing: Solving methods

Solving Methods


Branch and Bound


Bound


algorithm…)

Specific heuristic

The comparison analysis regarding exact and approximate method for the fleet assignment remains useful for the maintenance routing .

The use of column generation combined with branch and bound algorithm is highly recommended for solving the problem exactly. The pricing problem included in the column generation procedure could be treated as a shortest path problem. In this case , a column is equivalent to a pairing

Other airlines have implemented approximate methods for solving the crew pairing problem by using mainly genetic algorithm.

Scheduling

44

Crew assignment: Introduction

Once the crew pairing problem is solved, the second phase is crew assignment. It’s the process of assembling the pairings into longer schedule (usually on a monthly basis) and assigning individual crew members to this schedule.

The crew assignment problem is usually solved by using either bidline or rostering approach:

Bidline Rostering

The schedule assigned take into account vacation time, training and rest.

1.Generic schedules are built from pairing.

2.Crew members bid on theses schedules

3.Assignment based on seniority

1.Specific schedules are constructed trying to satisfy certain crew bids with priority based on seniority.

Or

Scheduling


Crew assignment: Rostering model

Decision variablesInput

P :set of dated pairings

K : set of crew members of given type

F : set of flights

Sk:set of schedules for employee k in K

Np: number of selected schedules that must contain p

Cs,k : cost of schedule s if it’s assigned to employee k ( represent the choices and the priority)

ap,s : 1 if pairing p is in the schedule s,0 otherwise

Xs,k: 1 if the schedule s is chosen for employee k,

0 otherwise

* For the cockpit crew rostering, the problem is solved by fleet family ( driven license) and for each crew type separately

Scheduling


Crew assignment: Solving methods

Solving Methods


Branch and Bound


Bound


algorithm…)

Specific heuristic

Basically, the approach used for solving crew pairing could be used for crew assignment. However many airlines still use heuristics to optimize the crew assignment.

Scheduling


Crew scheduling: Impact

For large airlines, the improvement in solution quality related to crew scheduling (pairing & assignment), translates to savings on the order of $50 million annually.

Beyond the economic benefits, crew scheduling optimization tools can be used in contract negotiations to quantify the effects of proposed changes in work rules and compensation plans.

Scheduling


Scheduling: challenges & opportunities

Integrated schedule

Scheduling


Schedule design Fleet assignment Fleet assignment Maintenance routing

Fleet assignment Crew pairing Maintenance routing Crew pairing

Crew pairing Crew assignment Schedule design

Fleet assignment

Maintenance routing

Fleet assignment

Maintenance routing Crew pairing

Revenue Management


Plan

Outline

Demand forecasting

Implementation

Network revenue management

Fare class mix

Revenue Management

Optimization


Outline

For maximizing the income revenue given the scheduled flight and capacities, the airline should sell the right seats to the right customers at the right prices and at the right time

The revenue maximization process is mainly made up of two components:

- Pricing ( or differential pricing)

- Revenue Management ( or Yield Management)

Customer segmentation

Price decision

Capacity allocation

Pricing Revenue Management

For most airlines, revenue management is the primarily tactical decision in the revenue maximization process. However, for low-costs, pricing tends to be the primarily tactical decision

Revenue Management


Product design

Outline: Pricing

The airline offer various product called “fare product or fare class” for each future flight departure. The traditional fare product structure is mainly defined by following restrictions :

Fare product

Advance purchase

Change feeNon- refundability

Saturday night

Number of days required between booking and flight

departure (7,14,21…)

Penalties of changes in itinerary after purchase

The option of refundability (or not )

The requirement to stay at Saturday night

Service amenities could been added into others characteristics for each product.

For each product, the airline associates a price allowing to :

- attract the right costumer by the right product.

- maximize the wiliness to pay for each consumer

Revenue Management


Outline: Revenue Management

Given the fare classes and the price associated to each fare class, the revenue management is the subsequent process of determining how many seats to make available at each fare level for maximizing the revenue

Revenue management system is mainly made up of two components (1)Optimization and (2)Demand forecasting.

Revenue Management


Optimization

The correct RM strategy is to manage the seat inventory of each flight departure to maximize total flight revenues generated by all the network.

In practice the airlines attempt to achieve this goal by implementing either of these approaches:

Max

Fare Class mix Network Revenue Management

RevenueiMax RevenueO-D

i: single flight O-D: itinerary origin destination

Vs

Maximization of the revenue generated by each single flight

Maximization of the revenue generated by the network

Revenue Management


Optimization

Implementing time

Because of its relative simplicity, the fare class mix is the most common approach used in the airline industry.

