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A realisation of an apartment dynamic pricing system

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Revenue management (RM) has been successfully employed by diverse industries to utilise vast data warehouses to forecast demand and supply and price products to maximise profits. The apartment industry, however, represents a new frontier for RM. This industry shares many characteristics with the hotel industry, but presents new challenges such as extremely long lengths of stay and relatively small transaction density. The objective of this paper is to introduce the implementation of an apartment dynamic pricing system with particular emphasis on setting optimal rental rates for new leases. Optimal rental rates are recommended as weekly rates based on unit type and lease term for a finite horizon of future weeks. This paper studies the characteristics of apartment firms, and discusses similarities and differences between the apartment and hotel industries from an RM point of view. It then provides the overview of an apartment dynamic pricing system, followed by a detailed description of its modules. Finally, it concludes with ideas for future enhancement to the system.Journal of Revenue and Pricing Management (2008) 7, 256-265. doi:10.1057/rpm.2008.11 Published online 22 February 2008
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A realisation of an apartment dynamic
pricing system
Jian Wang
n
Received (in revised form): 1st October 2007
n
Rainmaker Group, 5755 North Point Parkway, Suite 77, Alpharetta, GA 30022, USA
Tel: þ1 678 578 5704; E-mail: jwang@LetItRain.com
Jian Wang is Vice President of Research and
Development at the Rainmaker Group, which
develops pricing solutions for gaming resorts
and multi-family housing industries. He has
more than ten years of experience in designing
and building diverse pricing and revenue
management systems. Jian was principal
scientist and developer at Archstone-Smith
and Talus Solutions (now JDA). He has
published several papers in professional jour-
nals. He holds an MS in applied mathematics
and PhD in statistics from Clemson University.
ABSTRACT
KEYWORDS: apartment, dynamic pricing,
implementation, unconstrained demand
Revenue management (RM) has been successfully
employed by diverse industries to utilise vast data
warehouses to forecast demand and supply and
price products to maximise profits. The apartment
industry, however, represents a new frontier for RM.
This industry shares many characteristics with the
hotel industry, but presents new challenges such as
extremely long lengths of stay and relatively small
transaction density. The objective of this paper is
to introduce the implementation of an apartment
dynamic pricing system with particular emphasis on
setting optimal rental rates for new leases. Optimal
rental rates are recommended as weekly rates based on
unit type and lease term for a finite horizon of future
weeks. This paper studies the characteristics of
apartment firms, and discusses similarities and
differences between the apartment and hotel industries
from an RM point of view. It then provides the
overview of an apartment dynamic pricing system,
followed by a detailed description of its modules.
Finally, it concludes with ideas for future enhance-
ment to the system.
Journal of Revenue and Pricing Management
advance online publication, 22 February 2008;
doi:10.1057/rpm.2008.11
INTRODUCTION
An important and fundamental decision apart-
ment owners and operators have to make
frequently is to set ‘appropriate’ rental rates
for new and renewal leases. New leases are
signed by prospective tenants who make
advance reservations to lease an exposed unit
for a pre-determined number of months.
Exposed units are those units that are either
being vacant or to be vacant that the current
residents have given notice to move out but no
pre-leases have been signed yet. Renewal leases
apply to existing residents who are renewing
their current leases that are about to expire.
In traditional apartment management, ap-
propriate rents are often set with the objective
of maximising both occupancy and return on
investment. Rent is normally based on factors
such as the physical characteristics of a property,
its current vacancy rate and competitive
position in the marketplace, along with man-
agers’ prior experience. There is a variety of
literature addressing traditional apartment
rent setting. Sirmans and Benjamin (1991) per-
formed an extensive literature review regarding
apartment rent setting. Pagliari and Webb
(1996) built a regression model to set rental
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rates based on rent concessions and occupancy
rates. Among the existing literature, to our
knowledge, no effort has ever been made to set
rates to maximise total revenue growth.
