-
Andreas Fink *, Torsten Reiners
on substantial real-world data, using a simulation model to
assess optimization results for dierent scenar-
ios. The results indicate that the proposed approach can
signicantly improve eciency.
as well as the general demand for an improved service quality in
a competitive market. As carrental companies provide substitutional
products, price and service quality are critical success
* Corresponding author. Tel.: +49 40 42838 4706; fax: +49 40
42838 5535.
E-mail address: [email protected] (A. Fink).
www.elsevier.com/locate/tre
Transportation Research Part E 42 (2006) 2722921366-5545/$ - see
front matter 2005 Elsevier Ltd. All rights reserved. 2005 Elsevier
Ltd. All rights reserved.
Keywords: Car rental logistics; Transportation in car rental
networks; Minimum cost network ow model
1. Introduction
We consider the logistics processes in the short-term car rental
industry. This industry faces cer-tain developments such as a
disproportionate growth of car holding costs relative to pricing
levelsInstitute of Information Systems, University of Hamburg,
Von-Melle-Park 5, 20146 Hamburg, Germany
Received 19 March 2004; received in revised form 20 September
2004; accepted 29 October 2004
Abstract
Logistics management in the car rental business involves
short-term decisions about the transportation
and deployment of cars with regard to optimizing eet utilization
while maintaining a high service level. We
model and solve this problem by means of minimum cost network ow
optimization under consideration ofessential practical needs such
as multi-period planning, a country-wide network, customized
transportation
relations, eeting and deeeting, and car groups with partial
substitutability. Experiments were conductedModeling and solving
the short-termcar rental logistics
problemdoi:10.1016/j.tre.2004.10.003
-
is the description of an eective solution method that supports
decision making in short-termlogistics management under
consideration of essential practical needs. We disregard aecting
de-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 273mand from a revenue management perspective (by means of
pricing policies depending on theshort-term relation between supply
and demand); see Geraghty and Johnson (1997).The paper is organized
as follows: First, we describe the major system components and
core
processes of car rental operations and we introduce the
resulting decision problem (Section 2).Section 3 focuses on
modeling and solving the short-term car rental logistics problem.
Thisincludes determining the supply of available cars, forecasting
demand, balancing supply anddemand on the basis of a minimum cost
network ow model, and eventually validating thegenerated plan by
means of a simulation model. Computational results are presented in
Section4. In Section 5, we describe the architecture of an
integrated decision support system supportingcar rental logistics.
Finally, in Section 6, we summarize the lessons learned and discuss
require-ments for future research.
2. Problem description
In this section we present an overview of car rental operations
(network, eet, rental and logis-tics processes) and introduce the
core decision problems.
2.1. Network and eet
The major car rental companies operate cross national. However,
logistics management ismainly split in accordance with national
subsidiaries. Such organizations run a network of rentallocations
(stations), where customers can pick up (check-out) and return
(check-in) cars. Typi-cally, a national rental network exhibits
some hierarchical structuree.g., by means of groupingstations in
districts (pools), and districts in regions. Fig. 1 shows a
possible structure of a carrental network in Germany with four
regions, and, as an example, the Munich district, whichincludes all
stations in and around this city. The map also shows some depots,
marked by squares,factors. This underlines the importance of
optimizing car rental logistics in terms of the utilizationof the
eet of cars while maintaining a high degree of customer
satisfaction. In this regard, sophis-ticated control systems have
to be developed and used.According to the Economist Intelligence
Unit (2000) the car rental industry is polarized be-
tween the major international companies providing services to
both business and leisure custom-ers on the basis of international
networks including outlets at all major airports and city
centers,and small companies operating locally and primarily serving
the leisure market. While the generalconcepts described in this
paper may be applied to any car rental company that operates a
sub-stantial integrated network of rental locations, we are
inuenced by our work in an industry pro-ject with the German
subsidiary of a major international car rental company. Our focus
is on theshort-term deployment of passenger cars for a planning
horizon from a few days up to about twoweeks. In this context,
yield management basically involves optimizing car deployment with
re-gard to the number and type of deployed cars as well as the
incurred transportation costs dueto car movements between rental
locations and/or depots. The main contribution of this paperwhich
serve for the dispersal of new cars (eeting) and eventually
collecting cars once the holding
-
Hamburg
Berlin
Cologne
NORTH
EASTWEST District Munich
274 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292period expires (deeeting). Depots act as an
intermediate layer between stations on one side andmanufacturers
and resellers on the other.The car rental company is aliated with
dierent kinds of stations. A corporate station oper-
ates by means of sta and cars that are both part of the car
rental company. A station with auton-omous sta but without a
separate eet of cars is called corporate agent. In addition,
franchisepartner (licensee) stations as well as foreign stations
generally operate a separate eet of carsand are for the main part
autonomous regarding logistics management. Consequently, we focuson
corporate stations and corporate agents, where the car rental
company can centrally decideabout the deployment of their own
cars.
Munich
Frankfurt
SOUTH
Airport Munich
Landsberg
Fig. 1. Possible structure of a car rental network.A car rental
company usually operates up to about 15 car groups where each group
containsdierent cars with comparable quality (e.g., concerning size
and equipment). Each group repre-sents a homogeneous good with a
base rental fee per day (rate). In case that a customer madea
reservation for a certain group in advance and no corresponding car
being available at the timeof check-out an upgrade to a superior
car group can be granted by the station. In practice,
singleupgrades and double upgrades correspond to one or two
additional quality levels, respectively.There are some common rules
that dene feasible upgrade relations (see Table 1). Double
up-grades should only be granted if no car from a single upgrade
car group is available. Note thatthe rules are partly treated as
suggestions and the station sta may make exceptions to
satisfyparticular customers.
Table 1
Car groups
Group Type Rate Single Double Holding costs per day
A Sub-compact r1 B, J C h1B Compact r2 C D h2C Economy r3 D, K E
h3. . . . . . . . . . . . . . .
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 275Car rental companies generally enter into agreements with
car manufacturers and resellers,which dene criteria for the car
usage (in particular, in terms of a maximum holding periodand
mileage). For our purposes holding costs per day (including
interest, depreciation, mainte-nance, etc.) of a car of some car
group are assumed to be constant during the standard holdingperiod
(e.g., 6 months). If a car rental company continues to use some car
for rental operations inspite of an applicable deeeting criterion,
penalty costs may have to be taken into account.
