WO2005062195A1

WO2005062195A1 - Revenue management of callable products

Info

Publication number: WO2005062195A1
Application number: PCT/US2003/036824
Authority: WO
Inventors: Guillermo Gallego; Steven Kou
Original assignee: The Trustees Of Columbia University In The City Ofnew York
Priority date: 2003-11-18
Filing date: 2003-11-18
Publication date: 2005-07-07
Also published as: AU2003291055A1

Abstract

The present invention is directed to methods (10), apparatuses and media that use callable products (14) to enhance or maximize the revenue of perishable capacity providers such as airlines and hotels (11). The invention also provides algorithms or formulae with which the best possible callable prices (11) and the best possible reserved sales for low fare customers (15) can be determined (13). The revenue management methods allow for more aggressive bookings at low fares (16) that improve revenues and yield when high fare demand is low (16), and allows selected low fares bookings to be called if the high fare demand is high (18).

Description

REVENUE MANAGEMENT OF CALLABLE 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 the 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 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 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. 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 of managing revenue with callable products. Particularly for industries with perishable/constrained capacity and/or constrained inventory, the expected revenue with callable products can be significantly higher than in the traditional cases where sales at low fares are final. The present invention also provides for apparatuses, computer-readable storage mediums and formulae or algorithms that help to implement the present methods.

[0009] In one aspect of the present invention, a computer-implemented method for managing revenue from selling a product comprises: (a) receiving a customer request to purchase a callable product, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product; and (b) determining whether or not to exercise the call option on the underlying product, thereby managing revenue. In the present invention, the call option comprises a strike price and a fixed period of time. Thus, determining whether or not to exercise the call option of the underlying product can comprise: (i) determining whether a second customer has requested to purchase a specific product that is identical to the underlying product at a price higher than the strike price and (ii) determining whether or not an exercise of the call option and a selling of the specific product to the second customer will maximize profits; thereby managing revenue.

[0010] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) receiving a request to purchase a specific product from a customer; (b) sending to the customer an alternative to purchase the specific product as a callable product, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product, wherein the underlying product is identical to the specific product of (a); and (c) receiving a second request from the customer specifying purchase of the specific product or the callable product; wherein if the customer specified purchase of the callable product, sending to the customer information as to whether the call option on the underlying product has been exercised; thereby managing revenue.

[0011] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) receiving a customer request to purchase a callable product, wherein the callable product comprises (i) an underlying product, (ii) a call option on the underlying product, wherein the call option comprises a strike price and a fixed period of time and (iii) an alternative product, wherein the alternative product is provided to the customer if the call option on the underlying product is exercised; (b) determining whether or not to exercise the call option on the underlying product; and (c) exercising the call option on the underlying product at the strike price within the fixed period of time, and providing the customer with the alternate product, thereby managing revenue. This aspect where an alternative product is provided to the customer when the call option is exercised is contemplated because customers may be willing to receive a smaller compensation in terms of the strike price when an alternative product is provided. For example, a customer purchasing a callable product wherein the underlying product is an airline ticket or a concert ticket may desire having an alternate airline ticket or alternate concert seat if the seller repurchases the underlying product by exercising the call option. [0012] In the present invention, the call option component of callable products can comprise a right of a seller of the underlying product to buy back the underlying product at a strike price within a fixed period of time. The details regarding the strike price and the fixed period of time are generally established by the seller prior to offering the callable product for sale. However, it is contemplated that a potential buyer and a seller can negotiate what the strike price and the fixed period of time should be, which would therefore impact and involve a negotiation as to the price of the callable product itself. Also in the present invention, the strike price of the underlying product can be greater than the purchase price of the callable product.

[0013] In aspects where the callable product comprises an alternative product, the strike price of the underlying product can be less than the purchase price of the callable product. For example, assume a callable product is purchased for $100, and the callable product comprises an underlying product, an alternative product valued at $80, and a call- option with a strike price on the underlying product at $40. If the call option is exercised, the customer will receive $40 on the call option and the alternative product in exchange for the underlying product. Although the strike price for the underlying product is less than the price of the callable product, the customer still receives a premium due to receiving the alternative product. Further, the present invention contemplates that the call option can further comprise an overriding-right of the customer to refuse the exercising of the option by the seller.

[0014] In an aspect of the present invention, a computer-implemented method for managing revenue from selling a product comprises: (a) offering a callable product for sale within a first time period, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product, wherein the call option comprises a strike price and a fixed period of time; (b) receiving a request from a first customer to purchase the callable product; (c) sending to the first customer a confirmation of purchase of the callable product; (d) determining a price to sell the underlying product for sale as a specific product in order to maximize revenue; (e) offering the underlying product for sale as a specific product within a second time period; (f) receiving a request from a second customer to purchase the specific product; (g) sending to the second customer a confirmation of purchase of the specific product; and (h) exercising the call option on the underlying product at the strike price within the fixed period of time, and sending information to the first customer that the option has been exercised, thereby managing revenue from selling the underlying product. In relation to this aspect and related aspects, the specific product can be purchased at a price greater than the strike price of the underlying product, and the strike price of the underlying product can be greater than the purchase price of the callable product. Further, in relation to aspects of the present invention that comprise callable products with alternative products, the specific product can be purchased at a price greater than the strike price of the underlying product, and the strike price of the underlying product can be less than the purchase price of the callable product since consideration to the customer of the callable product is also provided by the alternative product.