Revenue management (RM) has emerged as
an alternative methodology in setting appro-
priate rental rates. ‘Appropriate’ is defined in
terms of RM as the optimal rental rates that
achieve maximum revenue for the apartment
firms. An apartment revenue management
system (RMS) is an application of RM
principles to the apartment industry to provide
an automated approach to setting optimal rental
rates in a systematic and informed manner. A
vast array of service industries has successfully
developed proprietary RMSs, but the apart-
ment industry represents a new frontier for
RM. The sophistication of an apartment RMS
varies with its capabilities, which range from
setting optimal rents for new and renewal leases
to evaluating the system’s performance. Unlike
the travel and hospitality industries, very few
papers related to apartment RMSs can be
found in the existing literature. Davidoff
and Small (2003) provide an overview of
the apartment RM concept by comparing the
hotel and apartment industries, suggest steps
that apartment firms need to take to implement
an RMS and predict the future of apartment
RMS software products.
The objective of this paper is to describe the
implementation of an apartment dynamic
pricing system with particular emphasis on
setting optimal rental rates for new leases. This
system has been helping leading apartment
operators offer prospective tenants a menu of
rent options that are set daily and expressed as
unit types, move-in weeks and lease terms.
In implementing this system, customers are
not explicitly differentiated at the time when
their requests are being made. They are instead
implicitly classified by their purchase behaviour
such as the desired times of year for move-in
and lease terms. It is important to point out that
fair housing laws generally require that two
people being offered the same product (eg unit
type, move-in date and lease term) at the same
time essentially must be quoted the same rates.
This legal restriction makes traditional market
segmentation approaches inappropriate. Custo-
mers are thus distinguished by a quote rate at
which they are willing to pay. In other words,
this system manipulates rent as the only variable
to encourage or discourage demand. Three
factors that influence the rent are considered in
the system: the capacity of the apartment, the
demand arriving process and the market
competition.
The remainder of this paper is organised as
follows: it starts with a study on the character-
istics of apartment-rental firms from an RM
point of view. Since apartment-rental firms are
in many ways similar to hotel firms, this study is
performed through a comparison of the simila-
rities and differences between the two industries.
It then outlines the system, followed by a
detailed description on the individual modules
of the system. Finally, it concludes with ideas for
further improvement of the system.
CHARACTERISTICS OF
APARTMENT-RENTAL FIRMS
On the surface, the apartment industry shares
many characteristics with the hotel industry.
Since the hotel industry has been successfully
using RM techniques for a number of years, it
would be of great benefit if the apartment
industry can simply adapt existing RM techni-
ques from the hotel industry. In this section, we
study the characteristics of apartment-rental
firms by noting the similarities and differences
between the apartment and hotel sectors from
an RM viewpoint.
It is obvious that both apartment and hotel
industries share the following characteristics:
Perishable products. Both offer rooms with
multiple types as products for customers to
stay in for a certain length of time. These
products are perishable in the sense that
occupied units have certain value (rental
income) until the moment they become
vacant. After that point, they are worthless
until they are occupied again.
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Realisation of an apartment dynamic pricing system
Constrained supply. Both face supply con-
straints. In other words, both have a
relatively fixed capacity with diverse room
types. When demand exceeds current in-
ventory, it would be almost impossible
to replenish extra inventory in a short
period of time to meet the demand. This
kind of situation, however, creates an
opportunity for market segmentation, and a
price structure that attracts more customers
who are higher on the ‘willingness to pay’
spectrum.
Advance consumption decisions. Consumers
routinely reserve the product before they
use it.
Censored demand observations. Both demand
processes are stochastic, and observations
are likely to be censored or constrained
due to product availability and/or pricing
constraints.
While it might not be obvious, the apartment
industry distinguishes itself with its own unique
features:
Longer lengths of stay. The most obvious
difference between hotel and apartment-
rental firms is that apartments have extremely
long length of stay. Hotel guests usually stay
just days, while apartment residents typically
stay for months. A hotel RMS can create
pricing strategies to dynamically control a
guest’s length of stay. Doing so enables a hotel
to avoid losing a week-long customer because
it already sold too many one-night stays. An
apartment-rental firm can also vary lease terms
to maximise value, but not to the same degree
as hotels, due to the inherent characteristic of
the lower volume of transactions. In addition,
the characteristic of a long lifecycle of product
consumption in the apartment industry has
added extra modelling complexity. For exam-
ple, an apartment RMS has to take into
account the diverse likelihoods of customer
behaviour, such as early termination of leases,
due to its longer-length-of-stay characteristic.
