System and method for forecasting using Monte Carlo methods

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First Claim
1. A method comprising:
 receiving, with a computer system using one or more processors, sales data for a set of stock keeping units (SKUs);
filtering, with the computer system, the sales data into a lowselling set of SKUs to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs;
creating, with the computer system, a set of clusters of SKUs from the lowselling set of SKUs;
generating, with the computer system, a dynamic linear model for use with each cluster in the set of clusters;
generating, with the computer system, a set of random data points from the sales data, wherein the set of random data points are chosen based around a prior mean and a covariance of the sales data;
fitting, with the computer system, the sales data for each cluster in the set of clusters to the dynamic linear model at each random data point in the set of random data points using a Monte Carlo method with an unscented Kalman filter, wherein the unscented Kalman filter uses an unscented transformation sampling technique to capture a true mean and the covariance of the sales data;
calculating, with the computer system, the sales of the lowselling SKUs based on the fitting at the each random data point in the set of random data points, wherein the unscented Kalman filter is calculated at the each random data point in the set of random data points for a time period T;
iterating, with the computer system, the calculating based on the unscented Kalman filter calculated at the each random data point in the set of random data points for a time period T+1, wherein after each iteration, generating a first forecast for the sales of the each cluster in the set of clusters for the time period T+1;
performing, with the computer system, additional iterations for the time period T+1 of a set of time periods to generate the first forecast for the sales of the each cluster in the set of clusters;
generating, with the computer system, for the time period T+1 of the set of time periods, a second forecast for the sales of the lowselling SKUs; and
ordering inventory based on the second forecast for the sales of the lowselling SKUs for the time period T+1 of the set of time periods.
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Abstract
A system and method for calculating demand forecasts is presented. Sales data for a set of SKUs is received. The sales data is filtered to contain only data for lowselling SKUs. A set of clusters of SKUs is created. A generalized dynamic linear model for use with each cluster in the set of clusters is generated. A set of random data points is generated. The dynamic linear model is fitted at each data point in the set of random data points using a Monte Carlo method. This fitting can be performed using an unscented Kalman filter method. Calculating a forecast for sales based on the fitting at each data point. Using the forecast for sales, inventory is ordered. Other embodiments are also disclosed herein.
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20 Claims
 1. A method comprising:
receiving, with a computer system using one or more processors, sales data for a set of stock keeping units (SKUs); filtering, with the computer system, the sales data into a lowselling set of SKUs to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating, with the computer system, a set of clusters of SKUs from the lowselling set of SKUs; generating, with the computer system, a dynamic linear model for use with each cluster in the set of clusters; generating, with the computer system, a set of random data points from the sales data, wherein the set of random data points are chosen based around a prior mean and a covariance of the sales data; fitting, with the computer system, the sales data for each cluster in the set of clusters to the dynamic linear model at each random data point in the set of random data points using a Monte Carlo method with an unscented Kalman filter, wherein the unscented Kalman filter uses an unscented transformation sampling technique to capture a true mean and the covariance of the sales data; calculating, with the computer system, the sales of the lowselling SKUs based on the fitting at the each random data point in the set of random data points, wherein the unscented Kalman filter is calculated at the each random data point in the set of random data points for a time period T; iterating, with the computer system, the calculating based on the unscented Kalman filter calculated at the each random data point in the set of random data points for a time period T+1, wherein after each iteration, generating a first forecast for the sales of the each cluster in the set of clusters for the time period T+1; performing, with the computer system, additional iterations for the time period T+1 of a set of time periods to generate the first forecast for the sales of the each cluster in the set of clusters; generating, with the computer system, for the time period T+1 of the set of time periods, a second forecast for the sales of the lowselling SKUs; and ordering inventory based on the second forecast for the sales of the lowselling SKUs for the time period T+1 of the set of time periods.  View Dependent Claims (2, 3, 4, 5, 6, 7)
 8. A system comprising:
