US 20060161504 A1 Abstract Generating a price schedule involves generating a graph (
50) having paths that include states (52) with values (54, 56, 58). The graph (50) is generated by determining the values (56, 58) of a successor state (52) from the values (56, 58) of a predecessor state (52). An optimal path is selected, and a price schedule is determined from the optimal path. Computing an elasticity curve involves having a demand model, values for demand model, and filter sets that restrict the values. Elasticity curves are determined by filtering the values using filter sets, and calculating the elasticity curve using the demand model. An best-fitting elasticity curve is selected. Adjusting a demand forecast value (56) includes estimating an inventory and a demand at a number of locations (24). An expected number of unrealized sales at each location (24) is calculated. An sales forecast value (56) is determined according to the expected number. Claims(22) 1-26. (canceled) 27. A method for computing an elasticity curve, comprising:
selecting a demand model having a plurality of variables; receiving a plurality of values for each variable; defining a plurality of filter sets, each filter set operable to restrict the values for at least one variable; determining an elasticity curve for each filter set by:
filtering the values for at least one variable using the filter set; and
calculating the elasticity curve from the filtered values by performing a regression analysis using the demand model as a regression equation;
measuring a quality value for each elasticity curve; and selecting an optimal elasticity curve according to the quality values. 28. The method of a dependent variable comprising a demand variable; and a plurality of independent variables comprising a price variable and time variables. 29. The method of the variables comprise a dependent variable and a plurality of independent variables; and determining the elasticity curve comprises using the demand model as a regression equation of the dependent variable over the independent variables. 30. The method of the values are associated with a plurality of products; and determining the elasticity curve for each filter set comprises:
determining an elasticity curve for each product using the values associated with the product;
measuring a quality value for each elasticity curve;
determining an unsatisfactory elasticity curve according to the quality values; and
eliminating the values associated with the unsatisfactory elasticity curve.
31. The method of the values are associated with a plurality of products; and determining the elasticity curve for each filter set comprises:
determining an elasticity curve for each product using the values associated with the product;
calculating an elasticity value from each elasticity curve; determining an unsatisfactory elasticity value; and
eliminating the values associated with the unsatisfactory elasticity value.
32. The method of 33. The method of 34. A system for computing an elasticity curve, comprising:
a database operable to store a demand model having a plurality of variables, a plurality of values for each variable, and a plurality of filter sets, each filter set operable to restrict the values for at least one variable; and a server coupled to the database and operable to:
determine an elasticity curve for each filter set by filtering the values for at least one variable using the filter set, and calculating the elasticity curve from the filtered values by performing a regression analysis using the demand model as a regression equation;
measure a quality value for each elasticity curve; and
select an optimal elasticity curve according to the quality values.
35. The system of a dependent variable comprising a demand variable; and a plurality of independent variables comprising a price variable and a time variable. 36. The system of the variables comprise a dependent variable and a plurality of independent variables; and the server is operable to perform a regression analysis using the demand model as a regression equation of the dependent variable over the independent variables. 37. The system of the values are associated with a plurality of products; and the server is operable to determine the elasticity curve for each filter set by:
determining an elasticity curve for each product using the values associated with the product;
measuring a quality value for each elasticity curve;
determining an unsatisfactory elasticity curve according to the quality values; and
eliminating the values associated with the unsatisfactory elasticity curve.
38. The system of the values are associated with a plurality of products; and the server is operable to determine the elasticity curve for each filter set by:
determining an elasticity curve for each product using the values associated with the product;
calculating an elasticity value from each elasticity curve; determining an unsatisfactory elasticity value; and eliminating the values associated with the unsatisfactory elasticity value.
39. The system of 40. The system of 41. Logic for computing an elasticity curve, the logic encoded in media and when executed operable to:
select a demand model having a plurality of variables; receive a plurality of values for each variable; define a plurality of filter sets, each filter set operable to restrict the values for at least one variable; determine an elasticity curve for each filter set by:
filtering the values for at least one variable using the filter set; and
calculating the elasticity curve from the filtered values by performing a regression analysis using the demand model as a regression equation; measure a quality value for each elasticity curve; and
select an optimal elasticity curve according to the quality values.