[0015] In all aspects of the present invention, the offering of products, including callable product, specific products and put-products, can occur via display on a website or via a listing by a server.

[0016] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) receiving a customer request to purchase a put-product, wherein the put-product comprises an underlying product and a put option on the underlying product; (b) sending to the customer a confirmation of purchase of the put-product; and (c) receiving notice from the customer information that the put option on the underlying product has been exercised.

[0017] In the aspects of the present invention relating to put-products, the put option component of the put-product can comprise a right of the customer to sell the underlying product at a strike price within a fixed period of time back to a seller of the put-product. The strike price of the underlying product can be less than the purchase price of the put-product, or the strike price of the underlying product can be greater than the purchase price of the put- product.

[0018] In one aspect, a computer-implemented method of purchasing a callable product comprises: (a) viewing a callable product by a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; (b) sending a purchase request to the seller for the callable product; (c) receiving a confirmation of purchase of the callable product; and (d) receiving information as to whether the call option on the underlying product has been exercised.

[0019] In all aspects of the present invention, the specific product, the underlying product (of both callable products and put-products) and the alternative product can have a perishable/constrained capacity and/or constrained inventory. For example, the specific product, the underlying product or the alternative product can comprise, 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.

[0020] In another aspect of the present invention, an apparatus for managing revenue from selling a product comprises: a means for offering one or more products comprising a callable product; a means for receiving a customer request to purchase the callable product, wherein the callable product comprises an underlying product and a call option on the underlying product, wherein the call option comprises a fixed period of time and a strike price; a means for sending to the customer a confirmation of purchase of the callable product; a means for determining whether or not to exercise the call option on the underlying product; and a means for sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue. In such an apparatus and related apparatuses, the means for determining can comprise (i) determining whether or not to exercise the call option within a fixed period of time, (ii) determining whether a second customer has requested to purchase a specific product that is identical to the underlying product at a price higher than the strike price or the purchase price of the callable product and (iii) determining whether or not the exercise of the call option and a selling of the specific product to the second customer will maximize profits; thereby managing revenue.

[0021] In another aspect, a computer-implemented method for managing revenue from selling a product comprises: (a) a means for receiving a request to purchase a specific product from a customer; (b) a means for sending to the customer an alternative to purchase the specific product as a callable product, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product, wherein the underlying product is identical to the specific product of (a); and (c) a means for receiving a second request from the customer specifying purchase of the specific product or the callable product; wherein if the customer specified purchase of the callable product, sending to the customer information as to whether the call option on the underlying product has been exercised; thereby managing revenue. [0022] In yet another aspect, an apparatus for purchasing a callable product comprises: a means for viewing a callable product for sale by a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; a means for sending a purchase request to the seller for the callable product; a means for receiving a confirmation of purchase of the callable product; and a means for receiving -information as to. whether- the_call.option_on the underlying. product has been exercised. [0023] In one aspect, a computer-readable storage medium containing a set of instructions for a host system comprises: a display routine for offering a callable product for purchase, wherein the callable product comprises an underlying product and a call option on the underlying product; an input routine for receiving a customer request for purchase of the callable product; a run routine for determining whether or not to exercise the call option on the underlying product; and a run routine for sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue. The run routine for determining whether or not to exercise the call option on the underlying product can comprise a mathematical formula or an algorithm for determining whether or not the exercise of the call option will maximize revenue. Such formula and algorithms are presented in the Examples and Figures herein.

[0024] In another aspect, a computer-readable storage medium containing a set of instructions for a client system comprises: a display routine for viewing a callable product available for purchase from a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; an input routine for selecting the callable 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 callable product and information as to whether the call option on the underlying product has been exercised by the seller.

[0025] In another aspect, a computer-implemented system for managing revenue by selling a product comprises: (a) a file server; and (b) a processor programmed for implementing instructions for: (i) offering a callable product, wherein the callable product comprises an underlying product and a call option on the underlying product; (ii) receiving and storing a customer request for purchase of the callable product; (iii) determining whether or not an exercise of the call option and a selling of the underlying product as a specific product to a second customer will maximize revenue; and (iv) sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue.

[0026] In one aspect, a computer-implemented method of managing airplane ticket revenue with callable products comprises: (a) offering a callable product, wherein the callable product comprises an underlying product and a call option on the underlying product, wherein the underlying product is an airplane ticket reservation; (b) receiving a request for purchase of me callable-product from.af st custo^ of the callable product to the first customer; (d) receiving a request for purchase of said airplane ticket reservation from a second customer; (e) determining whether or not an exercise of the call option and a selling of the underlying product as a specific product to the second customer will maximize revenue; (f) sending to the first customer information that the call option on said airplane ticket reservation has been exercised; and (g) sending to the second customer a confirmation of purchase of said first airplane ticket reservation, thereby managing revenue.