a user input device; a display device; one or more processors; and one or more nontransitory storage media storing computing instructions configured to run on the one or more processors and perform; receiving sales data for a set of stock keeping units (SKUs); filtering the sales data into a lowselling set of SKUs to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating a set of clusters of SKUs from the lowselling set of SKUs; generating a dynamic linear model for use with each cluster in the set of clusters; generating a set of random data points from the sales data, wherein the set of random data points are chosen based around a prior mean and a covariance of the sales data; fitting the sales data for each cluster in the set of clusters to the dynamic linear model at each random data point in the set of random data points using a Monte Carlo method with an unscented Kalman filter, wherein the unscented Kalman filter uses an unscented transformation sampling technique to capture a true mean and the covariance of the sales data; calculating the sales of the lowselling SKUs based on the fitting at the each random data point in the set of random data points, wherein the unscented Kalman filter is calculated at the each random data point in the set of random data points for a time period T; iterating, with the computer system, the calculating based on the unscented Kalman filter calculated at the each random data point in the set of random data points for a time period T+1, wherein after each iteration, generating a first forecast for the sales of the each cluster in the set of clusters for the time period T+1; performing, with the computer system, additional iterations for the time period T+1 of a set of time periods to generate the first forecast for the sales of the each cluster in the set of clusters; generating for the time period T+1 of the set of time periods, a second forecast for the sales of the lowselling SKUs; and ordering inventory based on the second forecast for the sales of the lowselling SKUs for the time period T+1 of the set of time periods.  View Dependent Claims (9, 10, 11, 12, 13, 14)
 15. At least one nontransitory storage media having computing instructions stored thereon executable to perform:
receiving sales data for a set of stock keeping units (SKUs); filtering the sales data into a lowselling set of SKUs to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating a set of clusters of SKUs from the lowselling set of SKUs; generating a dynamic linear model for use with each cluster in the set of clusters; generating a set of random data points from the sales data, wherein the set of random data points are chosen based around a prior mean and a covariance of the sales data; fitting the sales data for each cluster in the set of clusters to the dynamic linear model at each random data point in the set of random data points using a Monte Carlo method with an unscented Kalman filter, wherein the unscented Kalman filter uses an unscented transformation sampling technique to capture a true mean and the covariance of the sales data; calculating the sales of the lowselling SKUs based on the fitting at the each random data point in the set of random data points, wherein the unscented Kalman filter is calculated at the each random data point in the set of random data points for a time period T; iterating, with the computer system, the calculating based on the unscented Kalman filter calculated at the each random data point in the set of random data points for a time period T+1, wherein after each iteration, generating a first forecast for the sales of the each cluster in the set of clusters for the time period T+1; performing, with the computer system, additional iterations for the time period T+1 of a set of time periods to generate the first forecast for the sales of the each cluster in the set of clusters; generating for the time period T+1 of the set of time periods, a second forecast for the sales of the lowselling SKUs; and ordering inventory based on the second forecast for the sales of the lowselling SKUs for the time period T+1 of the set of time periods.  View Dependent Claims (16, 17, 18, 19, 20)
1 Specification
This disclosure relates generally to forecasting, and relates more particularly to forecasting sales for a retail business.
A retail business typically needs to stock items in a warehouse or store in order to sell the items. Storing too few of a particular item can be undesirable because if the item is sold out, then the retail business is not able to sell the item until it is in stock again. Storing too many of a particular item also can be undesirable because the amount of space in a warehouse or store is finite—storing too many of an item that does not sell takes away space from items that do sell. Therefore, it would be desirable to have a system that can more accurately forecast the sales of items for a retailer or distributor.
To facilitate further description of the embodiments, the following drawings are provided in which:
For simplicity and clarity of illustration, the drawing figures illustrate the general manner of construction, and descriptions and details of wellknown features and techniques might be omitted to avoid unnecessarily obscuring the present disclosure. Additionally, elements in the drawing figures are not necessarily drawn to scale. For example, the dimensions of some of the elements in the figures might be exaggerated relative to other elements to help improve understanding of embodiments of the present disclosure. The same reference numerals in different figures denote the same elements.