On the contrary, a hotel RMS often focuses
on customer behaviours prior to product
consumption because of the relatively short
average length of stay.
Fewer transactions. In contrast to the hotel
industry, an apartment-rental firm has less
traffic and thus fewer transactions. For every
hundred transactions that an apartment firm
has, a hotel may have thousands. An RMS is
a statistically based system. The more the
data we have, the more accurate the system
will be. In the implementation of any RMS,
the transaction data are often aggregated into
certain levels on which the data share a set of
common attributes. When the number of
levels increases, the amount of data in each
level would decrease. This kind of situation
with sparse data will prevent us from
obtaining accurate estimates. This problem
is also known as the ‘curse of dimensionality’
(Ha
¨rdle, 1990).
No repeat customers. An apartment firm rarely
sees the same resident move back in again
once he/she moves out. In contrast, it is
common for a hotel to see repeat customers.
In order to better accommodate these
customers, the concept of customer relation-
ship management has been proposed to
integrate with the existing RMS in some
hotel firms (Noone et al., 2003).
More renewals. Hotel firms rarely have
‘renewals’. Most of their guests stay for the
exact number of days as they have planned
before. It is uncommon for them to ‘extend’
or ‘renew’ to stay extra nights. It is, however,
very common for apartment tenants to
extend their stays. Apartment customers
often make monthly payments for a period
of time and then decide whether to
re-commit for another term at the same or
different rate.
More risky decisions. With typical hotel
transactions usually being a length of stay
no more than one week, each transaction
only represents a very small fraction of a
hotel’s total annual inventory. In contrast,
a typical apartment lease often represents a
length of stay for months. It ties up a much
larger portion of the firm’s total annual
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Wang
inventory. In addition, in the apartment
universe, the initial lease price influences the
subsequent rate and probability of a renewal.
Therefore, each apartment transaction is
more important and more risky than a
typical hotel transaction.
No group booking. Group booking is very rare
for apartment firms, but it happens often
with hotel firms when conferences are held
or groups of vacationers arrive. A hotel
RMS has to integrate some group optimisa-
tion functionality to decide if it is profitable
to accept a group booking or not.
No over-booking. Over-booking is a well-
studied and widely used technique to assure
the maximum utilisation of inventory in
hotel and airline RM industries. The
applicability of this technique is critically
built on a specific business practice: the
separation of a reservation from a particular
room or seat. For instance, when a guest
books a hotel room, he will not be assigned a
room number until he checks in. However,
this kind of practice does not prevail in the
majority of apartment firms. When prospec-
tive residents make a reservation, they are
typically given the unit numbers that they
will move into later. This kind of situation
makes it difficult for an apartment firm to
adapt the over-booking technique. Luckily,
no-shows or cancellations happen less fre-
quently in apartment industry, in which
over-booking becomes less critical.
No walk-ins. In the hotel industry, a
significant number of customers often walk
in and check into rooms on the same day.
This walk-in situation has added complexity
to demand forecasting. In order to get
accurate demand prediction, a hotel RMS
often updates demand forecasting more
frequently. Apartment firms rarely have
walk-in customers. This allows for less
frequency to perform demand forecasting.
Concessions. Apartments may offer ‘conces-
sions’ as incentives to attract and retain
customers. Typically, there are two kinds of
concessions: upfront and recurring. Upfront
concessions are offered when the customers
sign new leases, such as ‘free rent for the first
month’. Recurring concessions are amor-
tised evenly over the entire period of stay
after customers have moved in, such as ‘$50
off each month’. In the implementation of
an apartment RMS, often the ‘base effective
rents’, which are the net rents without
amenities and concessions, are considered.
This examination shows that apartment-rental
firms lack the characteristics of over-booking,
group booking, repeat customers and walk-ins
that hotel firms have; but it would be deceptive
to conclude that it is easier to implement an
apartment RMS than a hotel RMS. The distinct
features of a low volume of transactions, long
lengths of stay and extended decisions during
consumption in the apartment industry present
new challenges to traditional RM methodolo-
gies used in hotels and other industries.
To our knowledge, very few papers in the
literature deal with the issue of these features.