2.2. Rentals
A rental starts with a check-out at some station where the
customer signs the contract and endswith a check-in at the same or
a dierent station where the car is returned. Check-out data
in-cludes the planned check-in station and rental length. The
revenue due to a rental is composedby the base rate per day
(multiplied by the rental days) as well as additional services,
e.g., feesfor insurance, gasoline, or extra equipment. In case of
an upgrade, the revenue is based on therate of the car group
originally reserved. In general, the rate may depend on factors
such asthe season, day of the week, or special contracts with
certain groups or companies.Customers make reservations specifying
at least the check-out and check-in station and time as
well as the requested car group. The typical policy of car
rental companies is to accept reserva-tions for passenger cars
without examinationhowever, these reservations are usually not
bind-ing on either side. Achieving a high service level, in
particular providing all customers that hold areservation with a
car of the requested group (or an upgrade), is extremely important.
Althoughthis may be unprotable from a short-term perspective on
some cases, a high service level is cru-cial to build long-term
customer relationships in competitive markets.Achieving a high
utilization of cars is a main goal of the planning concepts
discussed in Section
3, but nonetheless requires the ecient execution of operations
processes. In particular, car rentalcompanies aim at a short
turnaround with regard to the time needed from a check-in until
acheck-out of the car is possible again (e.g., due to refueling and
cleaning). For standard casesthe turnaround time should be shorter
than 1 h. In general, there is a high degree of uncertaintyin the
processes throughout the day. For example, there may be delayed
check-ins, returned carsmay be in need of repair, reservations may
expire when no customer turns up (no-show), or alot of walk-in
customers may unexpectedly arrive. Furthermore, the current status
of cars is ofteninaccurately represented in the information system
(e.g., shortly after check-in or during turn-around). Balancing
supply and demand throughout the day is complicated by these
uncertainties.One consequence is that car rental companies usually
do not operate by xed and automated pre-assignments of specic cars
to (forecasted) customers, but by exibly handling the allocation
whenthe customer arriveswith some degree of manual forward planning
by a rough matching of res-ervations with the pool of available
cars for dierent groups.
2.3. Logistics processes
The typical life cycle of a car is illustrated in Fig. 2. New
cars are delivered from the manufac-turers to feasible depots where
the cars are prepared for rental operations including
supplement-ing special equipment and registering a vehicle license.
Cars are brought into the active eet
(eeting) using trucks (with a capacity of up to eight cars) from
the depots to designatedwith
-
276 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292respect to direct eetingstations within the districts.
This applies analogously for deeeting(transporting a car at the end
of the holding period from some station to some depot).Ideally,
foreseeable car shortages at some stations are balanced by
arranging eeting and
deeeting appropriately. Nonetheless, there is generally also the
need to schedule car transfersbetween stations. We distinguish
transfers via truckkeeping the mileage of the caror by drivingthe
car itself (by axle, carried out by station sta or sta from service
providers). While combiningseveral car transfers on one truck
usually leads to lower costs, it may also stand for
inexibilitybecause of longer transfer times, mandatory advance
planning procedures, and delays resultingfrom the combination of
more than one car transfer. Transportation by axle is typically
fasterand more exible but also more expensive than transportation
via trucks. Transportation by axlemay be combined with
transportation via truck as some designated stations may act as
collectionpoints where trucks drop and pick-up cars (in particular
in connection with eeting and deeet-ing). Note that transportation
services are for the most part assigned to external shipping
compa-nies on the basis of basic agreements, which include certain
service guarantees and cost structures.We generally found that
shipping companies charge xed costs per car depending upon the
trans-portation relation, the distance as well as the mode of
transport.The question marks shown in Fig. 2 indicate the logistics
processes that are the subject of this
paper. That is, we aim to optimize car deployment by means of
eeting, transfers between sta-tions, and deeeting, focusing on
short-term logistics decisions for a planning horizon from afew
days up to one or two weeks. We assume tactical and strategic
decisions as given. In partic-ular, there are generally xed
arrangements for the range of aggregate eeting and deeeting
con-
Fleeting
Defleeting
Transfer
Rental
Car Manufacturer
Reseller
Cars on yard
Station
DepotNew carsCars for saleand/or
Fig. 2. Life cycle of cars.tingents with xed charges per car
provided. Agreements with car manufacturers and
wholesalersdetermine to what extent the holding period of cars in
the active eet can be exibly adjusted toresolve shortages or to
reduce over-capacity. The strategic management of the purchase,
dispersal,and disposal of cars is an important issue of the car
rental industry; see Economist IntelligenceUnit (1997). More
detailed plans are generally determined through some hierarchical
eet plan-ning process. This mainly includes forecasting rental
demand as well as controlling the availabilityof cars at dierent
aggregate levels (in particular, with respect to the planning
horizon, regions,and car groups).The management of car deployment
is highly complex due to the connection of car availability
across time, the station network, and dierent car groups.
Furthermore, the detailed planning ofshort-term car logistics
involves thousands of potential rental cases each day. For these
reasons,eective decision support by appropriate information systems
seems indispensable. The literature
-
ply and demand from the perspective of short-term logistics
management. (As discussed in Section2.3, we assume strategic and
tactical decisions such as the station network or the available
car
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 277types as given. In Section 5, we outline the integration
of the proposed optimization model withina decision support system,
which also includes mid- and long-term planning functionality as
wellas aecting demand by exible rate adaptations in the sense of
revenue management.) On the onehand, revenue may be increased by
serving rental requests. On the other hand, we strive for anecient
deployment of cars with regard to transportation costs as well as
holding costs accordingto the number and type of used cars. These
conicting goals are integrated by the objective ofmaximizing prots,
as dened by subtracting the incurred variable costs from the
obtainedrevenue.We model and solve the car logistics problem on the
basis of a rolling planning horizon of one
week. Resulting plans are re-optimized each night on the basis
of new data, assuming that allcheck-outs and check-ins are
generally keyed into the information system not later than by
theend of the day. The assumption of time periods of half days
results in partitioning a week into14 periods. (Dierent planning
horizons or denitions of time buckets are of course possible.)We
aim at a robust car logistics plan, which provides the stations in
each period with enough carsof the dierent car groups, without
fully automating the detailed decisions in the stations duringthe
course of the day. The station sta should be enabled to handle
customer requests by exiblydeploying locally available cars. That
is, we do not propose an automatic assignment of speciccars to
customers by the decision support system. This is due to the
uncertainties of the actualthat considers the car rental business
mainly encompasses revenue management and pool controlsystems as
descriptive tools. Edelstein and Melnyk (1977) describe a pool
control system with thepurpose to clarify and evaluate alternatives
for, e.g., assigning cars within a pool of cities oraccepting
reservations. The system is a descriptive interactive tool that
leaves the actual deploy-ment decisions to the manager. A yield
management system was designed at Hertz by Carroll andGrimes (1995)
to combine various stand-alone decision support systems addressing
mainly tacti-cal and strategic questions concerning the eet size
and deployment as well as product design. Thisyield management
system supports decision making by gathering information from the
corre-sponding subsystems as well as presenting alternatives for
mid- and short-term planning. Gera-ghty and Johnson (1997) focus on
revenue management, especially capacity management,pricing, and
reservations control. Pachon et al. (2003) describe a prescriptive
model for daily eetplanning within a pool of neighboring rental
locations. All papers mentioned provide valuable in-sight into the
car rental business. However, the literature generally lacks
prescriptive optimizationmethods for short-term logistics
management under consideration of important requirementsfrom
practice such as multi-period planning, a country-wide network,
customized transportationrelations, eeting and deeeting, and car
groups with partial substitutability. Our aim is to pro-vide an
ecient solution method that takes these aspects into account and
eectively supportsdecision making in car rental logistics
management.
