Price determination method, price determination device, and program

Abstract

To efficiently estimate the optimum price of a product that may have multiple sales routes. [Solution] The price determination method obtains the potential demand for the product for each of multiple sales destinations and the price elasticity, which indicates the rate of change in the potential demand for the product when the base price of the product is changed, for each of multiple sales destinations for a product that can be sold at a price determined for each of the multiple sales destinations based on a base price common to the multiple sales destinations, calculates the estimated sales volume for each sales destination based on the potential demand for the product and price elasticity, and determines a base price for the product such that the total value of the estimated sales volumes for each sales destination is less than the sales limit for the product.

Description

[Technical Field]

[0001] The present disclosure relates to a price determination method, a price determination device, and a program. [Background technology]

[0002] Patent Document 1 discloses an information analysis device that supports appropriate pricing of products. This information analysis device derives sales performance for each area type based on area type data, which groups multiple geographically divided areas into areas with similar resident attributes, and sales performance data, which includes data indicating stores that sold the target product to customers, the sales price and sales volume of the target product at the store, and the customer's residential area. The information analysis device also identifies sales volumes for each area type corresponding to multiple sales prices of the target product based on the sales performance for each area type, derives price elasticity for each area type of the target product, and derives purchase frequencies, which indicate the number of purchasing customers who purchased a product at the target store for each area type and the purchase volumes of the target product for each area type. The information analysis device estimates the sales volume for each sales price of the target product at the target store for each sales price based on the price elasticity, the number of purchasing customers, and the purchase frequencies. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2017-228056 Summary of the Invention [Problem to be solved by the invention]

[0004] According to Patent Document 1, it is possible to estimate the sales volume when multiple sales prices are set for a product under analysis based on price elasticity, customer numbers, and purchase frequencies derived for each area type in areas with similar resident attributes. However, in commercial transactions, there are often multiple recipients of goods or services, and contracts setting out various arrangements such as transaction prices with each recipient are often different. Given this situation, there was a problem in that it was difficult with conventional technologies to determine prices taking into account the delivery routes when there are multiple recipients of goods or services. Patent Document 1 also does not anticipate a technology for optimally determining prices taking into account multiple recipients of goods.

[0005] The present disclosure has been devised in view of the above-described conventional situation, and aims to efficiently estimate the optimal price of a product that may have multiple sales routes. [Means for solving the problem]

[0006] The present disclosure provides a price determination method for a product that can be sold to each of multiple sales destinations at a price determined for each of the sales destinations based on a base price common to the multiple sales destinations, by obtaining the potential demand for the product for each of the sales destinations and price elasticity that indicates the rate of change in the potential demand for the product when the base price of the product is changed, calculating an estimated sales volume for each of the sales destinations based on the potential demand for the product and price elasticity, and determining a base price for the product such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit for the product.

[0007] The present disclosure also provides a price determination device comprising a processor and a memory, wherein the processor, in cooperation with the memory, acquires, for each of a plurality of sales destinations, a potential demand for the product that can be sold at a price determined for each of the sales destinations based on a base price common to the plurality of sales destinations, and a price elasticity that indicates a rate of change in the potential demand for the product when the base price of the product is changed; calculates, for each sales destination, an estimated sales quantity based on the potential demand for the product and the price elasticity; and determines a base price for the product such that the total value of the estimated sales quantities for each sales destination is equal to or less than the sales upper limit for the product.

[0008] The present disclosure also provides a program for causing a price determination device, which is a computer, to execute the following processes: for a product that can be sold to each of multiple sales destinations at a price determined for each of the sales destinations based on a base price common to the multiple sales destinations, acquiring the potential demand for the product for each of the sales destinations and price elasticity that indicates the rate of change in the potential demand for the product when the base price of the product is changed; and calculating an estimated sales quantity for each of the sales destinations based on the potential demand for the product and price elasticity, and determining a base price for the product such that the total value of the estimated sales quantities for each of the sales destinations is equal to or less than the sales upper limit for the product.

[0009] These comprehensive or specific aspects may be realized as a system, an apparatus, a method, an integrated circuit, a computer program, or a recording medium, or may be realized as any combination of a system, an apparatus, a method, an integrated circuit, a computer program, and a recording medium. [Effects of the Invention]

[0010] According to the present disclosure, it is possible to efficiently estimate the optimal price of a product that may have multiple sales routes. [Brief explanation of the drawings]

[0011] [Figure 1] A block diagram showing an example of the hardware configuration of a price optimization device according to an embodiment of the present invention. [Figure 2] FIG. 10 is a diagram showing an example of the data structure of parameter data stored in memory. [Figure 3] A diagram showing an example of the data structure of sales performance data stored in memory. [Figure 4] A diagram showing an example of the data structure of sales forecast data stored in memory. [Figure 5] A diagram showing an example of the data structure of optimal price data stored in memory. [Figure 6] An example of a demand-price curve [Figure 7] A conceptual example of the search area for estimated sales volume [Figure 8] Diagram showing an example contractual arrangement between a supplier and a reseller [Figure 9] 1 is a flowchart showing an example of the operation procedure of a price optimization device according to an embodiment of the present invention in chronological order. DETAILED DESCRIPTION OF THE INVENTION

[0012] 1. Background to this disclosure Recently, technological innovation, infectious diseases, demographic trends, and other factors have caused significant changes in relationships within and between social groups, particularly nations. This has led to greater social fluctuations, making it difficult to predict future economic activity, such as demand. Furthermore, the frequency and severity of weather phenomena and disasters caused by global warming are changing due to the progression of global warming, making it difficult to predict the impact on economic activity, such as demand, based solely on human experience and intuition. Therefore, there is a need for technology that can make robust predictions even in uncertain situations and enable effective decision-making and actuation. The present inventors have developed price optimization technology as one of the technologies that can enable decision-making and actuation. Price optimization technology consists of technology for predicting demand for a target product or service and technology for setting prices according to demand.

[0013] Dynamic pricing is known as a technology for setting prices based on predicted demand. Dynamic pricing aims to maximize sales by adjusting the price of a product (including services; the same applies below) based on predicted demand. It is being increasingly adopted in a variety of industries, including not only retail but also the entertainment industry. For example, if the price is fixed, a high product price tends to result in low sales volume and low profits, while a low product price tends to result in low profits even with a high sales volume. However, dynamic pricing makes it possible to dynamically adjust the product price based on demand. For example, during peak periods when demand is high, the product price can be increased to maximize sales, and during off-peak periods when demand is low, the product price can be decreased to reduce missed sales.