BRIEF DESCRIPTION OF THE DRAWINGS [0027] Figure 1 presents a flow diagram of a computer-implemented method of managing revenue where a customer converts a purchased specific-product into a callable product. [0028] Figure 2 presents a flow diagram of another strategy of computer- implemented methods of managing revenue with callable products. [0029] Figure 3 presents a flow diagram showing how management of callable products in relation to specific products can increase expected revenue. [0030] Figure 4 presents one apparatus for implementing the methods of the present invention. [0031] Figure 5 presents Proposition 3.1 of Example 2, which compares the revenues with and without a callable feature. [0032] Figures 6A and 6B present how the mean and the distribution of W(a, p) are computed, see Example 2. [0033] Figures 7A and 7B present calculations regarding the optimization with respect to a, the number of seats allocated to the low fare customers, see Example 3. [0034] Figures 8A-C present an Appendix to the Examples, where the Appendix provides proofs for Lemma 3.1 and Lemma 4.1.

DETAILED DESCRIPTION OF THE INVENTION [0035] A callable product is a product that has at least two components: (i) an "underlying product," and (ii) an option (a "call option") on the underlying product. The call option on the underlying product gives the seller (of the callable product) the right to

_ "exercise" _the_ call, option,, i.e., to buy back or repurchase the underlying product from the purchaser of the callable product. The right to exercise the call option is limited to a fixed time period and a fixed price (i.e., the "strike price" of repurchase for the underlying product. The call option component of the callable product therefore describes the fixed time period and the strike price, which are generally established at the time of purchase of the callable product. It is contemplated that the call option component itself can be purchased or sold as a separate product. In the present invention, 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 does not have an option (call option or put option) component. A specific product that is a component of a callable product that can be repurchased by the seller from the customer is thus called an "underlying product."

[0036] In addition to the underlying product and the call option, the callable product can further comprise an alternative product. An alternative product is a specific product that is given to the purchaser of a callable product only when the call option on the underlying product has been exercised. Hence, a specific product that is a component of a callable product that is given to the customer as part of the consideration of the repurchase of the underlying product (by exercising the call option) is an "alternative product." The alternative product, in addition to the strike price of the underlying product, are compensation given to the customer in exchange for the seller's repurchase of the underlying product. Thus, the alternative product is a product that is not identical to the underlying product, although the alternative product tends to be related or similar to the underlying product. Further, the strike price of the underlying product can be less than the purchase price of the callable product. For example, assume a callable product is purchased for $100, and the callable product comprises an underlying product that is an airplane ticket for NY to LA at 9AM on October 1, an alternative product for an airplane ticket for NY to LA at 2 PM on October 1 is valued at $80 (and hence, the alternative product is related or similar to the underlying product), and a call-option with a strike price on the underlying product is set at $40. If the call option is exercised, the customer will receive $40 on the call option and the alternative product in exchange for the underlying product. Although the strike price for the underlying product is less than the price of the callable product, the customer still receives a premium due to receiving the alternative product. Further, the present invention contemplates that the call option can further comprise an overriding-right of the customer to refuse the exercising of the option by the seller. [0037] Figure 1 is an illustrative example in which a seller can enable a host system to allow a customer who has purchased a specific product to convert the specific product into a callable product. The seller can offer the conversion for free or can charge for the opportunity, and the seller can allow certain specific products for conversion 1. This 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 callable 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, if the option is exercised with the fixed time period, the seller can inform the buyer via e-mail and deposit the amount of the strike price into the customer's account 4 and 5; or if the option is not exercised with the fixed time period, the seller informs the buyer that the option was not exercised 6. This basic model has numerous variations, as described herein.

[0038] Figure 2 is an illustrative example for the methods of managing revenue with a callable 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 third-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.).

[0039] The host system then receives a request from a customer for purchase of a product 11. The host system determines whether the product that is requested is a specific product, i.e., a product that does not have an option component, or a callable product. If the product that is requested is a specific product, then the host system sends 13 to the customer a choice or the opportunity to purchase a callable product which has as its underlying product component the requested specific product. The option component of the callable product can either provide the seller with the right to buy-back the underlying product from a purchaser or the callable product can be offered with an option override feature giving the customer the final power to allow or not to allow the seller to buy back the product. Both option varieties can be presented at 13. If the customer did not choose the callable product opportunity at 13, then the host system provides the customer with confirmation of purchase of the specific product..l5,__ „ .... [0040] Where the seller has final control of exercising the option, the seller generally aims to maximize revenue by setting the price of a specific product higher than the strike price of an underlying product. In this manner, the seller can take advantage of high-demand periods of a specific product, while already having hedged his/her position by selling the specific products as underlying product components in callable products at an earlier time. For example, a callable product was sold for $100 with an underlying product that has a strike price of $150 to a first customer. At a later time (within the fixed time period stated in the option component of the callable product), the demand is high for products related to X, and as such, a second customer is willing to purchase X for $200. The seller decides to exercise his/her option on X, and X is therefore repurchased from the first customer for $150 and is then resold to the second customer for $200. The benefit for the first customer is a profit of $50, which is in consideration for the possibility that the seller may not exercise the option, which in that case, the customer would have to retain the product at the expiration of the fixed time period. The benefit for the seller is the maximization of revenue with reduced organizational costs. The seller is not only hedged for periods of weak demand, but the seller can calculate the extent of hedging (i.e., by setting the number of callable products the seller wishes to sell; the strike price; and the duration of the fixed period of time) with relation to historical commercial trends. Further, as the seller knows the costs of hedging from the callable products, the seller is able to calculate with precision the price that specific products should be sold during periods of high demand (or low demand).

