JP5650144B2 - Simulation apparatus, method, and program - Google Patents

Description

  The present invention relates to a simulation apparatus, method, and program, and more particularly, to a simulation apparatus, method, and program for estimating the number of sales in a market event.

  A Bratberg Wisnyevsky model (B-W model) has been proposed as a model for estimating the number of units sold (Non-Patent Document 1). In this model, the number of sales of a brand under promotion is regressively modeled using information such as the regular price, actual price, and discount rate of the brand.

Blattberg, R.C. et al., “How retail price promotions work: empirical results”, Marketing Working Paper, no.42, University of Chicago, 1987.

  An object of this invention is to provide the simulation apparatus, method, and program which can estimate the sales volume in a market event accurately.

In order to achieve the above object, a simulation apparatus according to the present invention is a simulation apparatus for estimating the number of sales of each of a plurality of product classifications i in a marketing event, wherein the epoch t in each of the input marketing events is the simulation apparatus. Based on the discount rate dc _{i, t} and the number of sales x _{i, t} of a plurality of product categories i, for each product category i, the discount rate dc _{i, t} and the elapsed time Δt from the start of application of the discount rate _Using each of a plurality of functions f _j (dc _{i, t} , Δt _i ) that output a value indicating the effect on the number of sales by discount using _i as an argument, the number of sales x _i, the explanatory variables f _j when the dependent variable the _{t (dc i, t, Δt} i) by estimating the regression coefficients alpha _j for each of the explanatory variables for each of the commodity classification i f _j (dc _{i , t, Δ i)} and to generate a discount effects regression model using the regression coefficients alpha _j, the explanatory variable _{f j (dc i, t,} Δt i) and sales quantity x of the product category i based on the regression coefficients alpha _{j i,} a discount effects modeling means for calculating the residual epsilon _{i, t} for _t, sales quantity x _i of the plurality of commodity classification i of each epoch t in the marketing events the _input, based on _t, each epoch For t, for each product category i, the residual ε _i calculated by the discount effect modeling means with each of the sales quantity x _{j, t−1} of the plurality of product categories j one epoch before as an explanatory variable _{, t} as the explained variable, the regression coefficient γ _j for each of the explanatory variables x _{j, t-1} is estimated, so that the explanatory variable x _{j, t-1} and the regression for each product category i are estimated. Generate residual variation regression model using coefficient γ _j Based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation, the discount effect regression model for each product category i and the residuals And a simulation means for simulating the sales quantity x _{i, t} of the plurality of product categories i using a sales quantity estimation model integrated with a difference fluctuation regression model.

A simulation method according to the present invention includes a discount effect modeling means, a residual fluctuation modeling means, and a simulation means, and is a simulation method in a simulation apparatus for estimating the number of sales of each of a plurality of product categories i in a marketing event, The simulation device uses the discount effect modeling means to input the product classification based on the discount rate dc _{i, t} and the sales quantity x _{i, t} of the plurality of product classification i of each epoch t in the marketing event inputted. For each _i, a plurality of types of functions f _j (dc) that output a value indicating the effect on the number of sales by the discount with the discount rate dc _{i, t} and the elapsed time Δt _i from the start of application of the discount rate as arguments. _{i, t} , Δt _i ) as explanatory variables, the sales quantity x _{i, t} of the product category i By estimating a regression coefficient α _j for each of the explanatory variables f _j (dc _{i, t} , Δt _i ) when used as explanatory variables, the explanatory variables f _j (dc _{i, t} , A discount effect regression model using Δt _i ) and the regression coefficient α _j is generated, and the number of sales of the product classification i based on the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _j calculating a residual ε _{i, t} with respect to x _{i, t} , and sales quantity x _{i, t of the} plurality of product categories i of each epoch t in the input marketing event by the residual variation modeling means For each epoch t, for each product category i, the discount effect modeling means calculates each sales quantity x _{j, t-1} of the plurality of product categories j one epoch before as an explanatory variable. the dependent the residual epsilon _{i, t} was Use the explanatory variable x _j when a _few, by estimating a regression coefficient gamma _j for each of the _t-1, the explanatory variable x _j for each of the commodity classification _{i, t-1} and the regression coefficient gamma _j Generating a residual variation regression model, and for each product category i based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation by the simulation means. Performing a simulation of the sales quantity x _{i, t} of the plurality of product classifications i using a sales quantity estimation model in which the discount effect regression model and the residual fluctuation regression model are integrated. It is characterized by that.

The program according to the present invention is a program for estimating the number of sales of each of a plurality of product categories i in a marketing event, and the computer is used to input the plurality of product categories i of each epoch t in the inputted marketing event. discount rate dc _{i, t} and sales quantity x _i, based on the _t, for each of the commodity classification i, discount rate dc _i, the elapsed time Delta] t _i from the start applying the _t and the discount rate as arguments , Each of a plurality of types of functions f _j (dc _{i, t} , Δt _i ) for outputting a value indicating the effect on the sales quantity by discount is an explanatory variable _{, and} the sales quantity x _{i, t} of the product category i is an explained variable. The explanatory variable f _j (dc _{i, t} , Δt _i for each product category i is estimated by estimating the regression coefficient α _j for each of the explanatory variables f _j (dc _{i, t} , Δt _i). ) And the regression coefficient α _j And a residual effect ε _{i with} respect to the sales quantity x _{i, t} of the product classification i based on the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _{j. , t} for each product category i for each epoch t based on the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event. When each sales quantity x _{j, t-1} of the plurality of product classifications j before one epoch is an explanatory variable, and the residual ε _{i, t} calculated by the discount effect modeling means is an explained variable the explanatory variables x _j, by estimating a regression coefficient gamma _j for each of the _t-1, the explanatory variable x _j for each of the commodity classification _i, the residual variation with _t-1 and the regression coefficient gamma _j of Residual variation modeling means for generating a regression model, And the discount effect regression model and the residual variation regression model for each product category i are integrated based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation. This is a program for functioning as simulation means for simulating the sales quantity x _{i, t} of the plurality of product categories i using the sales quantity estimation model.

