Einführung in Verkehr und Logistik€¦ · Lohatepanont & Barnhart 2004, S. 19). Die...

WS 13/14 Einführung in Verkehr und Logistik 1 / 46

Einführung in Verkehr und Logistik

(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


Airline Planning Process12. Konzeptionelle Grundlagen

4

Über die weiteren Teilprobleme der Flugplanerstellung besteht in der Literatur, trotz

vielfach divergierender Terminologie, ein breiter Konsens. Im Rahmen der Netzwerk-

planung, häufig auch Schedule Design genannt, werden die angebotenen Flugstrecken,

die Frequenz der Flüge sowie ihre Abflugs- und Ankunftszeiten definiert (vgl. hier und

im Folgenden z.B. Erdmann et al. 2001, S. 117; Gopalan & Talluri 1998, S. 156f.;

Lohatepanont & Barnhart 2004, S. 19). Die Marktmodellierung oder das Forecasting

dient der Nachfrageprognose auf den Märkten der Fluggesellschaft und der Bewertung

des Netzwerks. Dieser Planungsphase wird eine besondere Bedeutung zugesprochen, da

sie die Grundlage nachgelagerter Entscheidungen, etwa im Rahmen der Ressourcenal-

lokation oder dem Pricing, darstellt (vgl. Grosche & Rothlauf 2007, S. 2).

Die Aufgabe der Flottenzuweisung bzw. des Fleet Assignments besteht darin, unter-

schiedlichen Flugzeugtypen (analog Flottentypen), die sich in zahlreichen Charakteris-

tika, wie ihrer Sitzkapazität, ihrer Reichweite, ihrer Nutzlast oder ihrem Treibstoff-

verbrauch aber auch hinsichtlich potenziell erzielbarer Erlöse unterscheiden, Flugstre-

cken (analog Legs)2 des zuvor generierten Flugnetzes zuzuordnen (vgl. Clarke et al.

1996, S. 249; Sherali et al. 2006, S. 2).3 Dem Fleet Assignment folgt die Aircraft Rota-

2 Als Leg wird der durch einen Start und die dazugehörige Landung definierte Teil eines Fluges bezeich-net (vgl. McGill & Van Ryzin 1999, S. 248). 3 Mittelfristig wird der Planungszeitraum auf eine repräsentative Standardperiode, z.B. eine Woche festgelegt, während kurzfristig konkrete Zeiträume (fully dated) betrachtet werden (vgl. Grothklags 2006,

Personal

Revenue Management

Flugnetz

Langfrist Mittelfrist Kurzfrist Implementierung

Kontrolle

Operations Control

Marktmodellierung

Crew Pairing

Crew Rostering

Revenue Management

Fleet Assignment Wochenplanung | fully dated

Aircraft Rotation

Pricing

Netzwerkplanung

Flottenplanung

3 J. 0 2 W. 1 J. 8 W. 6 M. 4 W.

Abbildung 1: Allgemeiner Flugplanungsprozess einer Fluggesellschaft

Quelle: in Anlehnung an Grothklags 2006, S. 3.

1See [Gro06].


Introduction to Revenue Management

Origin of Airline Revenue Management

I Airline Deregulation Act of 1978 (prices, schedule)I Low Cost Carrier (LCC) entered the market ! price pressureI American Airlines first launched special discount faresI Instruments of RM:

I Price DiscriminationI OverbookingI Capacity ControlsI Forecasting systems (not covered here)


Basics

I Revenue Management (RM) is also known as Yield ManagementI RM can be either quantity- or price-based depending on the control

variableI most airlines commit to fixed prices and tactically allocate quantityI LCC use price as the primary tactical variable

I Objective: utilization of additional yield according to individualwillingness to pay (WTP)

I Successful application also in other service areas: hotels, car rentals


Conditions conducive to RM2

I Demand variability and uncertaintyI Production inflexibility (variations in supply difficult)I Advance salesI Perishable inventoryI High fixed costs/low marginal costsI Customer heterogeneity (preferences)

2Talluri and van Ryzin (2005, pp. 13).