[0014] When a product is sold to a large number of resellers, the selling price of the product may differ for each reseller (hereinafter referred to as "resale route"). In such cases, it has been difficult for the seller to determine the price of the product. This is thought to be due to the fact that, for example, the contracts that stipulate various arrangements between the seller and the reseller differ for each resale route. Therefore, there is a need for technology that assists sellers in setting product prices because the contracts differ for each resale route.

[0015] Therefore, in the following embodiments, examples of a price determination method, a price determination device, and a program for efficiently estimating the optimal price of a product that may have multiple sales routes will be described.

[0016] Hereinafter, with appropriate reference to the drawings, embodiments specifically disclosing the price determination method, price determination device, and program according to the present disclosure will be described in detail. However, more detailed description than necessary may be omitted. For example, detailed descriptions of well-known matters and redundant descriptions of substantially identical configurations may be omitted. This is to avoid unnecessary redundancy in the following description and to facilitate understanding by those skilled in the art. Note that the accompanying drawings and the following description are provided to enable those skilled in the art to fully understand the present disclosure, and are not intended to limit the subject matter of the claims.

[0017] 2. Price optimization device configuration First, with reference to FIGS. 1 to 8, a configuration example of a price optimization device 1 as an example of a price determination device according to the present disclosure will be described. FIG. 1 is a block diagram showing an example of the hardware configuration of the price optimization device 1 according to the present embodiment. FIG. 2 is a diagram showing an example of the data structure of parameter data 21 stored in memory 20. FIG. 3 is a diagram showing an example of the data structure of sales performance data 22 stored in memory 20. FIG. 4 is a diagram showing an example of the data structure of sales forecast data 23 stored in memory 20. FIG. 5 is a diagram showing an example of the data structure of optimal price data 24 stored in memory. FIG. 6 is a diagram showing an example of an image of a demand-price curve. FIG. 7 is a diagram showing a conceptual example of a search area for estimated sales quantities. FIG. 8 is a diagram showing an example of an arrangement based on a contract between a supplier and a reseller.

[0018] 1, the input device IN1 and the display device OU1 are shown as separate entities relative to the price optimization device 1, but at least one of the input device IN1 and the display device OU1 may be included within the price optimization device 1. The price optimization device 1 is connected to an external device (not shown) via a network NW so that data communication can be performed between the external device and the price optimization device 1. The network NW may be, for example, a Wide Area Network (WAN), a Local Area Network (LAN), mobile communications such as Long Term Evolution (LTE), 4G, or 5G, power line communications, short-range wireless communications (e.g., Bluetooth (registered trademark) communications), or communications for mobile phones, and is not limited to those exemplified here.

[0019] The price optimization device 1 uses a potential demand prediction model obtained by machine learning to predict the potential demand of a product that corresponds to the prediction target for each of a plurality of sales destinations (hereinafter sometimes referred to as "resale destinations") from a seller (e.g., a store; the same applies hereinafter) that is a supplier of the product, and uses the prediction results to calculate a base price P' that maximizes the expected value of product sales. ref The price optimization device 1 is a computer device such as a desktop personal computer or a stationary server computer. Note that the price optimization device 1 is not limited to these computer devices, and may be a portable computer device such as a smartphone or a tablet terminal. The price optimization device 1 includes at least a processor 10 and a memory 20.

[0020] The processor 10 is configured by at least one of a central processing unit (CPU), a digital signal processor (DSP), a graphical processing unit (GPU), and a field programmable gate array (FPGA). The processor 10 functions as a controller that manages the overall operation of the price optimization device 1. The processor 10 performs control processing for overseeing the operations of each unit of the price optimization device 1, data input / output processing between each unit of the price optimization device 1, data calculation processing, and data storage processing. The processor 10 operates according to a program stored in the memory 20. The processor 10 uses the memory 20 during operation and temporarily stores data generated or acquired by the processor 10 in the memory 20. In the price optimization device 1, the processor 10 cooperates with the memory 20 to execute various processes (e.g., the processes of the flowchart shown in FIG. 9 ). The processor 10 cooperates with the memory 20 to realize the functions of the parameter input unit 11, the potential demand forecast / price elasticity estimation unit 12, and the price determination unit 16.

[0021] The parameter input unit 11 acquires various parameter data 21 input by the user based on the user's input operation using the input device IN1, for example, and stores the data in the memory 20. For example, if the upper limit L r Here, r is an identification number of the reseller, and is an integer equal to or greater than 1. Details of the parameter data 21 will be described later with reference to FIG. 2. The parameter data 21 is used when the price determination unit 16 determines the base price P' of the product. ref This is data that serves as one or more constraints necessary for the process of determining the sales quota t. For example, the sales quota L t,r , the reference price P of the relevant product tentatively assumed by the user (e.g., seller) ref , the sales price P for each resale destination (e.g., sales quota t) t,r In addition, the base price P refis a price set commonly to multiple resellers and is used as the basis for determining the price of the product at each reseller. As will be described later, the price of the product at each reseller is determined, for example, by a function using the base price.

[0022] The potential demand forecasting / price elasticity estimation unit 12 learns and estimates parameters of a potential demand forecasting model that predicts the potential demand of a product, using sales performance data 22 for each resale destination stored in memory 20. In addition, the potential demand forecasting / price elasticity estimation unit 12 uses the potential demand forecasting model obtained by estimation based on this learning to calculate the base price P of the product that does not depend on the resale destination. ref The potential demand prediction / price elasticity estimation unit 12 outputs the prediction results for each resale destination that predicts the potential demand corresponding to the product, and the price elasticity for each resale destination, which is a parameter that indicates the degree of impact when the base price of the product is changed, and stores them in memory 20 for each resale destination. The potential demand prediction / price elasticity estimation unit 12 has at least a data preprocessing unit 13, a learning unit 14, and an inference unit 15. The inference unit 15 has at least a demand prediction unit 15a and a price elasticity acquisition unit 15b.