According to the present invention, the product classification is based on the discount rate dc _{i, t} and the sales quantity x _{i, t} of the plurality of product classifications i of each epoch t in the marketing event inputted by the discount effect modeling means. For each _i, a plurality of types of functions f _j (dc) that output a value indicating the effect on the number of sales by the discount with the discount rate dc _{i, t} and the elapsed time Δt _i from the start of application of the discount rate as arguments. _{i, t 1} , Δt _i ) as explanatory variables, and the sales quantity x _{i, t} of the product category i as an explanatory variable for each of the explanatory variables f _j (dc _{i, t} , Δt _i ) by estimating the regression coefficients alpha _j, wherein explanatory variable for each product category _{i f j (dc i, t} , Δt i) to generate a discount effect regression models using and the regression coefficients alpha _j, the description variable _{f j (dc i, t,} Δt i) and the regression coefficient sales quantity x _i of the product category i based on alpha _j, calculates the residual epsilon _{i, t} for _t. One epoch for each product category i for each epoch t based on the number of sales x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event by the residual variation modeling means The explanation _when the sales quantity x _{j, t-1} of the previous plurality of product classifications j is an explanatory variable and the residual ε _{i, t} calculated by the discount effect modeling means is an explained variable variables x _j, by estimating a regression coefficient gamma _j for each of the _t-1, the explanatory variable x _j for each of the commodity classification _i, the residual variation regression model using _t-1 and the regression coefficient gamma _j Generate.

Based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation by the simulation means, the discount effect regression model and the residual fluctuation for each product category i The sales quantity x _{i, t} of the plurality of product categories i is simulated using the sales quantity estimation model integrated with the regression model.

  In this way, the sales quantity of the product classification is the explained variable, the discount effect regression model with multiple types of functions that output the value indicating the effect on the sales quantity by discount, and the residual is the explained variable, Sales at market events by simulating sales figures for multiple product categories using a sales quantity estimation model that integrates a residual fluctuation regression model with sales figures for multiple product categories one epoch before as explanatory variables The number can be estimated with high accuracy.

  As described above, according to the simulation apparatus, method, and program of the present invention, the sales quantity of the product classification is the explained variable, and multiple types of functions that output values indicating the effect on the sales quantity by discount are explanatory variables. Multiple sales quantity estimation models that combine the discount effect regression model and the residual fluctuation regression model with the residual as the explained variable and the sales quantity of multiple product categories one epoch before as the explanatory variable. By performing the simulation of the sales quantity of the product classification, an effect that the sales quantity in the market event can be estimated with high accuracy can be obtained.

It is the schematic which shows the structure of the sail simulation apparatus which concerns on embodiment of this invention. It is a figure which shows sale object brand information. It is a figure which shows the discount step simulation data of main brand groups. It is a graph showing the estimation result by a sale simulation model. Is a graph showing the value of the function f _1, f _2. Is a graph showing the value of the function f _3, f _4. Is a graph showing the value of the function f _5, f _6. It is a graph which shows the fitting result (estimated value of sales number) of the sales quantity of the brand A by the discount effect modeling part 25. It is a graph which shows the example of fitting of the residual of the brand A (estimated value of a residual). It is a graph which shows the estimated value of the sales volume of the brand A calculated using a sales volume estimation model. It is a graph which shows the example of the discount step simulation data of a main brand group. It is a graph which shows the simulation result of sale sales. It is a figure which shows the simulation result of sale sales. It is a flowchart which shows the content of the sail simulation process routine in the sail simulation apparatus which concerns on embodiment of this invention. It is a figure which shows an experimental result.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Outline of the invention>
The present invention relates to the construction of a sales quantity estimation model of a brand product handled on an E-Commerce site, particularly during a sale period, and a simulation of sale sales. The sales of the sale are modeled in advance by the sales quantity and discount variables of the major brands. These brands are discounted during the sale period, but the discounting steps (3 discount-> 5 discount-> 7 discount date) vary. The number of sales of the target brand product during the sale period is estimated by considering the change in the number of sales accompanying the discount, the influence of the past sales quantity of the brand, and the past sales quantity of other brands. By using the result of the sales volume estimation model, it is possible to simulate sales sales with the input as the discount step of the main brand group.

  The approach is regression modeling of the number of branded goods sold during the sale. However, since various discounts are performed during the sale period, there are sudden data fluctuations associated with discounts such as the number of sales rapidly increasing on the discount day. In the present invention, first, the fluctuation accompanying the discount is subjected to regression modeling, and the remaining portion (residual) is explained using autoregressive terms and past sales numbers of other brands.

<System configuration>
The sale simulation apparatus 100 according to the embodiment of the present invention uses a sale simulation model, the number of sales of the main brand group, and the discount data, and the linear regression simulation of the sales number estimation model of the main brand group and the sale sales. Build a model. In the execution of the sale simulation, the discount step data of the main brand group is input, and the expected sales during the sale period are output for each epoch (epoch is an interval of time series data. And).

  The sale simulation apparatus 100 is constituted by a computer having a CPU, a RAM, and a ROM storing a program for executing a sale simulation processing routine to be described later, and is functionally constituted as follows. Yes. As shown in FIG. 1, the sail simulation apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 30.