Price Discrimination (PD)

First-degree/perfect price discriminationI Each customer is charged according to its WTP

I Requires information on each customers WTP & ability to vary price bycustomer and unit

! Theoretical abstraction because of lack of information

Second-degree price discriminationI Discrimination by offering various possible purchase contracts

I Customers decide which contract to purchase

! Self-selection by customers

Third-degree price discriminationI 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 sameamount


q(r)

q*

r*r* r

q

q*q*

r

q(r)

q

r1

r2

r3

q1

q3

q2

I RM ! 2nd degree PDI Segmentation of customers

I self-selection

I Prices for almost similar goods differI Different ticket fares within the same class

of serviceI Economy, Business, First ClassI Restrictions apply

I Optimal strategy ! prices according toindividual WTPI Not feasibleI Instead several fare classes (FC) for each

service class


Fare Classes

I Varying ticket prices for identical product (flight from A to B)

I Up to 20 different fare classes on a single flight

I FC are represented by letters

I full fares: F - first class, C - business class, Y - economy classI discount fares economy class: M, B, K, H, Q, S, W

I Restrictions apply for cheaper tickets:

I Rebooking/Cancellation feesI Advance purchase requirementsI Trip length and length of stayI Saturday-night stay

I Restrictions provide necessary FencingI to separate demand of business and leisure travellersI to prevent that high-value customers buy-down to cheaper tickets

I Objective: additional demand through cheap tickets and better utilizationof capacity


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 continuouslydifferentiable and strictly monotonic decreasing inverse function:

r(q) = q�1(r)

Example: Linear PSFq(r) = a� b � r 0 � r � a=b

r(q) = a=b � 1=b � q 0 � q � a


Revenue function

u(q) = q � r(q)

Marginal revenue function

u0(q) = r(q) + q � r 0(q)

Assumption: The marginal revenue function is strictly monotonicdecreasing within its domain.

Example: Linear PSF

u(q) = a=b � q � 1=b � q2

u0(q) = a=b � 2=b � q

u00(q) = �2=b ! concave function


Objective Function: Maximizes Revenue

max u(q) = q � r(q)

Constraints

q � C

q � 0

Optimal Solution

Extreme value with disregard of the capacity constraint:

u0(q) = 0! q0

q� = minfC ; q0g und r� = r(q�)


Exampleq(r) = 400� 0:5r

C = 120

Solution:r(q) = 800� 2 � q

u(q) = 800 � q � 2 � q2

u0(q) = 800� 4 � q

) q0 = 200

) q� = minf120; 200g = 120

) r� = r(120) = 560

u� = 800 � 120� 2 � 1202 = 67:200 (= 120 � 560)


Capacity Controlling

I Revenue maximizing control of sales processesI Decision about acceptance/rejection of booking inquiriesI Single-leg or network flightsI Supports price discrimination and erroneous fencingI Types of controls:

I Booking limitsI Protection LevelsI 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 itI The value of capacity is measured by its expected opportunity cost

(displacement cost)

I Optimization problem regarding the acceptence of booking requests


Booking Limit3 bjI Limits the amount of capacity C that can be sold to any fare class jI Partitioned: available capacity is divided into seperate blocksI Nested: available capacity overlaps in a hierarchical manner, more

expensive fare classes have access to all the capacity reserved forcheaper fare classes

Protection Level yjI Specifies an amount of capacity to reserve (protect) for a particular

fare class j

Formal Relationship

bj = C � yj�1 j = 2; : : : ; n

3Talluri and van Ryzin (2005, pp. 28-30).


Relationship between bj and yj


ExampleAn airline is operating the flight legs A-B and B-C as well as thecombination of both A-B-C. The utilized aircrafts have a capacity of 100seats. For the purpose of price discrimination two fare classes areassigned to each flight leg. Overbookings are not taken into account. Thefollowing table shows the expected demand per flight leg and fare class:

Route Class W Class KA-B Price (EUR) 250 490

Demand 100 40B-C Price (EUR) 220 400

Demand 80 60A-B-C Price (EUR) 460 880

Demand 80 50

How many seats per flight leg in combination with a certain bookingclass should be sold?