[0023] The data preprocessing unit 13 determines the processing division t of the data based on the input operation of the user using the input device IN1, for example. The processing division here is the base price P ref This is the minimum unit when forecasting potential demand for each resale destination, and the base price P ref It is also the smallest unit when determining price elasticity, which indicates the degree of impact when a change in price is made. For example, the data preprocessing unit 13 determines the processing interval t to be, for example, one day (i.e., one day of the week) or one hour (i.e., one time period). Note that the value of the processing interval t is not limited to one day or one hour, and may be, for example, an eight-hour period in the morning, an eight-hour period in the afternoon, or an eight-hour period at night, or may be a number of hours (e.g., two, three, four, or six hours) that allows a day to be divided into multiple time periods.

[0024] The data preprocessing unit 13 references the past sales performance data 22 for each resale destination stored in the memory 20, and generates (preprocesses) learning preparation data by shaping the data of explanatory variables necessary for learning the parameters of the potential demand forecasting model according to the processing category t (see FIG. 3). The data of the explanatory variables and the learning preparation data may be the same, or the data of the explanatory variables may be configured as part of the learning preparation data. Shaping here is not limited to editing or adding data included in the sales performance data 22 for each resale destination, but may also include processing to attach (add) external data acquired from other external devices (not shown) (for example, trend information for stores, weather information, information indicating whether or not the onset of COVID-19 has occurred).

[0025] When there is missing data (i.e., missing data) in the past sales performance data 22 for each resale destination stored in memory 20, the data pre-processing unit 13 performs a process of complementing the missing data using data before and after the date and time of the missing data. For example, the data pre-processing unit 13 adds data from the first week when there are not enough days to calculate a one-week moving average, or complements the weather for a date and time when weather information could not be obtained. It goes without saying that examples of data complementation are not limited to these exemplified processes.

[0026] The learning unit 14 performs machine learning using the learning preparation data (see FIG. 3) generated by the data preprocessing unit 13 and a likelihood function that takes into account right truncation of actual sales figures that exceed the upper limit of the product sales figures. Here, right truncation refers to a situation in which an observed value that exceeds a certain upper limit is recorded as the upper limit. As a result of machine learning using the learning preparation data as input (for example, processing by the variational Bayes method using the likelihood function described above), the learning unit 14 calculates the reference price P ref The parameters of the potential demand forecasting model that predicts the potential demand corresponding to the product, and the base price P ref We estimate the price elasticity parameters corresponding to

[0027] Here, learning of parameters of a potential demand forecasting model using a likelihood function will be described.

[0028] First, let us assume that the actual sales volume for each processing section t has an upper limit (upper limit) due to supply constraints imposed by the seller (e.g., a store), and that the upper limit of the actual sales volume fluctuates depending on the processing section t. The actual sales volume, upper limit of the sales volume, and price for a certain time frame, processing section t, and resale destination r are respectively expressed as y t,r , l t,r , p t,r Let t be the processing interval (in other words, the sales quota) corresponding to the unit time for analyzing the sales of the product, and so on. The price optimization device 1 according to this embodiment determines the price that maximizes the expected value of sales of the product for a time point in the future from the present.

[0029] Optimal reference price P' ref To determine the potential demand for the product in the absence of supply constraints, t Furthermore, in this embodiment, the base price P ref Potential demand S when changing t,r To predict the price elasticity of demand, e r You need to get y t,r When the upper limit is reached, ^y t,r Yes t,r However, the actual sales volume y t,r In a general regression model with the objective variable, the actual sales volume y t,r In other words, the predicted value is obtained assuming that the actual sales volume after the stockout is zero, which results in an underprediction of potential demand.

[0030] Furthermore, while there are existing technologies that assume a normal distribution for demand forecasting, this assumption results in poor forecast accuracy when actual sales figures include values ​​near zero. Furthermore, linear models that employ a normal distribution cannot achieve nonlinear responses to multiple explanatory variables. Furthermore, while price optimization requires the estimation of price elasticity, conventional technologies have not introduced this parameter known as price elasticity. This price elasticity can be expressed, for example, as the slope of a line that approximates the distribution characteristics of sales volume and price, as shown in Figure 6. In other words, it is an index (parameter) that indicates the percentage by which a product's sales volume decreases when the price is increased, and the percentage by which a product's sales volume increases when the price is decreased.

[0031] To solve these problems, in this embodiment, the relationship between actual sales volume at the time when the upper limit of sales volume is exceeded and potential demand is modeled using a right-truncated likelihood function of a Poisson distribution. Also, to achieve nonlinear response, a forward propagation neural network (NN) is introduced in the learning process in the learning unit 14. Furthermore, a price elasticity parameter is added to the potential demand forecasting model, so that the price elasticity parameter is estimated in the inference results.

[0032] Specifically, the potential demand forecasting model is constructed by combining the output f of a forward propagation neural network (NN) and the base price P ref The relative price fluctuation Δp relative to the price was used to model the following equation (1). In equation (1), ^S t、r ,X, θ, and α respectively represent the potential demand for each resale destination, the feature quantity (see the example of data added in preprocessing in Figure 3), the NN parameters, and the price elasticity for each sales destination.

[0033]

number

[0034] If the sales quantity is less than the sales upper limit (i.e., the actual sales quantity is less than the sales upper limit), (S t、r <L t、r), no right truncation is performed, and the likelihood function M(S t、r |^S t、r ) is a normal P(S t、r |^S t、r ) where P represents the probability mass function. On the other hand, if the sales volume (quantity) is greater than or equal to the sales ceiling (i.e., the upper limit of the sales volume), then (S t、r ≧L t、r ), right-censored, and the likelihood function M(S t、r |^S t、r ) is expressed as the accumulation of the probability mass function from the upper limit of the sales volume to infinity. These relationships are expressed by the following equation (2). The likelihood function expressed by equation (2) is necessary for the learning unit 14 to learn and estimate the parameters of the potential demand forecasting model shown in equation (1) (i.e., to execute processing using the variational Bayes method).

[0035]

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[0036] The inference unit 15 calculates the reference price P ref The parameters of the potential demand forecasting model that predicts the potential demand corresponding to the base price of the product, as well as the price elasticity parameters corresponding to the base price of the product, are acquired from the learning unit 14 or the memory 20. The inference unit 15 also associates the prediction result of the probability distribution of the potential demand corresponding to the base price of the product and the price elasticity corresponding to the base price with the processing category t, adds it to the sales forecast data 23, and stores it in the memory 20.