3. Modeling and solving the car logistics problem
The car logistics problem is modeled with the objective of
maximizing prot by balancing sup-processes in the stations in
conjunction with the often delayed availability of events (in
particular,
-
278 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292check-ins) in the information system. In the following
sections, we describe the determination ofsupply and demand and
dene the decision model and a corresponding minimum cost networkow
model.
3.1. Supply
The determination of the supply of available cars throughout the
planning horizon is compli-cated due to the connection of car
availability across time and space. The option of car
transfersbetween stations and the partial substitutability of car
groups due to the possibility of upgradesmean that in theory almost
any particular car may serve any future rental request at some
arbi-trary station. This is related to the problem of deploying
empty freight cars in rail system net-works; see, e.g.,
Spieckermann and Vo (1995).It is reasonable to assume that the
information system of a car rental company provides at the
end of each day accurate data concerning the number of cars of
dierent groups being available ata station, the cars currently on
rent, which will become available at some station in the future,
andthe number of new cars of dierent groups being available at a
depot (with a eeting option). Thisprovides accurate data for the
initial period of the planning horizon. The availability of cars
insubsequent periods is inuenced by possible check-outs due to
future rental requests, whichmay or may not be served, as well as
check-ins due to cars currently on rent. Future rental re-quests
have to be estimated on the basis of demand forecasts (see the next
section), and one alsohas to rely on tentative check-in plans which
are requested at check-out and updated during therental time. In
combination, car availability may depend on uncertain check-in data
of forecastedrental requests. Therefore, the accuracy of data about
car availability decreases for future periods,which sets limits on
an adequate planning horizon for detailed car logistics planning.We
assume pre-dened eeting and deeeting contingents at the depots,
which dene upper and
lower bounds for how many new cars of dierent groups are
available and how many cars have tobe taken out of the active eet,
respectively. Specic cars may eventually become unavailable
forrental at the end of the contracted holding period or as a
result of a repair necessity. While onecan estimate the former
events, the latter ones are uncertain.
3.2. Demand
The planning of car logistics crucially depends on a sensible
demand forecast. The main prob-lem is that a substantial proportion
of rental requests are not due to a reservation. Therefore,
wegenerally need to establish detailed short-term forecasts of
rental requests over the planninghorizon.First of all, a forecast
of a rental request must include information about the check-out
station
and time as well as the requested car group. For rental requests
that are linked to a reservation wealso know, from the
corresponding reservation data, about the planned check-in station
and ren-tal length (and so we usually have an accurate estimate of
the revenue). However, to forecastwalk-in customers one has to rely
on past data to guess the check-in station and the rental
length.Consequently, forecast data becomes increasingly inaccurate
after the average rental length of vedays. In practice, the demand
forecast might be adapted by the local station sta, which may
have
additional information available that aect demand (e.g., some
new local event or weather
-
Thstatiosome location at some period) as well as short-term
demand forecasts (i.e., potential number of
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 279check-outs of some car group at some station in some
period), as elaborated in Sections 3.1and 3.2, respectively.
Moreover, we rely on cost parameters concerning holding costs per
dayand car group as well as transportation costs depending on the
dierent modes of transport.The objective is to maximize short-term
prots as measured by the revenue of the satised rentalrequests
minus the sum of the variable costs, considering additional or
saved car holding costs andthe incurred transportation costs.
Within the planning horizon of about one week, decision vari-ables
represent the number of cars of dierent car groups that are to be
moved between dierentlocations at dierent time periods. This
includes transfers between stations as well as eeting anddeeeting
(moving cars from depots to stations and vice versa) under
consideration of dierenttransportation options. A solution must
meet the constraints set by the availability of cars (initialand
inferred supply), the forecasted rental requests (demand), and the
allowed upgrade relations.Because of the size of problem instances
from practice it is crucial to devise an ecient solution
method. Our solution approach rests on modeling the problem as a
specic minimum cost net-
worke decision model is based on detailed data about the car
supply at the stations (corporatens and corporate agents) and
depots (i.e., number of available cars of some car group
atconditions). Nevertheless, detailed demand forecasts can at best
provide a reasonable basis for ashort-term planning horizon, while
mid- or long-term decision problemswhich are not subjectof this
papergenerally rely on aggregate data. Furthermore, inuencing
factors such as season-ality or local events are ignored in the
current model due to a restricted access to historic data.Within
the car rental logistics decision support system, as introduced in
Section 5, the forecastmodule may exploit aggregate data over a
long time period together with information about rel-evant
(external) events.We assume that linear regression functions can
map reservations to a forecast of rental re-
quests, i.e., to an estimate of the requested number of
check-outs of a car of some car group atsome station in some
period. We have identied four main factors that aect such a
regressionfunction: the station, the period (for which we forecast)
within a week, the lead time (betweenthe current period and the
period for which we forecast), and the car group. This results in
thefollowing general regression function (the subscripts/indices
represent factor combinations):
#check-outsstation;period;leadtime;group
astation;period;leadtime;group
bstation;period;leadtime;group#reservationsstation;currentperiodleadtime;group
The parameters a and b of these regression functions are
estimated on the basis of past data. Fur-thermore, we estimate a
walk-in factor that represents the average proportion of walk-in
customerrequests on the total demand (for each station, period
within a week, and car group). The lengthand the check-in station
of forecasted walk-in rental requests have to be guessed by
sampling frompast rentals with the same characteristic (for each
station, period within a week, and car group).The revenue of
forecasted walk-in rentals is estimated on the basis of the average
revenue per daythat has been obtained in the past for the relevant
car group.
