CA2450041A1 - Revenue management of flexible products - Google Patents

Abstract

The present invention is directed to methods, apparatuses and media that use flexible products to enhance or maximize the revenue of perishable/constrained capacity and/or inventory providers such as airlines and hotels. The invention also provides algorithms or formulae with which the conditions of maximizing revenue of flexible products can be determined in relation to specific products and in relation to situations involving repeated transactions where demand varies. The revenue management methods provide lower priced flexible products that attract additional customers who would otherwise not choose to purchase and enable companies to wait for uncertainty on specific product demand to be resolved before assigning alternative products, which thereby enables maximized use of capacity/inventory and generation of revenue.

Description

P-00057 (19240-187) REVENUE MANAGEMENT OF FLEXIBLE PRODUCTS
[0001] All patents, patent applications and publications cited herein are hereby incorporated by reference in their entirety. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art as known to those skilled therein as of the date of the invention described and claimed herein.

[0002] A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of tile patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.
BACKGROUND OF THE INVENTION

[0003] In a great number of industries, sellers have a perishable/constrained capacity and/or constrained inventory of a good for sale. Examples of perishable/constrained capacity include airlines selling seats on a flight, hotels renting rooms, theaters selling seats to an event and manufacturers selling capacity slots in a pure order-to-delivery environment. Examples of constrained inventory of goods for sale include fashion retailing where once inventory is ordered it cannot be replenished because lead times are longer than the sale horizon.

[0004] Airlines, hotels, and other service providers have, of course, long been aware of the risks presented by the combination of uncertain demand and immediately perishable capacity and a number of mechanisms have been proposed to help manage this risk. The most venerable of these mechanisms is overbooking, i.e., accepting more bookings on a flight than available capacity. Typically, overbooking has been considered a way for airlines to hedge against the risks of cancellations and no-shows. For this reason, overbooking models usually assume that the denied boarding cost of refusing a booked passenger is greater than the highest fare.

[0005] If the denied boarding cost is less than the highest fare, an optimal policy allows overbooking even in the absence of cancellations or no-shows. In this case, this overbooking is done with the purpose of improving revenues by bumping lower fare passengers in favor of NEWYORK 82388v2 "."."..,... ."""",. m. ...._.,.." r.~.,e .: ~qmarcn.:~wass-=.,.-..w....~o.~e,-~x .... .. . . .. . , ~~~~-~-~~,-~~--~-- ~--.~~----........._.._._....._.._.
,m-.,~.~..-~-.~._-._._.........

P-00057 (19240-187) higher fare passengers. However, this bumping strategy is inconvenient for passengers, inflexible for airlines, and may result in high involuntary denied boarding and reaccommodation costs if bumped passengers need to be rebooked on a competing flight.

[0006] Another mechanism to manage risk is the sale of deeply discounted "stand-by"
tickets. Stand-by passengers are only accommodated if the number of shows iiom guaranteed bookings is less than the available capacity. If a stand-by passenger is not accommodated on the flight he booked, he will be accommodated on a future departure for the same destination that does have available capacity. However, stand-bys are merely a hedge against no-shows and overbookings, rather than a strategy to improve capacity utilization.

(0007] Thomas Cook, formally of American Airlines, suggested a ''replane"
strategy. In this strategy, once airlines observe a high demand for high-fare tickets of a particular flight, they can call many customers to see whether they are willing to give up their seats for an alternative flight plus some compensation, even if the flight is not overbooked. However, this strategy for maximizing revenue suffers from (i) the operational costs of identifying the suitable customers willing to be shifted to alternative flights, (ii) the operational costs of shifting customer to alternative flights in an ad hoc manner (such as customer services, scheduling coordination, etc.), and (iii) the intangible costs of ill-will among low-fare customers who do not have the flexibility to give up their seats. Thus, an approach that maximizes revenue for industries with constrained capacity and inventory is desired, where the approach provides more efficient methods for capacity utilization, decreases operational costs and increases overall demand.
SUMMARY OF THE INVENTION

[0008] The present invention relates to computer-implemented methods for managing revenue from selling products, including the selling of flexible products and specific produ.ets.
Particularly for industries with perishable/constrained capacity and/or constrained inventory, the expected revenue with flexible products that are managed in relation to the demand levels of related specific products can be significantly higher than in the traditional cases where sales at low fares are final or in cases where flexible products are sold without proper revenue management. The present invention also provides for apparatuses, computer-readable storage mediums and formulae that help to implement the present methods.
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P-00057 (19240-187) (0009] In one aspect of the present invention, a computer-implemented method for managing revenue from selling a praduct comprises: (a) offering a flexible product for sale, wherein the flexible product comprises at least two alternative products, wherein a seller assigns one of the alternative products to a purchaser at a later date; (b) receiving a customer request for purchase of the flexible product; (c) determining which alternative product is to be assigned to the customer; and (d) informing the customer which alternative product the seller has assigned to the customer, thereby managing revenue from selling the product.

[0010] In the present invention, determining (how to manage revenue) can comprise, for example, observing specific demand for each specific product before assigning the customer an alternative product so as to maximize capacity and/or using a linear program and/or a column generation approach. Further, in the present invention, determining how to assign a particular alternative product of a flexible product, or when to assign, can comprise, for example, waiting until uncertainty on specific product demand is resolved before the customer is assigned an alternative product.

[0011] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) offering one or more flexible products and/or specific products for sale; (b) receiving a customer request for a specific product; (e) providing the customer with a first choice to purchase the specific product and with a second choice to purchase a flexible product; and (d) receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

(0012] In the present invention, where a flexible product comprises an alternative product that is also offered to consumers as a specific product, the price of the specific product can be greater than the price of the flexible product. Further, the present invention encompasses methods for managing revenue that include determining whether revenue can be maximized by selling a specific product as an alternative product.

(0013] In one aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) offering one or more flexible products and/or specific products for sale; (b) receiving a customer request for a specific product; (c) determining whether revenue NEWYORK 82388v2 ..,.".. .,~.. .?.,~ ..-=x,",,~R~~~ -------_.._...._ __-~,.
,.~,."~.~..m.~~.._.....~.....~~.~".

P-00057(19240-187) can be increased by selling a flexible product comprising the specific product as an alternative product, wherein if revenue cannot be increased by selling the flexible product, then sending a confirmation of purchase of the specific product to the customer, and wherein if revenue can be increased by selling the flexible product, providing the customer with a first choice to purchase the specific product and with a second choice to purchase the flexible product; and (d) receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

[0014] In the aspects of the present invention where a customer has purchased a flexible product, the invention encompasses informing or sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer occurs within a fixed period of time, wherein the fixed period of time is established as a component of the flexible product prior to or upon purchase of the flexible product.

[0015] In one aspect of the present invention, a computer-implemented method for managing revenue from selling a product comprises: (a) offering a flexible product within a fixed time period for purchase of the flexible product, wherein the flexible product comprises at least a first alternative product and a second alternative product; (b) receiving a first customer request fox purchase of the flexible product within the fixed time period for purchase of the flexible product; (c) receiving a second customer request for purchase of a specific product which is identical to the first alternative product after the fixed time period for purchase of the .flexible product; and (d) determining which alternative product is to be assigned to the first customer based on the second customer's request, thereby managing revenue. In this aspect, the determining can comprise dynamically allocating alternative products to customers after the fixed time period for purchase of the flexible product. Also in this aspect, the specific product can have a purchase price greater than the flexible product. In the present invention, the determining which alternative product is to be assigned in order to manage revenue can also comprise maximizing quantity of products sold.

[0016] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) offering for sale during a first time period at least a specific product and a flexible product, wherein the specific product is offered at a discount price, and NGWYORK 82388v2 ,..., ~,w .,~m-. .~>.,~.,:~-~,~.~,a,~,, , ,~-....._"~,.~ .~.~----_-.~.

P-00057 (19240-187) wherein the flexible product comprises the specific product as an alternative product; and (b) offering for sale during a second time period the specific product, wherein the specific product is offered at a price greater than the discount price in the first time period.

[0017] In yet another aspect, a computer-implemented method for buying a flexible product comprises: offering to buy a flexible product within a fixed time period, wherein the flexible product comprises at least two alternative products; and receiving information after the fixed time period as to which alternative product has been sold by the seller.

[0018] Within all aspects of the present invention, a flexible product can comprise a set of alternative products that have a perishable/constrained capacity and/or constrained inventory.
Further, a specific product can comprise a product having a perishable/constrained capacity and/or constrained inventory. Products that have a perishable/constrained capacity and/or constrained inventory can be, for example, any ticket reservation such as an airplane ticket reservation, a hotel room reservation, a concert ticket reservation, a theater ticket reservation, or an Internet webpage advertising space reservation, an air cargo reservation, or a vacation tour reservation. In one aspect of the present invention, a flexible product comprises at least two different airplane ticket reservations.

[0019] In one aspect, the present invention provides an apparatus for managing revenue from selling a product comprising: under control of a host system; means for offering for sale a flexible product; means for receiving a customer request for purchase of the flexible product, wherein the flexible product comprises at least two alternative products;
means for determining which alternative product is to be sold to the customer so as to maximize capacity; a.nd means for notifying the customer which alternative product of the flexible product the seller has sold to the customer.

[0020] In another aspect, an apparatus for managing revenue from selling a product comprises: under control of a host system; means for displaying or offering one or more products for sale; means for receiving a customer request for a specific product; means for determining whether revenue can be increased by selling a flexible product comprising the specific product as an alternative product, wherein if revenue cannot be increased by selling the flexible product, then sending a confirmation of purchase of the specific product to the customer, and wherein if revenue can be increased by selling the flexible product, providing the customer rrEwSroRCC sz3ss~z ~.,w.~~. ...~..~.~.~", .. . ., ,~"V~..~---_... .,~ ~.....__..__....m...-...

P-00057(19240-187) with a first choice to purchase the specific product and with a second choice to purchase the flexible product; and means for receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

[0021] In yet another aspect, an apparatus for purchasing a flexible product comprises:
under control of a client system; means far requesting a purchase of a flexible product, wherein the flexible product comprises at least two alternative products; and means for receiving information as to which alternative product of the flexible product has been assigned by the seller.

[0022] In one aspect, a computer-readable storage medium containing a set of instructions for a host system comprises: a display routine for presenting a flexible product available for purchase, wherein the flexible product comprises at least two alternative products;
an input routine for receiving a customer request for purchase of the flexible product; a run routine for determining which alternative product of the flexible product should be assigned to the customer so as to maximize revenue; and a run routine for sending to the customer information as to which alternative product of the flexible product the seller has assigned to the customer.

[0023] In another aspect, a computer-readable storage medium containing a set of instructions for a client system comprises: a display routine for viewing a flexible product available for purchase from a seller, wherein the flexible product comprises at least two alternative products; an input routine for selecting the flexible product for a purchase request; a run routine for sending the purchase request to a host system; and a storage routine for receiving and storing a confirmation of the purchase of the flexible product and information as to which alternative product of the flexible product has been assigned by the seller.

[0024] In yet another aspect, a computer-implemented system for managing revenue from selling a product comprises: a file server; and a processor programmed for implementing instructions for: offering a flexible product; receiving and storing a customer request for purchase of the flexible product; determining which alternative product of the flexible product to assign to the customer in order to maximize revenue; and sending to the customer information as NEWYORK $2388v2 P-00057 (19240-187) to which alternative product of the flexible product the seller has assigned to the customer;
thereby managing revenue.

[0025] In one aspect, the present invention provides a computer-implemented method for managing airplane ticket revenue from selling a product comprising: offering a flexible product, wherein the flexible product comprises a first airplane ticket reservation and a second airplane ticket reservation; receiving a request for purchase of the flexible product from a first customer;
sending a confirmation of purchase of the flexible product to the first customer; receiving a request for purchase of the first airplane ticket reservation from a second customer; sending to the first customer information that the second airplane ticket reservation has been assigned to the first customer; and sending to the second customer a confirmation of purchase of the first airplane ticket reservation.
BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 presents a flow diagram of a computer-implemented method of managing revenue where a customer converts a purchased specific-product into a flexible product.

[0027] Figure 2 presents a flow diagram of another strategy of computer-implemented methods of managing revenue with flexible products.

[0028] Figure 3 presents formulae relating to Example 1.

[0029] Figure 4 presents formulae relating to the second period problem without overbooking as described in Example 1.

[0030] Figure 5 presents formulae relating to the second period allocation problem with overbooking as described in Example 1.

[0031) Figure 6 presents a lemma and proof relating to the second period allocation with overbooking problem as described in Example 1.

[0032) Figure 7 presents an algorithm to compute optimal second period allocations and optimal expected profit with overbooking, as described in Example 1.