42. The logic of a dependent variable comprising a demand variable; and a plurality of independent variables comprising a price variable and a time variable. 43. The logic of the variables comprise a dependent variable and a plurality of independent variables; and the logic is further operable to use the demand model as a regression equation of the dependent variable over the independent variables. 44. The logic of the values are associated with a plurality of products; and the logic is further operable to determine the elasticity curve for each filter set by:
determining an elasticity curve for each product using the values associated with the product;
measuring a quality value for each elasticity curve;
determining an unsatisfactory elasticity curve according to the quality values; and
eliminating the values associated with the unsatisfactory elasticity curve.
45. The logic of the values are associated with a plurality of products; and the logic is further operable to determine the elasticity curve for each filter set by:
determining an elasticity curve for each product using the values associated with the product;
calculating an elasticity value from each elasticity curve;
determining an unsatisfactory elasticity value; and
eliminating the values associated with the unsatisfactory elasticity value.
46. The logic of 47-71. (canceled)Description This application claims benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application Ser. No. 60/238,676, filed Oct. 6, 2000. This invention relates in general to commercial environments, and more particularly to generating an optimized price schedule for a product. An important decision for a business to make is determining the prices of products, goods, or services offered by the business. Pricing decisions are important to a business's success or failure, since these decisions may have a critical impact on customer demand, profitability, and business operations. Informed pricing decisions, however, may be difficult to make, since these decisions may need to reflect a large number of business objectives and operating constraints, and may need to be made for a large number of items across a large number of sales locations. Moreover, pricing decisions may need to be frequently updated in order to adjust for rapid changes in business conditions, such as changes in inventory, demand, or a competitor's prices. Consequently, businesses may benefit greatly from price optimization, which may allow businesses to make effective pricing decisions. A business may generate a price schedule over a time horizon, and may optimize the price schedule in order to maximize the benefit of a product to the business. For example, a price schedule may be optimized to maximize expected profits or revenues over a time horizon, subject to operating constraints such as an allowed frequency of price changes, a maximum number of price changes, or an inventory target level. Optimizing price schedules, however, may be computationally difficult. As a result, previous techniques for generating an optimized price schedule have been inadequate. In accordance with the present invention, disadvantages and problems associated with generating price schedules have been substantially reduced or eliminated. In accordance with an embodiment of the present invention, a method for generating a price schedule includes generating a transition graph having paths. Each path has states, and each state has a price value, an inventory value, and a state value. The transition graph is generated by repeating the following for a number of stages until a last stage is reached. The price value of a successor state is determined. The inventory value of the successor state is calculated using the price value and the inventory value of a predecessor state. The state value of the successor state is calculated using the price value and the inventory value of the predecessor state. After the last stage has been reached, an optimal path is selected according to the state values of the states, and a price schedule is determined from the optimal path. In accordance with another embodiment of the present invention, a method for computing an elasticity curve includes selecting a demand model having a number of variables. A number of values for each variable are received. Filter sets that restrict the values for at least one variable are defined. An elasticity curve is determined for each filter set by filtering the values for at least one variable using the filter set, and calculating the elasticity curve from the filtered values by performing a regression analysis using the demand model as a regression equation. A quality value is measured for each elasticity curve, and an optimal elasticity curve is selected according to the quality values. In accordance with another embodiment of the present invention, a method for determining a sales forecast from an estimated demand and inventory includes defining a number of locations. An inventory and a demand are estimated at each location. An expected number of unrealized sales at each location is calculated using a difference between the demand and the inventory at the location. A sales forecast is determined using the expected number of unrealized sales. Certain embodiments of the present invention may provide one or more technical advantages over previous price scheduling techniques. Selling goods typically requires dynamic adjustment of a sales price over a time horizon. Given a forecast of product demand over time and a model of price elasticity, the present invention may calculate a price schedule that maximizes a business objective such as cumulative revenue, while satisfying business constraints such as a desired price behavior or an inventory target level. The present invention may generate price schedules that satisfy a variety of operating constraints. Price schedules are typically required to meet operating constraints such as a maximum number of price changes within a given time period of a time horizon, a maximum number of price changes over a time horizon, or a maximum price change over a time horizon. Price values may be constrained to meet specific price rules, for example, a price value must have a “9” in the cents position. Price values may be constrained to adhere to certain price reduction levels, such as 25%, 50%, or 75% off a base price. Constraints may be applied to the