[0037] The demand forecasting unit 15a calculates the base price P based on the potential demand forecasting model (see formula (1)) including the parameters obtained by the learning unit 14 executing the processing of the variational Bayes method, the price elasticity, and the base price of the product input by a user operation or the like as the prediction target. ref The demand forecasting unit 15a predicts the probability distribution of potential demand corresponding to the base price P ref The prediction results for each resale destination of the probability distribution of potential demand corresponding to the above are associated with the processing class t and added to the sales prediction data 23 in the memory 20 and stored.

[0038] The price elasticity acquisition unit 15b acquires the average value of the distribution as a price elasticity parameter from the distribution of price elasticity estimated by the learning unit 14 through the execution of the variational Bayes method process. ref It is a parameter that indicates the degree of influence on the predicted value of potential demand when changing the base price of a product (for example, the degree to which the predicted value of potential demand can change by changing the base price of the product). In other words, price elasticity is the degree to which the predicted value of potential demand changes when the base price P ref This is a parameter necessary to predict potential demand when the

[0039] The price determination unit 16 determines the standard price P of the product for each resale destination estimated by the potential demand forecast / price elasticity estimation unit 12. ref The reference price P' is calculated by optimizing the objective function (for example, maximizing sales) using the predicted probability distribution of potential demand and price elasticity corresponding to the price. ref The price determination unit 16 includes at least a constraint condition / objective function / sales upper limit setting unit 17, a mathematical optimization unit 18, and a price calculation unit 19.

[0040] The constraint / objective function / sales upper limit setting unit 17 determines the objective function and the sales upper limit L of the calculation performed by the mathematical optimization unit 18 based on the input operation of the user using, for example, the input device IN1. t,r The objective function is a function set as an evaluation index for the price determination unit 16 to appropriately calculate the price. In other words, the price determination unit 16 determines a price that optimizes (satisfies) the value that this objective function can take. The sales upper limit L t,r is the upper limit of the number of products sold that should be set for each resale destination, and is a variable necessary for the optimization process performed by the mathematical optimization unit 18, or may be a constant determined for each resale destination if it is determined in advance through negotiations between the seller (the supplier) and each resale destination. Note that, while maximizing sales is an example of optimizing the objective function, it is not limited to this, and it may also be, for example, leveling demand or minimizing product purchases.

[0041] Furthermore, the constraint / objective function / sales upper limit setting unit 17 additionally sets constraints for the mathematical optimization unit 18 to use when performing calculations, based on, for example, user input operations using the input device IN1. The constraints referred to here include, for example, system-related user restrictions and conditions for improving user acceptance. For example, a constraint may be set to different prices for weekends, holidays, and weekdays. Other constraints may include an upper price limit, a lower price limit, a set of set prices, the number of price fluctuations, the price fluctuation cycle, the price fluctuation unit (e.g., changing in 100 yen increments), and the price calculation target (e.g., a desire to calculate the optimal price for weekdays or holidays).

[0042] Furthermore, the constraint condition / objective function / sales upper limit setting unit 17 may set an objective function that can be used under a constraint condition based on the constraint condition, not limited to an input operation by a user using the input device IN1, for example. That is, the constraint condition / objective function / sales upper limit setting unit 17 may set the constraint condition and the objective function independently, or may set one based on the other.

[0043] Here, the objective function and price-related constraints set by the constraint / objective function / sales upper limit setting unit 17 will be described.

[0044] The constraint / objective function / sales upper limit setting unit 17 sets the objective function as the price p t、r and the product's base price P ref The probability distribution of potential demand for each resale destination corresponding to P(^S t,r =S;Δp t,r =0) to obtain the maximum expected value of the total sales of the product. This defined objective function is shown, for example, in equation (3). In equation (3), S(p t、r ) is the supply constraint and price elasticity e t,r The sales volume (quantity) is calculated by taking into account the above (see equation (5)), and is a positive real number as shown in equation (4). Also, as shown in equation (6), the base price P ref Relative price fluctuation Δp t,rThe relative price fluctuation Δp t,r is defined.

[0045]

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[0046] The objective function in equation (3) represents maximizing the expected value of "sales = supply quantity L × price p" for each processing section t, based on the probability distribution P of potential demand.

[0047]

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[0048] The constraint in equation (4) indicates that the supply volume is greater than or equal to 0 (zero) in all processing intervals t (i.e., time), or in other words, it limits the supply volume at the store so that it does not become a negative value. Here, equation (5) indicates that the supply volume, taking price elasticity into account, in the processing interval (i.e., time), does not exceed the upper limit of sales volume.

[0049]

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[0050]

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[0051]

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[0052] The constraint in equation (6) indicates that the supply quantity L is the smaller of the upper limit of the supply quantity or sales quantity in each processing section t, r (in other words, sales quota, resale destination r) taking into account price elasticity. As mentioned above, equation (7) expresses the relative price fluctuation Δp (i.e., the base price P refThis shows the definition of the ratio (relative ratio showing the extent to which the amount varies depending on the treatment category).

[0053] The constraint condition / objective function / sales upper limit setting unit 17 defines and sets the constraint conditions on the price by each of equations (8) to (10). Specifically, equation (8) defines the price p t、r For example, the price table p stored in the memory 20 i (not shown) Select flag from x i,t、r The set price is a discrete value, and the objective function is the set price p t、r Since this formulation is a special quadratic function of , this formulation falls into the category of mixed integer nonlinear programming problems.

[0054]

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[0055] Equation (8) expresses the price selection in each transaction interval (i.e., time). p i indicates a price divided by some unit (for example, the price policy of the user's store). For example, if the price is set in increments of 100 yen, a difference of 1 in i will result in a price difference of 100 yen. Note that p i The prices do not have to be separated by equal price ranges, but may be separated by unequal price ranges.

[0056]

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[0057]

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[0058] Equation (9) indicates that column i of the price table is either "0 (i.e. not selected)" or "1 (i.e. selected)." Equation (10) indicates that the sum of the values ​​in column i of the price table is always "1" for all processing intervals t and r (in other words, time and sales channel). In other words, equations (8) to (10) can be said to represent a one-hot vector whose length is the number of price options, that is, a vector in which only one element is 1 and the others are 0.