The input unit 10 receives time-series data of input observation values (sales). The observed value is a scalar value, that is, the time series data is a one-dimensional time series. For example, time-series data consisting of a set (n = 1,..., N) of an epoch t _n and an observed value (t _n ).

Further, the input unit 10 receives the inputted sale target brand information. The sale target brand information is sales data and discount data of main brand groups targeted for sale. For example, as shown in FIG. 2, the brand name, discount rate, and sales of each epoch t _n and each sale target brand. This is time-series data consisting of a set with the number (n = 1,..., N).

Further, the input unit 10 receives the input discounted step simulation data of the main brand group. The discount step simulation data of the main brand group is data for simulation. For example, as shown in FIG. 3, a set of epoch t _n and the brand name and discount rate of each brand to be sold (n = 1, ..., time series data consisting of N).

  The computing unit 20 includes a state space modeling unit 21, a state estimation unit 22, an event signal extraction unit 23, a regression modeling unit 24, a discount effect modeling unit 25, a residual variation modeling unit 26, and a sale simulation unit 27.

  The state space modeling unit 21 defines a state space model, and the state estimation unit 22 performs sequential estimation of state vectors. The event signal extraction unit 23 extracts an event signal indicating an event component related to a change in the sale or the campaign effect from the sequentially estimated state vector. Based on the extracted event signal, the regression modeling unit 24 performs regression modeling using the explanatory variables of the brand that is the sale target. At that time, regression modeling is performed only on brands that are highly reliable and important in the sale period, and main brand groups in the sale period are selected (main variable selection regression). A sale simulation model including a linear regression equation using the selected sale period main brand group and a regression coefficient estimated value is output to the discount effect modeling unit 25. The discount effect modeling unit 25 receives the number of sales of the sale target brand information and the actual data of the discount, and performs modeling of a variation portion associated with the effect of the discount on the number of sales of the brand. This result is sent to the residual fluctuation modeling unit 26, and the remaining part (residual fluctuation) is modeled. The sale simulation unit 27 integrates these two modeling results and constructs a sales quantity estimation model for each brand. These sales volume estimation models are used when executing the sales sales simulation. The sale simulation unit 27 receives the discount step simulation data of the main brand group as input data, and outputs the sales amount as a simulation result while estimating the number of sales for each epoch of each brand. Each processing operation will be described below.

  The state space modeling unit 21 defines a nonlinear Gaussian model in which time-series data is expressed in the state space, as will be described below, based on the definition of the state space model set in advance.

  First, nonlinear Gaussian modeling shown in the following equations (1) and (2) is performed.

However, _Xt is a state vector at time t, and normally an unobserved quantity is taken. And an object thereof is to estimate using the time-series data y _t the state vector X _t. w is a system noise vector, which is a white noise vector following a normal distribution. μ is observation noise, and is white noise according to a normal distribution. As shown in equation (2), y _t the observation value at time t, generated by the linear transformation H state X _t. Equation (2) shows the relationship between the state vector X _t and the observed values y _t by using the observed noise. f () is a non-linear part, and the type of f () varies depending on the model. State vector X _t is expressed by the following equation (3).

Where x _t , ..., x _{t−M + 1} , a ₁ , ..., a _M are variables related to the cyclic fluctuation component expressed in the autoregressive process, T _t , n _t , β _t This is a variable related to the nonlinear trend component. E _t and β ′ _t are variables relating to the event component. Therefore, the parameters to be estimated are 2 × M + 5 in total. F (X _t-1 ) and w of the state update equation using this state vector X _t are expressed by the following equation (4).

  Here, H in the observation equation (2) above is a vector of 1 row (2 × M + 5) columns, the 1st, (2 × M + 1) th, (2 × M + 4) th Element is 1 and others are 0. The state update formulas for the nonlinear trend term and event term are derived from the following formulas (5) to (7), respectively.

  This is called the first-order Gaussian Markov approximation for the time update of unknown variables, and is defined as a continuous system. If the equations (5) and (6) are solved simultaneously, a state update equation for the nonlinear trend component is derived, and solving the equation (7) leads to a state update equation for the event component. The first order Gaussian Markov approximation is similar to the Dynamic Model Compensation (DMC) method. The nonlinear trend component is a component that models a long-term unsteady component, and is expressed by the following equations (8) and (9).

However, (DELTA) shows the data interval of time series data. Here, by ^setting e− ^αΔ≡β , an equation similar to the above equation (4) is obtained. n _t represents the slope of the trend component T, which changes with time. Therefore, unlike the local constant trend (random walk model) and the local linear trend (constant slope), which are often adopted as trend models, it is possible to realize a non-linear change in trend with a small amount of noise. The event component is a component that models a local unsteady component, and is represented by the following equation (10).

Here, by ^setting e− ^γΔ≡β ′, an equation similar to the above equation (4) is obtained. β ′ is set to take a different value at the event time and at the normal time. For example, the value of β ′ is set according to the following equation (11).

This β 'value setting means that β' takes the boundary between the unsteady and steady regions in the first-order AR coefficient, and it becomes possible to take a signal with long-term memory (correlation) at the event. Usually, it means that no signal is taken. Switching between event and normal is done automatically. Switching to the event from the normal, using the technique of outlier detection using a normal distribution, the start of the event when a y _t is detected as outliers. Switching to normal time from the event, beta 'restless 0.9 near the minimum value of the range, carried out at the point where E _t approaches zero. For example, when β ′ becomes a value in the vicinity of 0.9, which is the minimum value in the range, for a predetermined number of times, the mode is switched to the normal time.

  As described above, the state space modeling unit 21 defines a type of f () as shown in the above-described equation (4) and defines H in the equation (2).