The terms “first,” “second,” “third,” “fourth,” and the like in the description and in the claims, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms “include,” and “have,” and any variations thereof, are intended to cover a nonexclusive inclusion, such that a process, method, system, article, device, or apparatus that comprises a list of elements is not necessarily limited to those elements, but might include other elements not expressly listed or inherent to such process, method, system, article, device, or apparatus.
The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “over,” “under,” and the like in the description and in the claims, if any, are used for descriptive purposes and not necessarily for describing permanent relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the apparatus, methods, and/or articles of manufacture described herein are, for example, capable of operation in other orientations than those illustrated or otherwise described herein.
The terms “couple,” “coupled,” “couples,” “coupling,” and the like should be broadly understood and refer to connecting two or more elements mechanically and/or otherwise. Two or more electrical elements can be electrically coupled together, but not be mechanically or otherwise coupled together. Coupling can be for any length of time, e.g., permanent or semipermanent or only for an instant. “Electrical coupling” and the like should be broadly understood and include electrical coupling of all types. The absence of the word “removably,” “removable,” and the like near the word “coupled,” and the like does not mean that the coupling, etc. in question is or is not removable.
As defined herein, two or more elements are “integral” if they are comprised of the same piece of material. As defined herein, two or more elements are “nonintegral” if each is comprised of a different piece of material.
As defined herein, “approximately” can, in some embodiments, mean within plus or minus ten percent of the stated value. In other embodiments, “approximately” can mean within plus or minus five percent of the stated value. In further embodiments, “approximately” can mean within plus or minus three percent of the stated value. In yet other embodiments, “approximately” can mean within plus or minus one percent of the stated value.
In one embodiment, a method can comprise: receiving sales data for a set of stock keeping units (SKUs); filtering the sales data to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating a set of clusters of SKUs from the set of SKUs; generating a dynamic linear model for use with each cluster in the set of clusters; generating a set of random data points; fitting the dynamic linear model at each data point in the set of random data points using a Monte Carlo method; calculating a forecast for sales of the lowselling SKUs based on the fitting at each data point in the set of random data points; and ordering inventory based on the forecast for sales of the lowselling SKUs.
In one embodiment, a system can comprise: a user input device; a display device; one or more processing modules; and one or more nontransitory storage modules storing computing instructions configured to run on the one or more processing modules and perform the acts of receiving sales data for a set of stock keeping units (SKUs); filtering the sales data to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating a set of clusters of SKUs from the set of SKUs; generating a dynamic linear model for use with each cluster in the set of clusters; generating a set of random data points; fitting the dynamic linear model at each data point in the set of random data points using a Monte Carlo method; calculating a forecast for sales of the lowselling SKUs based on the fitting at each data point in the set of random data points; and ordering inventory based on the forecast for sales of the lowselling SKUs.
In one embodiment, at least one or more nontransitory storage modules having computing instructions stored thereon configured perform the acts of: receiving sales data for a set of stock keeping units (SKUs); filtering the sales data to contain only data for lowselling SKUs, within the set of SKUs that have sales within a bottom twenty percent of the set of SKUs; creating a set of clusters of SKUs from the set of SKUs; generating a dynamic linear model for use with each cluster in the set of clusters; generating a set of random data points; fitting the dynamic linear model at each data point in the set of random data points using a Monte Carlo method; calculating a forecast for sales of the lowselling SKUs based on the fitting at each data point in the set of random data points; and ordering inventory based on the forecast for sales of the lowselling SKUs.
Turning to the drawings,
Continuing with
In various examples, portions of the memory storage module(s) of the various embodiments disclosed herein (e.g., portions of the nonvolatile memory storage module(s)) can be encoded with a boot code sequence suitable for restoring computer system 100 (
As used herein, “processor” and/or “processing module” means any type of computational circuit, such as but not limited to a microprocessor, a microcontroller, a controller, a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a graphics processor, a digital signal processor, or any other type of processor or processing circuit capable of performing the desired functions. In some examples, the one or more processing modules of the various embodiments disclosed herein can comprise CPU 210.