[0059] The mathematical optimization unit 18 calculates the base price P of the product read from the sales forecast data 23 in the memory 20. ref Using the predicted results of the probability distribution of potential demand for each resale destination and the price elasticity corresponding to the above, the mathematical optimization unit 18 calculates Δp (relative price fluctuation) that satisfies the constraint conditions set by the constraint condition / objective function / sales upper limit setting unit 17 and matches the objective function to the maximum extent. As an optimization process, the mathematical optimization unit 18 uses the calculated Δp (relative price fluctuation) to set the "reference price P ref × (1 + Δp)" to calculate the base price P' ref Calculate.

[0060] The price calculation unit 19 calculates the reference price P' ref Using the calculation results, the selling price P' based on the reference price P'ref predetermined for each resale destination is calculated. t,r (See Figure 8) for each resale destination, and the resulting sales price P' t,r is associated with the processing section t and added to the optimum price data 24 in the memory 20 and stored.

[0061] The memory 20 is configured using, for example, Random Access Memory (RAM) and Read Only Memory (ROM), and temporarily stores programs necessary for the operation of the price optimization device 1 and data acquired or generated during operation. The RAM is, for example, a work memory used during the operation of the price optimization device 1. The ROM, for example, stores and holds programs for controlling the price optimization device 1 in advance. The memory 20 also stores parameter data 21 (see FIG. 2), sales performance data 22 (see FIG. 3), sales forecast data 23 (see FIG. 4), and optimal price data 24 (see FIG. 5) as data referenced by the processor 10. Examples of the structures of these data will be described later with reference to each of FIGS. 2 to 5.

[0062] An example of the data structure of the parameter data 21 will now be described with reference to FIG.

[0063] The parameter data 21 is stored in the parameter data tables TB1a and TB1b shown in FIG. 2, and is calculated by the price determination unit 16 as the base price P' of the commodity. ref The parameter data table TB1a is configured to have records containing data that are one or more constraint conditions necessary for performing processing to determine the base price P ref The parameter data table TB1b has a record that associates the sales price Pr, sales limit Lr, the start date of the product sales period Start_t, and the end date of the product sales period End_t with Time_index "1". The parameter data table TB1b has a record that associates the sales price Pr, sales limit Lr, and type (type) for each route that indicates a resale destination (for example, resale destination "A") with Time_index "1". The type is the sales limit L for each resale destination. t,It indicates "manual" indicating that r is a value determined manually, or "auto" indicating that r is a value automatically set by the price optimization device 1. Note that in FIG. 2, only one row of each of the parameter data tables TB1a and TB1b is shown as an example of the parameter data 21, but it goes without saying that they include records having similar data items linked to other Time_index.

[0064] An example of the data structure of the sales performance data 22 will now be described with reference to FIG.

[0065] The sales performance data 22 includes at least records that associate data on actual sales and resale destinations (Routes) for each processing category, as shown in the sales performance data tables TB2a and TB2b in Fig. 3. The sales performance data table TB2a includes the upper limit L of sales for each resale destination. t,r The sales performance data 22 may further include data on the sales quantity upper limit and the actual sales quantity. If the sales quantity upper limit and the actual sales quantity are the same value, the product may be sold out, or the right truncation may have been applied. The sales performance data 22 may be stored in a table format such as the sales performance data table TB2a, or in another format. The sales performance data 22 may further include a sales performance data table TB2b that associates various data that are periodically sent from an external device (not shown) connected to the price optimization device 1 so as to be able to communicate data with the price optimization device 1, and that are additionally stored in the memory 20 by the data pre-processing unit 13.

[0066] Here, the data added by the data pre-processing unit 13, that is, the learning preparation data, will be described. The learning preparation data is configured to have records including a sales performance data table TB2a and a sales performance data table TB2b. The sales performance data table TB2b includes various data added by the data pre-processing unit 13 as data on various feature quantities. The data on various feature quantities includes, for example, at least feature quantity data generated from the sales performance data 22, feature quantity data generated from the processing category t, and feature quantity data acquired from an external device (not shown). The potential demand forecasting / price elasticity estimating unit 12 uses multiple pieces of this learning preparation data to learn parameters of a potential demand forecasting model that predicts the potential demand for products.

[0067] The feature data generated from the sales performance data 22 is data calculated by the data pre-processing unit 13 based on the records of the sales performance data 22 for each processing section t, and is, for example, data of the "one-week moving average of sales volume performance" (Sales_7d). In other words, the "one-week moving average of sales volume performance" is calculated by the data pre-processing unit 13. Note that the one-week moving average of sales performance is just one example, and other data may be used as long as it reflects sales performance. For example, it is possible to use sales performance for each processing section t. The period of sales performance to be used as feature data and the type of processed data to be used may be determined by the user's selection, taking into consideration the level of detail of the demand to be estimated, the load required for calculation, etc.

[0068] The feature data generated from the processing category t is data calculated by the data preprocessing unit 13 based on the records of the sales performance data 22 for each processing category t, and is, for example, data on "day of week," "year," "month," "day of year," "holiday flag," "timeslot," and "date." That is, "week," "year," "month," "day of year," "holiday flag," "timeslot," and "date" are calculated by the data preprocessing unit 13. "day of year" indicates the number of days from the first day of the year (New Year's Day) that the "date" corresponding to the corresponding processing category t falls on. The "holiday flag" is "TRUE" if the "date" corresponding to the corresponding processing category t is "a holiday," and is "FALSE" if the "date" corresponding to the processing category t is "not a holiday."

[0069] The feature data acquired from an external device (not shown) is data acquired by the data pre-processing unit 13 from an external device (not shown) that communicates data with the price optimization device 1, and is, for example, data such as a flag indicating "before_COVID." "before_COVID" is "TRUE" if the "date" corresponding to the relevant processing category t is a period before the onset date of the novel coronavirus disease, and is "FALSE" if it is a period after the onset date of the novel coronavirus disease.

[0070] An example of the data structure of the sales forecast data 23 will now be described with reference to FIG.

[0071] As shown in the sales forecast data table TB3 of FIG. 4, the sales forecast data 23 includes the base price P of the product for each resale destination (Route) and each processing category t. ref Potential demand S corresponding to r and its reference price P ref The price elasticity corresponding to rThe sales forecast data 23 is configured to have records including each piece of data. Like the parameter data 21 and the sales performance data 22, the sales forecast data 23 may be stored in a table format such as the sales forecast data table TB3, or may be stored in another format.