Lieberman (2004) points out the similar issue
of a low volume of transactions in ‘nontradi-
tional’ RM industries, such as commercial real
estate and self-storage, which have started to
explore RM opportunities.
MODULES
The levels of demand, inventory and market in
the apartment sector vary over time, and
managers are forced to act or react by dynami-
cally adjusting rental rates as uncertainty reveals
itself. This system described here is thus
modelled to forecast demand, inventory and
market changes over a finite planning horizon,
and to apply an estimation of price elasticity
of demand to explore the opportunity to
optimally set rental rates.
Specifically, this dynamic pricing system
formulates and solves a mathematical program-
ming problem in an attempt to optimally
balance demand and inventory while taking
into account the market situation. This system
can be regarded as the stochastic version of
‘dynamic price model with multiple products’
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Realisation of an apartment dynamic pricing system
(Bitran and Caldentey, 2003), with an exten-
sion to market competition.
The system consists of seven interdependent
modules: Data Aggregator, Statistics Updater,
Supply Forecaster, Demand Forecaster, Refer-
ence Rent Calculator, Rent Optimiser and
Rent Recommender. It can be operated in a
user-defined frequency, typically being in daily
batch run or on demand. Figure 1 illustrates the
relationships among these seven modules.
In this section, we describe the functionality
of each individual module. We begin our
description with the Data aggregator module.
Data aggregator
The Data aggregator is the critical link between
legacy property management systems and the
RMS. It defines and builds the basic data
elements that will be used by other modules. A
data element is the most discrete and con-
trollable unit that the system will deal with. It is
characterised by three dimensions: unit cate-
gory, lease term category and move-in week.
Unit category is defined as the collection of
apartment units with a common property-
specific attribute such as the number of
bedrooms.
Lease term category is defined as the bucket
of lease terms, which is similar to the length of
stay in a hotel RMS. It is also property-specific.
For instance, we can define three lease term
categories: short, medium and long. Short
may contain the lease terms of 1–3 months,
medium terms of 4–9 months and long terms
of 10 þmonths.
Move-in week is defined as the ‘week’
when a prospective resident would move in.
The meaning of week is not necessarily a
calendar week. For example, move-in week
could be defined as the days from Thursday to
Wednesday. Furthermore, it can also be
characterised by week type and month type
Data Aggregator
Stats Updater
Reference Rent
Calculator
Rent
Recommender
Rent Optimizer
Demand
Forcaster
Supply Forecaster
Figure 1: Module relationships
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Wang
attributes. A week type can be defined as the
beginning, middle or end of a month. It is
analogous to the day of week commonly used
in a hotel RMS. In a similar manner, a month
type can be defined accordingly.
Based on the three data dimensions defined
above, transaction data from an apartment’s
property management system will be fetched
and aggregated periodically. The system takes
into account a number of transaction types such
as move-ins, move-outs, notice-to-move-outs,
guest cards, leases, etc. These transaction data
will be used in the calculation of demand
forecast, supply forecast and business statistics.
Two kinds of transaction data are described:
guest cards and leases.
A guest card transaction records what a
prospective tenant prefers. Guest card informa-
tion may include the desired move-in and
move-out dates, the preferred unit type, the
monthly rents and concessions offered, and so
on. A guest card is said to be realised when
the prospect signs a lease and becomes a tenant.
A realised guest card is always tied to a
particular apartment unit. On the other hand,
a guest card is said to be unrealised when the
prospect does not sign a lease. Any unrealised
guest card is not associated with any particular
apartment unit.
A lease transaction represents a realised guest
card and records the action of a resident. A
lease transaction contains information such as
the apartment unit number that the resident
leases, the actual move-in and move-out dates,
the number of months of the lease term and so
forth. A lease transaction always associates the
resident with a specific, dedicated unit.
A wide variety of information can be
derived from the aggregated transactions,
including the numbers of guest cards, move-
ins, move-outs, early terminations, available
units and so on.
Statistics updater
The Statistics updater module estimates a
number of business statistics based on the
aggregated historical data. Each of the statistics
is estimated in the appropriate dimensions of
aggregation such as unit category, lease term
category, week type and month type. These
statistics are used for two purposes. One is to
provide an informed description of how
business has been recently, the other is to feed
the statistics produced by the module into the
subsequent modules.
