Transcript Them demand of car accommodations ,coach seats and sleepers

Journal of revenue and Pricing Management
Soheil Sibdari, Kyle Y.Lin
and Sriram chellappan
Received (in revised
from ):25th July ,2007
Multiproduct revenue management
An empirical study of Auto Train
at Amtrak
指導老師:李治綱博士
學生:陳慧瑛 N97D0021
Amtrak
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。
Amtrak鐵路公司是美國國營鐵路公司, 1971 年成立
每天有 265 輛列車在營運,列車行駛的路線橫越美國的 45 個州，所停靠
的車站也超過 500 個，每年運送城市裡的乘客數量和通勤者人數超過
7,500 萬人次。
傾斜技術在列車行駛到轉彎路段時一樣能夠很平順，讓乘客在搭乘這輛
列車時一路都感到非常舒適。
preface
• Amtrak that allows passengers to bring their vehicles on the
train
• Involves working with Amtrak ,provides the sales date of Auto
Train
• From the sales data ,built a mathematical model to develop a
pricing system for auto train.
• An algorithm was developed to calculate the optimal pricing
strategy that yields the maximum revenue .
• Introduced three pricing policies :
Myopic policy (seller ignores the effect of its current pricing ) –
– Static-price heuristic
– Pseudo-Dynamic heuristics
Introduce
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Auto train offered by Amtrak is a distinctive service in the US.
Passengers bring their vehicles on the train .(as a shuttle
between different place , virginia florida …)
Selling the tickets about 330 days before the train’s
departure date .
Vehicles: Cars vans/SUVs be accepts by Amtrak.
passengers : Different types of accommodations : Super Coach
Seat, superliner lower level Coach Seat ,Superliner Roomette
Superliner Accessible Bedroom, ….
The capacities of Accommodations are fixed and has a base
price with up to four discount levels
Introduce (II)
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In this paper, Dynamic pricing strategies in order to “maximise
the expected revenue of this service “
Two types of vehicle accommodations :cars & vans/Suvs
Two types of passenger accommodations :Super coach Seats &
Superliner roomette (sleepers)
Two types of tickets must be purchased .
For the vehicle depends of the type of vehicle the “party” (group of –
passengers )plans to bring .(交通工具部份視旅客們駕駛何款式)
– Passengers can choose their own accommodations .
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Either buy a coach seat for each passenger or share a sleeper
Complete reservation Includes two separate costs
– Base cost :boarding the Auto Train & cost of coach seats for all
passengers )
– upgrade cast : “ party” decides to upgrade to a sleeper
Related Researches
• 1997Gallego and van Ryzin- Multiproduct and continuous –
time dynamic pricing model -consider a finite-time(期限)
horizon during which the products can be sold and after
which the unsold products have no value .
• Amtrak requires manager to change the prices on a daily
basis
– Passengers make a multi-state decision
first :decide whether or not to ride the train
– Second :upgrading their accommodation
Amtrak can set its product prices at the beginning of each day.
use dynamic programming to determine each product’s optimal price at
the beginning of each day (變動規則決定每一產品的最佳訂價)
Related Researches (II)
• Amtrak different from railroad revenue management
problems :no networking (network-oriented nature and long
distance intercity trains) .
• Requires studying revenue management for bundled
products (Auto train)
• Additional resources of multiproduct revenue management
models :
– Maglaras and Meissner(2006),Talluri and R(2004),
You(1999),Ladany and Hersh(1978),talluri(1993).
Analysis of sales data (I)
•
Use Amtrak’s sales data to analyse the market.
– Data description
 sales data: 350tains departing between 10.2002 and
09.2003
– Three steps (collecting transaction data )
 Customer shopping :customers initiate search by entering
parameters (因素)-destination, date of departure …
 Results display :website responds the itinerary detailvehicle accommodation cost and coach seat cost …
 Customer decision: after comparing the options ,customers
decide to purchase the ticket and decide to upgrade the
purchase (replacing the regular coach seats with sleepers..)
– Complete reservation :includes tickets of vehicle and
passengers
 two records associated with each identification number
 Each record represents a transaction and contain time and
date of reservation. (a flag indicate whether the
reservation cancelled or purchased )
Analysis of sales data (II)
• data reconstruction
– Amtrak records the transaction price for each ticket
sale ,but does not record the price if no sale occur on a
specific day .
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If on a given day,a few tickets for car accommodations
and coach seats were sold ,no sales for van accommodation
and sleepers ,no documented information about van and
sleepers .
Lack of each accommodations daily price prevent up from
establishing a correct demand model
• Resolve lack of each accommodation’s daily
price
– Reconstructed the data
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Assign the transaction price as the price of the
accommodation for that day
if two price buckets have been charged for the car
accommodation during a day. Assume each of which
was active for half of that day.
No transaction ,last transaction and next transaction
are the same.assign that same price for the given day.
No transaction ,last transacgion and the next
transaction are diffferent .choose the price bucket of
the transaction that took place closer to the given
day.
•
Demand estimation
– reconsturcted data to estimate the daily demand
 Each accommodation from the opening day until the day deaprture
as a function of all accommodation price.