[0072] An example of the data structure of the optimum price data 24 will now be described with reference to FIG.

[0073] As shown in the optimal price data table TB4 of FIG. 5, the optimal price data 24 includes the optimal selling price P' of the product calculated by the price calculation unit 19 of the price determination unit 16 for each processing category t for each resale destination (Route). r The optimum price data 24, like the parameter data 21, the sales performance data 22, and the sales forecast data 23, may be stored in a table format such as the optimum price data table TB4, or in another format.

[0074] The input device IN1 is connected to the price optimization device 1 so as to be able to input and output data therebetween, and is a device that accepts input operations from a user of the price optimization device 1. A signal based on the input operation from the user is input from the input device IN1 to the price optimization device 1. The input device IN1 may be, for example, a mouse, a keyboard, a touch panel, or a combination of these.

[0075] The display device OU1 is connected to the price optimization device 1 so as to be able to input and output data therebetween, and displays the prediction results (i.e., the predicted value and price elasticity of the potential demand for the relevant product) and / or the price determination results (i.e., the calculation results of the optimal price using the above-mentioned prediction results) executed by the price optimization device 1. The display device OU1 is, for example, a Liquid Crystal Display (LCD) or an organic EL display. The input device IN1 and the display device OU1 may be configured as an integrated unit, in which case the input device IN1 and the display device OU1 are configured as a touch panel display.

[0076] Here, as shown in Figure 8, we will explain various examples of agreements (examples of parts of contracts) between a seller (ticket pool) that supplies a product (e.g., tickets for a concert, etc.) and multiple resellers (e.g., three parties) to whom the product is sold.

[0077] Between the ticket pool and resellers A, B, and C, the following arrangements have been made through closed voluntary discussions between the parties. (1) Agreement with reseller A The parameter data 21 is the sales limit L and the base price P ref Based on this, the sales price P from the ticket pool to reseller A A is "P A =P ref +3000", sales volume L A is "L A = No setting", the profit (kickback) that the ticket pool receives when one product is sold is P ref It states that: (2) Agreement with reseller B The parameter data 21 is the sales limit L and the base price P ref Based on this, the sales price P from the ticket pool to reseller B B is "P B =1.2P ref +300", sales volume L B is "L B : No setting", the profit (kickback) enjoyed by the ticket pool when one item is sold is 0.8P ref It states that: (3) Agreement with reseller C The parameter data 21 is the sales limit L and the base price P ref Based on this, the sales price P from the ticket pool to reseller C C is "P C =1.5P ref ", sales volume L C is "L C = (2 / 3)L”, the profit (kickback) enjoyed by the ticket pool when one product is sold is P ref It states that:

[0078] Here, like resale destination C, there is an upper limit L r In this case, in addition to the constraint that the total sales quantity of all resellers does not exceed the sales limit L of the entire ticket pool, the sales quantity of each reseller must not exceed the sales limit L r Include a constraint that the On the other hand, if there is no upper limit to the sales volume of resellers, such as resellers A and B, there is no need to impose any constraints on the sales volume of these resellers. However, in this case, the search area for the appropriate sales volume for each reseller may become narrow. This problem will be explained below using Figure 7 and formula (10). Note that, for simplicity of explanation, formula (11) uses only A and B as resellers out of A, B, and C shown in Figure 8. In formula (11), S' A sells the product to reseller A at a selling price of P A This is the predicted value of sales demand that shows how much sales demand can be expected if the price is changed by selling at (see equations (6) and (7)). Similarly, S' B sells the product to reseller B at a selling price of P B This is the sales demand forecast value that indicates how much sales demand can be expected if the product is sold at a different price (see equations (6) and (7)).

[0079]

number

[0080] In equation (11), S' A and S' B Since there is no upper limit for either, S' A and S' B The search is focused on areas where both the potential demand and the cost are simultaneously changed. As a result, the search area where a solution is found is the area shown as search area AR1 in Figure 7. Here, each term in equation (11) is the potential demand S A and S B Since this is a function of potential demand S A and S B As a result, the potential demand SA and S B If there is a large difference in the number of units sold by reseller A, the number of units sold by reseller B will be extremely limited. For example, S A =150, S B = 300, the optimal solution obtained from the search area AR1 is likely to be a solution that reduces the number of units sold by reseller A to about half the number of units sold by reseller B. Here, the profit after the price change is S' A +S' B If L is less than or equal to L, then the equation (12) holds. Therefore, the number of units sold by the more profitable resale destination A (see Figure 8) is severely limited.

[0081]

number

[0082] Therefore, in this embodiment, regardless of whether or not there is a sales upper limit for each resale destination, the value L indicating the sales upper limit is used. r The constraints are defined by adding the following equation for each resale destination. Here, the sales limit L for resale destinations that have a sales limit is r is added as a constant, and the upper limit L for resale destinations where there is no sales upper limit r is added as a variable. Equation (13) is r S', ​​which indicates the sales demand forecast value taking into account r This is the formula that expresses the upper limit of sales L r If is set as a variable, it is optimized simultaneously with the selling price.

[0083]

number

[0084] In the constraints of equation (13), the sales limit L r The optimal solution of S' is also searched. A and S' B A sales limit of some value for either or both of rTherefore, since the optimal solution is searched from outside the search area AR1, it is possible to find a better solution than the local optimal solution in the search area AR1.

[0085] 3. Operation procedure of the price optimization device Next, an example of an operation procedure executed by the price optimization device 1 according to this embodiment will be described with reference to Fig. 9. Fig. 9 is a flowchart showing an example of an operation procedure of the price optimization device 1 according to this embodiment in chronological order. A series of processes shown in Fig. 9 is mainly executed by the processor 10 of the price optimization device 1.

[0086] In Figure 9, the seller, who is the supplier, sets the sales limit L, which is the supply limit for the entire product, and the base price P ref , sales price for each resale destination P r (see FIG. 8), and profit distribution (see FIG. 8) are determined and stored as parameter data 21 in the memory 20 of the price optimization device 1 (step St1). r When (constant) is determined, the sales limit L for each resale destination is r (Constant) is stored as parameter data 21 in memory 20 of price optimization device 1 (Step St2). Note that Step S2 may be omitted.