[0033] Figure 8 presents an example of optimal second period allocations and optimal expected profit with overbooking, as described in Example 1.

NEWYORK 82388v2 P-00057(19240-187) (0034] Figure 9 presents another characterization of the optimal second-period allocations with overbooking.

[0035] Figure 10 presents "Corollary 2" and an example relating to the optimal second-period allocations with overbooking.

[0036] Figure 11 presents a model relating to second period dynamic allocation, as described in Example 1.

[0037] Figures 12, 13 and 14 present formulae relating to the problem of first period allocations, as described in Example 1.

[0038] Figure 15 and 16 describe how total demand for the flexible product and the two specific products, including both induction and cannibalization effects can be calculated.

[0039] Figure 17 presents Tables 3 and 4 of Example 1, which shows simulation results for demand induction and cannibalization.

[0040] Figure 18 presents equations (1), (2), (3) and (4) of Example 2, which relates to strategic pricing in perishablelconstrained markets with repeated transactions.

[0041] Figures I9 and 20 present formulae relating to the distressed inventory model, as discussed in Example 2.

[0042] Figure 21 presents Table l and Table 2 of Example 2, which shows the results of scenarios relating to the distressed inventory model.

[0043] Figure 22 presents computation towards equation (1) of Example 3 that represents the optimization problem faced by the network manager.

[0044] Figure 23 presents the column generation algorithm equation ( 1 ).

[0045] Figure 24 presents computation relating to the LP dual of equation ( 1 ) of Example 3.

[0046] Figure 25 presents computation relating to when a restricted LP is solved to optimality.

[0047] Figures 26 and 27 present computation relating to 2-column generation.
NEWYORK 82388v2 _..~.,.,. .... ..... ..,...~ . < ..,~, ...,~~,n",4 , ~. .~~,~.~"..,m..~,-,..-.. _ _-.._,~,.~ ...

P-00057(19240-187) [0048] Figure 28 presents revenue results directed to a case involving generic random networks.

[0049] Figure 29 presents computation and details relating to a demand model, as described in Example 3.
[4050] Figures 30A and 30B present plots relating to gain G~(T) as a function of time horizon T.
[0051] Figure 31 presents a plot where gain Gf(T) is a function of utility w.
[0052] Figure 32 presents a revenue plot where gain G f(T) is a function of utility w.
[0053] Figure 33 presents a plot of gain G f(T) vs. the ~ for the utility w =
1.
[0054] Figure 34 presents a plot of gain Gf(T') vs. the ~ for the utility w =
2.
[0055] Figures 35 and 36 present plots relating to the effect of discount on gain G f(T).
[0056] Figure 37 presents the results of an experiment relating to demand induction versus capacity utilization.
[0057] Figure 38 presents 'the gain curves for an entropy model.
[0058] Figures 39A-C present additional and alternative computations directed to the column generation algorithm.
[0059] Figure 40 presents one apparatus for implementing the methods of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0060] While flexible products offer advantages, there is the risk is that poorly managed flexible products could lead to revenue deterioration through cannibalization of higher fare demands. Sellers of flexible products require approaches that maximize profitability and prevent excess cannibalization.
[0061] The present invention provides a revenue management system or method for a variety of situations, including a case of a supplier with fixed perishable or constrained capacity/inventory offering a combination of flexible and specific products.
In this case, the problem of managing and pricing flexible products belongs to the field of revenue management.
1~3EWYORK 82388v2 ............. . _........_.__.._ .........._... ~_,.~. .....~."~".~y,.,.",~
r,~.~ ~ . , a..~«.»..m. . w~s m~...~.w.. .ate,., P-00057 (19240-187) The present invention often poses analyses in terms of an airline. However, one should bear in mind that the present invention is much more broadly applicable.
[0062] Airlines, hotels, and other service providers have, of course, long been aware of the risks presented by the combination of uncertain demand and immediately perishable capacity and a number of mechanisms have been proposed to help manage this risk. The most venerable of these mechanisms is overbooking (accepting more bookings on a flight than available capacity). Typically, overbooking has been considered a way for airlines to hedge against the risks of cancellations and no-shows. For this reason, overbooking models usually assume that the denied boarding cost of refusing a booked passenger is greater than the highest fare.
[0063] If the denied boarding cost is less than the highest fare, an optimal policy allows overbooking even in the absence of cancellations or no-shows. In this case, this overbooking is done with the purpose of improving revenues by bumping lower fare passengers in favor of higher fare passengers. However, this bumping strategy is inconvenient for passengers, inflexible for airlines, and may result in high involuntary denied boarding and reaccommodation costs if bumped passengers need to be rebooked on a competing flight.
[0064] Another relevant mechanism is the sale of deeply discounted "stand-by"
tickets.
Stand-by passengers are only accommodated if the number of shows from "guaranteed"
bookings is less than the available capacity. If a stand-by passenger is not accommodated on the flight he booked, he will be accommodated on a future departure for the same destination that does have available capacity. Stand-bys are similar to flexible products, with the difference that the stand-by ticket purchaser is not a priori guaranteed accommodation on one of a given set of flights. Thus stand-bys are usually analyzed as a form of "hedge" against no-shows and overbookings, rather than as a way to improve capacity utilization.
[0065) The flexible product approach proposed herein does not assume that passengers are necessarily indifferent among the alternatives within a flexible product.
In addition, the present invention allows the airline the ability to route passengers purchasing flexible products near departure rather than at the time of booking.
[0066] While flexible products appear to offer many advantages, a revenue management system is needed to determine how availability of these products should be managed for a seller offering both flexible and specific products, as provided by the present invention. An airline NEWYORK 82388v2 _._.,..., ~.,. , _..... _... _.._ ...__, .....". .. ,.,.-<...-...A,.~,~, ,~~m .~~._._ _ ",n,.N ""~» ~..,-.-.- __ _~~.r____~__.__~..,..._.~...,~"

P-00057 (19240-187) offering only flexible products, each of which consisted of a disjoint set of specific products could manage each flexible product as a single flight with capacity equal to the total capacity of the constituent specific products. However, when a supplier offers a combination of flexible and specific products, it is not clear what kind of booking limits or nesting structures should be used.
[0067] The present invention shows that there can be significant differences in profitability depending upon the booking control mechanism used, where revenue management can comprise booking control mechanisms. The present invention also shows that, under reasonable assumptions, the benefits from offering flexible products can make it worthwhile to consider them as part of the overall market offering.
[006$] The revenue management methods for selling flexible products enable customers to purchase combinations of underlying specific products as linked by a Boolean exclusive "or"
operation. Each underlying specific product is a set of one or more resources linked by a Boolean "and" operation. Thus, the concept of flexible products can be seen as extending the scope of revenue management to include combinations of resources linked by an exclusive "or"
operation. For example, a flexible can comprise the set of products (a, b, c and (d and e)) where either only a or b or c or (d and e) will be assigned to a customer.
[0069] A flexible product is a product that has a set of two or more "alternative products"
(which can also be denoted as "alternative products") that usually serve the same commercial market, where a purchaser of the flexible product will be assigned one of the alternative products by the seller at a later date (a date after the time of purchase of the flexible product). An alternative product is a specific product that is a member of a set of specific products, where each member of the set of specific products can be chosen by a seller to be assigned to the buyer as fulfillment of consideration for the purchase of a flexible product. The seller must inform the customer/buyer which alternative product has been assigned within a fixed time period, where the fixed time period is established as a component or trait of the flexible product. In other words, the seller will determine what the fixed time period is prior to or at the time of offering the flexible product for sale, and thus, the fixed time period is established prior to or upon sale of the flexible product. Alternatively, the fixed time period can be modified after sale of the flexible product upon negotiation between the buyer and seller, or the fixed time period can be modified unilaterally if agreed to upon purchase of the flexible product. In the present invention, NEWYORK 82388v2 P-00057(19240-187) a "specific product" is simply a single product or single product unit, where a product not only refers to goods, but also to property and services. For the purposes of the present invention, a specific product can be viewed as a product that is not sold as a flexible product to the same customer for the same consideration. Rather, flexible products are composed of a set of specific products, one or more of Which is assigned to the buyer of the flexible product, where the elements of this set are denoted as "alternative products."
[0070] As the flexible product usually comprises alternative products that have a perishable/constrained capacity and/or constrained inventory, the alternative products themselves often provide the fixed time period. For example, a flexible product is purchased March 1 st, and this flexible product comprises two alternative products X arid Y. Alternative product X is an airplane ticket reservation for a flight departing on March 29t~', and alternative product Y is an airplane ticket reservation for a flight departing on March 30~h. By the nature of the alternative products, the seller would have to assign either X or Y at a reasonable time prior to X, as the date of X is earlier than Y, such that the customer would be able to make the flight.
[0071] A seller can enable a host system to allow a customer who has purchased a specific product to convert the specific product into a flexible product. The seller can offer tile conversion: (i) at a discount with relation to the purchase price of the specific product (such that the customer thereby receives a monetary disbursement or account credit), (ii) for free or (iii) or can charge for the opportunity.
[0072) For (iii), the present invention provides an exception to the right or power of the seller to assign a particular alternative product. For a premium, the seller can choose to sell a flexible product where the buyer has the right to choose which alternative product with the set of alternative products he wishes to use, of course, within a fixed period of time. For instance, the buyer may be interested in paying additional money for the conversion due to buyer's uncertainty of whether he/she would be able to use the specific product in the future. For example, assume that the buyer has purchased a specific product A, where A is an airplane ticket reservation for a flight departing on June 1 S. The buyer, after purchase of A, fords out that he may not be able to fly on June l5tl'. To avoid flight cancellation or flight change costs, the customer may desire to convert A into a flexible product that has various alternative flights, all of which the customer knows he/she will be able to make (which can include the original specific NEVJYORK 82388v2 ____.-__~~_ . ----..~,-._ .,-.~. "m."~_ __~