 Determine the relationships between demand and accommodation
price.
– Address characteristics as seasonality
 Based on the observation ,booking follows a consistent pattern for
trains departing in Summer 2003
– Use the date of trains departing in Summer 2003 with total
of 38,545 transactions.
• Future demand from the past sale .
– Correlation between different combinations of reservations ,cancellations
and paid tickets between one week and two weeks before
– The result shows no significant relationship.
• Conclude that cannot learn about the future demand
based on past sales.
• Address the price sensitivity of demand for each
accommodation.
– The demand for Van accommodation is not sensitive to
the price level of any accommodation or the time before
departure .
– The number of daily reservations for Car
accommodation is independent from the price of van
accommodations .the correlation between the numbers
of reservations of car accommodation and the price
level less 0.50 than Van.
Them demand of car accommodations ,coach seats
and sleepers base on the price level of car
accommodations ,coach seats, sleepers ,not the
price of van accommodation
• Upgrading to sleeps is independent from the vehicle
accommodation price (Sleeper升級與交通工具無關)
– depends on the coach seat and sleeper price.
• TO verify
– “no relationship between the number of reservation for
sleepers and the price of car accommodations (,the same
situation for the price of van accommodations)
– The demand for car accommodations is a function of car
accommodation and coach seat prices.
– The demand for van accommodation is a function of van
accommodation and coach seat prices.
– The demand for coach seats is a function of car
accommodation ,van accommodation ,coach seat, and
sleeper prices.
– The demand for sleepers is a function of coach seat,
and sleeper prices.
No passenger can ride the train without carrying
a vehicle 1.daily demand for vehicle ,2.demand
of coach seats and sleepers.
• Determine the demand distribution of car
accommodation.
– Using the reconstructed data set ,calculated
the mean and the varianceof the number of car
accommodation reservations.
– Also observe that the sample mean and sample
variance of the number of reservation
Poisson distribution is appropriate to model
the demand distribution .
• Poisson distribution (poisson分配)
– Using a goodness-of-fit test from
Winston(1994) to test H0 .
– the total number of reservation for each
type of vehicle on a given day and for a
given price bucket follows a Poisson
distribution.(每一型式的交通工具預定的數量,在每一段
期間及每一規定的價格條件跟隨Poisson distribution 情形)
Siméon-Denis Poisson是個法國人，這名字翻譯起來
其實是唸作「布瓦松分配」最接近。
• Tested H0
– Price level=1(both car &coach seats)
corresponding test statistic is 1.7489 ,Degrees
of freedom =3, α=5.99,cannot reject H0
• adopt the Poisson distribute to model the
demand
– 5price levels for car accommodations and coach
seats ,there are 25 possible price combinations
in any day before the departure.
– tested 75 price combinations and reject less
than 5percent of them to follow Poisson
distribution at significance level α=0.5
• Demand increases as the departure date approaches.
• The average number of reservations almost stays flat from
the opening day through about 30days before departure
The model
• Discrete-time revenue (離散)management model
for a single-leg Auto train .
– Vehicle :car
– Passengers: coach seats and sleepers.
– During sales horizon :accommodations are fixed and
cannot be replenished
– Unsold accommodation have no salvagevalue after the
departure date.
– Cancellations and overbooking are not considered in this
model
– Use a monopolistic (獨占)model to address this problem
,do not consider indirect competition with other travel
industries .
Other pricing policies
• “current pricing -in this paper
– relies on employees’ knowledge and
experience
– Based on human decision .
– Can derive its performance using the
transaction data
• Myopic policy(缺乏遠見的政策，近視政策 )
– Seller ignores the effect of its current
pricing on future demand and revenue .
– Doesn’t take into account hot potential
sale might affect its inventory.
– Only objective is maximise the revenue
on the current day
• Static-price heuristic
– A fixed price each accommodation
– The strength of the policy is low operation
cost of price change
– Weakness is that this policy does not
respond to how well the sale goes (due to the
price is fixed ,didn’t know which period the sold are better than
the other time)
• Pseudo-dynamic heuristics
– Between dynamic programming and
static price policy, take into account the
current demand and determines the
price of accommodations .
– Using this price policy. Beginning of each
period ,the seller observes the
inventory levels and charges the
accommodations’price level .
Numerical results
• Computer program to calculate the “optimal
price “at the beginning of each period,Numerical
study ,the dynamic programming method improves
the expected revenue per train by 20%compared
to the average revenue
• The Best price buckets for car accommodations
,coach seats and sleepers .To summarise the
results for the last ten days before departure
Expected revenue generated by
different pricing policies
High performance
Daily demand from 330days before departure until 30days
before departure is almost constant and significantly low
compare
Pseudeo dynamci heuristic is more effective and
has the capability of learning from current sale
and correcting the pricing policy.
conclusions
• Mathematical model has been introduced
in order to maximise the expected revenue
over the sales horizon .
• Provided three other pricing policies to
compare the performance of the optimal
policy .
• The numerical study provides a manual for
the Amtrak revenue managers to
determine the optimal price .