[0041] This method of maximizing revenue of callable products is illustrated in

Figure 3. At 19, a host system receives a request from customer Z for purchase of a specific product. The host system accesses storage information to determine whether the requested specific product is currently an underlying product of a callable product of another customer 20. If the specific product is not currently part of a callable product, then the host system can complete the transaction and provide the customer with confirmation of purchase of the specific product 21, or if desired by the seller, present the customer with the choice to purchase a callable product that has the requested specific product as an underlying product 13.

[0042] If at 20, the specific product is an underlying product of a callable product, then the host system can determine whether the price of the specific product is greater than the strike price of the underlying product 22, and the host system can also determine whether _.proceeding to 23 jnakes economic sense (^e.^does he decision maximize revenue, where this can be determined either by mathematical formulae/algorithms (as disclosed in the Examples herein, or by human input decision making on the host system 22). If the decision to exercise the option on the callable product makes economic sense (i.e., does it maximize revenue and/or profit), then at 23 information is sent to the customer of the callable product that the option has been exercised (where the seller has the final right of exercise) or information is sent requesting exercise (where the customer has the final right of exercise). At 24, information is sent to the customer requesting purchase of the specific product that the purchase has been confirmed (or in the situation where only the specific product is only available via callable products where the customer has the final decision on the option, and all customers who own the callable products with the specific product as an underlying component decline the request for exercising the option, then at 24 information is sent to the customer informing him/her that purchase of the specific product is not possible).

[0043] In aspects where the customer has the final decision of whether the call option can be exercised by the seller, the seller can increase the price of the callable product as compared to callable products where the customer does not have any power over whether the call option is to be exercised.

[0044] Mathematical formulae and algorithms are presented in the Examples section that enable the calculation of revenue management with callable products. In other words, the formulae and algorithms can provide, for example, a determination of whether an exercise of a call option or put option on callable products or put-products will maximize revenue. Such formulae and algorithms can be incorporated into the methods, apparatuses and computer-readable media of the present invention.

[0045] If at 12, the customer did not request purchase of a specific product, and if the customer requested purchase of a callable product 16 and 14, then the host system provides the customer with confirmation of purchase of the callable product 17.

[0046] At 17, the confirmation of purchase includes confirmation of the fixed price

(strike price) and the fixed period of time of the option. Before expiration of the fixed period of time, the host system provides the customer with information regarding the exercise of the option 18. The information can be (1) where the seller has the final decision on the option, that the option on the underlying product was exercised or was not exercised, and if exercised, further information is provided as to payment to the customer of the amount of the strike price; and (2) where the customer has the final decision on the option, the seller sends information either requesting exercise of the option, or information that no request has been made to exercise the option.

[0047] Similar to the callable product, the present invention provides methods, apparatuses and media relating to the management of revenue with put-products. Put- products are related to callable products or can be considered to be variations of callable products. Put-products are identical to callable products, except that the option component of the put-product is different. For put-products, the option component ("put option") gives the customer or the buyer of the put-product the right to exercise the option, i.e., the right to sell the underlying product back to the seller of the put-product at a fixed price within a fixed time period. This differs from the aspect of callable products where the buyer/customer of the callable product has the final decision or the overriding decision feature on exercising the call option (note, in most aspects of callable products, the seller has the power to exercise the call option). In the aspect for callable products where the buyer has the final power on the call option, the seller still initiates the exercise of the option by requesting the exercise of the option to the customer. However, in the put-product, the buyer/customer can initiate the exercising of the put option by simply informing the seller that the underlying product of the put product is being sold-back, i.e., the put option is being exercised. Situations in which put-products can maximize revenue are situations where customers are uncertain whether they will have need of a product in the future, but the need is nevertheless important. In such a situation, the seller prices the cost of the put-product higher than the strike-price of the underlying product. The customer is willing, in effect, to pay a penalty in exercising the option for the benefit of knowing that he/she has control of the product. The seller is willing to sell such put-products from calculations of past historical commercial data, where the seller can vary the cost of the put-product, the strike price and the fixed time period to exercise the option, such that the seller can maximize and expect a range of revenue.

[0048] In all aspects of the present invention, the specific product or the underlying product (of both callable products and put-products) can have a perishable/constrained capacity and/or constrained inventory. For example, the specific product or the underlying product can comprise, 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. Further, in a related market to Internet advertising, 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 be connected to a hyperlink in the list. The highest bids are presented at the top of a list. In relation to a callable product, for example, Google can sell a callable product where a company such as Amazon may be interested in buying the rights to the first and second placement on the list in relation to the search term "DND". However, Amazon might purchase the second placement as a callable product, and Google may exercise the option of the second placement in light of a higher bid placed at a later time. Thus, the present invention also contemplates the use of callable and put-products to sell search term rights.

[0049] 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 sellers/service providers can be connected to a host system's Internet web page server, or any other suitable server, through any suitable Internet connections.

[0050] For example, Figure 4 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 software 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.

[0051] 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.

[0052] 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. EXAMPLES

[0053] In the Examples, a version of a revenue management model with two fare classes, where some units sold to the lower fare class can be called by the seller who can then use these units to satisfy demand from a high fare class. The Examples show that the expected revenue with callable products can be significantly higher than in the traditional case where sales at the low fare are final.