P-00057 (19240-187) product flight). The seller will offer the conversion based on a determination of whether the premium will maximize revenue. The buyer will choose the conversion based on a decision that the premium is less than the penalties of flight cancellation or flight changes.
[0073] In Figure l, the seller can allow certain specific products for conversion 1 (where the choice of specific products foa~ conversion, the choice of alternative products that compose a particular flexible product, the prices of the products and the fixed time period of the alternative products are determined by calculating whether such a conversion would maximize revenue;
such calculations can include the formulae and algorithms disclosed herein).
Offering or displaying the products for conversion can be easily implemented on the Internet. For example, the customer can click on a hyperlink (or input information on a webpage) of the allowed products for conversion to accept participation of the flexible product conversion 2. In 3, the host system confirms that the customer is indeed an owner of the specific product associated with the hyperlink, and sends a confirmation to the customer of the conversion. Later, the seller sends information 4 to inform the buyer as to which alternative product has been assigned. This basic model has numerous variations, as described herein.
(0074] Figure 2 is an illustrative example for the methods of managing revenue with a flexible product transaction, and as such, presents concepts generally applicable to the invention.
A host system 10, such as a server, presents a selection of products available for sale, either as passively displayed on a seller's website or in response to particular inquiries by a potential customer, where this interactive response can be displayed on the seller's website or on a tlurd-party website (for example, if the products are airplane ticket reservations, then the seller's website can be an airline's website and the third-party website can be a travel agency website, such as Expedia.com, etc.).
[0075] The host system then receives a request from a customer for purchase of a product 11. The host system determines 12 whether the product that is requested is a specific product or a flexible product. If the product that is requested is a specific product, then the host system determines (by programs or algorithms [which can comprise the formulae described herein), or by human decision making) 13 whether selling the specific product as a flexible product can maximize revenue. If it is determined that selling the specific product as a flexible product can maximize revenue, then the host system 14 presents the customer with the choice to purchase a NEWYORK 82388v2 _........ "..._...ri .._ . _....: "~.._...~__.._._, _..,H..... ,....___.,.,. ~
,",...,,~R. ey~".. ~----°--_--r ,;: ~--_ ~~~ i P-00057 (19244-187) flexible product that has the requested specific product as an alternative product. If it is determined that selling the specific product as a flexible product is unlikely to maximize revenue, then the host system provides 16 the customer with confirmation of purchase of the specific product. At 14, if the customer declined the opportunity to purchase the flexible product, then the customer is provided 1G with confirmation of purchase of the specific product.
[0076] At 12, if the product is not a flexible product, and if the product is a flexible product 17, then the host system provides 18 the customer with confirmation of purchase of the flexible product. The confirmation of purchase includes, for example, the time period in which the seller will inform 19 the customer which alternative product has been assigned.
[0077] A flexible product can be viewed as a menu of two or more alternatives offered by a supplier selling perishable/constrained capacity and/or constrained inventory. The supplier will assign customers who have chosen a flexible product to one of the alternatives at some later time prior to delivery. This contrasts with specific products where the customer chooses a specific alternative at the time of purchase.
[0078] One example would be an airline that offering a morning flight in addition to specific flights serving the same market. The airline would assign flexible customers to a specific flight shortly prior to departure. Flexible products have the advantage of increasing overall demand and enabling better capacity utilization. But without proper revenue management, flexible products can potentially cannibalize higher-paying specific demand.
The present invention provides conditions and algorithms for proper revenue management of flexible products. In Example 1, the invention provides such conditions and algorithms in the simple case of a single flexible product consisting of two specific products (i.e., two alternative products), which can be applied to more complex scenarios. Numerical simulation is used to determine the benefits from offering flexible products in this case and discuss extension of the approach to multiple products.
[0079] A flexible product can also be viewed as a set of two more alternatives serving the same market such that the seller will assign a purchaser of the flexible product one of the alternatives at a later date. This is in contrast to a specific product which, by definition, consists of a single alternative. For example, airline passengers typically book a specific flight. If their first choice is not available at an acceptable price, they may book on a less preferred alternative NEWYORK 82388v2 P-00057 (19240-187) or they may choose not to travel. However, in addition to these specific products, an airline could also offer flexible products, each of which consisted of two or more sets of flights serving the same market.
[0080] A customer purchasing a flexible product can be guaranteed service by one of the alternatives, however the airline ~.~ould does not have to inform the customer of the flight he will actually be traveling on until some later time. As an example of a flexible product, consider an airline with three morning flights from New York's Kennedy airport (JFK) to San Francisco International (SFO). One flight departs at 8:00 AM and arrives at 11:00 AM, the second departs at 9:00 AM and arrives at 12:30 and the third departs at 11:00 AM and arrives at 2:00 PM.
Customers can book seats on any one of the three flights as usual. However, in addition to these three specific products the airline might also offer a flexible product, say "JFK - SFO morning,"
at a discount.
[0081) Customers purchasing the JFK - SFO morning product would be guaranteed a seat on one of the three flights, but they would not be informed which flight until later. The airline would have the luxury of observing specific demand for each of the individual flights before assigning the flexible passengers to the morning departures.
[0082] Although we have couched the invention in terms of an airline in the paragraphs above, flexible products are contemplated in a number of other industries:
[0083] Internet Advertising: Internet service providers (ISP) such as Yahoo, MSN, and Lycos sell capacity on different properties to advertisers, where the properties consist of pages devoted to topics such sports, finance, weather, maps, ete. Advertisers can purchase space on individual properties or they can buy capacity on a cheaper run of network basis. If they purchase run of network, then the service provider can choose, effectively in real time, which property will host the advertisement.
[0084] Some advertisers have a strong preference for a certain property: for example, Nike might want its advertisements to appear on the sports page while American Airlines might want its ads to appear on the sports page. These advertisers will tend to purchase specific capacity. Other advertisers who are more indifferent regarding placement (or are simply more price sensitive) can purchase the cheaper run of network and take their chances on where their ads will be placed. The total capacity of an ISP is fixed and equal to the sum of the capacities of NEWYORK 82388v2 P-00057 (19240-187) its individual properties. Thus, run-of network is a flexible product while individual properties are specific products.
[0085] InteYnet Search Terms: In a related market, Google sells a fixed capacity of search terms. For example, upon a search for the term "DVD," various hyperlinks are then presented in a list. Companies or individuals place bids to be associated with search terms and strategies, such that they will connected to a hyperlink in the list. The highest bids are presented at the top of a list. In relation to a flexible product, Google can sell a flexible product where a company such as Amazon may be interested in buying the rights to the first, second or third placement on the list in relation to the search term "DVD". Thus, the present invention also contemplates the use of flexible products to sell search term rights.
[0086] Air Cargo: The majority of air cargo is sold on a reservation basis, similar to passenger sales. Shippers - primarily forwarders and consolidators - book capacity for their shipments on specific flights. This is known as a "flight-specific" booking.
However, in addition to flight-specific bookings, some earners offer "time-definite" products in which the carrier specifies only the pick-up time and the delivery tame. In this case, the carrier has the option to choose the flights it pleases to carry the shipment, subject only to the pick-up and delivery requirements. Here, the "time-definite" offering is a flexible product.
[0087] Tour Operators: European tour operators such as Airtours and Thompson sell tour packages that include both air transportation and lodging. For a popular destination such as Ibiza or the Costa del Sol, an operator will have space agreements with many different hotels.
When he books his tour, a customer can specify a particular property within the resort. Or, for a discount, he can specify a desired quality level (say three stars) and the tour operator will choose the property for him. Under this flexible product alternative, the tour operator will assign the customer to whichever property will maximize profitability.
[0088] Multiple Property Management: Major hotel chains such as Marriott, Sheraton, or Hilton often operate several properties within a single metropolitan location such as Manhattan or San Francisco. These chains have the opportunity to sell a general location-based product to travelers who are largely indifferent among the specific properties within the general location. The Disney corporation faces a similar opportunity at Disney World where they operate NEWYORK 82388v2 ."",... ,...~."." .z rc_..~ _ ., ,._-... .., ~.~.",e,.~,,m,~~",~~.~~~ .~
T~r.~.-._ P-00057(19240-187) a number of different hotels; some with specific themes. There are travelers who strongly prefer a particular hotel while others may be indifferent as long as the hotel is within Disney World.
[0089] Opaque Fares: Over the past decade, a number of Internet travel sellers such as Price-line and Hotwire have offered so-called opaque fares for hotels and airlines. Using an airline opaque fare, the purchaser buys a ticket (often at a discount) for a particular origin-destination and flight date without knowing the itinerary, airline, or exact flight-departure and arrival times. She is informed of these details only after the purchase is consummated. Opaque fares were created specifically as an inferior product that could fill capacity without excessively cannibalizing full-fare demand. While opaque fares resemble flexible products, it should be noted that they are not currently managed as such by the airlines and hotels.
Rather an airline or a hotel will make a certain amount of capacity available to a broker at a discount, which the broker will then seek to sell using an opaque fare. In general the airlines and hotels using opaque fares do not seek to maximize their total return from their capacity by jointly managing flexible and specific sales, as contemplated in the present invention.
[0090] Flexible products could potentially be used in any situation in which a company offers several products that some customers will consider as close substitutes while others have strong preferences for a specific product. For example, in made-to-order manufacturing, sellers could offer options under which a customer could either choose a specific slot or choose a cheaper flexible option under which delivery is guaranteed by some future date but the seller has the choice to choose the actual slot within that date.
[0091] Flexible products offer at least two advantages to sellers: risk pooling and demand induction.
[0092] Risk Pooling: Flexible products can improve capacity utilization since customers can be assigned to products after demand uncertainty about specific products has been largely resolved, allowing the supplier to hedge against demand and capacity unbalances.
[0093] Demand Induction: Most consumers may view flexible products as inferior to specific products. This potentially allows them to be sold at a lower price than the specific products without excessively cannibalizing specific product demand. At sufficiently low fares, flexible products may induce demand from a segment of the population that would have not purchased a specific product. The idea of offering an "inferior" product at a lower price to NEWYO12K 82388v2 iit 1 P-00057 (19240-187) stimulate demand is the motivation behind airline discount fares with advance-purchase and Saturday-night-stay restrictions. Moreover, airlines limit the availability of the discount fare inferior products to reserve capacity for full-fare demand.
[0094] Mathematical formulae are presented in the Example section that enables the calculation of revenue management with callable products. Such formulae can be incorporated into the methods, apparatuses and computer-readable media of the present invention.
[0095] The systems and methods of the present invention may be implemented using any suitable communication network. The methods can be implemented as a web site that is hosted on an Internet web page server, which can be any suitable server. A user's computer and servers or databases of sellersJservice providers can be connected to a host system's Internet web page server, or any other suitable server, through any suitable Internet connections.
[0096] For example, Figure 40 presents an illustrative example of how the systems and methods of the present invention can be implemented by an apparatus. In 30, the seller's or seller's service provider maintains servers and/or databases that can be connected to an Internet webpage server 31, which can be any suitable server. In 30, the servers and/or databases contain the information on products for sale, products that have been purchased, and the softwaxe routines that enable the determination of how to maximize revenue. The Internet webpage server 31 is a nexus at which information from the seller can be displayed or offered to customers (to the customer's computer 32), and at which customers can make purchase requests, selections or inquiries to the seller. The customer's computer can be connected to the Internet webpage server 31 or any other suitable server through any suitable Internet connections 33 and 34.
[0097] It is to be understood and expected that variations in the principles of the invention herein disclosed in an exemplary embodiment can be made by one skilled in the art and it is intended that such modifications, changes, and substitutions are included within the scope of the present invention.
[0098] The examples set forth below illustrate several embodiments of the invention.
These examples are for illustrative purposes only, and are not meant to be limiting.
NEWYORK 82388v2 . .....w..t___.__.. ._ ....... __ ....__~ ~~,~" .~:~~.",.,"~~.~. ~,.-~. ~.~
~,"~,.,~.,,.,.,~,"~.._ _.....,-,-_____..

P-00057(19240-187) ~sr s lvrnr .~c EXAMPLE 1: REVENUE MANAGEMENT OF FLEXIBLE PRODUCTS AND THE TVdO-PRODUCT PROBLEM
[0099) This example provides an analysis of the two-period, two-flight case for an airline offering a flexible product in addition to specific products. This example compares different control structures for flexible and specific bookings and derives algorithms for determining booking limits. The example shows, under some conditions, that it is optimal for a canier to allow overbooking when managing flexible bookings, even in the absence of no-shows or cancellations. The example presents a consumer choice model that models both the demand induction and cannibalization that may result from offering a flexible product. The example uses a simulation to compare results under the various control structures and for different pricing scenarios and provides insights into both the demand induction and risk pooling benef is that an airline could achieve from offering flexible products. Further, the example discusses the extension of the analyses to full airline networks with arbitrary specifications of flexible products. Although this example develops a model in the context of passenger airlines, the results extend directly to any industry that accepts bookings for multiple products or services using perishable/constrained capacity and/or constrained inventory.
[00100] Assume that an airline has two flights, say A and B, serving the same market, e.g., from the same origin to the same destination. Passengers book in two periods.
In the first period, the airline sells flexible product "(A;B)" in addition to specific products at discounted faxes.
[00101] In the second period the airline sells specific products "(A)" and "(B)" but not the flexible product (A;B). At the end of the second period the airline can allocate the customers who purchased (A;B) among flights A and B as it wishes. However, they must be accommodated on either flight A or flight B or the airline pays a denied boarding penalty to each passenger denied space. Additionally, specific passengers must be accommodated on the flight that they choose or the airline must pay a denied boarding penalty to each unaccommodated passenger.
[00102] In this model, we assume that flexible products are not sold during the second period. This corresponds to our assumption that flexible customers will be informed of their flight assignment some time (say 24 hours) prior to departure. In this case, the airline would not NEWYORK 82388v2 .,.-~~"~~~.~~.,.rv~.u_.._.-._... .~,»~..,. ..,»_._.~_....___._ __.~..._._..__~,.~