  In addition, the state space modeling unit 21 sets appropriate values for the diagonal components of the normalized system noise covariance matrix, which will be described later, and the observed noise variance.

The state estimation unit 22 performs sequential estimation of state vectors based on the input time-series data and the state space model modeled by the state space modeling unit 21. Since the model is a nonlinear, it performs sequential estimation of the state vector X _t by Normalized UKF was Unscented Kalman Filter and (UKF) based. A normal UKF algorithm includes generation of a sigma point sequence represented by the following equations (12) to (22), state update, and observation update (filter).

  Here, λ is a predetermined constant, and L is the number of dimensions of the state vector X. ￣y is the predicted value of the observed value, and ￣y = H￣X. v is a prediction error, and P is a covariance matrix of estimated error variance of the state vector X.

  In Normalized UKF used in this embodiment, ￣P, ^ P existing in the above normal algorithm is the sum of the variance values of all noises, that is, the sum of the diagonal components of the covariance matrix Q of the system noise w. Divide by the sum traceQ + r of the variance value r of noise μ. For example, ￣P in the above equation (22) is replaced with ￣P 'defined by the following equation (23).

  By this operation, the system noise covariance matrix Q in the equation (18) and the observed noise variance r in the equation (19) are normalized as shown in the following equations (24) and (25). . That is, the elements of the system noise covariance matrix Q and the observed noise variance r are all 1 or less. In addition, the sum of the elements of the system noise covariance matrix Q and the variance value of the observation noise is 1.

  Usually Q and r are unknown, and the setting of the variance of each noise largely depends on the analyst's experience. In general, the variance value of noise has a large effect on the estimation result of the state. Therefore, this amount is limited to 1 or less and the setting is facilitated to enable stable analysis.

  Also, the shape of the algorithm is appropriately changed by this series of normalization operations. However, by reducing the set value of α included in the above equations (15) and (16), the algorithm can be matched with the normal UKF algorithm. be able to. This is shown as follows.

Here, by setting α so that M · α ² becomes 1, the influence of the normalized number M on the generation of the sigma point sequence disappears. That is, the following equations (30) and (31) are obtained.

  The above equation (31) is normal sigma point sequence generation when it is assumed that the state follows a normal distribution. In this case, L + κ = 3 is often set.

  As described above, the state estimation unit 22 uses the normal time-series data of the input observation values and the covariance matrix ￣P ′, ^ of the estimated error variance of the normalized state vector X in the normal UFK algorithm. Sequential estimation of state vector X according to Normalized UKF algorithm (generation of sigma point sequence, state update, observation update) replaced with P ', normalized system noise covariance matrix Q', and observed noise variance r ' I do.

  The signal extraction unit 23 extracts an event signal due to a marketing event from the state vector X sequentially estimated by the state estimation unit 22.

Here, the state vector X _t is expressed by the following equation (32).

Among the elements of the state vector, x _t is a cyclic variation component, T _t is a nonlinear trend component, and _Et is an event component. The signal extraction unit 23 extracts an event component due to a marketing event (fluctuation component of the sale / campaign effect) as a characteristic signal of the target time series.

  The event signal extracted by the event signal extraction unit 23 is sent to the regression modeling unit 24. The regression modeling unit 24 performs regression modeling on the event signal using the explanatory variables of each brand created from the inputted sale target brand information. The model regression equation is expressed by the following equations (33) and (34).

Here, t is an epoch (time width) of time series data, and in the present embodiment, a unit of one day is assumed. α _{1, t} and x _{1, t} are the discount rate (0.3 for 3 discounts and 0.5 for 5 discounts) and the number of units sold, respectively, for brand 1 epoch t. When (1.0−α _{1, t} ) · x _{1, t} is regarded as an explanatory variable X ₁ created from brand 1, a normal linear regression equation represented by the above equation (34) is obtained. The X is a vector of explanatory variables X _i of each brand i, is → β, is a regression coefficient vector of the regression coefficient β _i of each brand i.

Here, the sale target brand information includes information on hundreds of brand groups, but only p ′ is used in the regression model of the above equation (33). In other words use only major brands group contributes to the variation of the event component E _t, the number of explanatory variables, that is, reducing the dimension of the model. As a result, the estimation accuracy of the estimation parameter → β is improved, and the prediction performance of the model is improved. Such a regression method is called primary variable selection regression.

  In the process of the regression modeling unit 24, a method called Elastic Net with Norm Restriction based on Elastic Net Regression (see Non-Patent Document 2), which is one method of principal variable selection regression, is used.

  Elastic Net Regression estimates the parameter → β that minimizes the loss function represented by the following equation (35).

Here → y average are normalized to 0, X _i is zero mean, and what norm is normalized to 1. This loss function can be rewritten by the following equation (36).

  This loss function has the same form as L1 regularized Lasso regression (see Non-Patent Document 3), and an estimation algorithm using Least Angle Regression (LARS) described in Non-Patent Document 4 can be applied. Lasso regression is called variable selection regression because it has the property that the regression coefficient of explanatory variables with strong collinearity is zero. However, you can't specify which variables are left out and the rest are zero. On the other hand, because Elastic Net has an L2 penalty, explanatory variables that show strong correlations have a property called grouping effect that gives the same regression coefficient. Since the algorithm level is more stable than Lasso regression, Elastic Net regression is used as variable selection regression in the present invention.

  Elastic Net with Norm Restriction considers the loss function expressed by the following equation (37).