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

maxF (x ; y) = 250xAB + 220xBC + 460xAC + 490yAB + 400yBC + 880yAC

xAB +xAC +yAB +yAC � 100 (A� B)

xBC +xAC +yBC +yAC � 100 (B � C)

xAB � 100xBC � 80

xAC � 80yAB � 40

yBC � 60yAC � 50

xAB ; xBC ; xAC ; yAB ; yBC ; yAC � 0 and integer

Optimal Solution: (F (x ; y) = 86100 EUR):

xBC = xAC = 0; xAB = 10; yAB = 40; yBC = 50; yAC = 50


Overbookings

I 50% of all reservations result in cancellations and no-showsI Objective: increasing the total volume of sales in the presence of

cancellationsI 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 availableI Airlines are obliged to compensate passengers for denied boarding


Terminology

Fleet (aircraft) type: A certain model of aircraft (e.g., BoeingB767-300)

Fleet (aircraft) family: A set of aircraft types with the same cockpitconfiguration and crew qualificationrequirements

Flight leg: An airport-to-airport flight segment

Through-flight: Two consecutive flight legs that are flown bythe 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 itslanding and the next take-off


Decision Problem

I Assigning aircraft types with different capacity to scheduled flightsI Depends on potential revenues, availability, operational costs,

equipment capabilitiesI 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)


Fleet Assignment Model (FAM)

I Foundation of analytical work in this fieldI 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 fleettype

2. Balance constraints - Ensure conservation of flow

3. Aircraft availability constraints - The number of available aircrafts ofeach type bounds their usage

4Hane et al. (1995).


Time-Space-Network5

(1d)) can be omitted from the formulation for the time–space network. The objective is to maximize therevenue or, equivalently, to minimize the assignment cost.

To be consistent with the existing literature as much as possible, we use the following notation through-out the remainder of this paper.

Notation

S set of stations in the network, indexed by s, o, or dF set of fleet types, indexed by f

L set of flight legs scheduled, indexed by l or {odt}, where o,d 2 S and t denotes the time when theflight takes off from o or is ready at d for the next take-off

N set of nodes in the network, indexed by {fst}, where f 2 F, s 2 S, and t denotes the event timeO(f) set of arcs for fleet type f that cross the aircraft count time-line, f 2 F

cfl cost of assigning fleet type f to leg l, f 2 F, l 2 L

Af number of available aircraft for fleet type f, f 2 F

xfl=1; if fleet type f covers leg l; f 2 F ; l 2 L0; otherwise

�(The decision variables xfl can also be denoted by xfodt for f 2 F, {odt} 2 L.)

yfstt 0 flow of aircraft on the ground arc from node {fst} 2 N to node {fst 0} 2 N at station s 2 S in fleettype f�s network, for f 2 F, where t 0 > t in general, and t 0 6 t for wrap-around arcs

t�, t+ the time preceding and succeeding t, respectively, in the time-line

Time

Stations

Station BStation A

A1

B1

D1

B2

C1

F1

E1

10:00am

9:00am

12:00pm

11:00am

A2

C2

D1

E2

F2

Arcs for Type 1

Arcs for Type 2

Wrap-aroundarcs for Type 1

Fig. 2. A two-type, two-station fleet-flow time–space network.

H.D. Sherali et al. / European Journal of Operational Research 172 (2006) 1–30 7

5See Sherali et al. (2005).


Properties

I Focuses on representing flight legs (arcs)I Model decides on feasible connectionsI Fleet type-dependent flight/turn-times ! network for each fleet typeI A directed flight arc belongs to the movement of an aircraft typeI 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 stationI Nodes represent arrivals and departures of a flight leg at a stationI Same-every-day fleet assignment ! moderate computational

complexity


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 atstation s and time point t̃

Ast leg(s) with arrival time t 2 Ts at station s

Dst leg(s) with departure time t 2 Ts at station s

Pst the predeccessor time point of t 2 Ts where the predeccessortime point of the first time point in Ts is the last time point inTs (wrap-around); j Pst j= 1