P-00057 (19240-187) sell flexible products during the last 24 hours. Furthermore, the possible inferiority of the flexible product to the consumer relies in part on the fact that there is a time lag between the time of purchase and the time when the specific product assignment occurs. For these reasons, the assumption that only specific products will be sold in the second period is reasonable for the airline case at least. However, there are other industries, such as Internet advertising, where the flexible product could well be sold up to the last minute before delivery.
This case is considered later.
[00103] This Example studies the problem of managing bookings for both flexible products and specific products in this simple setting under twa scenarios -when the airline allows overbooking and when it does not.
[00104] Define:
[00105] cA, cB = capacity of flights;
[00106] g = fare paid by flexible passengers during first period;
[00107] gA, gB = fare paid by specific passengers during first period;
[00108] , f , f = fare paid by specific passengers during second period;
[00109] Y= demand for flexible passengers during first period;
[00110] YA, YB = demands for specific passengers during first period;
[00111] DA, DB = demands for specific passengers during second period;
[00112] b = maximum number of flexible bookings accepted during first period;
[00113] blA, bjB = maximum number of flight specific bookings accepted during first period;
[00114] b'~, bB = maximum number of flight specific bookings accepted during second period;
[00115] d = gross penalty for each passenger denied boarding.
[00116] Assume that 0 < g < min(g'~, gB). Note that we have specified the overbooking penalty d as a gross penalty, that is it is the sum of the ill-will cost, reaccommodation cost, and direct cost paid per denied boarding. We assume for simplicity that this cost is independent of NEWYORK 82388v2 P-00057 (19240-187) the number and the mix of denied boardings. We further assume that d > jr > g' for, j = A, B. The assumption that the gross denied boarding cost exceeds all fares is standard, otherwise it is optimal for a revenue-maximizing airline to set no booking limit on a fare that exceeds the denied boarding cost.
[00117] In this model, the airline needs to decide how many units to make available for flexible and specific bookings during the first period and how to manage the remaining capacity during the second period. We assume that booking limits are set at the beginning of a period and cannot change during that period. The objective is to maximize the expected revenue net of denied boarding costs. We assume that the airline does not overbook in the first period, in other words, b'l Sc~, j = A,B, b > 0 and b + blA + bIB S CA + C&. This assumption is realistic because airlines typically reserve at least some capacity to satisfy the demand for higher fare products during the second-period.
[00118] The expected revenue during the first period is given by g'~E min(Y~, b~A ) + gBE
min(YB, b~B) + gE min(Y, b).
[00119] Let s' = min(, b'l) denote the number of seats booked by flight specific passengers, j = A, B during the first period and let s = min(Y, b) denote the number of flexible seats booked during the first period. Notice that (s~, se, s) is known at the beginning of the second period. Let ~' = c~ - s', j = A, B denote the residual capacity of the flights at the beginning of the second period and c(sA, sB, s) _ ~ + ~B - s > 0 denote the residual total capacity at the beginning of the second period. (For brevity, we will often write c for c(s'~, sB, s)). Given the vector ~ _ (~A, rB, c) of residual capacities, we want to determine how many seats, b'> 0, to make available for sale for flight j = A, B during the second period. Under a static control policy, the parameters b' , j = A, B are decided at the beginning of the second period before observing D', j = A, B. Later we will consider the case where bookings over the second period are managed dynamically.
[00120] Define (see Figure 3). We will concentrate on solving the second period problem and later return to address the first period problem.
[00121] Second Period Allocation Without Overbooking NEWYORK 82388v2 _...,.._ _,._,.___.....~.,.~.~~,,~~_~,,">~"-~~,..-...-_--.--...____.._..._~_.
_._,..._ P-00057 (19240-187) [00122] Here we will study the case where overbooking is not allowed. This could be a policy choice by the airline or it could be the result of a very high value of the denied boarding cost d. Since the second period expected profit is increasing (the terms increasing and decreasing are used in the weak sense) in b' S c' - s', j = A, Bvvhen bA + bB < c it follows that any optimal solution must satisfy bA + bB = c. Notice that b~ + bB = c is equivalent to allocating r~ - b' of the .s first-period flexible bookings to flight j = A, B at the beginning of the second period. Under this policy, flexible customers could be informed of their flight at the start of the second period without loss of revenue to the airline.
[00123] The second period problem without overbooking is shown in Figure 4.
[00124] We now argue by contradiction that EMSRA(k); k = l, ..., bA and EMSRB(k); k =
1, ..., bB represent, collectively, the c largest EMSR values in the set {EMSR'(x); 1 5 x <_ ~' ; j =
A, Bft. If not, then either EMSRA(bA+1) > EMSR~(bB) or EMSR'~(bA) < EMSRB(bg +1). In the former case, (bA+l; bB-1) is a better allocation, and in the latter case, (bA-1, bB+1) is a better allocation, contradicting the optimality of (bA, bB).
[00125] Finding the optimal allocation is similar to a bin-packing problem that reserves c seats for the most valuable second period bookings, as measured in terms of their EMSR values.
[00126] Example. If ~ _ $350; j = $330, DA follows a Poisson distribution with parameter 50, DB follows a Poisson distribution with parameter 40, ~ = 60, ~B
= 38 and c = 83, then (bA, bB) _ (47, 36) is an optimal allocation and h(60, 38, 83) _ $350 E
min(DA, 47) + $330 E
min(DB, 36) _ $27,470.09.
[00127] Moreover, EMSR~(47) = $239.16, EMSRB(36) = $250.00, EMSR~(48) _ $220.62 and EMSRB(37) _ $232.21. Thus, h(60 + 1, 38 + j, 84) = h(60, 38, 83) +
EMSRB(37) _ $27, 702.30 for all non-negative integers f and j. Finally, h(60, 38, 82) = h(60, 38, 83) - EMSRA(47) _ $27,230.93.
[00128] Theorem 1 suggests two simple algorithms to find an optimal allocation depending on the size of s relative to c + s. if s = 0, then b' _ ~', j = A, B
is optimal. This is, of course, the single-period solution when only specific products are offered. If s is small relative to c+s, then it is efficient to seek for the s smallest EMSR values and subtract those from the NEWYORK 82388v2 _ _ .._ .____ __ _.,.. . _ _ __~ ~_-- _.__ _ -_~

P-00057 (19240-187) allocation r'. On the other hand, if c is small, then it is more efficient to find the c largest EMSR
values.
[00129] Second Period Allocation with Overbooking [00130] Here we consider the situation where overbooking is allowed and there is a finite value of the denied boarding penalty, d. To compute (h' is denoted in the Figures with a carrot "~" over h) h'(~, rB, c) in this situation we need to study the marginal expected revenue for 0 _<
b' <_ ~' ; j = A,B. It is easy to see that an optimal solution will satisfy bA
+ b~, c axed that overbookings will occur only if b'~ + bB > c. The restriction to b' < r' is imposed without loss of generality because the expected marginal seat revenue net of overbooking costs is negative for b~
> ~' since < d.
[00131] We can write the second period allocation problem with overbooking as shown in Figure 5.
[00132) We will present two ways of obtaining an optimal solution for the second period allocation problem with overbooking. The first will start from an optimal solution without overbooking and sequentially increase the allocation (bA, bB) as long as the objective function H'(bA, bB c) continues to increase. This approach has the advantage that it calculates the incremental value of allowing overbooking as well as the optimal allocation.
The second approach is more direct since it does not require calculation of the optimal solution to the allocation problem without overbooking. However, it also does not directly compute the gain from allowing overbooking.
[00133] To develop the first algorithm, we require the lemma and proof shown in Figure 6.
[00134] From Figure 6, the last quantity is strictly larger than the expected marginal revenue minus denied boarding cost of the b$ + j + k'th booking. This shows that the allocation (bA - k +1, b~ + j + k - I ) has higher expected net revenue than the allocation (bA - k, bB +, j + k).
By repeating this argument, if necessary, we see that there exists an optimal solution of the stated form.
[00135] From Lemma l, we know we can start our search for an optimal allocation with over-booking from an optimal allocation without overbooking. Starting at the optimal allocation NEWYORK 82388v2 P-00057(19240-187) without overbooking, we can increase the allocations as long as the expected net marginal revenues calculated by equations (6) and (7) are positive. We can use this result to develop an algorithm to calculate the second period allocations when overbooking is allowed.
[00136] See Figure 7 for the "Algorithm to Compute Optimal Second Period Allocations and Optimal Expected Profit with Overbooking." See Figure 8 for an Example.
[00137] There is another, more direct, characterization of the optimal second-period allocations with overbooking that can simplify the calculation of the optimal allocations. See Figure 9 for Theorem 2 and Corollary 1. See also Figure 10 for an Example and Corollary 2.
[00138] It may be optimal to set allocations that allow overbooking in the second period, even in the absence of no-shows and cancellations. If the airline decides not to allow over-booking, it is constrained to set its booking limits bA and bB such that bA+bB
= cA+c~ - s'. On the other hand, if it allows overbooking, the number of possible booking policies is significantly expanded. Intuitively, allowing overbooking is optimal if the expected incremental gain from expanding the booking limits for the specific products outweighs the expected incremental risk of outcomes that would lead to bookings in the "overbooking region."
[00139] Second Period Dynamic Allocation [00140] In this section, we consider dynamically allocating seats in the second period.
Suppose that the second period consists of T time intervals, and assume that at most one request for the high fare product for either A or B (but not both) occurs during each time interval. This is identical to the booking model introduced by Lee and Hersh (T. Lee and Hersh, M., "A Model for Dynamic Airline Seat Inventory Control with Multiple Seat Bookings,"
Transportation Science, 27, 3 (1998) 252 - 265). See Figure 11.
[00141] We remark that it is easy to expand the dynamic formulation to time-varying arrival probabilities, time-varying fares, and to the case where flexible sales are allowed over the entire horizon, or a portion thereof. We also note that the second-period dynamic allocation approach will never result in overbooking.
[00142] First Period Problem [00143] We now turn to the problem of calculating the first period allocations. At the beginning of the first period we need to determine the booking limits (b~A , b1B , b). Recall that NEWYORK 82388v2 P-00057 (19240-187) the demands for discount flight specific products for A and B and flexible products in the first period are denoted by Y~, Y~ and Y, respectively with corresponding fares, g , gB and g. See Figures 12, 13 and 14 for the computations. From this point, we can iterate between reducing the values b~', j = A, B for a fixed b and increasing b for fixed b~', j = A, B
until total expected profit is no longer increasing. Our simulations indicate that this heuristic converges to what appears to be an optimal solution (our simulations also show that expected revenue is very flat around this locally optimal point). We use a similar heuristic for the case where overbookings are allowed in the second period, and when second-period bookings are managed dynamically.
[00144] Numerical Results [00145] In this section, we present numerical results for various settings of the problem parameters with and without overbooking. The purpose of these simulations is to gain insight into the benefits that an airline might achieve from flexible products, the relative magnitude of the risk-pooling and demand induction benefits of flexible products, and the benefits of allowing overbooking.
[00146] Risk Pooling Benefits [00147] In the first set of simulations we focus on estimating the risk-pooling benefits from flexible products. We consider two flights A and B with identical capacities, cA = cB = 100 and two booking periods. In the second periad, only full-fare specific bookings for A and B are received. The full fare is $200 and full-fare demand for each flight follows independent Poisson distributions with ~,2A = 75 and ~,2g = 25.
[00148] In the base case, we assume that only specific discount booking requests are received during the first period. Each discount passenger pays $150 and specific demands follow independent Poisson distributions with 7~1A = 80 and ?~1B = 40. In this case, the optimal booking limits for the two flights are bA = 31 and bB = 78 and the associated expected total revenue across both flights is $29,178.
[00149] To test the sensitivity of total expected revenue to the option of offering flexible products in the first period, we assume that the demand for flexible products follows a Poisson distribution with mean ~,~ _ ~,1A + x,18 = 120. In other words, we assume that when we offer a flexible product instead of the two specific products, the expected total demand for the flexible N&WYORK 82388v2 P-00057(19240-187) product is equal to the sum of the expectations of the specific products.
Since the flexible product is assumed to be inferior to the specific products, we would need to offer the flexible products at a lower fare to achieve the same level of demand. We then ask the question: how much can we discount the flexible product relative to the discount specific products and still make money? Let the flexible product fare ~ = a $150, where a <_ 1. We determine the total revenue obtained with the flexible product as a function of a. This provides a measure of the risk-pooling benefits provided by the flexible product, independent of any demand induction.
[00150] The "Static-Control Revenue" column in Table 2 shows the expected maximum revenue that could be gained from both flights assuming that only flexible products are offered in the first period and that static control without overboaking is applied to full-fare bookings in the second period. In other words, booking limits b~ and bB are set optimally at the beginning of the second period with bA + bB = c~ -+- cB - s where s is the number of flexible bookings accepted in the first period. Full-fare bookings for each flight in the second period are then given by min[b', D'] for i = A, B, where D' is unconstrained demand. The "Dynamic-Control Revenue" column shows the expected maximum revenue that could be achieved from full dynamic control of second period full-fare bookings using the dynamic program described in the section "Second Period Dynamic Allocation" above. Revenue under both control mechanisms is compared against the base case under which specific products are offered at a discount in the first period.
As expected, the expected total revenue from dynamic control of full-fare bookings is greater than that achieved from static control{however, it is interesting that in these cases, the vast majority of the benefits from flexible products can be achieved through static control.
[001511 Table 2: Expected revenue for different flexible fare levels, assmning no demand induction. The base case is offering only discount flight-specific products in the first period with a corresponding total revenue of $29,178.
Alpha Static ControlChange from Dynamic Change from Revenue ($) Base (l) Control Base (%) Revenue ($) 1 34,123 17.0 34,306 17.6 0.9 35,516 11.4 32,774 12.3 0.8 30,944 6.1 31.224 7.0 0.7 29,410 0.8 29,701 1.8 0.6 27,914 -4.3 28,205 -3.3 NEWYORK 82388v2 P-00057 (19240-187) [00152] Table 2 shows that the risk-pooling benefits provided by flexible products can be significant, even in the absence of any induced demand. Under static control, offering flexible products in the first period provides higher revenue than offering specific products as long as the fare for the flexible products is greater than 70% of the specific fare -assuming that total expected demand remains the same.
[00153] Demand Induction and Cannibalization [00154] For a more realistic estimate of the potential benefits of offering flexible products, we simulated the case when flexible products stimulated higher demand but also cannibalized demand from discount specific products. To simulate the effect of offering a flexible product, we use a simple consumer-choice model that estimates both demand induction and cannibalization in a consistent fashion. Specifically, we assume that the fraction of buyers with a maximum willingness-to-pay (w.t.p.) for specific products has a joint distribution over R2+ of g(w~, wB).
We further assume that the total number of buyers is a Poisson random variable with parameter ~., and that the willingness-to-pay distribution is independent of the total number of buyers.
Finally, we assume that, for each customer, the maximum willingness-to-pay for the flexible product is a function of his w.t.p.'s for the specific products according to:
w(wA, wB) = pwA + (1 p)we - p where p is the customer's probability that he will be assigned to flight A and p > 0 is his reduction in willingness-to-pay for the flexible product. Conceptually, p is the "value of information" that the buyer of the flexible product would pay to knave which flight he would be assigned to at the time of booking. In a fully general model, both p and p would be random variables, possibly correlated with w'~ and w&. However, for simplicity we assume that p = 1/2 (the maximum-entropy assumption) and that both p and p are constant across the population.
[00155] For this model, we have assumed no recapture among products. That is, if a customer does not find his first choice available, he does not purchase. While this is not fully realistic, it simplifies calculations and is fairly standard in revenue management analysis. It is also a conservative assumption - it tends to reduce the benefits of offering the flexible product since we have assumed that the customers who seek to buy the flexible product but cannot because of the booking limit are lost, where in reality some of them would be willing to buy the specific products.

