Scheduling and Revenue Management

Guideline on the use of Operations Research
in the airline industry
Nabil Si Hammou, Operations Research Analyst
n.sihammou@gmail.com

Scheduling and Revenue Management

April 2012

Abstract
 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
n.sihammou@gmail.com.
 Being an Operations Research Analyst, I am particularly interested in the
positions:
– Scheduling optimization specialist Nabil Si Hammou
– Revenue management optimization specialist Optimization Specialist
00.212.6.18.98.38.61
Nabil Si Hammou, April 2012 Best practices - Optimization process 2

Plan

Outline
( page 3..6)

Optimization Process Overview
( page 7..10)

Scheduling
(page 11..49)

Revenue Management
(Page 50..83)

Conclusion : Robustness
(page 84)


Outline
Context
 The 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
Context
 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:

Sales

Investment Operations
cost cost
Benefit


Outline
Airline management system
 To 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 Airport runway Airport charges Other regulations
hours length

Maintenance
requirement Airport
Facility constraints Passenger
behavior

Aircraft capacities connection time

Airline
Aircraft range Aircraft Demand
limitation Decision Competitor
Aircraft costs
System schedules

Passenger demand
Operational costs
Passenger Yield
Minimum turn time
Route Crew Managerial
characteristic availability constraint


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.

Decomposition
 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.

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

Best practices - Optimization process 8

Decomposition
 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).
9

Scope
 We focus in this presentation on the following subproblems :

A. Scheduling: B. Revenue Management:
1. Fleet assignment 3. Crew pairing 5. Optimization
2. Maintenance routing 4. Crew assignment 6. Forecasting

Scheduling


Scheduling

Fleet assignment


Scheduling
Fleet assignment: Introduction
 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.
06h00 10h30
Airport A
Which Which
aircraft type ? aircraft type ?

07h30 08h30 09h00 10h100
Airport B
Which Which
aircraft type ? aircraft type ?

Input Output
1.Schedule: set of flight legs with given departure and Assignment of fleet type to each flight leg of
arrival times. the schedule with profit maximization
2. Fleet: aircraft owned by the company (number of aircraft (expected revenue – operation cost) or cost
by type). minimization including spill cost
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) 13
Best practices - Optimization process

Scheduling
Fleet assignment: Introduction
Constraint
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…), ….


Scheduling
Fleet assignment: Time-space network
 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.

Time-space network
Airport C

Airport B

Airport A

Schedule cycle time
(week, day..)

: 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 Decision variables
F : set of flight legs to be operated fik :1 if flight leg i is assigned to fleet type k,
K: set of fleet types 0 otherwise.
Mk number of aircraft available of type k.
yak : number of aircraft of type k on the
Lk: the set of flight legs could be covered by the fleet type k. ground arc a
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


Scheduling
Fleet assignment: Modeling

Model

Minimizing costs ( operation & spill) min Cik f i k
k Ki F

subject to
Coverage constraint fi k 1 i F;
k K
Balance constraint k
yn fi k k
yn fi k k K n Nk;
i O ( k ,n ) i I ( k ,n )
k
Fleet availability constraint ya fi k Mk k K;
a CG ( k ) i CL ( k )

fi k 0;1 k K i Nk
Variable definition
k
ya 0 k K a Gk

* Additional restriction constraints are expressed throughout parameter definition


Scheduling
Fleet assignment: Solving methods

Solving Methods

Exact Methods Approximate Methods

Column
Brunch and Meta-heuristic
Generation & Specific
Bound ( genetic
Brunch and heuristic
algorithm…)
Bound

Solution time

Absolute
optimum

Implementing
time

flexibility
18

Scheduling
Fleet assignment: Solving methods
 Airline 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 Development
 Because 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.
1 2 3
Loading data Optimization Algorithm Report results
Initialization
Creating a
Reduced Master
Master model
Problem RMP

Fleet
availability Call solver library for solving RMP
Solver
(brunch and bound method)
Display the
fleet
Get the optimal assignment
Flight
schedule solution of RMP

Introduction to No
the best new C MP <=0
column
Restriction
Column generation
diagram Optima solution
found 20

Scheduling
Fleet assignment: Impact
 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.


Scheduling
Fleet assignment: Improvements / Future
 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


Scheduling

Maintenance routing


Scheduling
Maintenance routing: Introduction
 Given 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.

Maintenance Maintenan
Airport base ce base Airport Airport
4 9 10

Hub1
Airport
6
Airport
11

Hub3 Airport Airport
Hub2 Maintenance
Airport
5 7 8 base

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

1
Routing generation

2
Routing evaluation

3
Solving optimization model

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.