3.3. Network ow modelow problem, which makes available
polynomial time algorithms from network ow theory;
-
Figrouare awithdue teeti
g = g , . . . ,g , which dene eeting and deeeting options,
respectively. The corresponding
280 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 2722921 G
parameter values qi represent eeting and deeeting
contingents.Arcs (i, j) represent ow variables xij with regard to
dierent options for car deployment. If not
dened otherwise, we assume the parameter values as lij = 0, uij
=1, and eij = 0. For cars that are
neithrst of all, for each combination of some station s = s1, .
. . , sS, period t = t1, . . . , tT, and carp g = g1, . . . ,gG, a
stock node is dened that represents the number of cars of group g
thatvailable at station s at the beginning of period t. Some of the
stock nodes i are source nodesa positive supply qi which results
from the initial car stock as well as anticipated check-inso cars
on rent at the beginning of the planning horizon. In the same
manner, we introduceng nodes and deeeting nodes for each depot c =
c1, . . . ,cC, period t = t1, . . . , tT, and car groupsee, e.g.,
Ahuja et al. (1993) or Kennington and Helgason (1980). On the basis
of a directed graphthat consists of a set of nodes N and a set A of
arcs (i, j) that connect nodes, a general minimumcost network ow
model can be formalized as follows:
Minimize zx X
i;j2Aeijxij
subject toX
j:i;j2Axij
X
j:j;i2Axji qi 8i 2 N ;
lij 6 xij 6 uij 8i; j 2 AA node i 2 N comes with a parameter qi
that represents, if dierent from null, a positive (source
node) or a negative (sink node) amount of goods (in this case,
cars) in the sense of a given supplyor demand, respectively. In
total, the supply and demand of all network nodes must equal
eachother (i.e.,
Pi2Nqi 0. Arcs represent a potential ow of goods. The variable
ow quantity
xij on an arc (i, j) 2 A is restricted by a lower bound lij and
an upper bound uij. Each arc (i, j)has a cost parameter eij.
Multiplying this parameter by the ow quantity results in the costs
thatare incurred by the ow on a particular arc. Solving a minimum
cost network ow problem meansdetermining feasible (integer) values
for the arc ow variables xij in such a way that at each node ithe
quantity of in-ow minus out-ow equals qi and the sum of incurred
costs is minimized. Suchminimum cost network ow models can be
solved to optimality by ecient algorithms.Modeling the short-term
car rental logistics problem by means of a network ow model re-
quires on original transformation of the characteristics of the
described decision problem. Ourapproach is based on a time expanded
network (timespace network), where specic points in time(periods)
and space (stations and depots) are represented as corresponding
nodes. Arcs that con-nect these nodes are related to temporal and
spatial movements in the sense of dierent deploy-ment options. Time
expanded networks have been applied in application elds such as
railroadsystems (see, e.g., Kwon et al., 1998), air trac systems
(see, e.g., Gu et al., 1994), or freight ship-ping (see, e.g.,
Chardaire et al., in press). We must also take into account dierent
car groups andupgrade relations. Modeling this additional dimension
by means of multiple commodity typeswould lead to a multi-commodity
ow problem, which presumably cannot be eciently solvedto optimality
for realistic (i.e., large size) problem instances (see the
discussion in Section 6).Therefore, we integrate the possibility of
upgrades into a single-commodity minimum cost net-work ow model as
described below (note the example in Fig. 3).er deployed for a
check-out nor transported to a dierent location we dene, for all
locations
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 281(stations and depots), periods, and car groups, carryover
arcs that allow keeping cars on the yardin the sense of movement in
time. That is, such arcs connect (stock and eeting) nodes of the
sub-sequent period. Furthermore, for each station, period, and car
group, each stock node is con-nected to a corresponding rental node
(see the discussion below) that is traversed by cars thatare
actually deployed for rental requests with a preceding reservation.
Such a rental request is rep-resented by a reservation rental arc
between the applicable rental node (with respect to the check-out)
and the applicable stock node (with respect to the check-in).
Forecasted walk-in customersare represented by walk-in rental arcs
that connect two corresponding stock nodes. The costparameter eij
of a reservation rental arc is set to the negative value of the
expected revenue accord-ing to the reservation data, while the
costs of walk-in rentals are estimated on the basis of
historicaverage revenues. In each case, the destination node of a
rental arc is determined as follows: If theexpected check-in is
within the considered planning horizon at a station inside the
considered net-work, the arc leads to the corresponding stock node
of the period that follows the check-in period.(Our experiments
have shown that the followingnonetheless rather
conservativeapproachmay also be reasonable: A check-in before 8
a.m. or 1 p.m. still leads to assigning the arc tothe morning or
afternoon period, respectively, while later arrivals lead to the
subsequent period.)If the check-in is after the considered planning
horizon or at a station outside the considered net-work, the arc
ends at a virtual super-sink node, which means that such a car (ow)
cannot be usedagain within the planning horizon. Each rental arc
has an upper bound uij = 1. Eventually, theresulting ow on such
arcs, one or zero, indicates whether the rental request is served
(xij = 1)or turned-down (xij = 0). (Rental requests with identical
parameters can also be represented bya common arc with a resulting
upper bound larger than one.)For each combination of a station and
a period, upgrade arcs are introduced that start from the
superior car groups stock node and lead to the inferior car
groups rental node in accordance withthe feasible upgrade
relations. To prevent from unnecessary upgrades, we dene the cost
param-eter of upgrade arcs as a small value d > 0. (By
increasing this penalty factor, one can decrease theprobability for
granting upgradesin general at the cost of more transportation or
unfullledrental requests.) There are two reasons for distinguishing
between stock nodes and rental nodes(instead of directly connecting
stock nodes by upgrade arcs). First, this prevents a
concatenationof upgrades which would unintentionally result in the
transitive closure of the upgrade relations.Second, this restricts
upgrades to be applied in direct connection with a rental request
(but notbefore a transportation or while waiting at a station).