NEWYORK 82388v2 P-00057 (19240-187) [00156] For these simulations, we set the flight capacities at cA = cB = 100.
As before, we consider two periods. In the first period, both flexible products and discount specific products are offered. The total population of buyers in the first period has mean ~. = 444.
The willingness-to-pay of buyers for flights A and B are given by independent uniform distributions on (0, WA) and (0, WB) respectively. Figures 15 and 16 describe how total demand for the flexible product and the two specific products, including both induction and cannibalization effects can be calculated for this model. For our simulation, we set WA = I85 and WB = 168. In the second period, only full-fare specific products can book. The full fares for each flight are $200 and the discount faxes $150. The full-fare demands were assumed Poisson with parameters ?~2R = 75 and ~,2g = 25.
[00157] Tables 3 and 4 show the results for p = $10 and p = $30, respectively.
~,' for i =
A, B, f are the mean demands for each product including induction and cannibalization. bA, bB, and b are the optimal booking first-period booking limits for A, B, and the flexible product respectively. In each case, offering flexible products at a very low fare leads to a loss in total revenue because the loss from cannibalization exceeds the gain from demand induction.
[00158] However, at a sufficiently high fare, offering flexibles begins to show positive benefits. These benefits begin to decline when the flexible fare becomes high enough that it is no longer inducing enough new demand to outweigh cannibalization. When the flexible fare is equal to $150 - p, the benefit from offering flexibles drops to zero, since they no longer induce any additional demand.
[00159] We note that, for p = 10, the expected demand for all three products at any flexible fare g is the same as the expected demands for p = 30 at a fare g -$20.00. However, for p = 10, the value of b is higher at g then for p = 30 at g - $20.00, since flexibles are relatively more valuable at the higher fare. Consequently, the maximum achievable expected revenue is higher with the lower value of p. Similar reasoning shows that, for this choice model, maximum achievable expected revenue from offering flexible products is a decreasing function of p. See Figure 17 for Table 3, which shows simulation results for p = 10, and for Table 4, which shows simulation results for p = 30.
[OOlbO] Summary NEWYORK 82388v2 P-00057 (19240-187) [00161] In this example, we derived some revenue management approaches for a supplier offering both flexible and specific products. We showed that, under reasonable assumptions, optimal booking limits can exceed the total seating capacity available, even in the absence of no-shows or cancellations. We derived algorithms for computing booking limits on both specific and flexible products in the two-flight, two-period case; both when overbooking is allowed and when it is not. We also formulated a dynamic program for optimal acceptance of flexible and specific bookings on a booking-by-booking basis. We used simulation to show the potential benefits of flexible products both in terms of pure risk-pooling, and under a consumer choice model that represented both demand induction and cannibalization. While managing flexible products adds complexity to the revenue management problem, our simulation has shown that offering flexible products can significantly improve profitability. The increased profitability comes from two sources: (1) 'fhe lower price of the flexible product attracts additional customers who would otherwise not choose to purchase; and (2) Flexible products enable companies to wait for uncertainty on specific product demand to be resolved before the flexibles are assigned to products. This enables better usage of capacity.
[00162] Our simulations showed that under reasonable assumptions, the benefits of offering flexible bookings could be considerable - even when cannibalization from discount specific products is included. The benefits vary widely depending upon the unconstrained demand for specific products and how specific demand is distributed between flight alternatives.
The results suggest that flexible products would have the highest benefit when the constituent specific products have total demand that is low relative to capacity and when specific demand is unevenly distributed among flights (again relative to capacity.) For tl-~e parameters we chose, the value of overbooking was quite small relative to total revenue.
[00163] The present invention encompasses extending this Example's approach to a full network consisting of many flexible and specific products. The feasibility of serving any portfolio of flexible and specific bookings on a network of constrained capacities can be determined by solving a linear program. Also, a column generation approach can be used to determine the best set of flexible products to offer given a constrained network and a set of customer preferences. The benefits of offering flexible products changes as a function of total demand for a network with fixed capacity.
NEWYORK 82388v2 _____~._.~, ~ .

P-00057 (19240-187) [00164] Further, the present invention encompasses the incorporation of general consumer choice models. A flexible product is not only an economic substitute for each of the specific products it contains; those specific products are also substitutes for each other. Thus, we could expect that closing any of the availabilities of the products might increase demand seen for the others.
[00165j In this example, we have assumed that offering low-price flexible products can induce additional demand. Further, the present invention extends the models of this Example to where much of this induced demand would be drawn from competitors who ara not offering flexible products. In this case, a competitor who is unable to offer flexible products (due to a limitation in his booking system, say), may retaliate by lowering his own specific fares. The present invention also encompasses the case of two competing carriers, both of whom can offer flexible products in a market, but one of which has more frequencies.
(00166] In this Example, we have assumed that the airline has complete discretion on which specific product to assign a flexible customer. One variation would be to allow the flexible passenger to rank their alternatives. The airline could use one of a variety of schemes to match flexible customers with available flights in a way that best accommodates their stated preferences. Alternatively, airlines could book the flexible passengers to a flight at the time of booking - or any time thereafter.
(00167] This approach may make a flexible product more appealing to consumers, but this is a two-edged sword - anything that makes the flexible product more appealing increases cannibalization from the higher-fare specific products. The present invention provides methods of revenue management to determine how these tradeoffs would work in order to design the "right" portfolio of flexible products for an airline to offer.
[00168] Although in this Example, we have presented our analysis of flexible products entirely in a passenger airline context, the models and concepts of this Example is applicable to any seller of products or services who uses different elements of capacity and faces uncertain demand. For any such manufacturer, offering flexible products has the potential to both increase demand and better balance demand with capacity. Further, the present invention encompasses flexible products of contract manufacturing.
NEWYORK 82388v2 ... _.._ .. _...._..__ ~__ v...",;n."... ~...~.-----.~ _._._.._,_m~~,.r"_-"~"~_-.~_.__._ P-00057 (19240-187) EXAMPLE 2: STRATEGIC PRICING IN CONSTRAINED MARKETS WITH REPEATED
TRANSACTION
[00169] In this Example, a class of models are considered with the following four properties:
[00170] First, sellers have fixed capacity or a fixed inventory of a good fox sale.
Examples of fixed capacity include airline selling seats on a flight, hotels renting rooms, and manufacturers selling capacity slots in a pure order-to-delivery environment.
Examples of fixed inventory of goods for sale include fashion retailing where inventory is ordered once and cannot be replenished because lead times are longer than the sale horizon.
[00171) Second, buyers interact with sellers over a number of time periods to transact the good. The model is developed in terms of a capacity sale in which buyers are purchasing reservations for capacity to be consumed at a future time (as in airline reservations). The model is also applicable to inventory sales in which buyers receive the product at the time of purrchase (as in fashion goods).
[00172] Third, the value of unsold goods drops to zero at the end of the final period - i.e., there is no salvage value for the good. Positive salvage value can be incorporated by adjusting prices without loss of generality.
[00173] Fourth, buyers and seller will interact many times - buyer expectations and competitive actions by sellers will be influenced by observed past behavior.
This is one difference of this Example relative to the other Examples herein.
[00174] This Example provides a general model that can be used to manage revenue, and covers a wide number of real-world markets including airline seats, hotels, fashion goods, high technology goods, gas pipeline capacity sales, automobiles and many others. In many cases, tactical pricing and inventory availability policies have been developed in industry. However, these policies are based on a single transaction between a buyer and a seller.
This Example provides pricing and availability policies when there are multiple transactions and the behavior of buyers depends upon the availability that they have seen in the past.
[00175] Special cases of perishable, constrained capacity models that will be expanded upon include "revenue and yield management" and "markdown management". Revenue and NEWYORK 82388v2 P-00057 (19240-187) yield management problem is faced by airlines, hotels, rental cares, and other industries. In the revenue management problem, prices are generally assumed to be fixed and the seller's problem is to determine how much capacity to reserve for higher price, late-booking customers. In markdown management, the problem facing the seller is when and by how much to markdown unsold goods over a finite season. The number of times that goods can be marked down is usually limited and it is often assumed that the price of a good cannot be raised once it has been marked down.
[00176] In this Example, models will be developed in which capacity is limited and immediately perishable and buyers seek to reserve capacity ahead of time. The overall setting is similar to the revenue management problem with the two following differences.
[00177] First, we assume that buyers' assumptions about price and availability in each booking period are influenced by past outcomes. E-commerce has made pricing and inventory availability information easier for consumers to track over time and this supports the informational aspect of our assumption. Second, we look explicitly at competitive actions and behavior over time as being intrinsic rather than extrinsic to the analysis.
If a seller makes large amounts of capacity available at a low price during one instance of the problem, some buyers will assume that the seller will act the same way in the future and adjust their behavior accordingly. A recent example of this is the $2,002.00 rebate for every GM
vehicle, or the 0%
financing after September 11, 2002. These assumptions extend the analysis beyond a single interaction between buyer and seller to consider a sequence of interactions.
Thus, this Example and the present invention provide revenue management methods for the interaction of customer expectations with supplier inventory and pricing policy in the context of multiple interactions.
[00178] The Basic Model [00179] A seller has a fixed, perishable capacity C. Sales of this capacity occur over two periods. During period i, the supplier sells capacity at a price of r;. We assume that r~ and ~2 are announced ahead of time and known to both the seller and all buyers. At the end of period 2, the value of unsold capacity drops immediately to 0 - ie, there is no salvage value. (The zero salvage value assumption is without loss of generality. If there is a residual value r~3 c r2 then we can reformulate the problem to maximize the revenue in excess of salvage value by setting r, ~