EXAMPLE 1: A MODEL OF REVENUE MANAGEMENT USING CALLABLE PRODUCTS

[0054] In this example of one possible model of managing revenue of callable products, the selling horizon is divided into two booking periods. The first period is comprised of low fare bookings and the second of high fare bookings. More precisely, during the first period there is a demand for D units at price pz, and during the second period there is demand for D_H units at price pπ, where D_L and D_H are two non-negative integer- valued random variables and the two prices, P and pπ, are fixed constants with P_L < P_H. Here, for simplicity, we also assume that DL and DH are independent.

[0055] In one aspect of the invention, callable products provide low fare customers an opportunity to have their units called (during the second period) at a fixed price p e

, /?_#] announced by the seller. In this example, there is no charge associated with this opportunity, and this can be easliy implemented via the Internet. For example, the after a buyer purchases a ticket via the Internet, an additional web page is posted asking whether the buyer is willing to let the airlines to buy back the ticket in the future at a higher price p. The buyer can say yes or no. If the buyer says yes, then later when there is a need to recall the ticket (if such an occasion arises) the seller can send an e-mail to the buyer and a deposit of p dollars into the buyer's account.

[0056] For the seller the recall price (can also be called the strike price) p is a decision variable which can be chosen optimally to the seller's advantage. For the buyer, the decision of whether giving the seller such an option is based on the recall price p and the calculation of his/her reservation price during the second period. More precisely, let q be the probability that a low fare sale is callable. In general, q = g(p) is an increasing function of p, because the higher the^~callable ^"price p ^"the mofeTikely^~the buyerwill participate The terms-inereasing - and decreasing are used in the weak sense unless otherwise stated. In a theoretical analysis, one does not need to specify the particular function form of g(p). However, some possible cases for g(p) are provided herein.

[0057] The decision variables for the seller are p, the callable price, and a, the number of units available for sale at the low fare. Given a, sales at the low fare will be Sι(a) = min(D_£, ). The number of callable units, Vι{a), will be conditionally binomial with parameters S_L( I) and q; i.e. V (O = bino(S fα), q). Let c be the total capacity. Let the number of low fare customers who do not participate in the callable feature to be Y (a) = S_L(Λ) — V_L( I). (Note: variables herein with an apostrophe, i.e., V or q', can also be denoted with an overline instead of the apostrophe, i.e., V or q with an overline, see Figures). The capacity available for sale at the high fare is then c - V'_h(a) = c - bino(Sz/ ), q'), where q' = 1 - q. The number of units sold at the high fare is min(D_a c - V'rJ( )), and the number of units actually called is equal to min((Sι ) + D_H- cf, Y_L(O)). Thus, the expected revenue is given by r(a,p) - E[R(a,p)], where:

[0058] R(a,p) = _P S_L( ) + p_H™in(D_H, c - V_L(a)) - pm ((S_L(a) + D_H- c)⁺, V_L(a)). (1).

Note that q = g(p) ≡ 0 corresponds to the traditional revenue management case when sales are not callable, while q = g(p) ≡ 1 corresponds to the case that all sales are callable.

EXAMPLE 2: PROPERTIES OF THE MODEL

[0059] Let R(a) be the revenue corresponding to the strategy without the callable product. Since the number of units sold at the low and high fares are S (α)and min(c - Sz α), D_H), respectively, we have that R(a) = piβdia) + pj_ϊ{min(c - S_L(a), D_H)}. Figure 5 presents Proposition 3.1, which compares the revenues with and without a callable feature.

[0060] Remark: On the surface, Proposition 3.1 seems to be surprising, as it reminds one of the concept of "arbitrage" in finance, as the revenue gain by adding the callable feature is non-negative with probability one ("riskless"). It should be pointed out this is only possible because of the information asymmetry. More precisely, the airlines have information about who may be willing to buy high fare tickets even when the plane is full, while it is difficult for customers to gain that information. In addition, even if, by chance, a few customers do have such information, they may not be able to use the information if tickets are non-transferable. [0061] The next question is that, although it is good to have a "riskless" gain in revenue, the bottom line is how big the gain is. To answer this question, both the mean and the distribution of W(a, p) shall be computed. This is conducted and shown in Figures 6A and 6B. In the Figures, references are made to proofs shown in an Appendix; the Appendix is shown in Figures 8A-8C. In the remaining Examples, it is demonstrated that by choosing the seat allocation a and the recall price p in an optimal way, the revenue gain can be substantial.

EXAMPLE 3: OPTIMIZATION

[0062] The optimization with respect to a, the number of seats allocated to the low fare customers is first calculated. See Figures 7 A and 7B. In summary, the following result is provided: Theorem 4.1 - There is an optimal solution a and p = g(p ) that maximizes r(a, p) that can be found by solving the equation (7) [see Figure 7B] for every a e [a(0), c], and then choosing the largest value for r(a, p).

[0063] Remark: Three interesting points of the callable tickets are worth mentioning: (1) Even if the option to participate in the callable program is offered at no cost, the buyer's utility is at least as large, resulting in a win-win situation. This is made possible mainly because the callable feature enables the buyer to share the possible revenue from the high fare demand that would otherwise be lost. (2) The operational cost of the callable tickets can be quite low, if implemented with via the web and e-mails. (3) The callable features only targets those, self-selected, customers willing to participate.

