Einführung in Verkehr und Logistik [1.15ex] (Bachelor) [1.15ex

Transcription

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Einführung in Verkehr und Logistik
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(Bachelor)
Revenue Management and Fleet Assignment
Univ.-Prof. Dr. Knut Haase
Institut für Verkehrswirtschaft
Wintersemester 2013/2014, Dienstag 10:15-11:45 Uhr, Phil E
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2. Konzeptionelle
Grundlagen
Airline
Planning
Process1
Langfrist
Mittelfrist
Implementierung
Kurzfrist
Kontrolle
3 J.
6 M.
1 J.
8 W.
4 W.
2 W.
0
Flottenplanung
Netzwerkplanung
Flugnetz
Marktmodellierung
Fleet Assignment
Wochenplanung | fully dated
Aircraft Rotation
Revenue
Management
Operations
Control
Pricing
Personal
Revenue Management
Crew Pairing
Crew Rostering
Abbildung 1: Allgemeiner Flugplanungsprozess einer Fluggesellschaft
Quelle: in Anlehnung an Grothklags 2006, S. 3.
1 Seedie
Über
weiteren Teilprobleme der Flugplanerstellung besteht in der Literatur, trotz
[Gro06].
vielfach divergierender Terminologie, ein breiter Konsens. Im Rahmen der Netzwerk-
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Introduction to Revenue Management
Origin of Airline Revenue Management
I
I
I
I
Airline Deregulation Act of 1978 (prices, schedule)
Low Cost Carrier (LCC) entered the market
! price pressure
American Airlines first launched special discount fares
Instruments of RM:
I Price Discrimination
I Overbooking
I Capacity Controls
I Forecasting systems (not covered here)
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Basics
I Revenue Management (RM) is also known as Yield Management
I RM can be either quantity- or price-based depending on the control
variable
I most airlines commit to fixed prices and tactically allocate quantity
I LCC use price as the primary tactical variable
I Objective: utilization of additional yield according to individual
willingness to pay (WTP)
I Successful application also in other service areas: hotels, car rentals
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Conditions conducive to RM2
I
I
I
I
I
I
Demand variability and uncertainty
Production inflexibility (variations in supply difficult)
Advance sales
Perishable inventory
High fixed costs/low marginal costs
Customer heterogeneity (preferences)
2 Talluri
and van Ryzin (2005, pp. 13).
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Price Discrimination (PD)
First-degree/perfect price discrimination
I Each customer is charged according to its WTP
I Requires information on each customers WTP & ability to vary price by
customer and unit
!
Theoretical abstraction because of lack of information
Second-degree price discrimination
I Discrimination by offering various possible purchase contracts
I Customers decide which contract to purchase
!
Self-selection by customers
Third-degree price discrimination
I Customers are divided into groups based on identifiable characteristics
(students, children, retiree)
I
Prices differ for different groups, all members of a group pay the same
amount
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I RM ! 2nd degree PD
I Segmentation of customers
q
I self-selection
q(r)
I Prices for almost similar goods differ
I Different ticket fares within the same class
q*
r*
of service
I Economy, Business, First Class
I Restrictions apply
r
q
I Optimal strategy ! prices according to
q1
q(r)
q2
individual WTP
I Not feasible
I Instead several fare classes (FC) for each
q3
r1
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r2
r3
service class
r
Fare Classes
I
I
I
Varying ticket prices for identical product (flight from A to B)
Up to 20 different fare classes on a single flight
FC are represented by letters
I full fares: F - first class, C - business class, Y - economy class
I discount fares economy class: M, B, K, H, Q, S, W
I
Restrictions apply for cheaper tickets:
I
I
I
I
I
Rebooking/Cancellation fees
Advance purchase requirements
Trip length and length of stay
Saturday-night stay
Restrictions provide necessary Fencing
I to separate demand of business and leisure travellers
I to prevent that high-value customers buy-down to cheaper tickets
I
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Objective: additional demand through cheap tickets and better utilization
of capacity
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Deterministic 1-Fare-Class Problem
Price-Sales-Function (PSF)
r
Offer price
q
Demand
q(r )
Price Sales Function
q(r ) is continuously differentiable and exhibits an also continuously
differentiable and strictly monotonic decreasing inverse function:
1
r (q) = q
(r )
Example: Linear PSF
q(r )
=
a
r (q)
=
a=b
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br
1=b q
0r
a=b
0qa
Revenue function
u(q) = q r (q)
Marginal revenue function
u 0 (q) = r (q) + q r 0 (q)
Assumption: The marginal revenue function is strictly monotonic
decreasing within its domain.