NEWYORK 82388v2 P-00057 (19240-187) r; - ~3 for i E jl, 2, 3~.). We denote the case in which rl > ra the markdown management problem and the case in which r, < r2 the revenue management problem.
[00180] We assume that there is a population of potential customers D. Each customer within this population can be characterized by a willingness to pay vector (W~, W2) where W;
denotes his willingness to pay in period i for capacity. There are three possibilities.
[00181] First, Wl = W~. The willingness to pay of a buyer is the same in the fist period as the second. This buyer's behavior will be driven entirely by the prices being offered in the two periods and his belief on capacity availability in period 2.
[00182] Second, Wj > W2. This buyer is willing to pay more in period 1. This would characterize markdown markets in which the value of the object purchased declines over time -such as fashion goods as well as some industrial markets where the buyer is willing to pay a premium to lock-in future capacity and eliminate supply uncertainty.
[00183] Third, WI < W2. This buyer is willing to pay more in period 2. This is considered to be a characteristic of some airline passengers who may be uncertain during period 1 about their need to travel, but have that uncertainty resolved in period 2.
[00184] We assume that the willingness to pay in the two periods has a joint density function f with the support on R2+. Note that this model is general - for example, as a special case, D could consists of two independent populations; one of which has W> > 0 and W2 = 0, the other which has WI = 0 and W2 > 0.
[00185] Denote the unconstrained the demand in period i by Dt. In each period, the seller can choose to accommodate demand up to his level of unsold capacity, or he may choose to set a sales limit, 0 <_ bl <_ C on the amount of capacity that he allows to be sold.
Then, expected total revenue is given by: TR(bl, b~ _ ~IEjmin(Dl, b~)J + rZEmin jD~, b2, max(C -Dl, C - b~)J.
[00186] We assume that sellers are seeking to determine to values of b; to maximize total revenue (for simplicity, we will assume throughout that variable costs for the seller are zero -this is appropriate for sellers who are seeking to dispose of existing inventory - such as a retailer who has already purchased fashion goods or a hotel selling rooms) given their capacities, prices, and uncertain knowledge of demand. We denote b'~ (where b' is also depicted, including some figures, as b with a carrot ~ over it) as tactically optimal if it maximizes total revenue assuming a NEWYORK 82388v2 i ~___ P-00057(19240-187) single instance of the problem. Since capcity is perishable, we will always have b'2 ~ C, In addition, see Figure 18 for equations (1) and (2).
[00187] In equation (2), G2 is the c.d.f. on D2, here assumed to be continuous and strictly increasing on R+ (hence invertible). These conditions are standard results from the basic newsvendor problem and revenue management problem. This Example focuses on the case of multiple instances where buyers and seller interact repeatedly over time. Each instance may correspond to capacity availability in each period, and hence, the unconstrained demand in each period will change far each instance. Let D;(~) indicate unconstrained demand in period i during instance n > 0, p;(n) indicate buyers' probability of availability during instance n, and b;(n) the amount of capacity that the seller will offer for sale at price ~; during instance n. Let x;(n) denote sales and y;(n) = xl(n)lD;(n) the fraction of unconstrained demand in period i that is satisfied in instance n. Then, it is reasonable to expect that a buyer's posterior probability that capacity will be available in period n will be a function of the fraction of total demand that was satisfied in past interactions: See equations (3) and (4) in Figure 18. Explicitly considering this process of expectation formation will lead to pricing and availability policies that can differ significantly from those that are tactically optimal.
[OOI88] Situations are also considered in which there is more than one supplier. In these cases, the supplier is denoted by a superscript capital letter. Thus, x;A(n) indicates sales from supplier A during period i on interaction n. Absence of a superscript will indicate that we are dealing with a single supplier.
[00189] Strategic Pricing of Distressed Inventory [00190] Marking down prices on obsolete or distressed inventory is a time-honored in many industries. Inventory may become distressed because it is physically perishable - as in airline seats or "sell it or smell it" goods such as fish or meat.
Alternatively, inventory may become distressed because it becomes unseasonable or obsolete as new models are released - as in fashion goods or high tech electronic goods. In this part of the Example, the invention provides the optimal pricing of distressed inventory in the presence of buyers whose expectation of future discounts may influence current behavior.
[00191] 'The Distressed Inventory Model. In the distressed inventory model, prices are lower in the second period than the first, ~Z < ~l, and inventory perishes at the end of the second NEWYORK 82388v2 P-00057 (19240-187) period. The optimal tactical policy is for sellers to allow all of their unsold capacity to be sold at the price r2, that is b'2 = C This corresponds to intuition - making the distressed available for sale at any price r2 > 0 is more profitable than allowing it to "perish"
unsold. However, the solution can be considerably different when we consider future interactions between buyers and sellers.
[00192) In this case, a buyer will either purchase the capacity at the full price in the initial period or choose to "wait for the sale" and hope to purchase the capacity at the discount price in the second period. For a particular buyer, the decision to purchase in period 1 or wait until period 2 will depend upon the prices in the two periods, his willingness to pay for capcity, the cost of waiting and his estimate of the likelihood that the capcity will be available in period 2. If buyers believe that sufficient capacity will be available in period 2, and their willingness to pay does not change, then they will all wait for the sale and purchase at the lower price. If, on the other hand, buyers believe that there is a low chance that capacity will be available in period 2, then some buyers "lock in" their purchases in period 1 while others will wait until period 2 in hopes of getting the lower price. In a repeated interaction between buyers and sellers, it is reasonable that buyers will form their expectations about the availability of distressed inventory based on their past interactions. This will provide an incentive for sellers to limit the amount of distressed inventory that they offer. See Figures 19 and 20 for the mathematical resolution of the distressed inventory model.
[00193] Numerical Examples. To see the impact of customer expectation formation, consider the following example where D follows a Poisson distribution with parameter 7~: C =
100; ~I =1 ~ 0; ~1, = 250; p~(0) = 1; p2(0) = 0; p~(h + 1) = pl(n) + a(y;(n) -pa(~)).f°~ all n > 1. In addition, we will assume that the willingness to pay is the same in the two periods and is given by an exponential distribution with rate 1/100 (mean = 100), that a = 1, and that bl(n) = C'. For comparison purposes, the expected revenue that would be achieved from offering a single fare at $150, i.e., b2(n) = 0, would be $8,367 with ~,~(n) = 55.8 for all h.
[00194] Table 1 in Figure 21 shows the results of a sample path for the case ~2 = 50 and b2(n) = 100. As expected, the tactical policy of making all remaining capacity available for sale at ~2 results initially in a significant revenue increase. However, as buyers learn to anticipate that distressed inventory will be available and adjust their behavior accordingly, cannibalization of NEWYORK 82388v2 P-00057 (19240-187) full-fare business begins to occur. Averaging the results of a simulation over 1000 sample paths results in an estimated expected equilibrium revenue equal to $5,968.40 with a standard error of $16.22. This average represents 71.3% of the benchmark with b2(n) = 0.
[00195] The example in Table 1 illustrates that the tactically optimal solution of selling all distressed inventory at a discount price can lead to a suboptimal solution when the impact on customer expectations is taken into account. Now, consider the case where the seller sets a higher distressed inventory price r~ = 100 and sets a booking limit b2(n) =

50. Table 2 in Figure 21 shows a sample path for this case. Again, the seller initially realizes a substantially increased revenue. As buyers learn to anticipate that distressed inventory will be available and adjust their behavior accordingly, cannibalization of full-fare business begins to occur.
In this case, however, the demands and sales oscillate between two states during the first few instances - one in which total demand is split between the two classes, and one in which virtually all demand is for the discounted capacity. Our simulation over 1000 sample paths indicates that the system converges to an expected equilibrium revenue of $7,789 (93.1% of benchmark revenue) with a standard error of $59.50. Again, the seller would be worse off from selling distressed inventory, even at the higher fare and with the limit in place.
[00196] The above examples assume that consumers are totally myopic and base their expectations on the last realization. However, we have observed that the limiting behavior of the system seems to be the same under exponential smoothing updates of probabilities for all positive values of a. It is also interesting to observe that while the fluid limit approximation can display oscillatory behavior, its limiting average behavior is very close to that of the corresponding stochastic system. The present invention also encompasses a system to determine the extent to which demands seen by the suppliers in each period are driven by the non-linear dynamics of the system as opposed to the intrinsic uncertainty.
[00197] Summary [00198] This Example provides revenue management methods that consider the behavior of demand and price over time, the nature of optimal policies on the part of the seller, the existence and nature of equilibria, and the implications for seller profitability and buyer expenditure compared to alternative policies. Also encompassed are: the optimal static and dynamic sales limit policies on the part of sellers; the kind of behavior that prices, demands, NEWYORK 82388v2 P-00057 (19240-187) sales and total revenue display under various static policies over time; how different expectation formation mechanisms affect the evolution of the system - possibilities for h > 1 include ~z ~~~ --- ~i~.~ --1) -f- ~~~~i~ _ 1~ - P,~y " 1~~ figs some a: wit~~ (1 ~ fx < 1 ~i~n~~ - ~t~_.rj-.0 ~3~~f~ - 1)~~~' how the seller can set an optimal (or even sensible) policy, in the case when he does not have full knowledge of f, but only observes unconstrained demand (D;(n)) in each period n, and in the case if the seller cannot observe demand but only sales in each period (x;(n));
what conditions is there an equilibrium for which p;(h) _ ,y;(n) for i = 1, 2, and under what conditions does the system approach such an equilibrium; whether the results change in any significant fashion if the seller faces a production cost function for the good; whether the seller could also change the prices r;(h); when there is a switching cost to the buyer (e.g., airline miles); and situations that have more than one seller - if buyers do not switch sellers based on availability, then there is no impact, but if buyers choose sellers based on past availability, then the nature of the optimal policy is likely to change.
EXAMPLE 3: DETERMINISTIC ANALYSIS OF THE FLEXIBLE BOOKING PROBLEM
[00199] In this Example, the present invention provides formulae that can be used in the revenue management methods herein. The formulae resolve the deterministic flexible booking problem in a network. The details of the model are as follows. The network consists of m resources and the capacity of the resources is given by a a vector c E R"'+.
This network offers n specific products. The vector p E Rm+ denotes the revenue derived from the specific products, i. e.
p~ denotes the revenue from the sale of 1 unit of the j-th specific product, j = 1, ..., h; and A E R' x n denotes the capacity utilization matrix, i.e. A~ , i = l, ..., m, j = 1, ..., n, denotes the amount of resource i required by 1 unit of the specific product j. ~Ve will denote the set of specific products by N.
[00200] The network also offers f flexible products. Each flexible product k =
l, ..., f, is described by a set Nk a N of specific products and network manager has the flexibility of assigning the demand for the flexible product k to any of specific products included in the set Nk.
Let hk = ~N~ ~ denote the number of specific products constituting the k-th flexible product and let Ck denote the submatrix of A obtained by picking the columns of A
corresponding to Nk. In the NEWYORK 82388v2 P-00057 (19240-187) airline context, the specific products are combinations of specific flights, or an itinerary, that serve a particular origin-destination (O-D) pair and a flexible product is a collection of alternative itineraries serving a given O-D pair. The revenue from the flexible products is given by a vector ~ E Rf+ and the set of all flexible products is denoted by F. See the section "Computational Results for a Real Airline Network" in this Example for an example of a real airline network.
[00201] The demand for the specific and flexible products is assumed to be given by a choice model. Specifically, we assume that when a subset S c N a F of products is offered by the network, the arrival rate for specific products is given by ~,(S) E Rn+
and the arrival rate for flexible products is given by y(S) E Rf+. Specific choices for ~,(S) and y(S) are discussed in Section "Column generation algorithm" in this Example and Figures 39A-C.
[00202] The time horizon for the problem is T, i.e. the network resources have to be sold over the time horizon [0, T] and are worthless after T. We will assume that the assignment of the demand for flexible products to particular specific products is made at time T. The goal of the network manager is to choose a sequence Sl c N a F, l = l, ..., L, of subset of products to offer and corresponding time intervals t(S~), l = l, ..., L, over which to offer these sets in order to maximize the revenue. See Figure 22 for computation towards equation (1) that represents the optimization problem faced by the network manager.
[00203] The decision variables in (1) are the times {i(S) : S c N v F, and the composition variables z, i. e. the number of variables are 2n+r + Efk=I nk -1. Since there are only m + f + 1 constraints in the problem, at most m + f + 1 of the exponentially many variables in ( 1 ) can take a positive value. Moreover, suppose the k-th flexible product is offered for any period then at least one of the components of the zk vector must be strictly positive. On the other hand if the k-th flexible product is never offered then the row corresponding to k in the constraint E,~~y(S)t(S~ - U
= 0 is effectively redundant and can be dropped without affecting the solution. Thus, we have the following result. Lemma l: There exists an optimal solution of the LP (1) with t(S) > 0 for at most m+ 1 subsets S c N a F.
[00204] Since the number of variables that will be positive at the LP optimal solution is relatively modest, namely m + l, a column generation ought be an efficient algorithm for solving NEWYORK 82388v2 P-00057 (19240-187) ( 1 ). In the next section, the Example provides a column generation algorithm that works well for some restricted classes of consumer choice models:
[00205] 2 Column generation algorithm (00206] See Figure 23 for the column generation algorithm equation (1). See Figure 24 for the LP dual of (1). Notice that we have kept all the z variables in the restricted LP. This is not necessary - zk must be included only if the k-th flexible product is offered by some set S E
~o~.
(00207] Suppose the restricted LP is solved to optimality. See Figure 25 for the resolution.
For column generation to be successful one must be able to efficiently solve (4) for all values of the dual variables (u, v, /~. This is impossible for arbitrary assignments of the demand rates {~,(S), y(5~~, S c N a F. We focus on the following special case presented in Figures 26 and 27.
[00208] Therefore, one can restrict attention to set of the form SS = { j ~ N
: x~ <_ S ~ a { k a F : yk _< S} for 5 >_ wl. The result now follows by recognizing that the sets SS are identical for w~ S
<wt+ul=1,...,n+f [00209] The characterization of the "minimum set" in Lemma 2 leads to the column generation algorithm displayed in higure 23.
(00210] The optimal basis for the restricted primal corresponding to the index k is a feasible basis for the restricted primal corresponding to the index k + 1 and, therefore, can be used as the starting basis. Typically, the re-optimization only requires 1-4 pivot steps.
[00211] Pe>~formance analysis of the LP solution i>z a stochastic >zetwo~k [00212] In this Example, we are mainly concerned with the deterministic analysis of the network flexible booking problem. However, in any real network the t, the demand for the flexible and specific products is, likely to be random. In this section, the performance of a feasible LP-based policy in a stochastic network is provided.
[00213] We assume that when the network manager offers a set S c N ~ F
requests for a specific product j E S n N arrive according to a Poisson process with rate 7~~(S) and requests for flexible products k a S n F arrive according to a Poisson process with rate y;(S), where ~,(S') and y(S) are defined by (5) and (6) respectively.
NEWYORK 82388v2 ___.~~. J