Here, β ′ _i = β _i / | X ′ _i |, that is, β ′ _i is a regression coefficient when the normalized explanatory variable X _i is restored. Since | X ′ _i | is the norm of the explanatory variable i, the larger this value, the smaller β ′ _i . That is, the loss function of the above equation (37) is variable selection regression that selects only explanatory variables that have a large norm and contribute to minimization of the square error. This loss function is rewritten as (38) below.

This corresponds to the weighted L1 norm and L2 norm penalty terms, has both adaptive Lasso (see Non-Patent Document 5) and Elastic Net properties, and regression coefficients are estimated by the LARS algorithm. Note that the extracted event signal _Et is assigned to → y.

Regression modeling unit 24, an event signal E _t which is extracted, based on the explanatory variables X _i brand i created from for sale brand information, according to the above (38) equation, the algorithm LARS, each explanatory variable Estimate the regression coefficient β _i of X _i . At this time, the norm is large and the β regression coefficients event signal E _t contribute explanatory variables other explanatory variables to minimize square error is estimated to be zero. The regression modeling unit 24 selects a set of brands having a corresponding regression coefficient β greater than 0 as a main brand group in the sale period. A regression coefficient vector → β consisting of an estimated value of the regression coefficient β _i for the main brand group in the selected sale period and the linear regression expression of the above equation (34) are output as a sale simulation model.

(Non-Patent Document 2): Regularization and variable selection via the elastic net, Hui Zou and Trevor Hastie, 2005
(Non-Patent Document 3): The Elements of Statistical Learning, Trevor et al., 2009
(Non-Patent Document 4): Least Angle Regression, Bradley Efron et al., 2004
(Non-Patent Document 5): The Adaptive Lasso and its Oracle Properties, Hui Zou, 2006

  Here, FIG. 4 shows a graph representing the estimation result by the sail simulation model. The variable component of the sale is modeled by the sum of its average value and the estimated sales for the major brands.

  Major brands will be discounted in different ways during the sale. Information on this discount step (date of 3 discount → 5 discount → 7 discount) and actual sales data are sales target brand information.

  When the discount effect modeling unit 25 acquires the discount rate and the sales volume data of the sale period main brand group from the sale target brand information, the sales volume of each main brand is set as an explanatory variable, and a function f described later is set as an explanatory variable. Modeling of the fluctuation part accompanying discounting is performed based on the linear regression equation shown in the following equation (39). Note that the linear regression equation shown in Equation (39) is an example of a discount effect regression model.

Here, the six functions f _{j, j = 1,..., 6} output values indicating the variation effect on the sales volume by the discount dc at time t. These functions f are the following functions using the discount rate dc _{i, t} of the brand i and the elapsed time Δt _i from the start of application of the discount rate as arguments.

First, as shown in FIG. 5, the function f ₁ indicated by the discount pulse A is a pulse-type function whose value increases with an increase in the discount rate, and the function f ₂ indicated by the discount pulse B is an increase in the discount rate. This is a pulse-type function whose value decreases with time. The value of the function is the discount rate itself (for example, 3 discount days will be 0.3 and the others will be 0.0). Note that FIG. 5 shows the function values when the discount rate increases stepwise.

Further, as shown in FIG. 6, the function f ₃ indicated by the discount step A is a step-type function whose value increases with an increase in the discount rate, and the function f ₄ indicated by the discount step B is an increase in the discount rate. It is a step-type function whose value decreases with. The value of the function takes the discount rate itself (for example, 3 discount periods are 0.3 and 5 discount periods are 0.5). Note that FIG. 6 shows the value of the function when the discount rate increases stepwise.

Further, as shown in FIG. 7, the function f ₅ indicated by the time attenuation A is a non-linear function in which the value attenuation becomes slower as the discount rate increases, and the function f ₆ indicated by the time attenuation B is the discount rate. This is a non-linear function that decays faster as the value increases. For example, the value of the function f5 is −log (Δt _i ) × (1.0−dc _{i, t} ), and the value of the function f 6 is −log (Δt _i ) × dc _{i, t} . Note that FIG. 7 shows function values when the discount rate increases stepwise.

In addition, α _{j, j = 1, ..., 6} are estimated parameters (regression coefficients), and these are estimated under the constraint of positive values (to facilitate interpretation of regression models). . At that time, selective regression of each function (that is, selection of the function to be used) is performed. This process is performed for all the main brands, and an estimated value ^ α _j of the regression coefficient for each function f _{j is obtained} for each main brand.

That is, the discount effect modeling unit 25, for each main brand i of the sale period main brand group, the sales quantity x _{i, t} and the discount rate dc _{i, t of the} main brand i obtained from the sale target brand information and the explanatory variable f _{j. , j = 1,..., 6} and the regression coefficient α _{j for} each explanatory variable f _{j, j = 1 ,.} And a difference (residual ε _{i, t} ) between the actual sales quantity and the estimated value of sales quantity (Σα _j f _j (dc _{i, t} , Δt _i )).

And the estimated value ^ α _j of the regression coefficient of each explanatory variable f _j, which is determined for each major brand i, the estimated value of the sales number _{(Σα j f j (dc i} , t, Δt i)), and actual sales number (Residual ε _{i, t} ) is sent to the residual fluctuation modeling unit 26. FIG. 8 shows the result of fitting the sales quantity of the brand A by the discount effect modeling unit 25 (estimated value of the sales quantity).

When the residual variation modeling unit 26 receives the residual portion ε _{i, t} in the sales quantity estimation of each main brand i (i = 1,..., P ′) from the discount effect modeling unit 25, the residual variation modeling unit 26 Residual fluctuations are modeled for each major brand i, with the residual of the sales quantity as the explained variable and the sales quantity one epoch before all the major brands as the explanatory variable. The residual ε _{i, t} is subjected to regression modeling by a linear regression equation shown in the following equation (40). Note that the linear regression equation shown in the equation (40) is an example of a residual variation regression model.