Scheduling
Constraints
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 ..)


Scheduling
Maintenance routing (1): Routing generation
 At 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.

Overnight
Day 1 day 1 Day 2 Overnight
day2

05h00 13h30 15h05 16h05 17h10 18h10 6h20 7h20 14h25 15h25 17h00 21h30
Routing 1 LAX JFK JFK ORD ORD JFK JFK JFK IAD IAD JFK JFK LAX LAX

06h15 07h45 09h00 12h00 13h10 15h40 09h10 12h00 13h10 15h40 17h00 18h30
Routing 2 JFK
BOS JFK JFK ATL ATL JFK JFK ATL ATL JFK JFK BOS BOS


Scheduling
Maintenance routing (1): Routing generation
 Automated 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 Creating all one day routing

2 Building routing by attaching one day routing

3 Examination of constraint satisfaction

4 Establishing a list of potential routing candidate

 This generation could be enhanced by using constraint programming
techniques


Scheduling
Maintenance routing (2): Routing evaluation
 The 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 :

Objective function

Maximizing
Minimizing pseudo- Maximizing through
maintenance
cost values
opportunities


Scheduling
Maintenance routing (3): Optimization model
 After 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
R: set of feasible routings 1. Xr :1 if routing r is chosen. 0 otherwise
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

Model

Minimizing costs min Cr * X r

subject to
Coverage constraint
l ,r * Xr 1 l L
r R

Fleet availability constraint Xr N
r R
Variables definition
Xr 0,1 r R

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


Scheduling

Solving Methods


Column
Branch and Meta-heuristic
Bound ( genetic
Branch and heuristic
algorithm…)
Bound

 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:
a. Crew pairing b. Crew assignment


Scheduling
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.

Time
Cockpit crews: charged with flying the aircraft

Cabin crews: responsible for in-flight passenger safety and service.
36

Scheduling

Cockpit

Authorized for One fleet
type The crew scheduling
problem is solved
VS separately for the
Cabin
cockpit crew and
Able to work on
Different cabin crew
fleet type

Cockpit

Cockpit crew
size depends on fleet type
Scheduling trends to
be Individual for
VS cabin crew and per
Cabin
Number of team for cockpit
Cabin crew size crew
passengers
depends on
on board

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

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

 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.


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

Constraints
Feasibility others
C.1 Flights in a pairing must be sequential in time and space; C.7 Flight covering
C.2 The elapsed time between the arrival of a flight leg and the departure C.8 Fleet restriction
of the subsequent flight leg in the pairing is bounded by a maximums
and a minimums threshold: for cockpit crew
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

Overnight
C2.a Rest
9h30 12h00 13h10 15h40 16h10 19h10 9h10 12h10 12h30 14h00 15h00 16hh30
JFK ATL ATL JFK JFK MIA C2.b MIA JFK JFK BOS BOS JFK

C6 C6
C1
Sign In : Sign out : C3
08h00 Duty Period 1 19h25 Sign In : Sign out :
08h10 Duty Period 2 16h40

C4 C5.Time Away From Base
40

Scheduling
Crew pairing: Costs

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

Example of a pairing cost structure in Europe

Pairing cost

Maximum of

Minimum guaranteed Time away from base
Sum of duty cost
pairing pay cost
Duty cost= Max of
Total flying time
cost

Total duty time cost

Minimum
guaranteed per day
Nabil Si Hammou, April 2012 41

Scheduling
Crew pairing: Optimization model

All possible feasible pairings are
generated based on rules and regulations.
Pairing
generation
Generators are normally equipped with filters to
identify and select good potential pairings

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


Scheduling
Crew pairing: Optimization model
F = Set of flights 1. Xp :1 if pairing p is chosen. 0 otherwise
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


Column
Bound ( genetic
algorithm…)
Bound

 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.
44

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

 The crew assignment problem is usually solved by using either bidline or
rostering approach:
Or
Bidline Rostering

1.Generic schedules are built from pairing. 1.Specific schedules are constructed trying to
satisfy certain crew bids with priority based on
2.Crew members bid on theses schedules
seniority.
3.Assignment based on seniority


Scheduling
Crew assignment: Rostering model
P :set of dated pairings Xs,k: 1 if the schedule s is chosen for employee k,
K : set of crew members of given type 0 otherwise
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

* 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


Column Meta-heuristic
Branch and Generation & Specific
( genetic
Bound Branch and heuristic
algorithm…)
Bound