[0064] The analysis above depends heavily on the assumption that h(q) is convex, but it may be that we can do with less. Fix a and consider EW(a, p) and let us think of optimizing with respect to p. If we make the assumption that q = 0 at p = P then we conclude that W(a, p_L) = 0 and W(a, p_H) = 0. Indeed, W(a, P_L) = 0 because there are no callables and W(a, p_H) = 0 because although there may be callables we cannot make money out of them since p = pπ- Now, the function EW(a, p) is non-negative and it is zero at both P_L and pπ- Suppose that EW( , p) is differentiable with respect to p, then there must be at least one p at which the derivative must vanish. If this point is unique, then that point must be the maximizer of EW(α, p). Thus, we have the following result.

[0065] Theorem 4.2 If q = g(p_L) = 0, EW(a, p) is continuously differentiable with respect to p, then there is a unique root for equation (7), then p(a) necessarily maximizes EW( , p): - [0066] If there is a unique root for each a e [a(0), ..., c} then we can find the unique p that maximizes expected revenue for each a and then select the best pair.

[0067] Comparison with Existing Practices

[0068] Airlines typically overbook to hedge against cancellations and no-shows. An airline may be tempted to overbook even in the absence of cancellations and no shows if the spread between the fares is larger than the compensation needed to persuade low fare customers to give up their seats. This bumping strategy can be made operational in several ways. The crudest is to allow passengers to show up at the gate and then compensate them to go home or take a different flight. A more subtle way of doing this is to call and bribe passengers before they go to the airport. This is the idea behind the "re-plane" concept introduced by Thomas Cook formally at American Airlines.

[0069] There are several advantages of the callable program over the bumping strategies described above. First, although some of the low-fare customers may be willing to do so for a small compensation, others may require much larger compensation and considerable ill-will from involuntarily denied boardings. As a result, the actual monetary and intangible costs may be difficult to determine.

[0070] For the callable product, a low fare ticket is recalled only if the customer agrees to do this, i.e., by purchasing the callable product in the first place, the customer agrees to allow the seller to recall the ticket.

[0071] Secondly, the operational costs of shifting customers to alternative flights

(such as customer services, scheduling coordination, etc.) can be quite significant. There is very little operational costs associated with the callable tickets, as the airlines do not have any obligation to the participated customers after paying the price p, which is already incorporated in the revenue function and the revenue function is shown to be bigger than that without the callable feature.

[0072] Third, a seller can choose the recall price p optimally, while it is hard to choose the optimal compensation (i.e. deciding whether the compensation should be a free flight or just a coupon of some monetary values) for customers who lost their seats due to overbooking.

[0073] Fourth, the use of callable products does not preclude the using of other strategies, and a seller can combine it with the existing bumping or re-plane practices to increase the revenue even more. For example, if all the recallable units are not enough to satisfy the excess high fare demand, then the airline can "re-plane" or bump passengers.

[0074] Finally, there is another twist that can help recall even more tickets, if needed, by simply putting a green or red icon on the web site, where the green icon indicates that the airline is willing to allow low fare passengers to cancel their paid reservations with little or no cost. The idea is to take advantage of the fact that the valuations of certain low fare passengers may change and those who prefer not to travel would be happy to recover the low fare they initially paid. EXAMPLE 4: MODELING DEMAND DETAILS AND DEMAND INDUCTION

[0075] The analyses in the previous Example does not require the specification of particular distributions for the demands D_H and D_L,' and a particular function for the participation function g, where the participation probability q = g(p). hi this Example, some possible choices for D , D_L and g are presented which will be used in numerical analysis.

[0076] Tτe Demands D and D_L

[0077] Assume that sales are done through the Internet, and assume that only a low- fare customer with the reservation price P_L ≤ R_L will buy a unit during the first period, where R_L is a random variable representing the willingness to pay of low fare customers during the first period. (Of course, if the customer does not want to purchase at all, then she/he just needs her/his reservation price to be zero.) Here, assume that each buyer has the independent and identically distributed reservation price, and hence one can simply use one notation R_L to denote the reservation price. Later, we shall relax the condition P ≤ R_L and analyze the case where some customers may have speculative purposes, and, therefore, the purchasing decisions may also be influenced by the buyer's perception of the (subjective) probability of their units being called, which leads to possible calculation of the speculative profits.

[0078] Similar setting can be postulated for the high-fare customer with a reservation price RH, where R represents the willingness to pay of low fare customers during the second period.

[0079] If we further assume that both low-fare and high-fare customers come according to a Poisson processes. Then D has a Poisson distribution with the parameter X_LP(RL ≥ PL), and D_H has a Poisson random variable with the parameterλflP(RH ≥ PH)-

[0080] The Participation Function g: [0081] The customer will make a decision of whether giving the seller such an option based on both the recall price p and the calculation of his/her reservation price during the second period R ( "R ' " can also be denoted as R with a tilde symbol over the R). In general, q = g(p) depends on both R '_L and p. There are many possible forms of g. For example, if the seller does not screen the low fare customers for their willingness to participate in the call program (meaning any low fare customers who want to participate will be allowed to do so immediately after they purchase the low fare ticket), and the buyer is risk-neutral, then g(p) = P(R '_L < P I RL ≥ P_L), where which is the conditional (homogeneous and subjective) probability that a low fare customer accepts the call offer given that he buys at the low fare

PL.