The business statistics estimated by the
module include:
Demand and rent seasonality, which depict
the effects of different seasons on demand and
rent. Apartment reservation data commonly
exhibit a high degree of seasonality. For
instance, demand during the summer season
usually appears higher than other seasons in
the northern markets.
Demand average, which represents the
estimates of the average de-seasonalised
demand by removing seasonal factors.
Booking pace curve, which characterises the
pace at which demand arrives during the
booking horizon by days left prior to a
move-in week.
Early terminations, which estimates the
number of leases that might be terminated
early.
Renewal fraction, which approximates the
fraction of expiring leases that are likely to
be renewed.
Average lease term, which describes the
average length of lease terms.
In estimating each of these statistics, observa-
tion data are pooled in a proprietary approach
in an attempt to circumvent the data sparseness
issue. It is worthwhile to address the issues of
demand unconstraining.
Demand seasonality, demand average and
booking pace curve statistics all use the data of
unconstrained demand. Data censoring is
commonly seen in RM. For example, Liu
et al. (2002) list three censoring constraints:
capacity limitation, stay controls and rate
controls. There are a variety of papers that
address the issue of demand unconstraining.
Talluri and Van Ryzin (2004) review some
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Realisation of an apartment dynamic pricing system
parametric and nonparametric approaches to
correcting censored demands.
Although demand unconstraining has be-
come an important process in RM practice, no
rigorous definition of unconstrained demand
has been given in the literature. Unconstrained
demand is often described as the ‘true’ demand
that would be satisfied if there were no
censoring limitations within a rate class. Under
the context of dynamic pricing RM however,
this description seems inappropriate, because
no specific rate classes are defined and used.
Therefore, to meet our needs, we define
unconstrained demand as the demand for the
reference rent that would be realised if there
were no capacity limitation. In other words,
unconstrained demand would be observed
when inventory were available and the offered
rate happened to be the same as reference rent.
Reference rent is defined here as the ‘economic
value’ of an apartment unit in the marketplace,
which is often perceived from the viewpoint of
an apartment operator. It is analogous to the
concept of ‘rack rate’ in the hotel industry. The
actual rental rates offered are often optimised
around the reference rents.
Denote d(t,r) as the unconstrained demand
for the reference rent rat time t. Given the
definition of unconstrained demand above, it
would be easy to identify a censored demand if
the reference rent were known. In reality,
however, the reference rent is unknown. We
use r
ˆto denote its estimate. In the ‘Reference
rent calculator’ section below, we describe how
to estimate the value of r
ˆ
. In addition, denote p
as the offered rate at time t, which is observable
and known. An estimator for unconstrained
demand d(t,r) can be expressed as follows:
^
dðt;^rÞ¼ ^
Dðt;pÞGð^r;pÞ
where D
ˆ(t,p) represents the estimate of un-
constrained demand for the offered rent p,
which is only censored by the capacity
limitation. G(r
ˆ
,p) is the estimate of the price
elasticity effect, comparing the offered rent p
with the estimate of reference rent r
ˆ
.
Note that although the estimation of d
ˆ(t,r
ˆ)
involvestheuseofthepublishedratep,weexpect
that a good estimate of d
ˆ(t,r
ˆ) should be invariant
of the value of pused. In addition, D
ˆ(t,p)and
G(r
ˆ
,p) should be nonincreasing and nondecreas-
ing, respectively, when pincreases for a fixed r
ˆ
.
The estimation of D
ˆ(t,p) can adapt some
existing unconstraining approaches such as the
expectation maximisation method (Dempster et
al., 1997). The estimation of G(r
ˆ
,p), on the
other hand, relies on the underlying assump-
tion of elasticity model. When elasticity b(o0)
is assumed to be constant, one approach to
estimate G(r
ˆ
,p) can be formulated as
Gð^r;pÞ¼1b1
^r
p

It can be easily seen that G(r
ˆ
,p)¼1 when
p¼r
ˆ;G(r
ˆ
,p)>1 when p>r
ˆ; and G(r
ˆ
,p)o1 when
por
ˆ
. In addition, it can be shown that this
function of G(r
ˆ
,p) is increasing with respect to
pas expected.