In the depicted embodiment of
Network adapter 220 can be suitable to connect computer system 100 (
Returning now to
Meanwhile, when computer system 100 is running, program instructions (e.g., computer instructions) stored on one or more of the memory storage module(s) of the various embodiments disclosed herein can be executed by CPU 210 (
Further, although computer system 100 is illustrated as a desktop computer in
Forecasting is a key problem encountered in inventory planning for retailers and distributors. In order to buy inventory in advance, retailers or distributors would like an estimate of the number of units a distinct item for sale (also known as a stock keeping unit or a “SKU”) is going to sell in a certain time period. To clarify the difference between an item and a SKU, an item might be, for example, an iPad. But each specific configuration of the iPad (screen size, memory size, color, radio, and the like) is a different SKU. Each SKU typically has a unique identifier. Buying fewer quantities of a SKU than is needed leads to lost sales opportunities, hence lower revenue, because items that could have been sold were not in stock. Buying too many of a particular SKU units also can lead to lost sales opportunities because the cost of buying the unused inventory might not be compensated for by income from other sales to customers and can lead to lost opportunity costs (e.g., items that do not sell occupying space in a warehouse or store in place of items that could have been sold).
In general, a retailer or distributor wants to forecast the number of units it will sell so it can accurately purchase the units on a timely basis. One method of forecasting examines past sales of an item. Past sales can reveal both local level and seasonal patterns. Local level patterns refers to sales in the recent past, as sales of a certain SKU in the recent past can be important in forecasting future sales. Seasonality refers to periodic events that can influence sales. Seasonality can refer both to general seasonality (e.g., sales might be higher during the autumn because of the holiday season), and to product seasonality (e.g., some products are generally used only during certain times of the year.) For example, swimwear might be more popular in the summer, while Christmas decorations are more popular in the fall and winter.
With reference to
Yaxis 410 is the range of values for sales. Data series 430 represents the sales for each time period represented by Xaxis 420. Yaxis 410 can be in a variety of different formats. In some embodiments, Yaxis 410 can represent actual sales. In some embodiments, Yaxis 410 can represent sales rankings. Using rankings as opposed to actual sales might result in more reliable and accurate data in some embodiments. For modeling purposes, two timeseries might be considered similar if they rise and fall in unison. A rank correlation metric such as a Pearson correlation or a Spearman correlation can be used to measure similarity between timeseries. For display purposes, Yaxis 410 can be linear or logarithmic.
As described above, a retailer would take data such as that illustrated in
There are several different methods that can be used to generate sales forecasts for SKUs. Some methods involve placing a SKU in a cluster of SKUs and generating a forecast for the cluster of SKUs.
Many methods of generating a sales forecast assume that the distribution of demand has a Gaussian distribution. For example, several of the methods referenced above use one or more dynamic linear models that are fitted using a Kalman filter.
The Kalman filter is optimized for Gaussian distributions and might not work very well for lowselling items, which typically have inconsistent demand that are more easily modeled as having a Poisson distribution. A Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.
Briefly, a Kalman filter works in a twostep process. In a prediction step, the Kalman filter produces estimates of current state variables along with their uncertainty. Once the outcome of the next measurement is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. Because of the algorithm'"'"'s recursive nature, it can be executed in realtime using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.
The basic Kalman filter is limited to a linear assumption. However, lowselling items are often nonlinear and are best modeled using a Poisson distribution.
Retail sales often have a “long tail” distribution. That is, a relatively small number of products make up the majority of sales of a retailer. At one exemplary retailer, it has been found that approximately 71% of items, sold have a maximum weekly sales of approximately 5 or less.
There have been methods aimed at using the Kalman filter for nonlinear assumptions. For example, the extended Kalman filter uses a linking function to transform the nonlinear data into a linear form for Kalman filtering purposes. However, when the models are highly nonlinear, the extended Kalman filter can give particularly poor performances. In the extended Kalman filter, the state distribution is approximated by a Gaussian random variable which is then propagated analytically through the linearization of the nonlinear system. These approximations can introduce large errors in the true posterior mean and covariance of the transformed random variable, which can lead to suboptimal performance and possibly divergence of the filter.