 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

Maintenance
Schedule design Fleet assignment Fleet assignment
routing

Fleet assignment Crew pairing Maintenance
Crew pairing
routing

Crew pairing Crew assignment Schedule Fleet Maintenance
design assignment routing

Fleet Maintenance
Crew pairing
assignment routing


Revenue Management


Revenue Management
Plan

Outline

Optimization

Network revenue
Fare class mix
management

Demand forecasting

Implementation


Revenue Management
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)

Pricing Revenue Management

Customer Product Price Capacity allocation
segmentation design decision

 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
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 :

Advance Number of days required
The option of refundability (or
between booking and flight
not ) purchase
departure (7,14,21…)

Fare
Non- refundability Change fee
product

The requirement to stay at Saturday night Penalties of changes in itinerary
Saturday night after purchase

 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:

Fare Class mix Network Revenue Management

Maximization of the revenue Maximization of the revenue
generated by each single flight Vs generated by the network

Max Revenue i
Max RevenueO-D

i: single flight O-D: itinerary origin destination


Revenue Management
Optimization
 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.

Fare Class mix Network Revenue Management

Interdependence
of flights

Absolute
optimum

Implementing
time


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


Revenue Management
Control types

 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

 Booking limits are controls that limit the  Bid-price control sets a threshold
amount of capacity that can be sold to any price such that a request is
particular class at a given point in time. accepted if and only if its revenue
exceeds the threshold price

Revenue Management
Modeling:

Input Output
Deterministic Random Optimal policy of selling the flight seats at each
J :set of fare class time given the remaining flight capacity ( best
Dj,t : demand of fare
Pi : price associated to fare allocation of flight capacity on fare classes)
class j at period t<=T
class I (Pi > Pi+1)
C : flight capacity
T : flight date

Assumptions

Or

Static Model Dynamic Model
(Non overlapping demand) (Overlapping Non overlapping)

59

Revenue Management
Static model:
 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
Input Decision policy (Control policy)
Deterministic Random U(j,x): Quantity of demand to accept given
remaining flight capacity. x
J :set of fare class Dj: demand of fare
Pi : price associated to class j Or
fare class i (Pi > Pi+1) Booking limit controls Bid price controls
C : flight capacity limitj (x) : maximum Bid Price (x,j): price
number of demand of threshold for accepting
fare class j..1 to accept the demand during the
given remaining capacity stage j given the
at the start of stage j remaining capacity x 60
Nabil Si Hammou, April 2012

Revenue Management
Static model: method solving
 The optimal policy related to the revenue management model could be found by
using either dynamic programming or heuristics.

Solving Methods


Dynamic Heuristics
Programming ( EMSR…)

Solving time

Absolute
optimum

Implementing
time


Revenue Management
Static model: method solving
Dynamic Programming (EMSR Expected marginal seat revenue…)

Model Model

EMSR-a : version a EMSR-b : version b
j
k2
Yk k1 k2
1 S j Dk
k2
Pk 2 Pk1 * P rob(D 1
k Yk ) k 1
1 j
and pk * E[ Dk ]
k2
Pk 2 Pk1 * P rob(D 1
k Yk
1
1) p*
j
k 1
j
j
E[ Dk ]
Yj Ykj 1
k 1
k 1
Pj 1 p* * P rob(Sj
j Y jj 1 )

Pj 1 p* * P rob(Sj
j Y jj 1 1)

Optimal policy Optimal policy Optimal policy
Booking limitj (x) Bid Price (x,j): (x,j)
Bid Price Booking limitj (x) Booking limitj (x)

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

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

Overlapping demand

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

Dynamic model

Dynamic
Programming


Revenue Management
Static model Vs Dynamic model
 The choice of dynamic model versus static models depends mainly on which set
of approximations is more acceptable and what data is available

Assumptions Data availability

Non overlapping
Vs Markovien arrivals
demand

Or

Static Model Dynamic Model

Revenue Management
Impact
 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.
Interdependence between flights

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

 Revenue maximization over a network of connecting flights requires to jointly
manage the capacity controls on all flights
Latest version of
Network Revenue Management revenue management system65

Revenue Management
Optimization: Network revenue management
Definition

 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

 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.


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 Virtual Nesting Bid price

Maximum of seats on each Mapping to virtual class of
single flight for each itinerary single flight and use nesting
control of single flight
Used only for computations Complexity of mapping
Simpler, popular
Not used for control


Revenue Management
Modeling:

Input
Deterministic Random
M :set of single flight Dj(t) :1 if the product j is realized in
N : set of product (itinerary O-D with fare class). the period t. 0 otherwise
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

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

Complexity of dynamic
programming for network Approximation
revenue management 68

Revenue Management
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.