Note that this modeling of upgrades leads,for each car that is used
in connection with an upgrade, to irrevocable group degradation
until theend of the planning horizon. As a result, the model is
slightly more restrictive than the underlyingapplication. However,
this does not severely aect the soundness of the model as we assume
anaverage rental length of ve days in connection with a planning
horizon of about one week.Fig. 3 illustrates the basic structure of
the network ow model by means of an example for two
stations, one depot, and two car groups, where car group B is a
feasible upgrade option for cargroup A. At station 1 in period 2,
there are two rental requests for a car of group A, both of
whichwith an estimated check-in at station 2 in some future period
k. While the reservation rental arcstarts at the rental node and
thus can be served by the superior car group B, a walk-in
customermust not receive an upgrade. Therefore, the walk-in rental
arc starts at the stock node.Every reasonable transportation option
between stations is represented by a transportationarc. Such arcs
are connected to stock nodes. Essentially in conformance with
industry practices
-
282 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292A A
stat
ion
1st
atio
n 2
A
period 1 period 2 period k
...+1
+10
+10
A A
A
A
B B
B B
B
B
upgrad
e
+5
A A+3
A A
A
A
B B
B B
B
B
keep on yard
+4
transportation (axle)
A A
B+20 B B
...
depo
t 1
fleet
ing +10
transportation (truck)
fleeting
defleeting
reservation rental arc
walk-in rental arc
...
...
stock node
rental nodetransportation costs are assumed to be proportional
to the number of cars according to the par-ticular cost parameter
value depending upon the transportation relation, the distance as
well asthe mode of transport. Possible upper bounds (transportation
capacities) and destination nodes(in accordance with the
transportation times) are dened depending on each specic
transporta-tion relation. Consequently, one can exibly map dierent
modes of transport such as by axle(expensive, fast, exible) or via
truck (cheap, not so fast, some minimum lead time due to
advanceplanning) with regard to dierent distances and network
structures.For each depot and car group, eeting arcs and deeeting
arcs from depot nodes to stock nodes
of specic stations and vice versa represent eeting and deeeting
options, respectively, which alsoincludes the actual transportation
(eeting is usually done via truck). Car holding costs are takeninto
account by means of the cost parameters of eeting and deeeting
arcs. That is, the costparameters of eeting and deeeting arcs
represent the transportation costs plus the additionalor minus the
saved holding costs. Minimum and maximum eeting and deeeting
contingentsprimarily result from the supply and demand at the depot
nodes, but can also be constrainedby suitable lower and upper
bounds on specic arcs from depots to stations and vice versa.
Someminimum lead times may have to be taken into account, which
restricts the periods where eetingarcs may start and lead to. If
deeeting takes longer than the planning horizon, such arcs are
con-nected to corresponding depot nodes at period T (to allow for
deeeting even at the end of theplanning horizon). Fleeting and
deeeting contingents that are not pre-assigned to specic depots
depo
t 1
defle
etin
g A-
10A A
B B B
-
15......
Fig. 3. Basic structure of the network ow model.
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 283are represented, for each car group, by virtual
super-eeting nodes and super-deeeting nodes.These nodes are
connected to corresponding depot eeting and deeeting nodes,
respectively.In order to balance supply and demand, we introduce a
general super-sink node that eventuallyabsorbs all remaining cars
at the end of the planning horizon in accordance with the resulting
neg-ative supply value.Solving the network ow model generates ow
values for each arc (variable), which essentially
results in a short-term car logistics plan with regard to
proposed transfers between stations as wellas eeting and deeeting
decisions. Reservation rental arcs with no ow indicate the possible
needfor special action to enable serving such rental requests.
Detailed examinations of the resultingsolution are possible by
means of sensitivity analysis. For example, one can evaluate the
eectof modifying the initial availability of cars at some station,
or determine the additional revenuethat is a necessary to serve an
unserved rental request.The introduced network ow model does not
comprise all aspects of the short-term car logistics
problem and thus should be embedded in a more general decision
support system, which providesthe eet manager with a exible
interactive planning environment. In particular, a solution of
thenetwork ow model does not determine specic cars for deeeting.
Moreover, detailed restrictionswith regard to the transportation
options (e.g., xed track routes throughout a day or a minimumtruck
loading) cannot be represented. Therefore, the core optimization
model must be comple-mented by appropriate pre- and
post-optimization steps depending on the specics of the
practicalsituation. First, particular cars with a deeeting status
may be scheduled separately before solvingthe network ow model.
Second, the results of the network ow optimization should be
adaptedregarding detailed transportation procedures. In general,
the planning process may involve dier-ent scenarios (e.g., dierent
demand estimations or dierent eeting and deeeting
contingents),which are evaluated by a combined application of the
network ow optimization, pre- andpost-optimization steps, and a
simulation system.
3.4. Simulation model
For a given scenario the described network ow model generates a
schedule how cars should bedeployed. Due to the uncertainties of
the rental operations throughout the day it is reasonable
toevaluate the generated car logistics plan by means of simulation
experiments before being imple-mented in practice. Fig. 4 shows the
combined iterative application of demand forecast, networkow
optimization, and simulation experiments as elements of a general
logistics planning process.Simulation experiments are based on
initial data in a global database (in particular, information
about the state of the car eet and existing reservations at the
day of planning), which is developedthrough a simulation of seven
days. Based upon a rolling planning horizon of one week, the
se-quence of forecast, optimization, and simulation is executed
each day until a whole week has beensimulated. The results of the
detailed simulation of car rental operations for 24 h, considering
thescheduled car transfers as well as eeting and deeeting decisions
due to the network ow optimi-zation, lead to modied data, which
serves as input for the next iteration. Depending on the out-come
the whole process can either be repeated using a variation of the
input parameters (e.g.,adapted eeting and deeeting contingents), or
the deployment plan can be put into practice.To enable the
assessment of the application of an optimized car rental logistics
planning incomparison to historic processes, we distinguish between
two modes of simulation. In replay
-
mode, historic processes (rentals, transfers, eeting, and
deeeting) are simulated in accordancewith historic data. This mode
is mainly used to obtain reference values such as the incurred
costs
Forecast
Anticipated rentals
OptimizationDatabase Simulation
Logistics PlanReservations, fleet
7 days7 daysResults: car fleet, pending transports and rental
s
24 hoursInput from stations Yes: Apply
Repeat until a week is simulated
Assessment
Logistics Planning Process
Accepted?
No: Repeat with changed input parameters
Fig. 4. Logistics planning process.
284 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292and revenues as well as the resulting service level.