In response to those criticisms of the extended Kalman filter, the unscented Kalman filter was developed. The unscented Kalman filter uses a deterministic sampling technique called the unscented transformation that picks a minimal set of sample points (also known as sigma points) around the mean. Typically, the number of sigma points is 2L+1, where L is the dimension of the augmented state. These sigma points are then propagated through the nonlinear functions, from which the mean and covariance of the estimate then can be recovered. The result is a filter which captures the true mean and covariance of the data more accurately than the extended Kalman filter.
However, it has still been found that the unscented Kalman filter still can be inaccurate for Poisson distribution models of highdimensions. In other words, analyzing the data for many different SKUs at once is not very accurate for the unscented Kalman filter.
An embodiment solves the above problems by using Monte Carlo methods with the unscented Kalman filter to produce more accurate estimations. Monte Carlo methods rely on repeated random sampling to obtain numerical results. In some embodiments, instead of using 2L+1 sigma points calculated in a specific manner, one performs an unscented Kalman filter using many randomly chosen points around a mean and covariance.
A flowchart illustrating the operation of a method 300 of using Monte Carlo methods to produce a forecast is presented in
Sales data regarding a set of SKUs is received (block 302). The sales data is filtered to produce data only for “lowselling” SKUs, for processing by an embodiment (block 304). As stated above, the methods presented below are optimized for lowselling items. Highselling items often are linear, and accurate forecasts can be produced using other methods. In some embodiments, “lowselling” SKUs are those where the maximum weekly sales of the SKU are below a certain threshold. This threshold can be five items in some embodiments. The threshold also can be other higher or lower values. The threshold also can be determined as a percentile score. In some embodiments, SKUs that are in the bottom 20 percentile of sales could be considered “lowselling.” In other embodiments, lower or higher percentiles can be used, such as bottom 50%, bottom 40%, bottom 30%, bottom 15%, bottom 10%, bottom 5%, or bottom 1%.
Thereafter, the data can be grouped or clustered (block 306). As describe above, there can be a large number of SKUs that are lowsellers. For very large retailers, the number can be in the millions. To simplify calculations, SKUs are grouped in one of a variety of different manners. Exemplary grouping manners can use the categories to which a SKU belongs. In some embodiments, the groups (or clusters) contain between 50 and 300 SKUs.
A dynamic linear model (DLM) is chosen (block 308). This DLM can be a generalized DLM, chosen such that it works well for a large variety of different types of goods. Other methods of forecasting use DLMs specifically chosen for a type of good, or use many different DLMs with different weights, in an attempt to obtain an accurate result. Embodiments can use a generalized DLM tuned for accuracy across a large number of goods.
The data for the cluster is fitted to the DLM using Monte Carlo methodology with an unscented Kalman filter. In general, the Monte Carlo methodology involves sampling the DLM at a large number of random data points. In some embodiments, the number of random data points used can be over 1000. The large number of data points allows more accurate values to be obtained.
To more thoroughly explain this, it can be useful to discuss the details of the unscented Kalman filter in more detail. As described above, the Kalman filter is a recursive estimator that uses an estimated state and a current state to compute an estimate, with no need for a history of observations or estimates. The Kalman filter has two phases, a predict phase and an update phase. The predict phases uses a state estimate from the previous time to product an estimate at the current time. In the update phase, measurement information at the current time is used to refine the prediction to arrive at a new estimate for the current time. These steps are repeated at each time T. The formulas is as follows:
x_{k}=F_{k}x_{k1}+B_{k}u_{k1}+w_{k1 }
Where F_{k }is the state transition model applied to the previous state x_{k1}; B_{k }is the controlinput model applied to control vector u_{k}; and w_{k }is the process noise which is assumed to be drawn from a zero mean multivariate normal distribution.
The predicted state is as follows:
x_{kk1}=F_{k}{circumflex over (x)}_{k1k1}+B_{k}u_{k1 }
The predicted estimated covariance is as follows:
P_{kk1}=F_{k}P_{kk1}F_{k}^{T}+Q_{k1 }
Where P_{kk1 }is the covariance at point k given the covariance for point k−1 and F_{k}^{T }is the transpose of the F matrix at point k.