Example: Linear PSF
u(q)
u 0 (q)
u 00 (q)
= a=b q
= a=b
=
2=b
1=b q 2
2=b q
! concave function
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Objective Function: Maximizes Revenue
max u(q) = q r (q)
Constraints
q
q
C
0
Optimal Solution
Extreme value with disregard of the capacity constraint:
u 0 (q) = 0 ! q0
q = minfC ; q0 g und r = r (q )
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Example
q(r ) = 400
0:5r
C = 120
Solution:
r (q) = 800
u(q) = 800 q
u 0 (q) = 800
2q
2 q2
4q
) q0 = 200
) q = minf120; 200g = 120
) r = r (120) = 560
u = 800 120 2 1202 = 67 200 (= 120 560)
:
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Capacity Controlling
I
I
I
I
I
Revenue maximizing control of sales processes
Decision about acceptance/rejection of booking inquiries
Single-leg or network flights
Supports price discrimination and erroneous fencing
Types of controls:
I Booking limits
I Protection Levels
I Bid prices
I Principles:
I Capacity is allocated to a request if its revenue is greater than the
value of the capacity required to satisfy it
I The value of capacity is measured by its expected opportunity cost
(displacement cost)
I Optimization problem regarding the acceptence of booking requests
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Booking Limit3 bj
I Limits the amount of capacity C that can be sold to any fare class j
I Partitioned: available capacity is divided into seperate blocks
I Nested: available capacity overlaps in a hierarchical manner, more
expensive fare classes have access to all the capacity reserved for
cheaper fare classes
Protection Level yj
I Specifies an amount of capacity to reserve (protect) for a particular
fare class j
Formal Relationship
bj = C
3 Talluri
yj
1
and van Ryzin (2005, pp. 28-30).
j = 2; : : : ; n
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Relationship between bj and yj
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Example
An airline is operating the flight legs A-B and B-C as well as the
combination of both A-B-C. The utilized aircrafts have a capacity of 100
seats. For the purpose of price discrimination two fare classes are
assigned to each flight leg. Overbookings are not taken into account. The
following table shows the expected demand per flight leg and fare class:
Route
A-B
B-C
A-B-C
Price (EUR)
Demand
Price (EUR)
Demand
Price (EUR)
Demand
Class W
250
100
220
80
460
80
Class K
490
40
400
60
880
50
How many seats per flight leg in combination with a certain booking
class should be sold?
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Linear Optimization Model
xij
number of seats in class W on flight leg i-j (i.e., A-B, B-C or A-C)
yij
number of seats in class K on flight leg i-j
max F (x ; y )
xAB
xBC
250xAB + 220xBC + 460xAC + 490yAB + 400yBC + 880yAC
=
+xAC
+xAC
+yAB
+yBC
+yAC
+yAC
xAB
xBC
xAC
yAB
yBC
yAC
xAB ; xBC ; xAC ; yAB ; yBC ; yAC
Optimal Solution: (F (x ; y ) = 86100 EUR):
100
100
100
80
80
40
60
50
(A
(B
B)
C)
0 and integer
xBC = xAC = 0; xAB = 10; yAB = 40; yBC = 50; yAC = 50
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Overbookings
I 50% of all reservations result in cancellations and no-shows
I Objective: increasing the total volume of sales in the presence of
cancellations
I Contrary to RM overbooking does not optimize the customer mix
(i.e., best allocation of price or capacity)
I Amount of sold tickets exceeds the amount of seats actually available
I Airlines are obliged to compensate passengers for denied boarding
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Terminology
Fleet (aircraft) type:
A certain model of aircraft (e.g., Boeing
B767-300)
Fleet (aircraft) family:
A set of aircraft types with the same cockpit
configuration and crew qualification
requirements
Flight leg:
An airport-to-airport flight segment
Through-flight:
Two consecutive flight legs that are flown by
the same aircraft
Itinerary:
A sequence of one or more flight legs
Fare class:
A particular type of fare restriction
Turn time:
Minimum time an aircraft needs between its
landing and the next take-off
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Decision Problem
I Assigning aircraft types with different capacity to scheduled flights
I Depends on potential revenues, availability, operational costs,
equipment capabilities
I Too small aircraft = spilled (lost) customers (insufficient capacity)
I Too large aircraft = spoiled (unsold) seats (high operational costs
per seat)
I Challenging task ! complexity of airline schedules and depending
airline processes (crew scheduling, maintenance, RM)
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Fleet Assignment Model (FAM)
I Foundation of analytical work in this field
I Usually formulated as a mixed integer program (MIP)
I Construction as time-space-network
Basic FAM4 main constraints
1. Cover constraints - Each flight leg is assigned to exactly one fleet
type
2. Balance constraints - Ensure conservation of flow
3. Aircraft availability constraints - The number of available aircrafts of
each type bounds their usage
4 Hane
et al. (1995).