Some biggest airlines have recently implemented the network revenue management in order to increase the revenue by taking into account the interdependence between flights.

Absolute optimum

Interdependence of flights

Fare Class mix Network Revenue Management

Revenue Management


Optimization: Fare class mix

Fare class mix (called also leg-based Revenue Management) consists to allocate optimally the capacity of each single flight leg to different fare classes.

Definition

Revenue Management


Bid-price control sets a threshold price such that a request is accepted if and only if its revenue exceeds the threshold price


The capacity allocation control could be implemented within the reservation system under one of these decision forms :

Booking limits Bid price

Partitioned Nested

Remained flight capacity

Tim

e

Bid Price

Booking limits are controls that limit the amount of capacity that can be sold to any particular class at a given point in time.

Control types

Revenue Management



Output Input

J :set of fare class

Pi : price associated to fare class I (Pi > Pi+1)

C : flight capacity

T : flight date

Dj,t : demand of fare class j at period t<=T

Deterministic Random

Assumptions

Static Model (Non overlapping demand)

Dynamic Model (Overlapping Non overlapping)

Or

Optimal policy of selling the flight seats at each time given the remaining flight capacity ( best allocation of flight capacity on fare classes)

Modeling:

Revenue Management

59


The static model is mainly based on the assumption of Non overlapping demand :

- demand for the n classes arrives in n stages, one for each class, with classes arriving in increasing order of their revenue values.

Non overlapping demand

Static model

Decision policy (Control policy) Input

J :set of fare class

Pi : price associated to fare class i (Pi > Pi+1)

C : flight capacity

U(j,x): Quantity of demand to accept given remaining flight capacity. x

Dj: demand of fare class j


Booking limit controls Bid price controlsOr

limitj (x) : maximum number of demand of fare class j..1 to accept given remaining capacity at the start of stage j

Bid Price (x,j): price threshold for accepting the demand during the stage j given the remaining capacity x

Static model:

Revenue Management


Solving Methods


Dynamic Programming

Heuristics ( EMSR…)

The optimal policy related to the revenue management model could be found by using either dynamic programming or heuristics.

Implementing time

Absolute optimum

Solving time

Static model: method solving


Revenue Management


Dynamic Programming (EMSR Expected marginal seat revenue…)

EMSR-a : version a EMSR-b : version b

j

k

jkj

kkkkk

kkkkk

kk

YY

Y

and

Y

kkY

1

1

21

)1Prob(D*PP

)Prob(D*PP

2

1112

2

1112

2

1

j

kkj DS

1

j

k

k

j

k

kk

j

DE

DEp

p

1

1*

][

][*

)Prob(S*P 1*1

j

jjjj Yp

)1Prob(S*P 1*1

jjjjj Yp

Model Model

Optimal policy Optimal policy

Even though the higher solution quality provided by the dynamic programming and its simplicity, many airlines still use approximate methods : EMSR

Bid Price (x,j):

Optimal policy

Static model: method solving


Revenue Management


Booking limitj (x) Bid Price (x,j) Booking limitj (x) Booking limitj (x)

Unlike static model, dynamic model allows for an arbitrary order of arrival with the possibility of interspersed arrivals of several classes. (overlapping demand).

In addition to other assumptions retained by the static model, the dynamic model requires assumption markovien arrivals

Overlapping demand

Dynamic model

Dynamic Programming


Dynamic model

Revenue Management


The choice of dynamic model versus static models depends mainly on which set of approximations is more acceptable and what data is available

Data availabilityAssumptions

Non overlapping demand

Markovien arrivalsVs

Static Model

Dynamic Model

Or


Static model Vs Dynamic model

Revenue Management


Effective use of fare class mix combined with other technique of RM (overbooking) have been estimated to generate 4%-6% incremental increase in revenue.

The fare class mix (leg-based RM approach ) is used to maximize revenues on each flight leg. For connecting itinerary demand, the lack of availability of any one flight leg seat in the itinerary limits sales.

Impact


Revenue maximization over a network of connecting flights requires to jointly manage the capacity controls on all flights

Interdependence between flights

Network Revenue Management

Revenue resulted from leg-based RM approach is not necessarily the maximum of the total revenues on the airline’s network

Latest version of revenue management system

Revenue Management


O-D control represents a major step beyond the fare class mix capabilities of most third-generation RM systems, and is currently being pursued by the largest and more advanced airlines in the world.