The unscented Kalman filter uses a set of sigma points chosen based on the mean. These sigma points are propagated through the nonlinear functions and the covariance of the estimate is then recovered. Typically, only a small number of sigma points are chosen, typically 2L+1, where L is the dimensionality of the augmented state. The sample points are chosen around the mean as follows (where x_{a }is the augmented mean)
x_{0}=x_{a }
x_{i}=x_{0}+(√{square root over ((L+λ)P_{k1k1}^{a}))}_{i }for i=1 . . . L
x_{i}=x_{0}−(√{square root over ((L+λ)P_{k1k1}^{a}))}_{i }for i=L+1, . . . ,2L
Although the unscented Kalman filter is more accurate than previous methods, it has been found to still diverge in certain cases.
Therefore, an embodiment uses Monte Carlo methodology. A set of random points are generated (block 310). The random points are chosen based around the prior mean and covariance. A large number of random points may be chosen. In some embodiments, over 1000 random points are generated.
Calculating expected value and covariance, steps that are part of the Kalman filter method, generally involve integrals. Integrals can be difficult to calculate for nonlinear functions, such as those involved in a Poisson distribution. The Monte Carlo method involves evaluating those integrals at each of the random points in the set of random points.
In some embodiments, a Cholesky decomposition is used in conjunction with the Monte Carlo method (block 312). (Connector block 311 is for illustrative purposes and only serves to connect block 310 with block 312.) The Cholesky decomposition involves decomposing a matrix A into a lower triangular matrix as follows:
A=LL*
In other words, matrix A is decomposed into a lower triangular matrix L and its conjugate transpose L*. Applying the Cholesky decomposition to a vector of uncorrelated samples, u, produces a sample vector Lu, with the covariance properties of the system being modeled. The Cholesky decomposition can be calculated in a variety of different manners known in the art.
The unscented Kalman filter can be calculated at each of the random points instead of the sigma points. Once the DLM has been calculated at the random samples points for a time T, the process can be repeated again for the next time period T+1 (block 314). After each iteration, the DLM can generate a forecast for sales, which is then used to order goods for a retailer/distributor (block 316).
Turning ahead in the figures,
In a number of embodiments, system 500 can include receiving module 502. In certain embodiments, receiving module 502 can perform block 302 (
In a number of embodiments, system 500 can include filtering module 504. In certain embodiments, filtering module 504 can perform block 304 (
System 500 can include clustering module 506. In certain embodiments, clustering module 506 can perform block 306 (
System 500 can include DLM choosing module 508. In certain embodiments, DLM choosing module 508 can perform block 308 (
System 500 can include random generation module 510. In certain embodiments, random generation module 510 can perform block 310 (
System 500 can include Cholesky module 512. In certain embodiments, Cholesky module 512 can perform block 312 (
System 500 can include iteration module 514. In certain embodiments, iteration module 514 can perform block 314 (
System 500 can include ordering module 516. In certain embodiments, ordering module 516 can perform block 316 (
Although the above embodiments have been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes can be made without departing from the spirit or scope of the disclosure. Accordingly, the disclosure of embodiments is intended to be illustrative of the scope of the disclosure and is not intended to be limiting. It is intended that the scope of the disclosure shall be limited only to the extent required by the appended claims. For example, to one of ordinary skill in the art, it will be readily apparent that any element of
Replacement of one or more claimed elements constitutes reconstruction and not repair. Additionally, benefits, other advantages, and solutions to problems have been described with regard to specific embodiments. The benefits, advantages, solutions to problems, and any element or elements that can cause any benefit, advantage, or solution to occur or become more pronounced, however, are not to be construed as critical, required, or essential features or elements of any or all of the claims, unless such benefits, advantages, solutions, or elements are stated in such claim.
Moreover, embodiments and limitations disclosed herein are not dedicated to the public under the doctrine of dedication if the embodiments and/or limitations: (1) are not expressly claimed in the claims; and (2) are or are potentially equivalents of express elements and/or limitations in the claims under the doctrine of equivalents.