P-00057(19240-187) [00214] It is easy to establish that the optimal value of the LP (1) is an upper bound on the expected revenue achievable in the stochastic network. On the other hand, optimal solution 1(S*I
t*~), d = l, ..., L}of the LP yields a feasible policy defined as follows.
[00215] (a) Select a permutation ~ of (1, ..., L) and open sets in the order {S~~l~, : l = l, ..., L} for a period {t*~~~,: l = 1, ..., L}.
[00216] (b) At the beginning of the time interval corresponding to the set S*~
open all products included in the set S*t. At any time t E [0, T], let x(t) ~ R" and y E R~ denote respectively the number of specific; and flexible products sold.
[00217] At any arrival epoch update the state (x, y), i. e. if the arriving request is for a specific product, increment the appropriate component of x by 1, else increment the appropriate component of y by 1. If there exists an integer composition vector z such that y = Uz and Ax + Cz _< c, accept the arriving request. Otherwise, reject the request, reset the state (x, y) to the original value and close the product corresponding to the current request.
[00218] Remark l: Note that in order to implement the policy one needs to solve a integer program at every arrival epoch.
[00219] In our computational experiments with the above feasible policy, we considered network with rrz = 5 resources, n = 10 specific products and f = 4 flexible products. All the other problems data such as the matrix A, the sets Nk, k = 1, ...,,f, and the revenue vectors r and p, were randomly generated. For each random instance of the underlying network we simulated the performance of the LP-based policy as the time horizon T and the total capacity c are simultaneously scaled up by a factor a = 1, I0, 100, 1000. For each scale factor the revenue generated by the above policy was averaged over 500 trials. In every random instance of the network, we found that the permuting the sets {S*I} did not improve the performance of the optimal policy. Therefore, we report results for the identity permutation.
[00220] Figure 28 displays the result of the results for generic random network instance.
In the plot ,cc denotes the average expected reveue, i.e. 1/aT E[R(aT)], where R(aT) is the random return of the policy over [0, aT], the upper and lower bounds, labeled fc ~ 2 0-respectively, are given by . 1/aT E[R(aT)] + . 2I(aT)2 Var[R(aT)], and the lp opt denotes the optimal value of the LP. From the plot it appears that as the scale factor a T
~o the average NEWYORK 82388v2 P-00057 (19240-187) revenue appears to asymptotically reach the LP optimal. Thus, for large time horizons T the LP
solution is a good approximation for the achievable revenue rate. This result is consistent with similar scaling results for networks with only specific products.
(00221] Computational Yesults far a peal airline network [00222] In this section we report the results of our computational experiments with a subset of American Airlines flights from JFK, LGA, STL, ORD to SFO. The details of the flights in this model is shown in the Table below:
O-D Pair Flight Time Capacity Revenue (p) I LGA -~ O_RD 6:OOAM - 8:17AM 172 194 2 LGA --~ ORD 7:00 AM - 9:32AM 172 I 94 3 LGA --~ ORD 8:30AM - I 1:OOAM 172 194 4 ORD -~ SFO 9:33AM - 2:16PM 134 287 ORD -~ SFO 1 I :5I AM - 4:25PMI 34 567 6 ORD -~ SFO 1:47 PM - 6: I I 34 567 7 JFK -~ SFO 7:30AM -1:49PM 160 567 8 JFK -~ SFO 3:45PM - 5:12P1VI 160 567 9 LGA -~ STL 6:1 OAM -8:50AM I 76 121 LGA -~ STL 7:SOAM - I0:40AM I72 121 1 I JFK -~ STL 9:20AM -12:11 AM 172 121 12 STL --~ SFO 4:08PM - 8:29PM I 76 278 13 STL -~ SFO 7:40PM -12:13AM 176 278 (00223] There were n = 26 specific products consisting of all the 1-hop flights shown in the Table above and all 2-hop flights from NYC to SFO satisfying time constraints. There were f = 5 flexible products consisting of the O-D pairs: NYC to SFO, NYC to STL, NYC
to ORD, ORD to SFO, and STL to SFO. The set Nk for each flexible product was set equal to all the flights that served the correponding O-D pair.
[00224] The details of the demand model used is sho~m in Figure 29. In this section we study the effect of model parameters, such the time horizon T, the utility u, the discount factor y, etc, on the gain Gf (T). In the sequel we will refer to the LP of the form (1) that includes (resp.
excludes) flexible products as Flex-LP (resp. NoFlex-LP). Thus, Rf(1') (resp.
Rnf(T)) is the optimal solution of the Flex-LP (resp. NoFlex-LP) with horizon T.
[00225] Gain Gf (T) as a function of time horizon T:

NEWYORK 82388v2 .._...___.",...."...- r,~,,., ~,: .~~"~"F~,~ _._... _.__..... _._ -_-..~_.~ _ _..._ P-00057 (19240-187) [00226] In the first set of numerical experiments we studied the gain Gf (T) as a function of the time horizon T, all other parameters being held constant. In particular, the total capacity c was held constant. A typical plot for the gain G f (T) as a function of the time horizon T (all other parameters held constant) is show in Figure 30A. The gain curve starts out flat, next, it enters a phase where it does not have any noticiable trend, and finally monotonically decreases to zero. In the particular instance shown in Figure 30 the slope of the gain curve is negative immediately after the flat section but this is not always the case.
[00227] In order to gain insight into the shape of the gain curve, we plot the Rf (T) and R"f(T) as a function in T in Figure 30B. From LP duality it follows that Rf (T) = of (T) 'c + (3f (T)T
and Rnf (T) = unf (T)'c + (3"f (T)T, where (uf (T), [3f (T)) (resp. {unf (T), (3nf (T))) are the optimal dual variables corresponding to the capacity constraints and time constraint in Flex-LP (resp.
NoFlex-LP). Since the optimal dual variables (uf (T), (3f (T)) and (u"f (T), ~3nf (T)) are piecewise constant function of T and the capacity c is held constant, it follows that Rf (T) and R~f (T) are piecewise linear functions of T.
[00228] For all T suffciently close to 0, the capacity constraints are slack in both Flex-LP
and NoFlex-LP. Thus, Rf (T) _ [3f (T)T and Rn f (T) _ (3~f (T)T, and the gain Gf~ (T') _ [(Rf (T) - R"f (T)) I Rf (T)) x 100 = [([if- (3,~f) ~ (3Y,fj x 100, a constant. Since the capacity constraints are slack in this interval, any gain is mainly explained by the phenomenon of demand induction instead of a more efficient use of the capacity by flexible products. We will return to this issue in later sections.
[00229] The erratic behavior of the gain curve begins at time To when a capacity constraint becomes active in either of the two LPs. (In Figure 30A this break point occurs at T« = 80). Since Rf (T) and Rnf (T) are concave, it :follows that the right derivative of the gain curve at T = T~ is positive if the capacity constraints becomes active in the NoFlex-LP and vice versa. Although subsequence changes in slopes can be explained in a similar manner, it appears that it is impossible to predict the shape of the gain curve without expolicitly solving the LP.
[00230] The gain curve once again becomes predictable for all times T , T1 when all capacity constraints are active in FIexLP. (In Figure 30A this occurs at TI =
245). For T , Tf, the gain decreases monotonieally because the Rnf (T) increases at a faster rate.
When all constraints NEWYORK 82388v2 ...__~_,_...~..~._ _.. . ~_.'._.. ~'~ ._.

P-00057 (19240-187) are active in NoFlex-LP (in Figure 30A this occurs at T = 3G0), Rf (T) = Rnf (l') and the gain drops to zero.
[00231] In summary, the gain curve Gf(T) has an initial constant section where the gain is primarily explained by demand induction, followed by a unpredictable region where gain has a contribution from both demand induction and better utilitization, and then a final monotonically declining section where the NoFlex-LP gradually catches up. Thus, for small T
the manager should offer flexibles to attract demand, and for very long horizon T the flexibles do not add any benefit since the entire capacity can be sold to the higher revenue customers purchasing specific products. Therefore, for low arrival rates are low, as is the case when the utility w is small, one should expect that more flexible products will be offered and the gains will remain positive over a larger time horizon T. We should also expect a similar behavior when the outside alternative (i.e. the products offered by the competition) becomes more attractive. We examine these issues in the next sections. We also attempt to separate the effects of demand induction and capacity utilization.
[00232] Before leaving this section, we examine the nature of the optimal collection of products for Flex-LP. For the instance shown in Figure 30A and Figure 30B, the optimal solution of Flex-LP from T = 1 to T = 85 was constant and consisted of a single set. At T = 85, a new set was added. As T increased, the group of optimal sets changed gradually by the addition of new sets or the . phasing out of sets that appeared before. When a new set S is added, the corresponding time t(S) is initially small; subsequently, t(S) increases, as T
increases, until it reaches a maximum, and then decreases until the set is phased out. After T =
3G0, the time at which Gf (T) drops to zero, the optimal collection of sets remains constant.
(It should be noted that the LP often has multiple optimal solutions, so solving each LP
separately will lead to optimal sets that are not consistent. To correct this, the new LP was solved with the optimal solution of the previous LP as its starting variables.) (00233] Gain Gf (T) as a function of utility w:
(00234] In this section we report on the results of our experiments where we changed the utility w derived from the journey. From (14) and (15) it follows that the arrival rate is an increasing function of the utility w. Since the total capacity c is fixed, the flexible products are likely to become less attractive as the arrival rate increases, or equivalently w increases - the NEWYORK 82388v2 P-00057 (19240-I87) network would not like to waste valuable resources on a low revenue alternative. On the other hand, when the utility is low, flexible products should become attractive because of the demand induction effect, and consequently, the gain Gf (T) due to flexibles will be high. Moreover, since reducing rates is equivalent to scaling capacity up, we expect that for low values of w flexible products will remain attractive over a larger time horizon T.
[00235] Out experimental results are consistent with the above analysis. From the plot of revenue vs. T shown in Figure 32 it is clear that revenue is an increasing function of w. On the other hand, gain Gf (T) plotted in Figure 31 is, on the whole, a decreasing function of w. The gain curves corresponding to different value of w tend to cross in the indeterminate range of the time horizon that was identified in the previous section. In this range capacity utilization effects dominate (see subection "demand induction vs. capacity utilization" for details) and the network offers flexible products, not to enhance demand, but to better manage capacity. Thus, the gains are high even for high value of the utility w. In fact, capacity utilization effect explains most of the gain for the case with w = 3. The Table below lists the number of flexible products in the optimal collection or set.
T _ w=1 ~_ w=2 w=3 ~~

51 4 3 _ l0I 4 2 1 [00236] For fixed utility w, the number of flexibles used decreases with the time horizon T
{this is consistent with results in the previous section); and, for a fixed time horizon T, the number of flexibles used decreases with w.
[00237] In summary, flexibles are especially attractive for low values of utility w and small time horizon T because of the demand induction effect - the network can improve the revenue by at least about 8% by offering flexible products. At intermediate values of T, the demand induction is not as important and it is not as clear to what extent are flexibles beneficial.
For large T, one can sell all the capacity to customers demanding specific products and flexibles are completely unattractive.