[0082] Notice that if R'_L = R_L, then q = g(p) = 1 - P(R_L > p) I P(R_L > PL )- hi particular, q = 1 - (b - p) I (b - a) if R_L is uniformly distributed between (a, b), resulting in p = h(p) = b - (l - q)(b - a) which is linearly increasing, and hence convex, in q.

[0083] On the other hand, if demand of the low fare ticket is very large, then the seller can afford to be more selective; for example, the seller can even turn away some low fare customers who are not willing to participate in the call program by not selling the tickets to them. In this case, the resulting callable probability is even higher: P(R 'L < p \ RL ≥PL) < g(p) = q ≤l- [0084] Scenario Example

[0085] Suppose that c = 100. For simplicity, we shall assume for now that the reservation prices of the low fare and high fare customers are the same during both periods, i.e. , R'_L = R and R'_H = RH. The willingness to pay distributions for the two fares are uniformly distributed between $0 and $300 for the low fare and between $0 and $600 for the high fare. Suppose the low fare is p = $150 and the high fare is p_H = $300. The optimal revenue under the traditional revenue management is approximately $21,462 with a standard deviation of about $1,513. These numbers were obtained by simulating the revenue under the optimal booking policy in the absence of callable products.

[0086] A callable price of p = $180 and a = 55 improved the expected revenue to approximately $21,753 with a standard deviation of about $1,579. The improvement in expected revenue was about 1.36%. [0087] Demand Induction [0088] The above analysis assumes that a buyer would only purchase at price P_L if R

≥PL. The buyer may, however, be willing to purchase at an even lower price if he feels that it is likely that he will make money. To see this, consider again a buyer with R_L < p. If the buyer's subjective probability that the unit will be called is s, then the surplus obtained by purchasing the unit at price p_L is s(p - P_L) + (1 - S)(R_L ~ P_L)- This quantity is non-negative as long as R ≥PL - (p ~P_LW(1 - s). Demand is thus induced by those customers with R_L e \P_L ~ (p ~ PL)S/(1 - s), P_L) and the probability that a buyer will agree to a call given that he makes a purchase has to be adjusted accordingly. The earlier case corresponds to the pessimistic prior s = 0.

[0089] If s = 10%, the expected profits increase to $21,832 at p = $182.50 with a - 55 bookings at the low fare. The actual ratio of calls to sales was approximately 6%. If customers correctly estimate the equilibrium s = 6% the expected profits drop to $21,808 or 1.58% more than without callable products.

[0090] The present invention also contemplates, as discussed supra, that the buyer has the discretion or final decision making power to sell back the underlying product. Under this variation, low fare customers whose valuation for the unit drops after purchase can sell the unit at their discretion at a price p_ < p. The seller may put a cap on the number of units he is willing to buy at p. This is like giving the buyers a conditional put option. Because a put gives buyers downside protection this may induce additional demand.

[0091] Further, the present invention also contemplates the situation where the event is cancelled after observing sales at the low fare, such that the buyer will pay p dollars to customers to agree to the call and p_L + d to those who do not. Here d is the cost penalty for involuntarily denying the service. Thus, the savings will be equal to (P + d - p) times the number of calls sold. ;

Claims

WE CLALM:

1. A computer-implemented method for managing revenue from selling a product comprising: (a) receiving a customer request to purchase a callable product, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product; and (b) determining whether or not to exercise the call option on the underlying product, thereby managing revenue.

2. The method of claim 1, wherein the call option comprises a strike price and a fixed period of time.

3. The method of claim 2, wherein the determining occurs within the fixed period of time and wherein the determining comprises (i) determining whether a second customer has requested to purchase a specific product that is identical to the underlying product at a price higher than the strike price and (ii) determining whether or not an exercise of the call option and a selling of the specific product to the second customer will maximize profits.

4. A computer-implemented method for managing revenue from selling a product comprising: (a) receiving a customer request to purchase a callable product, wherein the callable product comprises (i) an underlying product, (ii) a call option on the underlying product, wherein the call option comprises a strike price and a fixed period of time and (iii) an alternative product, wherein the alternative product is provided to the customer if the call option on the underlying product is exercised; (b) determining whether or not to exercise the call option on the underlying product; and (c) exercising the call option on the underlying product at the strike price within the fixed period of time, and providing the customer with the alternate product, thereby managing, revenue.

5. A computer-implemented method for managing revenue from selling a product comprising: (a) receiving a request to purchase a specific product from a customer; (b) sending to the customer an alternative to purchase the specific product as a callable product, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product, wherein the underlying product is identical to the specific product of (a); and (c) receiving a second request from the customer specifying purchase of the specific product or the callable product; wherein if the customer specified purchase of the callable product, sending to the customer information as to whether the option on the underlying product has been exercised; thereby managing revenue.

6. The method of claim 1, 4 or 5, wherein the call option comprises a right of a seller of the callable product to buy back the underlying product at a strike price within a fixed period of time.

7. The method of claim 6, wherein the strike price of the underlying product is greater than the purchase price of the callable product.

8. The method of claim 7, wherein the call option further comprises an overriding-right of the customer to refuse an exercising of the call option by the seller.