Definition

Optimization: Network revenue management

Network revenue management (called also Origin–Destination Control) is to manage the seat inventory by the revenue value of the passenger’s O-D itinerary on the airline’s network

Revenue Management


Control types


The capacity allocation control could be implemented in the reservation system by the extension of controls defined for the fare class mix. A product in this case is an origin-destination itinerary fare class combination.

Partitioned Booking limits Bid priceVirtual Nesting

Maximum of seats on each single flight for each itinerary

Used only for computationsNot used for control

Mapping to virtual class of single flight and use nesting

control of single flight

Complexity of mapping Simpler, popular

Revenue Management


Modeling:


Input

M :set of single flight

N : set of product (itinerary O-D with fare class).

ai,j : 1 if the single flight i used by the product j.

Xi : reaming capacity of single flight)

t: time ( running from1 to T).;

pj: price of product j


Dj(t) :1 if the product j is realized in the period t. 0 otherwise

Decision policy

Uj(t):1 if we accept a request for product j in period t 0 otherwise.

Complexity of dynamic programming for network revenue management

Approximation

Revenue Management

68

Dynamic Programming

Modeling:


One of the most popular approximation used in the practice is based on the aggregation of the expected future demand

substitute the future demand by its expected value.

Input

M :set of single flight

N : set of product (itinerary O-D with fare class).

ai,j : 1 if the single flight i used by the product j.

Xi : remaining capacity of single flight i

pj: price of product j

E[Dj ]:expected value of the future demand of the product j

Decision variable

Yj : maximum number of demand for product j ( ODIF itinerary with fare class ) to accept. “partitioned booking limits”

Deterministic linear model

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Modeling: deterministic linear model


NjDEY

MiXYa

tosubject

YP

jj

jj

Nj

ji

j

Nj

j

][0

*

*max

,

Maximizing total revenues

Single flight capacity constraint

Itinerary demand limit constraint

Model

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Solving Methods


Branch and Bound


Bound


algorithm…)

Specific heuristic

The comparison analysis regarding exact and approximate method for the fleet assignment remains useful for the network revenue management.

The use of column generation combined with branch and bound algorithm has already demonstrated its powerful for some airlines to solve the deterministic linear model of network revenue management.

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BidePricei=for each single flight capacity constraint i



Primal solution Dual solution

Partitioned booking limits =Primal solution

Definition of bid price

Primal solution size

Definition of dual solution

Dual solution size >

Bid price control the most useful control

i

Definition partitioned booking

limits

Definition of primal solution

limitj=Xj

for each product j ( itinerary with fare class)

Bid price= Dual solution

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By using bid price control, the decision policy becomes:

i legflight of price bid:

jproduct of price:

:with

i

jP

Some airlines have also used these values of bid price for the fleet assignment and/or fleet planning ( demand-driven dispatch). The bid price value associated to a single flight represent the marginal value of revenue would be generated in case of increasing the flight capacity by one seat.

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j

ijp

itinerrary iflight single if jproduct of demand Accept the

otherwiseReject

Modeling: deterministic linear model improved


The deterministic linear model makes one particularly hard assumption: demand is deterministic.

In order to incorporate the stochastic information into the deterministic linear model, airlines could replace the expected value of demand in the mathematical model by simulating many times the randomized demand.

The bid price become the average of bide prices related to each sample. This approach is called the randomized linear programming model

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Impact


Simulation studies of airline hub-and-spoke networks have demonstrated notable revenue benefits from using network revenue management over leg-based revenue management (fare class mix).

While the potential benefit may be high, network RM poses significant implementation and methodological challenges such as volume of data, organizational challenges.. .

Revenue Management


Other Alternatives

Optimization

In addition to the incremental revenue generated by optimization models either fare class mix or network revenue management, the airline could also enhance its incomes by :

- Taking into account the cancellation and non-show passenger in the process of the capacity allocation control ( overbooking)

- Improving the quality of optimization model inputs ( forecasting)

A 10% improvement in forecast accuracy can translate into 0.5% incremental increase in revenue generated from the RM system.

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Introduction

Demand forecasting

Forecasting Inventory Control

Optimization models use stochastic models of demand and hence require an estimate of the complete probability distribution or at least parameter estimates (e.g., means and variances) for an assumed distribution..

The outputs of the forecasting module are fed to the optimization module for producing RM controls such as booking limits, bid prices...

Optimizationsystem

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Forecasting

Demand forecasting

For RM, airlines are mostly interested in forecasting demand at various levels of aggregation (flight leg fare class vs. origin-destination fare class; fare class vs. booking class).