NEWYORK 82388v2 ,. _,-.1,_.._~._.._,__._M_.. __..._ ~",~ _..~...n P-00057 (I9240-187) [00238] Effect on outside alternative on the gain G f (t):
(00239] In this section, we report the results of our experiments exploring the effect of competition, or the outside alternative, on the gain Gf (T). We capture the effect of competition by altering the rates g~ , j = l, ..., n, and hk, k = 1, ..., k. Recall that (see (14) and (15)) we had initially set g; / g~ = hk, I hk = 20. In this section, we iteratively set g~
I g~ = hk, l hk = ~, where ~ _ {5, 10, 15, 20, 25}. For the choice model described by (5) and (6) it is clear that increasing ~ has the effect of making increasing the rate of customers that leave the network without purchasing any product, i. e. the outside alternative becomes ever more attractive.
[00240] Figure 33 plots the gain Gf (T) vs. the ø for the utility w = 1 and Figure 34 is the same plot for w = 2 (Note that the gain curve corresponding to ~ = 20 is the same as that in Figure 30A). From these plots it is clear that increased competition has the effect of shifting the gain curve up and to the left. For ~ small, i. e. when the outside alternative is not very attractive, the network manager (as used herein, "network manager" is encompassed by a host server or system, or other computer-implemented methods used to provide revenue management) has a captive customer pool and there is no incentive for offering flexible; thus, the gain Gf (T) is small. AlI the gain in this scenario is explained by capacity utilization effects rather than demand induction. On the other hand, for large ~, i.e. in highly competitive environments, the network manager attempts to capture customers by offering a cheaper flexible alternative; hence, the large gains. In this scenario the manger is atttempting to enhance demand by offering flexible products.
[00241] Effect of discount on gain Gf (T):
[00242] In this section we set revenue rk = (1 - s) min~~k ip~} for E E i0, 0.25, 0.5, 0.75}
and investigated the relation between s and G~~ (T). As Figure 35 and Figure 36 illustrate, increasing the discount on flexibles decreases the gain. Interestingly though, even offering 75%
discount on produces a positive gain fox certain time horizons T. In particular, when w = 0.5 (see Figure 35) a 75% discount produces positive gains over the same range as a 0%
discount.
[00243] Demand induction vs. capacity utilization:
[00244] As we have alluded to before, there are two distinct phenomena associated with offering flexible products. Since offering flexible products increases the number of offered NEWYORK 82388v2 ._ .... ____...._ _...._...r.....w.".~..,~,,~,.,~. . -.. ,~~~

P-00057(19240-187) products, the choice model given by (5) and (6) entails that total arrival rate will increase. This increase in arrival rate is likely to result in an increase in revenue. We will refer to this as the demand induction phenomenon.
[00245] Flexible products allow the network manager to better utilize the capacity by both allocating flexible customers to those resources that are under-utilized and removing flexible customers from resources that are over-utilized. Consequently, one is able to accept a larger fraction of the incoming demand, and therefore, increase revenue. This phenomenon will be referred to as improved capacity utilization.
[00246] From the experimental results detailed above, it appears that the demand induction effect dominates for small T and the improved capacity utilization effect appears to be the primary explanation for increase in revenue for moderate to large values of T. In order to better understand how much of the gain is caused by demand induction, we conducted an experiment where we assigned all the rate of a flexible product k to the specific product j E N
that had the highest revenue, and solved the corresponding NoFlex-LP. This situation represents an extreme demand induction effect where all the induced demand pays the highest possible revenue.
[00247] The result of this experiment is shown in Figure 37. The gain curve labeled Flex gain is a plot of the gain due to offering flexible products and the curve labeled Demand gain plots the gain due to enhancing the demand for certain specific products as described in the above paragraph. Up until T ~ 150, the Demand gain curve is higher than Flex gain. However, after T > 150, Flex gain dominates, suggesting that for T > 150, the gain is due to a better use of capacity rather than to demand induction. We can conclude that as T increases, the effects of demand induction become less significant.
[00248] Entropy model:
[00249] Up until this point, we have implicitly assumed that the customers to the network are one-time customers, and therefore, the particular assignment of flexible products to specific products has no impact on the arrival rate for flexible products. In this section we introduce a model for incorporating the effect of the current assignment decisions on future rates. We assume that the customer for a flexible product k knows that the probability of being assigned to NEWYORK 82388v2 ,~" .. _...,.. ~.. _.._..__h_.._.w.."",~,",>"," ~ ,~ ~..._. ..... _... __ -,~, .~. .. . .

P-00057 (19240-187) specific product j E Nk is given by pk~, j E Nk, and the corresponding rate for a flexible product is given by:
.. _~ .. _ _ .
r,,~. -. cre,,.~9 ~,~~, ~><. ._. ra°~, -~ r~~,i ..._ ~1F ;~~~'~;_ ~r a;y, a _ i':, ~;'~ :,... ...... ~~ vrx °~~' t . ) 12 ..j ~ s o ~- , Y,3a ',-f. :,..
~rlea,.~~.. l~ta~ . ~ f. .~~, .~"~,,~,i<..~ _~ ~~~.r. ~..:~~s,_.~};1T ~~h cIES_, y'r~Al~.,.l.~~.l~t, r~~i~~;~, :~~:~~'~.~~(a~ ~,x .
,~ .. f~ k~ .>F
[00250] In this model, the entropy term H(p) penalizes uncertainty, i.e. if there is an equal probability of being assigned to all the specific products (in which case the buyer of the specific product has no idea of what he is getting), the rate will be lower than if there is a high probability of being assigned to a particular specific product (in which case the buyer of the flexible product can be fairly certain of what he is getting.) The rates g~, j = 1, ..., h, for specific products are still given by (14).
[00251] Figure 38 shows the gain curves for the entropy model. Reasonable gains were produced when the buyer of a flexible product can be fairly certain of which product he is buying, i. e. when the probability of a flexible product being assigned to a certain specific product is high. When the probabilities were uniform, i.e. when the customer has no idea what product he is buying, the maximum gain was less than 1%. When the customer could be 99%
certain of buying a certain product, the maximum gain was a little less than 4%. So it seems that an airline might actually make less money when it has greater flexibility in assigning the flexible products because this can decrease the willingness of customers to buy the flexible product.
NEWYORK 82388v2 __._._.r~~........ _.

Claims (28)

1. A computer-implemented method for managing revenue from selling a product comprising:
(a) offering a flexible product for sale, wherein the flexible product comprises at least two alternative products, wherein a seller assigns one of the alternative products to a purchaser at a later date;
(b) receiving a customer request for purchase of the flexible product;
(c) determining which alternative product is to be assigned to the customer;
and (d) informing the customer which alternative product the seller has assigned to the customer, thereby managing revenue from selling the product.

2. The method of claim 1, wherein the determining comprises observing specific demand for each specific product before assigning the customer an alternative product so as to maximize capacity.

3. The method of claim 1, wherein the determining comprises using a linear program and/or a column generation approach.

4. The method of claim 1, wherein the assigning comprises waiting until uncertainty on specific product demand is resolved before the customer is assigned an alternative product.

5. A computer-implemented method for managing revenue from selling a product comprising:
(a) offering one or more flexible products and/or specific products for sale;
(b) receiving a customer request for a specific product;

(c) providing the customer with a first choice to purchase the specific product and with a second choice to purchase a flexible product; and (d) receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

6. The method of claim 5, wherein the price of the specific product is greater than the price of the flexible product.

7. The method of claim 5, wherein the flexible product comprises the specific product as an alternative product.

8. The method of claim 7, further comprising before step (c) determining whether revenue can be maximized by selling the specific product as an alternative product;

9. A computer-implemented method for managing revenue from selling a product comprising:
(a) offering one or more flexible products and/or specific products for sale;
(b) receiving a customer request for a specific product;
(c) determining whether revenue can be increased by selling a flexible product comprising the specific product as an alternative product, wherein if revenue cannot be increased by selling the flexible product, then sending a confirmation of purchase of the specific product to the customer, and wherein if revenue can be increased by selling the flexible product, providing the customer with a first choice to purchase the specific product and with a second choice to purchase the flexible product; and (d) receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

10. The method of claim 1, 5 or 9, wherein the informing ar sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer occurs within a fixed period of time, wherein the fixed period of time is established as a component of the flexible product prior to or upon purchase of the flexible product.

11. A computer-implemented method for managing revenue from selling a product comprising:
(a) offering a flexible product within a fixed time period for purchase of the flexible product, wherein the flexible product comprises at least a first alternative product and a second alternative product;
(b) receiving a first customer request for purchase of the flexible product within the fixed time period for purchase of the flexible product;
(c) receiving a second customer request for purchase of a specific product which is identical to the first alternative product after the fixed time period for purchase of the flexible product; and (d) determining which alternative product is to be assigned to the first customer based on the second customer's request, thereby managing revenue.

12. The method of claim 1 or 11, wherein the determining comprises maximizing quantity of products sold.

13. The method of claim 11, wherein the determining comprises dynamically allocating alternative products to customers after the fixed time period for purchase of the flexible product.

14. The method of claim 11, wherein the specific product has a purchase price greater than the flexible product.

15. A computer-implemented method for managing revenue from selling a product comprising:
(a) offering for sale during a first time period at least a specific product and a flexible product, wherein the specific product is offered at a discount price, and wherein the flexible product comprises the specific product as an alternative product; and (b) offering for sale during a second time period the specific product, wherein the specific product is offered at a price greater than the discount price in the first time period.

16. A computer-implemented method for buying a flexible product comprising:
offering to buy a flexible product within a fixed time period, wherein the flexible product comprises at least two alternative products; and receiving information after the fixed time period as to which alternative product has been sold by the seller.

17. The method of claim 1, 5, 9, 11, 15 or 16, wherein the flexible product comprises a set of alternative products that have a perishable/constrained capacity and/or constrained inventory.

18. The method of claim 5, 9, 11 or 15, wherein the specific product has a perishable/constrained capacity and/or constrained inventory.

19. The method of claim 1, 5, 9, 11, 15 ar 16, wherein the flexible product comprises an airplane ticket reservation, a hotel room reservation, a concert ticket reservation, an internet webpage advertising space reservation, an air cargo reservation, or a vacation tour reservation.

20. The method of claim 5, 9, 11 or 15, wherein the specific product comprises an airplane ticket reservation, a hotel room reservation, a concert ticket reservation, an Internet webpage advertising space reservation, an air cargo reservation, or a vacation tour reservation.

21. The method of claim 19, wherein the flexible product comprises at least two different airplane ticket reservations.

22. An apparatus for managing revenue from selling a product comprising:
under control of a host system;
means for offering for sale a flexible product;
means for receiving a customer request for purchase of the flexible product, wherein the flexible product comprises at least two alternative products;
means for determining which alternative product is to be sold to the customer so as to maximize capacity; and means for notifying the customer which alternative product of the flexible product the seller has sold to the customer.

23. An apparatus for managing revenue from selling a product comprising:
under control of a host system;
means for offering one or more flexible products and/or specific products for sale;
means for receiving a customer request for a specific product;
means for determining whether revenue can be increased by selling a flexible product comprising the specific product as an alternative product, wherein if revenue cannot be increased by selling the flexible product, then sending a confirmation of purchase of the specific product to the customer, and wherein if revenue can be increased by selling the flexible product, providing the customer with a first choice to purchase the specific product and with a second choice to purchase the flexible product; and means for receiving a customer input specifying purchase of either the first choice or the second choice; wherein if the customer input specifies the second choice, sending information to the customer as to which alternative product of the flexible product the seller has assigned to the customer.

24. An apparatus for purchasing a flexible product comprising:
under control of a client system;
means for requesting a purchase of a flexible product, wherein the flexible product comprises at least two alternative products; and means for receiving information as to which alternative product of the flexible product has been assigned by the seller.

25. A computer-readable storage medium containing a set of instructions for a host system comprising:
a display routine for presenting a flexible product available for purchase, wherein the flexible product comprises at least two alternative products;
an input routine for receiving a customer request for purchase of the flexible product;
a run routine for determining which alternative product of the flexible product should be assigned to the customer so as to maximize revenue; and a run routine for sending to the customer information as to which alternative product of the flexible product the seller has assigned to the customer.

26. A computer-readable storage medium containing a set of instructions for a client system comprising:

a display routine for viewing a flexible product available for purchase from a seller, wherein the flexible product comprises at least two alternative products;
an input routine for selecting the flexible product for a purchase request;
a run routine for sending the purchase request to a host system; and a storage routine for receiving and storing a confirmation of the purchase of the flexible product and information as to which alternative product of the flexible product has been assigned by the seller.

27. A computer-implemented system for managing revenue with flexible products comprising:
a file server; and a processor programmed for implementing instructions for:
offering a flexible product comprising a set of alternative products;
receiving and storing a customer request for purchase of the flexible product;
determining which alternative product of the flexible product to assign to the customer in order to maximize revenue and sending to the customer information as to which alternative product of the flexible product the seller has assigned to the customer, thereby managing revenue.

28. A computer-implemented method for managing airplane ticket revenue from selling a product comprising:
offering a flexible product, wherein the flexible product comprises a first airplane ticket reservation and a second airplane ticket reservation;
receiving a request for purchase of the flexible product from a first customer;
sending a confirmation of purchase of the flexible product to the first customer;

receiving a request for purchase of the first airplane ticket reservation from a second customer;
sending to the first customer information that the second airplane ticket reservation has been assigned to the first customer; and sending to the second customer a confirmation of purchase of the first airplane ticket reservation.