inventory age as described by the time the products are stored in inventory. The present invention may generate price schedules that satisfy these and other operating constraints. The present invention may allow for optimization of a variety of business objectives. Objectives may include, but are not limited to, margin and revenue considerations, opportunity costs of capital, inventory carrying costs, inventory age, costs of implementing price changes, impact on profits of substitute products, or opportunity costs of allocated shelf-space, or any other suitable objective. The present invention may be extended to incorporate an uncertainty of a demand forecast or an elasticity model in order to achieve certain statistical guarantees of performance of computed price schedules. The invention may be extended to compute price schedules of portfolios of products while considering price constraints between these products, or price schedules for groups of locations given price constraints between locations in the group. The present invention may efficiently generate an optimized price schedule using a “quantized dynamic programming” technique. A transition graph with paths representing possible price schedules may be generated using quantized dynamic programming. An optimal path of the transition graph is selected in order to determine an optimized price schedule. The present invention may improve the efficiency of the optimization by quantizing values associated with the transition graph at various degrees of granularity. Quantizing the state values reduces the size of transition graph, which may improve the processing time and power required to determine an optimal path of the transition graph. The present invention may take into account the elasticity of a product in order to improve the accuracy of the optimization. The elasticity of a product describes a change in the demand of a product in response to a change in the price of the product. The present invention may take into account the effect of unrealized sales due to supply limitations, which may improve the accuracy of the optimal path. An unrealized sale is predicted where there is a demand for a product, but no inventory, and may result when inventory is distributed across a group of locations that are being optimized together. Typically, aggregate values only take into account a total demand and a total inventory and do not account for supply limitations. The present invention may be used to compute an optimal sequence of product markdowns for liquidating merchandise, which may enable sellers to better plan and more profitably manage inventory, such as at the end of a product lifecycle. Given initial inventory and price values, a price schedule of product markdowns that maximizes business objectives while satisfying business constraints may be calculated. The price schedule may be used to maximize margin capture rates while reducing margin degradation and to provide accurate estimates of both margin capture rates and margin degradation factors. In addition, the present invention may be used to determine optimal start and end dates of a markdown horizon, or to determine which products should be put on a markdown plan. The present invention may be used to guide the decision of how many units of which product should be acquired for subsequent sale. Systems and methods incorporating one or more of these or other advantages may be well suited for modern commercial environments such as those associated with marking down the price of a product to achieve a predetermined inventory target. Other technical advantages are readily apparent to those skilled in the art from the following figures, descriptions, and claims. For a more complete understanding of the present invention and its advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: Company A server A database Locations A state State value In the illustrated example, transition graph The values Similarly, inventory values Additionally, constraints may be used to reduce the number of successor states A minimum and a maximum number of price changes may be used to control the number of times price value Constraints may be placed on inventory values The values describing the product are quantized at step Generating a price schedule includes generating transition graph Transition graph At step -
- S
_{i }represents the stage, - P
_{i }represents the price at stage s_{i}, - c
_{i }represents the inventory of state q_{i } - v
_{i }represents the value of state q_{i}, - h
_{i }represents accumulated state history of state q_{i}. Set Q is defined as the set of all states q_{i}. While the state history may include various aspects relating to an optimal path to the state such as a number of price changes, the state representation as expressed by Equation (6) abstracts away the details of the state history. Different representations of a state may be used. Unless otherwise noted, the components of a state are labeled using the state's annotation. For example, the state q′ has components labeled (s′,p′,c′,v′,h′).
- S
State value v Initial conditions and data are received at step Initial data may include a demand forecast F -
- C
_{E}=elasticity constant - p
_{0}=base price on which forecast F_{s }is based Transition**53**from a predecessor state**52**to a successor state**52**may be defined by a state-transition function expressed by Definition (9) that has a state-transition operator : (*s,p,c,v,h*)(*s′,p′,c′,v′,h′*), if and only if (9) - s′=s+1,
- p′εP,
- c′=γ
_{c}(max(0, c−F_{s}·E(p,s))), - V′=V+p·(c−c′),
- h′ captures the new state history and modifies h according to the transition, and
- the transition to the new state is consistent with any additional constraints that may be imposed.
Definition (9) provides an example of a state-transition function. Transition**53**, however, may be defined in any suitable manner. In addition, constraints may be placed on transition**53**in order to limit the successor states**52**of a state**52**. Any of the components of state**52**may be constrained. A constraint may, for example, prohibit drastic or frequent changes in the price values. A price-adjusted demand forecast F_{s}·E(p,s) may be adjusted to take into account unrealized sales that occur at one or more sales locations**24**. A method for adjusting the price-adjusted demand forecast is described in more detail in connection withFIG. 7 .