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 attime point t 2 Ts


Objective function: Minimizes total costs

minX

f2F

X

i2L

cfixfi

Cover constraintsX

f

xfi = 1 8 i 2 L

Balance constraints

yfsp +X

i2Ast

xfi �X

i2Dst

xfi = yfst 8 f 2 F ; s 2 S ; t 2 Ts ; p 2 Pst


Aircraft availability constraint

X

i2Ot̃

xfi +X

s2S

yfst̃ � Qf 8 f 2 F

Domains of variables

xfi 2 f0; 1g 8f 2 F ; i 2 L

yfst � 0 and integer 8f 2 F ; s 2 S ; t 2 Ts


Small Example

Leg specific data

leg i origin o destination d departure t arrival t flight time1 HAM FRA 360 410 502 HAM MUC 420 500 803 FRA HAM 500 550 504 MUC HAM 540 620 80

Fleetfleet f name quantity

1 A320-200 12 B737-500 13 E195 1

Cost cfifleet f i=1 i=2 i=3 i=4

1 2700 3200 2700 32002 2800 3100 2800 31003 1900 2600 1900 2600


Solution

Variable values xfi :

I x22 = x24 = x31 = x33 = 1I 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 � 3100I HAM - MUC - HAM: E195 ! costs: 2 � 1900


Why a simultaneous approach?

I Planning processes are usually examined separately from one anotherI Combining two ore more processes might lead to superior solutions! cost savings, revenue increase

I Integrating RM in FA: Provides the possibility to account fordemand variability

I Idea: Enable airlines to fit the fleet type to demand on a certain legI 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 aircraftsbetween two flight legs

! For simplification we disregard differing planning horizons in thefollowing case study


Model assumptions

I The model is solved for a predefined (short) period of time! usually for 1 day (same daily schedule)

I Demand is independent between flight legsI Network revenue Rfi is the solution of a RM model

! Here: analytic solution according to slides 10-11

I Aircraft availability is neglected to reflect a strategic decision processI The model decides on the optimal fleet composition for a given

networkI Result: Optimal assignment of fleet types to legs such that the

contributed profit minus fixed costs is maximized


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 iaccording to revenue function u(q)

q�fi = minfCf ; qfi0g

Rfi Profit contribution for fleet type f on flight leg i

Rfi = Rfi(q�fi)


Variables

zf = 1, if fleet type f is chosen (0, otherwise)

Objective function

maxX

f2F

X

i2L

Rfixfi �X

f2F

X

s2S

CAf yfst̃ �X

f2F

CFf zf


Cover constraintsX

f2F

xfi = 1 8i 2 L

Balance constraints

yfsp +X

i2Ast

xfi �X

i2Dst

xfi = yfst 8 f 2 F ; s 2 S ; t 2 Ts ; p 2 Pst


Linking constraint

X

s

yfst̃ � B � zf 8f 2 F

Domains of variables

xfi 2 f0; 1g 8f 2 F ; i 2 L

zf 2 f0; 1g 8f 2 F

yfst � 0 and integer 8f 2 F ; s 2 S ; t 2 Ts


Case Study

I Airline: Air Berlin (AB)I Period: Monday (Summer schedule 2011)I Airports S considered: 4 - HAM, DUS, NUE, STRI Number of flight legs L: 42I 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 restrictedI linear PSF: rfi(qfi) = qmaxi � 2 � qfi

I qmaxi = 200+ " with " a normal distributed random variable with� = 0 and � = 256

6To account for variability in demand (Listes and Dekker 2005).


Results

Airline Legs Aircrafts Surplus Revenue Costs PassengersAB 42 8 76.301 205.340 129.040 3.345

I Assumption: all possible fleet types are available and can be chosen

! Results do not reflect the actual AB fleetingI Fleet type 1: 6 aircrafts of CRJ-700I Fleet type 2: 2 aircrafts of CRJ-900


Resulting network


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 undG. 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 fordetermining 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.


Literature II

Talluri, K.T. und G. Van Ryzin:The Theory and Practice of Revenue Management.

Springer Verlag, 2005.

Einführung in Verkehr und Logistik€¦ · Lohatepanont & Barnhart 2004, S. 19). Die...

Documents

Transcript of Einführung in Verkehr und Logistik€¦ · Lohatepanont & Barnhart 2004, S. 19). Die...