Deterministic linear model

Input Decision variable
M :set of single flight Yj maximum number of demand
:
N : set of product (itinerary O-D with fare class). for product j ( ODIF itinerary with
ai,j : 1 if the single flight i used by the product j. fare class ) to accept.
Xi : remaining capacity of single flight i “partitioned booking limits”
pj: price of product j
E[Dj ]:expected value of the future demand of the
product j


Revenue Management
Modeling: deterministic linear model

Model

Maximizing total revenues
max Pj * Y j
j N

subject to
Single flight capacity constraint ai , j * Y j Xj i M
j N

Itinerary demand limit constraint
0 Yj E[ D j ] j N


Revenue Management

Solving Methods


Column
Bound ( genetic
algorithm…)
Bound

 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.


Revenue Management

Primal solution Dual solution

Definition Definition of primal Definition of bid Definition of
partitioned booking solution price dual solution
limits

Partitioned booking limits =Primal solution Bid price= Dual solution

limitj=Xj BidePricei= i
for each product j ( itinerary with fare class) for each single flight capacity constraint i

Primal solution size > Dual solution size

Bid price control the most useful control

Revenue Management

 By using bid price control, the decision policy becomes:
Accept thedemandof product j if p
j i
single flight i itinerrary j
Rejectotherwise

with :
Pj : price of product j
i : bid price of flight leg i

 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.


Revenue Management
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 74

Revenue Management
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
Optimization
Other Alternatives

 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.


Revenue Management
Demand forecasting
Introduction
 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..

Forecasting Optimization Inventory
system Control

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


Revenue Management
Demand forecasting
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).

 Usually, airline needs also to forecast other quantities such as, cancellation
and no-show rates ….
 The input requirements of the optimization module drive RM forecasting
requirements


Revenue Management
Demand forecasting
Forecasting methods :
 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.

Revenue Management
Demand forecasting
Forecasting methods : practices
 Because of its relative simplicity, exponential smoothing tends to be the most
common methods used for demand forecasting in the airline industry.
Exponential
smoothing

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

Weighted combined forecast

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

Number of
Logit Model Origin point
connections presence

Fare “logarithm(fare))” 80

Revenue Management
Implementation
Change assessment
 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.

Revenue-opportunity
assessment.

Investment Implementation
cost Benefit
Preimplementation phase Post implementation phase

Current RM system V0 New RM system V1

Leg based control Network control

Booking limit control Bide price control

…
…
.

.
…
.

Exponential smoothing Kalman filter & Exponential smoothing

 Simulation methodology is the most common method used in practice for
revenue-opportunity assessment 81

Revenue Management
Implementation
Revenue-opportunity assessment : Simulation
 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.

VS

82

Revenue Management
Challenges / Future

Choice-based revenue
Airline alliances
management


Conclusion


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 Vs Robust schedule

1.Develop a new schedule in case of 1.Integrate the expected recovery
irregular operations to reassign costs in the objective of the usual
resources and adjust the ﬂight schedule process.
schedule .
2.The usual schedule becomes more
2.Keep the usual schedule process resilient to disruptions and easier to
invariable repair when replanning is necessary.

Thanks for your interest


CV: Nabil Si Hammou
 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
n.sihammou@gmail.com.
Nabil Si Hammou
Optimization Specialist
00.212.6.18.98.38.61
87

Information sources
Seminars & references

Seminar organized by Air France Seminar organized by AGIFORS
Operations Research within Air Advancement of Operations
France Research in the airline industry

The global Airline industry A Unified Column Generation Revenue Management Optimization
Mr P. Belobaba, Mrs C. Approach for Crew Pairing and at Air Canada
Barnahart crew restoring at Lufthansa Mr J.Pagé
Mr N.Howak

Airline Operations and Scheduling Operations research and scheduling at Revenue Management O-D control
Mr M. Bazargan American airlines at KLM
Mr T.Carvalho Mr A.Westerhof

Demand Forecasting Computational Intelligence in
The Theory and Practice of Revenue
at United Airlines Integrated Airline Scheduling Management
Mr K.Usman Mr T. Groshe Mr K. Talluri, Mr G.Ryzin

88

Best practices on the optimization process
in the airline industry
Nabil Si Hammou, Optimization Specialist

Scheduling and Revenue Management

April 2012

Scheduling and Revenue Management

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Andere mochten auch

Andere mochten auch (18)

Ähnlich wie Scheduling and Revenue Management

Ähnlich wie Scheduling and Revenue Management (20)

Scheduling and Revenue Management