In evaluation mode, initial data is given as be-fore, but rental
requests are stochastically generated on the basis of demand
forecasts. Further-more, the transfers between stations as well as
the transports between stations and depots andvice versa due to
eeting and deeeting decisions, respectively, are generated using
plans due tothe network ow optimization.Since the simulation is
more detailed than the network ow model (in particular by
estimating
and using the exact time when a customer appears at the station
counter instead of using timebuckets of half days) and depends on
stochastic inuences, the implementation of the generatedcar
logistics plan is not always completely feasible. For example, if a
customer unexpectedly ex-tends the rental length a previously
planned transfer of this particular car may become impossible.In
such cases we abandon the respective element of the plan, while in
practice there may be thepossibility of some exible short-term
action to improve matters. Such deviating developmentsof the rental
and logistics operations are eventually taken into account at the
next iteration ofthe planning process (i.e., at the end of each
day).Fig. 5 demonstrates the basic simulation process in more
detail. Following the model initializa-
tion, a generator calls a procedure every specied time unit to
handle the queued events in theevent calendar. Such events are
primarily due to the start and the end of rentals and transports.
Generator event_checker
Loo
p
Check_eventMethod rental_end (rental_nr)
Method transport_start (transport_nr)
Get planned rental agreement Assign carUpdate fleet, region,
stationCreate real agreement
Reading Data
Create Model
Start Simulation
Call event
Event Calendar
Method rental_start (rental_nr)
Update fleet, region, station
Get planned transportCheck if transport can be performedUpdate
fleet, region, station
transport_end (transport_nr)Update fleet, region, station
Method
Fleeting, defleetingTransfer between stations (by truck, per
axle)
Fig. 5. Simulation process.
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 285For each event, a corresponding procedure has to be
executed, which adapts the state of the sim-ulation model. During
the simulation every event is recorded and eventually stored in the
data-base together with accumulative data (e.g., revenues, costs).
Report generators produce variousreports for dierent purposes of
logistics management. The simulation model has been imple-mented
using the simulation system eM-Plant from Tecnomatix. By means of
an ODBC interfaceto a relational database, the simulation system
obtains all relevant data and nally writes back thenew state of the
car eet after simulation.
4. Results
Our results are based on data of the German subsidiary of one of
the major international carrental companies. We generalize some of
our ndings from this case study. The problem data ischaracterized
by the following parameters: There are a few hundred stations and
about ten de-pots. The active eet typically includes up to 18,000
cars from 15 car groups. There are up to3000 new rentals
(check-outs) each day. Therefore, we have to consider about 20,000
rental re-quests simultaneously, for a planning horizon of one
week.
4.1. Forecast quality
The parameters of the regression functions introduced in Section
3.2 were estimated on real-world data that cover the past rental
operations for a period of 4 months. Each combinationof some
station, some period (for which we forecast) within a week, the
lead time (between thecurrent period and the period for which we
forecast), and the car group leads to a specic regres-sion
function, which maps the number of reservations to an estimate of
the number of potentialcheck-outs. Despite processing several
gigabytes of data, each least-squares estimate results
fromconsidering only 16 data points (one for each week).The quality
of the demand forecast was evaluated taking into account the
coecient of deter-
mination (r2) and the expected forecast error (s2
p). As an example, we consider the forecast of
rental requests for car group B for a Monday at some large
airport station. Carrying out thedemand forecast on Friday evening
means applying the following regression function: #check-outs =
6.26 + 0.97 * #reservations. This regression function comes with a
coecient of determina-tion of r2 = 0.84 and thus a rather high
correlation between the number of reservations and thenumber of
check-outs. If we need to carry out the forecast already on
Wednesday evening oneexpects that the parameter b is larger than
one taking into account the reservations yet to be re-ceived. This
is conrmed by the following regression function for the described
scenario: #check-outs = 14.06 + 1.21 * #reservations. For this
regression function the coecient of determinationdrops to r2 =
0.49. In the considered scenario, the t-statistics values for the
slope regression coef-cients are 8.5 and 5.0 when forecasting with
a look-ahead of two (Friday) or four (Wednesday)periods,
respectively, which means statistical signicance (assuming a level
of signicance of 99%and a degree of freedom of 14 which corresponds
to a theoretical t-value of 3.0).Fig. 6 illustrates the eects of
the look-ahead period on the forecast quality for the same
scenario as discussed before (with an average number of
check-outs per day of about 45). Theexpected forecast error (
s2
p) approximately doubles throughout the planning horizon of
oneweek. That is, the expected forecast error is critical, at least
for a look-ahead of more than very
-
286 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292few days. (For a look-ahead of more than ve days the
regression becomes statistically insignif-icant.) The situation
worsens for small stations with only a minor number of check-outs
per day.However, such forecast errors partly oset each other with
regard to dierent car groups that mayserve as substitutes due to
upgrades. The same eect is to be expected when aggregating over
dif-ferent stations (in the same district or region). Therefore,
the demand forecast is useful to estimatesuch aggregate demand
values for a planning horizon of one week (which is important to
decideabout eeting and deeeting contingents), while detailed
short-term forecasts for the next fewdays allow balancing supply
and demand at the stations on the basis of planning individual
cartransfers between stations. This is in agreement of using a
rolling planning horizon of one week
0
2
4
6
8
10
12
1 2 3 4 5 6 7Look-ahead [days]
Fore
cast
err
or
Fig. 6. Expected forecast error depending on the look-ahead
period.with a re-optimization each night on the basis of new
data.There are two main options to improve the forecast quality.
First, one may estimate the param-
eters of the regression functions on the basis of a larger data
set (covering complete data aboutoperations of some years), which
should lead to an improved forecast quality. This option
includesapplying medium range forecast models, which would also
allow taking into account eects of sea-sonality, local events, and
specic incentive plans. Second, we observed that information
systems ofcar rental companies often do not include complete
information about all relevant events. Forexample, the sta in small
stations sometimes misses to key-in local reservations into the
global res-ervation system (partly handling them in a paper and
pencil manner). Moreover, not every check-out that is due to a
reservation is actually labelled accordingly, and not all rental
requests that areturned-down at the counter (usually in connection
with a walk-in customer) are recorded. Car ren-tal companies should
generally take action to completely record all relevant business
processes intheir information system, which might substantially
improve the general forecast quality.
4.2. Optimization by means of the network ow model
Beside transportation costs, car holding costs due to the active
eet constitute the main costfactor in car rental operations.