The above equation (40) means the fitting of the residual by the sales number x _{i, t−1} of the brand i one epoch before and the sales number x _{j, t−1} of the other brand j one epoch before. In other words, it is an estimation model for the residual of the sales volume taking into account the influence of the own brand from the past and the influence of other brands, and γ _j is an estimation parameter representing the degree of contribution. FIG. 9 shows an example of fitting of the residual of brand A (estimated value of residual). A fluctuation (residual) obtained by removing a portion resulting from the discount from the fluctuation in the sales quantity of the brand A is regression-fitted with the past sales quantity (one epoch before) of the brand A and other brands.

The residual fluctuation modeling unit 26 calculates the residual ε _{i, t} obtained by the discount effect modeling unit 25 and the explanatory variables x _{j, t−1} (j = 1,..., P ′) for each main brand i. Based on the above equation (35), the regression coefficient γ _j of each explanatory variable x _{j, t−1} is estimated by a normal Elastic Net algorithm. Estimated values _{ circumflex over (γ)} _{j of} each regression coefficient estimated for each major brand i and residual estimated values _{ circumflex over (ε)} _{i, t} (= Σγ _j × _{j, t−1} ) are sent to the sale simulation unit 27.

The sale simulation unit 27 receives from the discount effect modeling unit 25 and the residual fluctuation modeling unit 26 the modeling result of the fluctuation part (discount effect regression model) and the modeling result of the residual fluctuation part (residual fluctuation regression model) accompanying the discount. Then, they are integrated, and an estimated model of the sales quantity x _{i, t} of brand i at time t shown in the following equation (41) is constructed.

  FIG. 10 shows the estimated value of the sales volume of the brand A calculated by the above equation (41).

  In addition, a sales sales simulation model using a model for estimating the number of sales of main brand groups is expressed based on the following equation (42).

The sale simulation unit 27 uses the sales quantity estimation model of the above equation (41) based on the discount step simulation data of the main brand group and the initial value of the sales quantity of each main brand given in advance, for each epoch t. Calculate the estimated value ^ xi _{, t} of the number of units sold for each major brand i. In addition, the sale simulation unit 27 uses the simulation model of the above equation (42) based on the discount step simulation data of the main brand group and the calculated estimated sales number ^ xi _{, t} of each main brand. The sales sales E _t is estimated for each epoch t.

  Here, an example of discount step simulation data of the main brand group is shown in FIG. In this example, a discount rate of 3 discount → 5 discount → 7 discount is applied to 18 brands by different steps. Some brands remain at 3 discounts throughout the sale.

  FIG. 12 shows a simulation result of sales sales corresponding to the input of the discount step simulation data. The solid line indicates the actual sales component, and the broken line indicates the simulation result value.

  Thus, when the simulation data of the discounting step of the main brand group is input, the sales quantity of each brand and the predicted sales of the sale (see FIG. 13) for each epoch are calculated in order, and finally, during the sale period. The sales forecast curve is output by the output unit 30. By considering the results of the simulation, it will be possible to search for discount steps for major brands that will improve the sales of the sale, which will be an important source of information for the upcoming sale.

<Operation of sale simulation device>
Next, the operation of the sail simulation apparatus 100 according to the present embodiment will be described. First, when time-series data composed of observed values (sales) at times t _{1 to} t _N is input to the sale simulation apparatus 100, the time-series data input by the sale simulation apparatus 100 is stored in a memory (not shown). ). When sales target brand information (sales quantity and discount rate of each brand) is input to the sales simulation device 100, the sales simulation device 100 stores the input sales target brand information in a memory.

  Then, the sail simulation processing routine shown in FIG.

  First, in step S101, time-series data of input observation values is acquired. In step S102, the state space modeling unit 21 sets and normalizes the nonlinear Gaussian model of the above formulas (1) and (2) based on the definition of the preset state space model. The system noise covariance matrix Q ′ and the observed noise variance r ′ are set to appropriate values.

  In step S103, the state estimation unit 22 uses the nonlinear Gaussian model set in step S102, the normalized system noise covariance matrix Q ′, and the observed noise variance r ′ to normalize UFK. In accordance with the algorithm, the generation of the sigma point sequence, the state update, and the observation update are sequentially performed using the time series data of the observation values acquired in step S101, and the state vector X is sequentially estimated.

In the next step S104, the event signal extraction unit 23 extracts an event signal indicating an event component from the state vector X sequentially estimated in step S103. In step S105, the inputted sale target brand information is acquired. In step S106, the regression modeling unit 24 calculates the regression coefficient β _i of each brand i of the sale target brand group based on the event signal extracted in step S104 and the sale target brand information acquired in step S105. In addition to the estimation, the main brand group for the sale period is selected from the brand groups to be sold. As a result, the sale simulation model of the above equations (33) and (34) using the regression coefficient β _i of the main brand group in the sale period is generated.

In the next step S107, the discount rate and sales quantity data of the sale period main brand group are acquired from the sale target brand information acquired in step S105. In step S108, based on the discount rate and sales volume data of the sale period main brand group acquired in step S107 by the discount effect modeling unit 25, for each brand i in the sale period main brand group (39 ), The regression coefficient α _j for each function f _j of the linear regression equation is estimated, and the residual ε _{i, t} is calculated.

In step S109, based on the number of sales in the sale period main brand group acquired in step S107 by the residual fluctuation modeling unit 26, for each brand i in the sale period main brand group, the linear regression equation (40) above. The regression coefficient γ _j with respect to the sales quantity x _{j, t-1} one epoch before each brand j is estimated, and the residual ε _{i, t} ′ is calculated.