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5
Time-Space-Network
H.D. Sherali et al. / European Journal of Operational Research 172 (2006) 1–30
Station A
Station B
Stations
A2
9:00am
Arcs for Type 1
A1
C1
10:00am
E2
C2
11:00am
E1
Wrap-around
arcs for Type 1
B1
12:00pm
F1
B2
D1
D1
Time
5 See
Arcs for Type 2
Sherali et al. (2005).
F2
7
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Properties
I
I
I
I
I
Focuses on representing flight legs (arcs)
Model decides on feasible connections
Fleet type-dependent flight/turn-times
! network for each fleet type
A directed flight arc belongs to the movement of an aircraft type
3 types of arcs:
(1) Ground arcs: represent aircrafts staying at the same station
(2) Flight arcs: represent flight legs
(3) Wrap-around arcs: connects the last event of the day with the first
event of the day
I A network time-line is associated with each station
I Nodes represent arrivals and departures of a flight leg at a station
I Same-every-day fleet assignment ! moderate computational
complexity
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Sets
L
set of flight legs indexed i
S
set of stations indexed s
F
set of fleet types indexed f
Ot̃
set of legs whose time span contains the time point t̃ (e.g. 3 am,
for counting purposes)
Ts
temporal ordered set of departure and arrival time points at
station s and time point t̃
Ast
leg(s) with arrival time t
Dst
Pst
2 Ts at station s
leg(s) with departure time t 2 Ts at station s
the predeccessor time point of t 2 Ts where the predeccessor
time point of the first time point in Ts is the last time point in
Ts (wrap-around); j Pst j= 1
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Parameters
cfi
costs of leg i if covered by aircraft of fleet type f
t̃
time point for measuring the number of aircrafts
Qf
available number of aircrafts of fleet type f
Variables
xfi
= 1 if fleet type f covers leg i (0, otherwise)
yfst
number of aircraft of fleet type f on the ground of station s at
time point t 2 Ts
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XX
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Objective function: Minimizes total costs
min
2 2
cfi xfi
f F i L
X
Cover constraints
8i 2L
xfi = 1
f
X X
Balance constraints
yfsp +
2
i Ast
xfi
2
i Dst
xfi = yfst
8 f 2 F s 2 S t 2 Ts p 2 Pst
;
;
;
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X X
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Aircraft availability constraint
2
xfi +
2
yfs t̃
Qf
8f 2F
s S
i Ot̃
Domains of variables
xfi
yfst
2 f0 1g
0 and integer
;
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8f 2 F i 2 L
8f 2 F s 2 S t 2 Ts
;
;
;
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Small Example
Leg specific data
leg i
1
2
3
4
origin o
HAM
HAM
FRA
MUC
destination d
FRA
MUC
HAM
HAM
arrival t
410
500
550
620
flight time
50
80
50
80
Cost cfi
Fleet
fleet f
1
2
3
departure t
360
420
500
540
name
A320-200
B737-500
E195
quantity
1
1
1
fleet f
1
2
3
i=1
2700
2800
1900
i=2
3200
3100
2600
i=3
2700
2800
1900
i=4
3200
3100
2600
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Solution
Variable values xfi :
I x22 = x24 = x31 = x33 = 1
I x11 = x12 = x13 = x14 = x21 = x23 = x32 = x34 = 0
Objective value Z :
I c22 x22 + c24 x24 + c31 x31 + c33 x33 = 10000
Results:
I HAM - FRA - HAM: B737-500 ! costs: 2 3100
I HAM - MUC - HAM: E195 ! costs: 2 1900
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Why a simultaneous approach?