Consequently, the logistics management in car rental companies
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 287generally aims at reducing the eet size as far as
possible and keeping transportation costs to areasonable amount
without inducing too many turned-down rental requests. Even if
loweringthe service level might be protable in the short-term in
certain situations, maintaining a high ser-vice level (e.g., above
99%) is extremely important from a long-term perspective (with
regard tobuilding stable customer relationships and a resulting
strong market share). Under considerationof these essential demands
of practical logistics management we are primarily interested in
meansfor reducing the eet size without signicant negative side
eects. Therefore, we analyze, rst, theeect of applying the network
ow model in comparison to the present manual practices, and,second,
modifying upgrade restrictions in order to increase the overall eet
utilization.A typical problem instance leads to a network ow model
with more than 100,000 nodes and
3,000,000 arcs (variables). The resulting problem instances were
solved by using the network sol-ver of ILOG Cplex (version 6.6).
The data structure of the network model was constructed on thebasis
of real-world data stored in a relational database, which was
accessed through an ODBCinterface, using the programming language
C++ and accessing Cplex in the form of a dynamiclink library (dll).
We used a standard personal computer with an 1.8 GHz CPU and 512 MB
mainmemory. All problem instances considered were solved to
optimality in about 1 min, requiringabout 300 MB of main memory.
That is, computation time is no critical factor for the
scenariosexamined, which allows an integration of the network
optimizer in an interactive decision supportsystem.Assuming demand
forecast data as deterministic data and solving the network ow
model to
optimality for dierent eet sizes should result in an upper bound
for the potential prot increase.However, our analysis of real-world
data has shown that a signicant proportion of check-outs inpractice
are not handled in accordance with the allowed upgrade relations,
which complicatescomparing real-world conditions with results from
the network ow optimization. For example,the comparative assessment
is problematic if in practice up to 10% of rental requests have
notbeen served by a car from a feasible group, while the solution
of the network ow model includesup to 3% of rental requests that
are turned-down fully conforming to the feasible upgrade options.A
deployment plan that conforms to strict rules but turns-down a few
rental requests may be per-fectly adequate if it enables the
station sta to serve these requests by disregarding some of
theserules.We examine the eects of eet size reductions with regard
to the percentage of rental requests
that are turned down as well as the resulting prot change.
Hypothetical eet size reductions aregenerated by applying rules
such as if there are initially three cars of some group at some
station,remove one of these. By using dierent rule sets we created
various reduced eet size scenariosthat match the data points shown
in Fig. 7. The depicted results are typical for various
periodsconsidered in dierent experiments. Starting with an initial
eet size from practice of 100%(e.g., 15,500 cars), according to the
upper diagram one might save more than 20% of the cars(e.g., more
than three thousand cars) before the service level drops below 99%.
That is, in theorywe are able to signicantly reduce the active eet
size without losing a high service level. The lowerdiagram
illustrates the eects of analogue eet size reductions on the
revenue as well as the rev-enue minus the additional transportation
costs (in each case normalized with reference to the rev-enue
obtained for the initial eet size). As may be expected, lost
revenues and additionaltransportation costs are only moderately
aected at the critical point where the service level begins
to drop sharply, since the optimized deployment plan generally
gives preference to the most
-
288 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 27229296.00%
96.50%
97.00%
97.50%
98.00%
98.50%
99.00%
99.50%
100.00%
10000 11000 12000 13000 14000 15000 16000
Fleet size
Serv
ice
leve
l
98.00%
98.50%
99.00%
99.50%
100.00%
ison
to in
itial
reve
nueprotable rental requests. Without disclosing tangible and
detailed revenue and cost gures in thispaper, in our experiments
reductions of car holding costs oset lost revenues and additional
trans-portation costs by a factor of more than ten. Assuming car
holding costs of 10 Euro per day, thisresults in a prot increase of
more than a million Euro per year by means of reducing the
averageeet size by a few hundred cars. The general protability of
the proposed approach even holds ifthe currently suboptimal
forecast quality is taken into account.In order to assess the
impact of upgrades we examine the eect of modifying upgrade
restric-
tions. In comparison to the existing upgrade rules from
practice, we consider two alternative sce-narios. On the one hand,
we prohibit all kinds of upgrades. On the other hand, we use
thetransitive closure of upgrade options in the sense that a rental
request may be served by anycar with a quality that is not lower
than the requested car group. Fig. 8 shows that the possibilityof
granting upgrades is crucial to achieve a high service level. In
case that one enables all conceiv-able upgrade options, the eects
on the service level and resulting prot gures are slightly betterin
comparison with present practices. Consequently, more upgrade
exibility constitutes an op-tion for increasing protability in
connection with an improved eet utilization. However, notethe
possible long-term aspects of loose upgrade rules. Namely, if the
probability of being granteda valuable upgrade is high enough,
customers might be tempted to make reservations for cargroups of
lower quality than actually wanted, which results in overall
revenue degradation.
96.00%
96.50%
97.00%
97.50%
10000 11000 12000 13000 14000 15000 16000Fleet size
Red
uctio
n in
com
par
Revenue Revenue - transportation costs
Fig. 7. Inuence of eet size reductions.
-
90.00%
ice
lev
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 28975.00%
80.00%
85.00%
10000 11000 12000 13000 14000 15000 16000
Fleet size
Serv
98.50%
99.00%
99.50%
100.00%
100.50%
101.00%
venu
e m
inus
tran
spor
tatio
n co
sts
Normal upgrades All upgrades95.00%
100.00%el
Normal upgrades All upgrades No upgrades4.3. Validation per
simulation
We analyzed the eects of implementing the car logistics plan
from the network ow model bysimulation experiments. As a basis for
comparison we used the simulation model to replay rentaland
logistics processes of periods of one week based on historic data.
With regard to this referencemeasurement, we validated optimized
car logistics plans by assessing the results in comparison toboth
the historic processes as well as the network ow scenario.We found
that the general potential for improvement due to the network ow
optimization is
conrmed by results from simulation experiments. As an example,
some simulation experimentfor a given week may result in an
approximate revenue of 3 million Euro and transportation costsof
less than 100,000 Euro. Removing one thousand cars from the active
eet, and simulating thesame seven day period on the basis of the
car logistics plan generated by the network ow model,essentially
led to a rental service level of 99.9% with about the same
transportation costs and anacceptable upgrade ratio of about
16%.
5. Decision support system
In Fig. 9 we propose the system architecture of a car rental
logistics decision support system.We distinguish between a core
system database and an events database. Core data are xed over
a
98.00%10000 11000 12000 13000 14000 15000 16000
Fleet size
Re
Fig. 8. Inuence of upgrade rules.