  When the discount step simulation data of the sale period main brand group is input to the sale simulation apparatus 100, the sale simulation apparatus 100 stores the input discount step simulation data of the sale period main brand group in the memory. The

Then, in step S110, discount step simulation data of the input sale period main brand group is acquired. In step S111, the sale simulation unit 27 integrates the regression model using the regression coefficient α _j estimated in step S108 and the regression model using the regression coefficient γ _j estimated in step S109. A model for estimating the number of sales is constructed for each brand i in the main brand group during the sale period. Based on the discount step simulation data of the sale period main brand group acquired in step S110 by the sale simulation unit 27 and the initial value of the sales quantity of each main brand given in advance, estimation of the sales number constructed is estimated. Using the model (the above equation (41)), the estimated value ^ x _{i, t} of the sales quantity of each main brand i is calculated for each epoch t. Further, the sales simulation unit 27 calculates the discount of each major brand i estimated in step S106 based on the discounted step simulation data of the major brand group and the estimated sales number ^ xi _{, t} of each major brand. In accordance with the sale simulation model to which the regression coefficient β _i is applied (the above equation (42)), the sale sales E _t is estimated for each epoch t, output by the output unit 30, and the sale simulation processing routine is terminated.

<Experimental result>
Next, experimental results using the simulation method described in this embodiment will be described. An experiment to generate a sales volume estimation model from time series data on the discount rate and sales volume of each brand on a certain EC site every day, and to estimate the sales volume of each brand using the time series data of the discount rate of each brand Went.

  FIG. 15 shows the evaluation results of the simulation for estimating the sales volume using the sales volume estimation model described in the present embodiment. As a comparison method, the sales volume was estimated using only the discount effect regression model.

  As shown in FIG. 15 above, the adjusted explanation rate is higher in all brands than in the comparison method, and the improvement in modeling accuracy by the sales number estimation model used in the present embodiment was confirmed. .

  As described above, according to the sale simulation apparatus according to the present embodiment, the discount effect using the sales quantity of the main brand as the explained variable and the plural types of functions f indicating the effect on the sales quantity by the discount as the explanatory variable. Using a sales model estimation model that integrates a regression model and a residual fluctuation regression model that uses the residual ε as an explanatory variable and the sales volume of all the main brands one epoch before as an explanatory variable, By simulating the sales volume, it is possible to accurately estimate the sales volume in the market event.

  When estimating the number of branded products sold during the sale period, the fluctuations associated with the discount and the rest are separately regression modeled, and the results are finally integrated. In addition, we modeled the sudden increase in sales volume on the day of discount and the decrease in sales volume over time since the discount using a non-linear function, and the ripple effect from the past sales volume of other brands Incorporate into the estimation model. Thereby, the number of sales in a market event can be estimated accurately.

  Further, according to the present embodiment, it is possible to predict a promotion effect such as a sale or a campaign by simulation. The input data is the discounting step for each brand (3 discount → 5 discount → X discount date), and the expected sales of the sale are output while estimating the number of sales of each brand for each epoch. By considering the simulation results, it is possible to search for an optimal discount step considering the influence relationship of the number of sales between brands.

  In addition, by estimating the regression coefficient of the regression model for the event signal so that only the explanatory variable that has a large norm and contributes to the minimization of the square error with the event signal is selected, the time series data of sales It is possible to accurately generate a regression model for an event signal based on a market event extracted from.

  In addition, the state vector X including the cyclic fluctuation component, the non-linear trend component, and the event component is sequentially estimated according to the normalized UFK, and a signal indicating the event component is extracted. A stationary signal can be extracted.

  In addition, by sequentially estimating the state vector X in accordance with the normalized error variance covariance matrix normalized, the system noise covariance matrix, and the normalized UFK using the observed noise variance values, the state of the nonlinear model can be determined. A vector can be estimated.

  In addition, the state estimation algorithm used in this embodiment is based on the Unscented Kalman Filter (UKF) that accurately estimates the time-series state modeled in a nonlinear Gaussian type, and the total noise variance value that exists in the model A method of normalizing the sum of to 1 is used. This enables stable analysis and state estimation by limiting the total sum of all noise variance values present in the model to 1.

  The present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

  For example, a value of 0 to 1 is assigned to the normalized system noise covariance matrix and the observed noise variance value, and the normalized system noise covariance matrix and the observed noise variance value are assigned. Using each of these combinations, it is possible to sequentially estimate the state vector and specify an optimal variance value. In this case, the event signal may be extracted from the state vector estimated under the optimum variance value.

  Moreover, although the case where a brand was used was demonstrated to an example as an example of goods classification, it is not limited to this. For example, a regression model having event components as explained variables may be generated using explanatory variables for each product classification such as product names and product categories. In this case, regression modeling may be performed so as to explain the event signal by an explanatory variable using the discount rate and the number of sales of the product category. Further, for each product category, a discount effect regression model may be generated with the sales quantity of the product category as the explained variable and the function f as the explanatory variable. Further, for each product category, a residual fluctuation regression model may be generated in which the residual of the sales quantity of the product category is the explained variable and the sales quantity of each product category is the explanatory variable.

  Moreover, although the case where the event signal is extracted from the state vector X sequentially estimated according to the normalized UFK has been described as an example, the event signal may be extracted by another method. Further, an event signal extracted in advance from time series data of sales may be given as an input to the regression model generation device. In this case, the state space modeling unit 21, the state estimation unit 22, and the event signal extraction unit 23 are not necessary.