9. A computer-implemented method for managing revenue from selling a product comprising: (a) offering a callable product for sale within a first time period, wherein the callable product comprises (i) an underlying product and (ii) a call option on the underlying product, wherein the call option comprises a strike price and a fixed period of time; (b) receiving a request from a first customer to purchase the callable product; (c) sending to the first customer a confirmation of purchase of the callable product; (d) determining a price to sell the underlying product for sale as a specific product in order to maximize revenue; (e) offering the underlying product for sale as a specific product within a second time period; (f) receiving a request from a second customer to purchase the specific product; (g) sending to the second customer a confirmation of purchase of the specific product; and (h) exercising the option on the underlying product at the strike price within the fixed period of time, and sending information to the first customer that the call option has been exercised, thereby managing revenue from selling the underlying product.

10. The method of claim 9, wherein the specific product is offered at a price greater than the strike price of the underlying product, and wherein the strike price of the underlying product is greater than the purchase price of the callable product.

11. The method of claim 10, wherein the offering is via display on a website or via a listing by a server.

12. A computer-implemented method for managing revenue from selling a product comprises: (a) receiving a customer request to purchase a put-product, wherein the put-product comprises an underlying product and a put option on the underlying product; (b) sending to the customer a confirmation of purchase of the put-product; (c) receiving notice from the customer information that the put option on the underlying product has been exercised, thereby managing revenue.

13. The method of claim 12, wherein the put option comprises a right of the customer to sell the underlying product at a strike price within a fixed period of time back to a seller of the put-product.

14. The method of claim 13, wherein the strike price of the underlying product is less than the purchase price of the put-product.

15. The method of claim 13, wherein the strike price of the underlying product is greater than the purchase price of the put-product.

16. A computer-implemented method for purchasing a callable product comprising: viewing a callable product by a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; sending a purchase request to the seller for the callable product; receiving a confirmation of purchase of the callable product; and receiving information as to whether the call option on the underlying product has been exercised.

17. The method of claim 1, 4, 5, 9, 12, or 16, wherein the specific product or the underlying product has a perishable/constrained capacity and/or constrained inventory.

18. The method of claim 1, 4, 5, 9, 12, or 16, wherein the specific product or the underlying 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.

19. An apparatus for managing revenue with a callable product comprising: a means for offering one or more products comprising a callable product; a means for receiving a customer request to purchase the callable product, wherein the callable product comprises an underlying product and a call option on the underlying product, wherein the call option comprises a fixed period of time and a strike price; a means for sending to the customer a confirmation of purchase of the callable product; a means for determining whether or not to exercise the call option on the underlying product; and a means for sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue.

20. The apparatus of claim 19, wherein the means for determining comprises (i) determining whether or not to exercise the call option within a fixed period of time, (ii) determining whether a second customer has requested to purchase a specific product that is identical to the underlying product at a price higher than the strike price and (iii) determining whether or not the exercise of the call option and a selling of the specific product to the second customer will maximize profits.

21. An apparatus for purchasing a callable product comprising: a means for viewing a callable product for sale by a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; a means for sending a purchase request to the seller for the callable product; a means for receiving a confirmation of purchase of the callable product; and a means for receiving information as to whether the call option on the underlying product has been exercised.

22. A computer-readable storage medium containing a set of instructions for a host system comprising: a display routine for offering a callable product for purchase, wherein the callable product comprises an underlying product and a call option on the underlying product; an jnput..routine_fo.r_receiving_a customer.request-fQr_purchase_.of.the_callable_product; a run routine for determining whether or not to exercise the call option on the underlying product; and a run routine for sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue.

23. The medium of claim 22, wherein the run routine for determining whether or not to exercise the call option on the underlying product comprises a mathematical formula or an algorithm for determining whether or not the exercise of the call option will maximize revenue.

24. A computer-readable storage medium containing a set of instructions for a client system comprising: a display routine for viewing a callable product available for purchase from a seller, wherein the callable product comprises an underlying product and a call option on the underlying product; an input routine for selecting the callable 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 callable product and information as to whether the call option on the underlying product has been exercised by the seller.

25. A computer-implemented system for managing revenue with callable products comprising: (a) a file server; and (b) a processor programmed for implementing instructions for: (i) offering a callable product, wherein the callable product comprises an underlying product and a call option on the underlying product; (ii) receiving and storing a customer request for purchase of the callable product; (iii) determining whether or not an exercise of the call option and a selling of the underlying product as a specific product to a second customer will maximize revenue; and (iv) sending to the customer information as to whether the call option on the underlying product has been exercised, thereby managing revenue.

26. A computer-implemented method of managing airplane ticket revenue with callable products comprising: (a) offering a callable product, wherein the callable product comprises an underlying product and a call option on the underlying product, wherein the underlying product is an airplane ticket reservation; (b) receiving a request for purchase of the callable product from a first customer; (c) sending a confirmation of purchase of the callable product to the first customer; (d) receiving a request for purchase of said airplane ticket reservation from a second customer; (e) determining whether or not an exercise of the call option and a selling of the underlying product as a specific product to the second customer will maximize revenue; (f) sending to the first customer information that the call option on said airplane ticket reservation has been exercised; and (g) sending to the second customer a confirmation of purchase of said first airplane ticket reservation, thereby managing revenue.