-
- holding cost/period- fleeting/defleeting date
290 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292Events Database
Reservation/Rental/Transport: - check-out station/date -
check-in station/date - car group/extras
Car Status:- on yard- on rent- on transport
Data Warehouse
Strategic Planning
EvaluationAnalysis Tools
Logistics Planning Process
Tactical-operational Planning
Forecast
OptimizationSimulation
Decision Support System
DatabaseManagementSystemFleetInformation:
- id- group/type
NetworkStation/Depot/Region:
- name/id- location
Core System Databasecertain period (such as the station network,
car groups with holding costs, and basic informationabout the cars
in the active eet). Data about incoming reservations, check-outs
and check-ins,and the start and end of transports are stored in the
events database.In addition to the described logistics planning
process, we propose the implementation of a data
warehouse that stores aggregate data for further processing by
appropriate analytical tools. Onthe one hand, resulting insights
(e.g., with regard to the protability of specic stations or the
con-tribution of dierent customer segments) will be a valuable
input for strategic planning. On theother hand, aggregate data
(e.g., concerning empirical distributions for the length and
reliabilityof transportation processes or probabilities for the
unexpected extension of the rental length) mayalso be used in the
logistics planning process. In particular, the data warehouse may
provide long-term data for enhancing the demand forecast model.
6. Conclusion
In this paper we considered logistics management in the car
rental business. After giving anoverview of car rental operations,
we presented a novel quantitative decision model to ecientlysolve
short-term car rental logistics problems by means of network ow
optimization. Our deci-sion model includes essential practical
aspects such as multi-period planning, a country-widenetwork,
specic transportation relations, eeting and deeeting, and dierent
car groups.Experiments were conducted on substantial real-world
data, using a simulation model to assess
Fig. 9. Architecture of a car rental logistics decision support
system.
-
A. Fink, T. Reiners / Transportation Research Part E 42 (2006)
272292 291optimization results for dierent scenarios. Our
experience from an industry research project indi-cates that the
approach can signicantly improve prots by reducing the costs for
the eet of carsand limiting transportation costs.From a practical
point of view, the crucial requirement for the implementation of
our approach
is the availability of an integrated information system with
data about the current state of the ren-tal system as well as a
sensible short-term demand forecast model. From a methodological
pointof view, modeling and solving the problem by means of a
multi-commodity network ow formu-lation may pose an interesting
research subject. In such a model, dierent commodity types
rep-resent the various car groups. As rental requests can be served
by dierent car groups according tothe allowed upgrade relations,
the sum of respective ow variables is linked to corresponding
de-mand data. Because of the large network size, special techniques
such as DantzigWolfe decom-position and Lagrangian relaxation may
have to be exploited to solve the problem to optimality ina
reasonable time horizon; cf. Kennington and Helgason (1980) or
Minoux (1986).A crucial question of car rental logistics is the
degree of central vs. local planning. Implement-
ing a nation-wide car logistics plan restricts the degrees of
freedom for local actions. On the onehand, our proposal
intentionally does not prescribe the operations in the stations
during thecourse of the dayin particular, we do not recommend
centrally assigning specic cars to custom-ers. However, our
empirical experience is that local planning of car transfers often
leads to anuncoordinated and inecient use of the rental network
resources. The local cause for car transferscan only be avoided by
means of an eective car logistics planning and implementation,
whichprovides the stations with adequate availability of cars
throughout each day. Central planning de-pends on the availability
of rather complete and accurate data in information systems. The
qualityof data can be improved by technical and organizational
measures. From a technical point ofview, the use of transponder
systems and the global positioning system may contribute to
theautomatic representation of the status of each car at each time
in the information system. More-over, the planning and execution of
car transportation via truck in collaboration with externalshipping
companies requires online interfaces between relevant information
systems. From anorganizational point of view, there are two main
sources of information that we have to deal with:the customers and
the companys sta in rental stations. For both we need to introduce
reasonableincentives for making available their mental knowledge as
data in the information system.To increase the information about
short-term demand, one must think about incentives for cus-
tomers to make serious reservations in advance. Today,
reservations are usually not binding oneither side, which means
that customers often make reservations at dierent car rental
companiesand eventually select only one (e.g., by entering the rst
station with an empty queue at the coun-ter upon arrival at the
airport). For a car rental company it is dicult to introduce
penaltycharges for no-shows. First, non-binding reservations are
the norm in the car rental business. Sec-ond, if a customer expects
that enough cars are available at the station even without a
reservationthe customer might be tempted to refrain from making
reservations. Therefore, car rental compa-nies generally strive to
make it as easy as possible to make reservations (e.g., by phone or
by web),in combination with incentives such as the possibility of
being granted an upgrade (which is notpossible for walk-in
customers).Considering the station sta, a strong negative incentive
to key-in information about a check-in
may arise in case that the station sta must reckon with a
decision from central planning that a
particular car (e.g., an attractive sports car which might
attract additional walk-in customers) will
-
soon be transferred to a dierent station. However, the check-in
must eventually be keyed-in withthe correct check-in time. Thus, if
station performance is measured by taking into account thecosts of
unutilized cars the station sta may indeed strive to properly enter
data about the avail-ability of this car for the general network as
soon as possible. In this respect we draw attention tothe
importance of a deliberate measurement of station performance by an
incentive-compatibleassignment/sharing of costs (in particular,
holding and transportation costs) and revenues inthe context of
intertwined central and local decisions. This poses a rather
complex problem, which
Pachon, J.E., Iakovou, E., Ip, C., Aboudi, R., 2003. A synthesis
of tactical eet planning models for the car rental
industry. IIE Transactions 35, 907916.
292 A. Fink, T. Reiners / Transportation Research Part E 42
(2006) 272292Spieckermann, S., Vo, S., 1995. A case study in empty
railcar distribution. European Journal of Operational Research
87, 586598.is even more true in the case of licensees, which
might over-exploit resources of the franchise sys-temin this case
by stockpiling cars of otherswhile under-investing in own resources
(see, e.g.,Dnes, 1996 for a general economic analysis of franchise
systems).
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Modeling and solving the short-term car rental logistics
problemIntroductionProblem descriptionNetwork and
fleetRentalsLogistics processes
Modeling and solving the car logistics
problemSupplyDemandNetwork flow modelSimulation model
ResultsForecast qualityOptimization by means of the network flow
modelValidation per simulation
Decision support systemConclusionReferences