  In addition, the case where a sales simulation model is constructed by generating a regression model with event components as explanatory variables has been described as an example, but the present invention is not limited to this, and a sales simulation model generated in advance is used as an input. May be given. In this case, the state space modeling unit 21, the state estimation unit 22, the event signal extraction unit 23, and the regression modeling unit 24 are unnecessary.

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

DESCRIPTION OF SYMBOLS 10 Input part 20 Calculation part 21 State space modeling part 22 State estimation part 23 Event signal extraction part 23 Signal extraction part 24 Regression modeling part 25 Effect modeling part 26 Residual fluctuation modeling part 27 Sale simulation part 30 Output part 100 Sale simulation apparatus

Claims (3)

A simulation device for estimating the number of sales of each of a plurality of product categories i in a marketing event,
Based on the discount rate dc _{i, t} and the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event, the discount rate dc _{i, t} and the corresponding rate for each product category i Each of a plurality of types of functions f _j (dc _{i, t} , Δt _i ) that outputs a value indicating the effect on the number of sales by discounting with an elapsed time Δt _i from the start of application of the discount rate as an explanatory variable By estimating the regression coefficient α _j for each of the explanatory variables f _j (dc _{i, t} , Δt _i ) when the sales quantity x _{i, t} of the product classification i is an explained variable, A discount effect regression model using the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _j is generated for each classification i, and the explanatory variable f _j (dc _{i, t} , Δt _i ). against and sales quantity x _i of the commodity classification i based on the regression coefficients α _j, in _t And the discount effect modeling means for calculating the residual ε _{i, t,}
Based on the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event, for each epoch t, the plurality of product categories one epoch before for each product category i Each of the sales numbers x _{j, t-1} of _j is an explanatory variable, and the explanatory variable x _{j, t-1} when the residual ε _{i, t} calculated by the discount effect modeling means is an explanatory variable. Residual fluctuation modeling means for generating a residual fluctuation regression model using the explanatory variable x _{j, t-1} and the regression coefficient γ _j for each product category i by estimating a regression coefficient γ _j for each of the product categories i When,
Based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation, the discount effect regression model and the residual variation regression model for each product category i are integrated. Simulation means for simulating the sales quantity x _{i, t} of the plurality of product categories i using a sales quantity estimation model;
Including a simulation apparatus. A simulation method in a simulation apparatus for estimating the number of sales of each of a plurality of product categories i in a marketing event, including discount effect modeling means, residual fluctuation modeling means, and simulation means,
The simulation apparatus includes:
Based on the discount rate dc _{i, t} and the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the marketing event input by the discount effect modeling means, the discount is calculated for each product category i. A plurality of types of functions f _j (dc _{i, t} , Δt) that output a value indicating the effect on the number of sales by the discount with the rate dc _{i, t} and the elapsed time Δt _i since the application of the discount rate as an argument each of _i) as an explanatory variable, the commodity classification i of sales quantity x _i, the explanatory variable f _j (dc i when the the dependent variable _{t, t,} a regression coefficient alpha _j for each Delta] t _i) By estimating, a discount effect regression model using the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _j is generated for each product category i _, and the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _j Calculating a residual ε _{i, t} for the sales quantity x _{i, t} of the product category i;
1 for each product category i for each epoch t based on the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event by the residual variation modeling means. Each of the sales numbers x _{j, t-1} of the plurality of product classifications j before the epoch is an explanatory variable, and the residual ε _{i, t} calculated by the discount effect modeling means is the explained variable. explanatory variable x _j, by estimating a regression coefficient gamma _j for each of the _t-1, the explanatory variables x _{j, t-1} and the residual variation regression model using the regression coefficient gamma _j for each of the goods classification i A step of generating
Based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation by the simulation means, the discount effect regression model and the residual fluctuation regression for each product category i Simulating the sales quantity x _{i, t} of the plurality of product categories i using a sales quantity estimation model integrated with the model;
The simulation method characterized by including and performing. A program for estimating the number of units sold for each of a plurality of product categories i in a marketing event,
Computer
Based on the discount rate dc _{i, t} and the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event, the discount rate dc _{i, t} and the corresponding rate for each product category i Each of a plurality of types of functions f _j (dc _{i, t} , Δt _i ) that outputs a value indicating the effect on the number of sales by discounting with an elapsed time Δt _i from the start of application of the discount rate as an explanatory variable By estimating the regression coefficient α _j for each of the explanatory variables f _j (dc _{i, t} , Δt _i ) when the sales quantity x _{i, t} of the product classification i is an explained variable, A discount effect regression model using the explanatory variable f _j (dc _{i, t} , Δt _i ) and the regression coefficient α _j is generated for each classification i, and the explanatory variable f _j (dc _{i, t} , Δt _i ). against and sales quantity x _i of the commodity classification i based on the regression coefficients α _j, in _t Discount effect modeling means for calculating the residual ε _{i, t,}
Based on the sales quantity x _{i, t} of the plurality of product categories i of each epoch t in the input marketing event, for each epoch t, the plurality of product categories one epoch before for each product category i Each of the sales numbers x _{j, t-1} of _j is an explanatory variable, and the explanatory variable x _{j, t-1} when the residual ε _{i, t} calculated by the discount effect modeling means is an explanatory variable. Residual fluctuation modeling means for generating a residual fluctuation regression model using the explanatory variable x _{j, t-1} and the regression coefficient γ _j for each product category i by estimating a regression coefficient γ _j for each of the product categories i And the discount effect regression model and the residual variation regression model for each product category i based on the discount rate dc _{i, t} of the plurality of product categories i of each epoch t input for simulation. Integrated sales piece Using the estimated model, the sales quantity of the plurality of product category i x _i, a program to function as a simulation means for simulating the _t.