The input requirements of the optimization module drive RM forecasting requirements

Usually, airline needs also to forecast other quantities such as, cancellation and no-show rates ….

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Forecasting methods :

Demand forecasting

Forecasts may be made by using different types of models and each technique may be used to forecast a variety of behaviors.

In terms of forecasting methods, the emphasis in RM systems is on speed, simplicity, robustness and accuracy, as a large number of forecasts have to be made and the time available for making them is limited.

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Forecasting methods : practices

Demand forecasting

Because of its relative simplicity, exponential smoothing tends to be the most common methods used for demand forecasting in the airline industry.

Some vendors have combined the exponential smoothing with other methods such as Kalman filter or linear regression to improve the demand forecasting quality.

Exponential smoothing

Exponential smoothing

Kalman filter

Weighted combined forecast

For modeling passenger choice behavior, some vendors have regressed this behavior as multinomial logit model that contains following variables:

Logit Model

Outbound displacement

Number of connections

Elapsed time

Origin point presence

Fare “logarithm(fare))”

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Change assessment

Implementation

Before implementing a new optimization or forecasting system, the airline should analyze the potential revenue impact of changing to new RM system: revenue-opportunity assessment.

Current RM system V0 New RM system V1

… .

Preimplementation phase Post implementation phase

Investment cost Benefit

Leg based control Network control

Booking limit control Bide price control

Exponential smoothing Kalman filter & Exponential smoothing

Revenue-opportunity assessment.

Simulation methodology is the most common method used in practice for revenue-opportunity assessment

Implementation

… .

… .

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Revenue-opportunity assessment : Simulation

Implementation

By modeling the current control processes , the planned control processes and customer behavior, a reasonably estimation of revenue benefits of changing to a new revenue management system can be obtained via simulation.

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VS

82

Challenges / Future

Choice-based revenue management Airline alliances

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Conclusion


Robustness

Substantial progress in optimization techniques and computing power has allowed significant progress to be made in the optimization of :

- aircraft and crew scheduling

- revenue management.

The schedule planning and optimization processes at airlines produce plans that are rarely executed exactly as planned on a daily basis because of disruptions.

To respond to the disruptions, airlines must replan and create feasible and cost-effective recovery plans in a short period of time. Two approaches are possible:

Schedule recovery Robust scheduleVs

1.Develop a new schedule in case of irregular operations to reassign resources and adjust the flight schedule .

2.Keep the usual schedule process invariable

1.Integrate the expected recovery costs in the objective of the usual schedule process.

2.The usual schedule becomes more resilient to disruptions and easier to repair when replanning is necessary.

Conclusion


Thanks for your interest


Being an Optimization Specialist with strong background in the use of operations research and forecasting methods in the airline industry, I am particularly interested in the positions:

– Scheduling optimization specialist– Revenue management optimization specialist

During my professional career, I have developed optimization programs to support decision making system in different industries.

– Crew scheduling within Royal Air Maroc : reduction of operating cost by 250.000€ annually.

– Transportation scheduling within L'Oreal France : reduction of transportation cost by 8%

– …. I would welcome the opportunity to discuss with you the potential for making a

significant contribution in optimizing the scheduling and revenue management process. Feel free to call me at 00.212.6.18.98.38.61 or email me at [email protected].

CV: Nabil Si Hammou

87

Nabil Si HammouOptimization [email protected]

Seminars & references

88

Seminar organized by Air France

Operations Research within Air France

Seminar organized by AGIFORS

Advancement of Operations Research in the airline industry

Airline Operations and Scheduling

Mr M. Bazargan

The global Airline industry

Mr P. Belobaba, Mrs C. Barnahart

Computational Intelligence in Integrated Airline Scheduling

Mr T. Groshe

The Theory and Practice of Revenue Management

Mr K. Talluri, Mr G.Ryzin

Operations research and scheduling at American airlines

Mr T.Carvalho

Revenue Management Optimization

at Air Canada

Mr J.Pagé

Revenue Management O-D control

at KLM

Mr A.Westerhof

Demand Forecasting

at United Airlines

Mr K.Usman

A Unified Column Generation Approach for Crew Pairing and

crew restoring at Lufthansa

Mr N.Howak

Information sources

April 2012

Best practices on the optimization process in the airline industry

Scheduling and Revenue Management

Nabil Si Hammou, Optimization Specialist

[email protected]

mailto:[email protected]

scheduling and revenue management

Documents

optimization algorithms

optimization processscope

revenue management process

practices of airlines

airline schedule

revenue management page

airline group

efficient management