[0087] The processor 10 refers to the memory 20 and reads and acquires the sales performance data 22 (step St3). The processor 10 generates information data (i.e., learning preparation data) necessary for learning in the learning unit 14 for each processing section t of the sales performance data 22 (see FIG. 3) based on at least one of the sales performance data 22 acquired in step St3 and data communication with an external device (not shown) (step St4). The necessary information data generated in step St4 is, for example, "example data added in preprocessing" as shown in FIG. 3.

[0088] The processor 10 performs machine learning using the learning preparation data (see FIG. 3) obtained by the series of processes from step St1 to step St4 and a likelihood function that takes into account right truncation for sales figures exceeding the upper limit of the product sales figures (step St5). For example, as a result of machine learning using the learning preparation data as input (for example, the variational Bayes method using the likelihood function described above), the processor 10 calculates the product base price P ref Potential demand S corresponding to r The parameters of the potential demand forecasting model that predicts the standard price of the product, P ref The price elasticity corresponding to r Estimate the parameters of

[0089] The processor 10 calculates the potential demand forecast model including the parameters obtained in step St5, the price elasticity, and the base price P of the product input by a user operation or the like as the forecast target. ref Based on this, for each resale destination, the base price P ref Potential demand S corresponding to r In addition, the processor 10 calculates the average value of the distribution of price elasticity e from the distribution of price elasticity estimated by executing the process of the variational Bayes method in the machine learning of step St5 for each resale destination. r The processor 10 acquires the base price P of the product obtained in step St6 as a parameter of ref Potential demand S corresponding to r The predicted probability distribution of and its reference price P ref The price elasticity corresponding to r and are added to the sales forecast data 23 in association with the processing category t and are stored in the memory 20.

[0090] Here, if a resale destination that satisfies condition K1 exists, the processing of processor 10 proceeds to step St7 as processing corresponding to that resale destination. In other words, if there is no setting of a sales upper limit Lr for each resale destination (in other words, if there is a resale destination for which the processing of step St2 has been omitted), processor 10 adds and sets the sales upper limit variable Lr defined in equation (12) for the resale destination that satisfies condition K1 so that the sales upper limit is automatically calculated during optimization in step St9, which will be described later (step St7).

[0091] On the other hand, if a resale destination that satisfies condition K2 exists, the processing of processor 10 proceeds to step St8 as processing corresponding to that resale destination. That is, if a sales upper limit Lr is set for each resale destination (in other words, if there is a resale destination for which the processing of step St2 has been executed), processor 10 sets, for the resale destination that satisfies condition K2, an objective function for the calculation performed by mathematical optimization unit 18 and constraint conditions when mathematical optimization unit 18 performs the calculation, based on an input operation by the user using input device IN1, for example (step St8). Note that processor 10 may determine and automatically set constraint conditions necessary for the calculation performed by mathematical optimization unit 18 based on instructions specified in advance by the user in a setting data file or the like, rather than based on an input operation by the user.

[0092] The processor 10 calculates the sales upper limit L, which is a constant (see step St2) or a variable (see step St7) that is a supply limit for each resale destination. r Based on the total sales volume for each resale destination, the optimal price P' for the product from the perspective of the seller (the supplier) is ref Specifically, the processor 10 performs optimization to determine the estimated sales quantity (S' r =S r *(1+e r (P' r -P r ) / P r )) is the sales limit L r and the total estimated sales volume (S' A +S' B) is the price P' that maximizes sales without exceeding the overall sales limit L. ref Determine.

[0093] The processor 10 calculates the price P' ref Using this, the selling price P r (see FIG. 8) is calculated and output to the display device OU1 for display (step St10).

[0094] (Other variations) The above-described embodiment describes a configuration for estimating latent demand for products that are commercially distributed and sold through monetary transactions. However, the concept of the above-described embodiment can be applied to all goods provided to customers, regardless of whether monetary transactions are involved. For example, novelty goods distributed free of charge are not subject to "sale," but they cannot be provided in quantities greater than the supply. By estimating latent demand for such goods using the method of the above-described embodiment, it is possible to estimate demand assuming that the number of goods provided does not reach the supply. In other words, sales are an example of provision, and products are merely an example of goods. Note that, if the purpose is solely to estimate latent demand, estimating price elasticity is not necessarily required. If only estimating latent demand is desired, the procedure described in the above-described embodiment can be performed without parameters related to price elasticity, and therefore a detailed description thereof will be omitted.

[0095] Furthermore, in this embodiment, the goods for which potential demand is estimated are not limited to tangible objects. For example, goods also include rights such as access rights to tourist facilities such as observation decks and rights to use public transportation, which cannot be provided in quantities greater than the supply quantity. Furthermore, the object for which potential demand is estimated may be a service with an upper limit on the number that can be provided, such as services provided to customers at hotels, hospitals, beauty salons, etc. In this case, the supply quantity is the upper limit on the number of services that can be provided, which is determined by the number of employees and facilities, and is not necessarily the number of tangible objects such as paper tickets that are actually supplied.

[0096] In the above-described embodiment, optimization is performed with the objective of maximizing sales, but other objective functions may be set. For example, the objective may be maximizing profits or sales volume.

[0097] In the above-described embodiment, the procedure for predicting potential demand and price elasticity taking right truncation into consideration was described, and the potential demand and price elasticity calculated by this method were used. However, the potential demand and price elasticity calculated by other methods, such as conventional techniques using binomial distribution, may also be used. Furthermore, the potential demand and price elasticity may be manually set by the user.

[0098] Summary of the Disclosure The above description of the embodiments discloses technical concepts corresponding to the following items.

[0099] (Item 1) For a commodity that can be sold at a price determined for each of a plurality of sales destinations (resale destinations) based on a base price common to the plurality of sales destinations, the potential demand (S r ), and price elasticity (e r ) and Calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the commodity for each of the sales destinations, and calculating a base price (P ref ) to determine Pricing methodology. As a result, according to this price determination method, while price fluctuations were not possible in contracts in which fixed prices and profits were individually determined between suppliers and customers (sales routes), it is now possible to appropriately determine the price of a product using the estimated sales volume and sales upper limit for each customer, and to efficiently estimate the optimal price for a product that may have multiple sales customers.