- C
The following summary outlines a method for determining an optimal final state. The method expands transition graph
At step _{0}.
Initially, set K is defined as {q Successor states Values for the successor state Quantization may be applied in any suitable manner. For example, price values may be stored as quantized values, and inventory values may be stored as exact precise values. When different states are compared using Equation (11), the inventory values may be compared after quantization. If the quantized values are the same, the two successors can be regarded identical according to Equation (11). At step A price schedule is determined from the optimal path at step In one embodiment, the present invention may be used to compute an optimal sequence of product markdowns for liquidating merchandise, which may enable sellers to better plan and more profitably manage inventory, for example, at the end of a product lifecycle. Given initial inventory and price values, a price schedule of product markdowns that maximizes business objectives while satisfying business constraints may be calculated. Elasticity module -
- D=demand
- P=price
- α=promotional variable
- t=time
- c
_{E}=elasticity constant K, q, β, and γ are constants, K>0, and it is expected that c_{E}<0, β>0, and γ<0. Equation (1) may be rewritten as Equation (2): 1*n*(*D*)=1*n*(*K*)+*c*1*n*(*P*)+*q*1*n*(1+α)+β1*n*(*t*)+γ*t*(2) Equation (2) may be used as a regression equation, where 1n(D) is the dependent variable and 1n(P), 1n(1+α), 1n(t), and t are the independent variables.
At step Data for a product may be grouped in data rows, where each data row includes data for a specific stage in time. A data row may include, for example, the following values: Product Identifier, Stage Number, Sales, Price, Revenues, and Promo. Product Identifier identifies the product, and Stage Number identifies the stage. Sales describes the number of units of the products sold during the stage, Price defines the price per unit, and Revenues describe the revenues generated from the sale of the product. Promo describes the number of units sold during a promotion for the product, such as a temporary price reduction. Other or additional values may be used to calculate an elasticity curve. For example, a seasonal index variable that describes how a time of year, such as the Christmas season, affects the demand for a product may be used. The values for Sales may be used as the values for demand D. Values for Price and Stage Number may be used as the values for price P and time t. Promotion variable a measures the significance of a promotion, and may be defined using Equation (3):
Filter sets are defined at step
According to the filter set of Table 1, a data row is removed if Sales is less than Min Sales or Revenues is less than Min Revenues. The data rows for a product are removed if number of data rows for the product is less than Min Rows. Promo Filter is used to define promotion variable α, as shown in Equation (3). Data rows that include values that are within a first or last percentile given by Perc Filter are removed. Steps At step The quality of the elasticity curve is determined to be acceptable or not at step At step Steps At step Unrealized sales, or stockouts, may be determined in order to predict sales. An unrealized sale is predicted where there is a demand at a location, but no inventory. An unrealized sale may be expressed as a difference between a demand value and an inventory value at any given location The method performs a significant adjustment to the demand forecast when inventory levels and forecasted demands are aggregated across a number of locations This method may be applied as part of the computation of the optimal price schedule, particularly if the estimate is not accurately performed as a preprocessing step. This may be the case if the demand value at each stage of the price scheduling horizon is dependent on a price value, and the future inventory values are dependent on the demand value. As has been outlined above, the prediction of sales in turn depends on the inventory values, leading to a circular dependency. The circular dependency may be resolved by taking the effect of distributed inventory on projected sales into account at each step of the computation of a price schedule. At step Alternatively, steps The expected number of unrealized sales E(M) may be calculated at step At step Alternatively, the computation in Equation (17) may be performed by using an incomplete beta-function. The inner sum of Equation (17) may be denoted by J, and Equations (21) through (28) may be used to describe the steps to transform J into a form that may be efficiently computed using a standard procedure for the incomplete beta-function.
At step The present invention may efficiently generate an optimized price schedule by using dynamic programming. In dynamic programming, transition graph Although the present invention has been described with several embodiments, a myriad of changes, variations, alterations, transformations, and modifications may be suggested to one skilled in the art, and it is intended that the present invention encompass such changes, variations, alterations, transformations, and modifications as fall within the scope of the appended claims. Referenced by
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