Demand forecaster
The Demand forecaster module predicts the
remaining unconstrained demand for a finite
planning horizon, which will be fed to the
Rent optimiser module. A remaining uncon-
strained demand forecast represents the level of
demand that will arrive at the reference rent,
disregarding the constraint of inventory avail-
ability. An important virtue of demand is based
on the assumption that customers making
reservations may identify themselves by three
quantities: the booking day, the length of stay
and the move-in week.
It is well known that forecasting accuracy
will significantly impact the profits of the
RM industry. Research on the appropriate
RM forecasting techniques has thus received
extensive attention from both academic and
industrial researchers; but most of the published
papers are related to hotel and other RM
industries. At the time of this writing, no
literature on forecasting modelling has been
found for the apartment industry. The inherent
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Wang
problem of data sparseness in the apartment
RM industry presents challenges to finding the
appropriate RM forecasting techniques.
A heuristic forecasting model is used to
predict the unconstrained remaining demand on
the level of unit category, lease term category
and move-in week. The basic assumption
underlying this model is that a similar pace of
historical demand would be followed. This
modelling procedure is similar to the methodol-
ogy of pick-up forecasting strategy (Talluri and
van Ryzin, 2004), but is formulated in top-
down manner. The idea behind the pick-up
method is to predict incremental bookings over
short intervals of time prior to service based on
recent booking activity, and then aggregate these
increments to obtain a forecast of total demand
to come. On the contrary, our method estimates
the total demand and then disaggregates the
remaining demand based on related statistics.
Supply forecaster
The Supply forecaster module predicts the
numbers of units available for lease for a finite
horizon of future weeks. This module does not
take into account an over-booking strategy as
in the hotel industry. Specifically, the weekly
inventory for a given future week is equal to
the number of capacity minus the number of
units to be occupied, plus the number of units
to be vacant.
The units to be occupied represent those
units that will be dwelled by both current
residents and prospective tenants. The prospec-
tive residents here consist of either new leases
to be signed or renewal leases to be extended.
The number of renewal leases is estimated by
applying the statistics of renewal fraction to the
number of expiring leases from current or
future residents. The units to be vacant, on the
other hand, denote any occupied units that
might become available due to any early
termination of leases.
Reference rent calculator
The Reference rent calculator is a module to
estimate reference rents. From an apartment
RM aspect, setting reference rents establishes
the base threshold around which optimal rental
rates will be determined. In other words,
optimal rents will be derived from reference
rents as the result of balancing demand and
supply under the objective of maximising
revenue growth.
In actual implementation, the reference
rents for the current day are estimated on the
level of Unit Category and Lease Term
Category, which will be projected into future
Move-in Weeks by using the rent seasonality
statistic. A number of methodologies can be
used to estimate the reference rents. One
method can be to use surveys along with
expert judgment, but this approach tends to be
subjective, costly and biased. An alternative is
to utilise a rule-based approach. This method
utilises a set of business rules based on the
values of some specific indicators. The indica-
tors are selected to better reflect the reality of a
property and its competitive influences. The
use of indicators breaks the limitation of a
traditional RMS to rely on internal data only.
Two main indicators are described as follows:
Market composite, which reflects current
market pricing. Estimating market composite
involves identifying the ‘right’ competitors,
shopping their current rates, positioning their
rates and weighing their relative importance.
This indicator enables an apartment firm to
understand and respond to customer beha-
viour in an informed manner.
Leasing velocity, which gauges the speed that
exposed units are being leased. For instance,
if the value of the leasing velocity is too high,
that is, the exposed units are being leased too
fast, it is reasonable to suspect that the price
being offered may be too low.
It is worthwhile to emphasise that the con-
sideration of leasing velocity is helpful. Market
composite merely reflects the external market
changes. By only taking into account this
indicator, we are unable to justify the estimated
reference rents, especially when the estimation
of market composite is skewed.
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Realisation of an apartment dynamic pricing system
An extreme example is to assume that all
competitors were making an irrational decision
by dramatically dropping their rents. The
corresponding market composites would be-
come small, which could thus produce low
reference rents. When considering the perfor-
mance of leasing velocity however, if we see
that units are already being leased too fast, we
might not want to follow our competitors to
decrease the reference rents. That is, we now
have an additional indicator to validate the
rationality of this rate decrease.