[0100] (Item 2) The price determination method comprises: a constraint that the total value of the estimated sales volume for each of the sales destinations must be equal to or less than the sales upper limit of the product, and the base price is determined by mathematical optimization using the maximization of sales or profits based on the estimated sales volume of the product for each of the sales destinations and the sales price of the product as an objective function; Pricing methodology described in item 1. This makes it possible to determine the base price of the product so as to maximize sales or profits under the constraint that the total estimated sales volume for each customer is equal to or less than the upper sales limit for the product.

[0101] (Item 3) If the sales destination includes a sales destination for which a sales upper limit for the product has been set in advance, the constraint conditions include a constraint that the estimated sales quantity for the sales destination is equal to or less than the set sales upper limit. Pricing methodology described in item 2. As a result, according to the price determination method, if a sales upper limit is set in advance for each individual sales destination, the optimum price of the product can be estimated by giving priority to that agreement.

[0102] (Item 4) If the sales destination includes a sales destination for which a sales upper limit for the product is not set in advance, the constraint conditions include a constraint condition in which the estimated sales quantity of the sales destination is a variable. Pricing methodology described in item 2. As a result, according to the price determination method, when a sales destination does not have a pre-set upper limit for the product, the optimal price for the product can be estimated by varying the estimated sales quantity to that destination.

[0103] (Item 5) The potential demand is calculated by a prediction model trained using learning preparation data including sales performance data of the product (sales performance data table TB2a) and attribute data related to sales of the product (sales performance data table TB2b). Pricing methodology described in item 1. As a result, the price determination method can improve the accuracy of predicting the potential demand and price elasticity of the product for each customer.

[0104] (Item 6) A processor and a memory, The processor, in cooperation with the memory, For a commodity that can be sold to each of a plurality of buyers at a price determined for each buyer based on a base price common to the plurality of buyers, obtain a potential demand for the commodity for each buyer and a price elasticity that indicates a rate of change in the potential demand for the commodity when the base price of the commodity is changed; calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the product for each of the sales destinations, and determining a base price for the product such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit of the product; Pricing device. As a result, the price determination device can appropriately determine the price of a product using the estimated sales volume and sales upper limit for each sales destination, even though price fluctuations were not possible in contracts in which fixed prices and profits were individually determined between the supplier and the sales destination (sales route), and can efficiently estimate the optimal price for a product that may have multiple sales destinations.

[0105] (Item 7) The price determination device is a computer. a process of acquiring, for each of a plurality of sales destinations, a potential demand for the commodity that can be sold at a price determined for each of the sales destinations based on a base price common to the plurality of sales destinations, and a price elasticity that indicates a rate of change in the potential demand for the commodity when the base price of the commodity is changed; calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the commodity for each of the sales destinations, and determining a base price for the commodity such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit of the commodity; program. As a result, the program makes it possible to appropriately determine the price of a product using the estimated sales volume and sales cap for each sales destination, even though price fluctuations were not possible in contracts in which fixed prices and profits were individually determined between the supplier and sales destination (sales route), and to efficiently estimate the optimal price for a product that may have multiple sales destinations.

[0106] Although the embodiments have been described above with reference to the accompanying drawings, the present disclosure is not limited to such examples. It is clear that a person skilled in the art can conceive of various modifications, alterations, substitutions, additions, deletions, and equivalents within the scope of the claims, and it is understood that these also fall within the technical scope of the present disclosure. Furthermore, the components in the above-described embodiments may be combined in any manner without departing from the spirit of the invention. [Industrial Applicability]

[0107] The technology disclosed herein is useful as a price determination method, a price determination device, and a program for efficiently estimating the optimal price of a product that may have multiple sales routes. [Explanation of symbols]

[0108] 1. Price optimization device 10 processors 11 Parameter input section 12 Potential Demand Forecast / Price Elasticity Estimation Section 13 Data preprocessing section 14 Learning Department 15 Reasoning part 15a Demand Forecasting Department 15b Price Elasticity Acquisition Section 16 Pricing Department 17 Constraints / Objective Function / Sales Upper Limit Setting Section 18 Mathematical Optimization Department 19 Price Calculation Department 20 memory 21 Parameter Data 22 Sales performance data 23 Sales forecast data 24 Best Price Data

Claims

1. For a commodity that can be sold to each of a plurality of buyers at a price determined for each buyer based on a base price common to the plurality of buyers, obtain a potential demand for the commodity for each buyer and a price elasticity that indicates a rate of change in the potential demand for the commodity when the base price of the commodity is changed; calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the product for each of the sales destinations, and determining a base price for the product such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit of the product; Pricing methodology.

2. The price determination method comprises: a constraint that the total value of the estimated sales volume for each of the sales destinations must be equal to or less than the sales upper limit of the product, and the base price is determined by mathematical optimization using the maximization of sales or profits based on the estimated sales volume of the product for each of the sales destinations and the sales price of the product as an objective function; The method of claim 1 .

3. If the sales destination includes a sales destination for which a sales upper limit for the product has been set in advance, The constraints include a constraint that the estimated sales quantity of the customer is equal to or less than the set upper sales limit. The method of determining a price according to claim 2.

4. If the sales destination includes a sales destination for which a sales upper limit for the product has not been set in advance, The constraints include a constraint using the estimated sales volume of the customer as a variable. The method of determining a price according to claim 2.

5. The potential demand is calculated by a prediction model trained using learning preparation data including sales performance data of the product and attribute data related to sales of the product. The method of claim 1 .

6. A processor and a memory, The processor, in cooperation with the memory, For a commodity that can be sold to each of a plurality of buyers at a price determined for each buyer based on a base price common to the plurality of buyers, obtain a potential demand for the commodity for each buyer and a price elasticity that indicates a rate of change in the potential demand for the commodity when the base price of the commodity is changed; calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the product for each of the sales destinations, and determining a base price for the product such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit of the product; Pricing device.

7. The price determination device is a computer. a process of acquiring, for each of a plurality of sales destinations, a potential demand for the commodity that can be sold at a price determined for each of the sales destinations based on a base price common to the plurality of sales destinations, and a price elasticity that indicates a rate of change in the potential demand for the commodity when the base price of the commodity is changed; calculating an estimated sales volume for each of the sales destinations based on the potential demand and price elasticity of the product for each of the sales destinations, and determining a base price for the product such that the total value of the estimated sales volumes for each of the sales destinations is equal to or less than the sales upper limit of the product; program.

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