I Planning processes are usually examined separately from one another
I Combining two ore more processes might lead to superior solutions
! cost savings, revenue increase
I Integrating RM in FA: Provides the possibility to account for
demand variability
I Idea: Enable airlines to fit the fleet type to demand on a certain leg
I But: Planning horizons differ for both problems (see previous slide)
I Difficult to adjust fleet types due to demand changes at short notice
! swapping = short run interchange of already assigned aircrafts
!
between two flight legs
For simplification we disregard differing planning horizons in the
following case study
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Model assumptions
I The model is solved for a predefined (short) period of time
!
usually for 1 day (same daily schedule)
!
Here: analytic solution according to slides 10-11
I Demand is independent between flight legs
I Network revenue Rfi is the solution of a RM model
I Aircraft availability is neglected to reflect a strategic decision process
I The model decides on the optimal fleet composition for a given
network
I Result: Optimal assignment of fleet types to legs such that the
contributed profit minus fixed costs is maximized
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Mathematical formulation
Parameters
CAf
Fixed cost per aircraft of fleet type f
CFf
Fixed cost of fleet type f
B
Large number
Cf
capacity of fleet type f (number of seats)
qfi0
optimal quantity of sold seats for fleet type f on flight leg i
according to revenue function u(q)
qfi
Rfi
= minfCf ; qfi0 g
Profit contribution for fleet type f on flight leg i
Rfi
= Rfi (qfi )
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Variables
zf
= 1, if fleet type f is chosen (0, otherwise)
XX
Objective function
max
2 2
Rfi xfi
f F i L
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XX
2 2
f F s S
CAf yfs t̃
X
2
CFf zf
f F
Cover constraints
X
2
xfi
=
1
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8i 2 L
f F
X X
Balance constraints
yfsp +
2
i Ast
xfi
2
i Dst
xfi
= yfst
8 f 2 F s 2 S t 2 Ts p 2 Pst
;
;
;
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X
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Linking constraint
yfs t̃
B zf
8f 2 F
s
Domains of variables
xfi
zf
yfst
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2 f0 1g
2 f0 1g
0 and integer
;
;
8f 2 F i 2 L
8f 2 F
8f 2 F s 2 S t 2 Ts
;
;
;
Case Study
I
I
I
I
I
Airline: Air Berlin (AB)
Period: Monday (Summer schedule 2011)
Airports S considered: 4 - HAM, DUS, NUE, STR
Number of flight legs L: 42
Fleet-types available: 15
(Do-328 TP, Q-400, CRJ-700, CRJ-900, E175, E195,
B737-500, B737-300, A319-100, B737-700, A320-200,
B737-800, A321-200, B777-200 BL, B777-200H GW)
I Maximum quantity of aircrafts per fleet-type: not restricted
I linear PSF: rfi (qfi ) = qmaxi 2 qfi
I qmaxi = 200 + " with " a normal distributed random variable with
= 0 and = 256
6 To
account for variability in demand (Listes and Dekker 2005).
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Results
Airline
AB
Legs
42
Aircrafts
8
Surplus
76.301
Revenue
205.340
Costs
129.040
Passengers
3.345
I Assumption: all possible fleet types are available and can be chosen
!
Results do not reflect the actual AB fleeting
I Fleet type 1: 6 aircrafts of CRJ-700
I Fleet type 2: 2 aircrafts of CRJ-900
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Resulting network
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Literature I
Grothklags, S.:
Flottenzuweisung in der Flugplanung: Modelle, Komplexität und Lösungsverfahren.
Doktorarbeit, Universität Paderborn, Paderborn, 2006.
Hane, C.A., C. Barnhart, E.L. Johnson, R.E. Marsten, G.L. Nemhauser und
G. Sigismondi:
The fleet assignment problem: solving a large-scale integer program.
Mathematical Programming, 70(1):211–232, 1995.
Klein, R. und C. Steinhardt: Revenue Management, Band 1.
Springer Verlag, Heidelberg, 2008.
Listes, O. und R. Dekker: A scenario aggregation–based approach for
determining a robust airline fleet composition for dynamic capacity allocation.
Transportation science, 39(3):367–382, 2005.
Sherali, H.D., E.K. Bish und X. Zhu:
Airline fleet assignment concepts, models, and algorithms.
European Journal of Operational Research, 172(1):1–30, 2006.
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Literature II
Talluri, K.T. und G. Van Ryzin:
The Theory and Practice of Revenue Management.
Springer Verlag, 2005.
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Einführung in Verkehr und Logistik [1.15ex] (Bachelor) [1.15ex

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