The addition of leasing velocity is in essence
an attempt to fine-tune the estimation of
reference rents. It protects us from the
abnormal changes of outside world. Further-
more, we will see that leasing velocity also
complements the restrictive capability of Rent
optimiser in the next section.
Rent optimiser
The Rent optimiser module calculates opti-
mised rents, from which the optimal rental rates
will be derived in the Rent recommender
module.
This module formulates a revenue optimisa-
tion problem. It attempts to set optimal rental
rates around projected reference rents by
balancing demand and supply forecasts. A
crucial element embedded in the module is
the use of price elasticity. Denote r
ˆas the
estimate of reference rent and d
ˆits correspond-
ing unconstrained demand. When elasticity
b(o0) is assumed to be constant, the optimised
rent pand its corresponding demand dwill
satisfy the following relationship:
p¼Dð^r;
^
d;d
;bÞþ 11
b

^r
where D(r
ˆ
,d
ˆ,d,b) represents the amount of
rate change, which is a monotonically decreas-
ing function of d. In particular, D(r
ˆ
,d
ˆ,d,b)
tends to be zero as d-0 and approaches to
Nas d-þN.
The range that optimised rents can vary is
limited by the values of elasticity. It can be
shown that the upper bound of optimal rents in
the above model is (1/b)r
ˆ
. According to this
relationship, if the reference rents are set too
low, the optimised rents cannot be adjusted as
high as desired by this Rent optimiser module.
In other words, the use of elasticity requires
that reference rents be appropriately estimated.
For the example in the above section, it can be
seen that the addition of leasing velocity does
indeed help improve estimating reference rents,
which will thus enhance optimised rent setting.
Rent recommender
The optimised rates computed from the Rent
optimiser module are in the aggregation level of
unit category, lease term category and move-in
week.Inactualleasingoperations,however,pro-
spective customers are offered optimal rates in the
form of unit type, lease term and move-in week.
The Rent recommender module recommends
optimal rents by disaggregating optimised rents.
Note that different pricing requirements on
the distribution of optimal rates across unit
types and lease terms can result in different
disaggregating procedures. For example, one
common pricing policy specifies that the
optimal rates should be distributed in inverse
proportional to the lengths of lease terms. That
is, the longer the lease term is, the cheaper the
optimal rent should be.
CONCLUSION
This paper describes the realisation of an
apartment dynamic pricing system with parti-
cular emphasis on setting optimal rental rates
for new leases. This system has been success-
fully used in production environments by
several leading apartment operators for years.
An average of a 3 per cent revenue increase has
been reported by these apartment operators.
This system can be further enhanced by
employing the following two aspects:
Expiration management. Some apartment
operators have expressed a strong interest in
controlling the duration of the residents’ stay
more effectively. Specifically, they want to
leverage pricing mechanisms to influence
&
2008 Palgrave Macmillan Ltd, 1476-6930 $30.00 1–10 Journal of Revenue and Pricing Management 9
Wang
prospective residents’ preferences in choosing
the lease terms to stay. As a result, more leases
could be encouraged to expire during peak
demand seasons (eg summer) so that addi-
tional demand at that time can be accom-
modated, at a corresponding higher rental
rate. Similarly, fewer leases could be encour-
aged to expire during off-peak seasons
so that there will be less risk to waste vacant
units.
Performance measurement. Monitoring system
performance closely always enables analysts
to identify and solve issues early. For
example, it would be very valuable to
measure the accuracy of the demand forecast.
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&
2008 Palgrave Macmillan Ltd, 1476-6930 $30.0010
Realisation of an apartment dynamic pricing system
... Apartment communities belong to the service industry, but they have their own characteristics (Wang 2008). For example, the duration of a tenant is continuous. ...
... In traditional apartment management, rents are often set with the objective of maximizing occupancy and return on investment. Rents are normally determined by such factors as physical characteristics of a property, its current vacancy rate and competitive position in the market place, along with managers' prior experience (Wang 2008). Sirmans and Benjamin (1991) performed an extensive literature review about the setting of apartment rents. ...
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S ummary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
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