指导老师李治纲博士.ppt

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,Soheil Sibdari, Kyle Y.Lin and Sriram chellappan Received (in revised from ):25th July ,2007,Journal of revenue and Pricing Management,Amtrak,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,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 trains 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),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 . 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 products 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 Amtraks 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 detail-vehicle 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 . 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 accommodations daily price Reconstructed the data 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),Simon-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, =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 =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 . Doesnt 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 ,didnt 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 sel