Cigarette life cycle dynamic studying and judging method based on multi-dimensional index and multi-method fusion

Abstract

The invention provides a cigarette life cycle dynamic studying and judging method based on multi-dimensional index and multi-method fusion, and belongs to the technical field of market analysis and commodity life cycle management in the tobacco industry. Expansion is carried out according to a logic chain of data preparation, core index construction, multi-method judgment, result fusion correction and conclusion output; through multi-dimensional index mining, multi-method cross validation and experience fusion, the subjectivity and one-sidedness problems of traditional cigarette life cycle research and judgment are solved, a more accurate and interpretable product stage judgment tool is provided for enterprises, and the method has remarkable practical value and technical innovation.

Description

Technical Field

[0001] This invention relates to the field of market analysis and product lifecycle management technology in the tobacco industry, and in particular to a dynamic assessment method for the cigarette lifecycle based on the fusion of multi-dimensional indicators and multiple methods. Background Technology

[0002] For general commodities, their life cycle can generally be divided into four stages: entry, growth, maturity, and decline, corresponding to the initial stage upon market launch, the middle stage, and the stage before market withdrawal. However, as a state-controlled commodity with clear planning attributes, cigarettes' life cycle does not entirely align with that of general commodities. For example, when cigarettes first enter the market, certain thicker cigarette specifications may not have few external competitors; or while a general commodity entering its decline stage usually signifies its end, cigarette specifications can continue to see sales growth through strategy adjustments or intervention. Therefore, the cigarette life cycle needs to be redefined based on its unique characteristics. Research has divided the cigarette life cycle into four stages: entry, growth, stability, and decline. These correspond to cigarette specifications entering the market, gradually reaching their peak, and finally entering a period of decline.

[0003] Against the backdrop of intensifying market competition and diversified consumer demand in the tobacco industry, accurate assessment of the cigarette product lifecycle is a core prerequisite for companies to formulate marketing strategies. However, existing technologies suffer from the following pain points:

[0004] 1. Over-reliance on single indicators. Traditional judgments often rely on single indicators such as sales volume or absolute sales revenue, without comprehensively considering key factors such as market share, penetration capability, and time dimension, leading to misjudgments at different stages;

[0005] 2. High degree of subjectivity. Some methods rely on qualitative assessments based on expert experience, lacking data-driven objective quantitative models, and the results are easily influenced by subjective preferences;

[0006] 3. Weak dynamic adaptability: It fails to effectively integrate multi-dimensional dynamic indicators (such as coverage breadth and relative growth trend), making it difficult to capture the turning points in the product life cycle in a timely manner. Summary of the Invention

[0007] To address the above technical issues, this invention provides a dynamic assessment method for the cigarette lifecycle based on the fusion of multi-dimensional indicators and multiple methods. This method enables automated and precise determination of the stage of cigarette specifications, improving enterprises' responsiveness to market trends.

[0008] The technical solution of this invention is:

[0009] A dynamic assessment method for the cigarette lifecycle based on the fusion of multi-dimensional indicators and multiple methods includes:

[0010] 1. Construction of a multi-dimensional indicator system. Based on cigarette specifications, key derivative indicators such as market share, relative growth rate, and penetration rate are extracted from four dimensions: sales performance, competitiveness in different market categories, regional coverage, and time accumulation. This forms a three-dimensional framework that covers market position, expansion capabilities, and time cycle.

[0011] 2. Cross-validation method for lifecycle determination. Using relative growth rate and relative market share, the four stages of the lifecycle are assigned to four quadrants, achieving a quadrant positioning method with growth rate as the vertical axis and market share as the horizontal axis. A lifecycle index is constructed by combining indicators such as sales volume, sales revenue, penetration rate, and time to market, and thresholds are set to divide the stages. Using time as the independent variable and relative growth rate as the dependent variable, a Gompertz function with an added decay term is fitted, and the inflection point of the curve is used to identify the stage.

[0012] 3. Dynamic correction mechanism. Consistency verification is performed on the interim conclusions output by the three methods. Disputed samples are voted on by domain experts to correct model biases and form a final judgment result that is primarily data-driven and calibrated with experience.

[0013] Furthermore,

[0014] The specific steps are as follows:

[0015] Step 1, Data Collection

[0016] Two types of core data were collected: performance data of the specifications themselves and market environment data, and then the data was cleaned.

[0017] The second step is to construct indicators.

[0018] 1) Regarding sales volume, including

[0019] (1.1) Increment and growth rate (1.2) Sales growth rate ratio (1.3) Sales share ratio (1.4) Relative growth rate (1.5) Relative share;

[0020] 2) Regarding sales revenue

[0021] (2.1) Increment and growth rate (2.2) Sales growth rate ratio in terms of sales volume (2.3) Sales share ratio in terms of sales volume (2.4) Relative growth rate in terms of sales volume (2.5) Relative share in terms of sales volume;

[0022] 3) Regarding the coverage rate of prefecture-level cities

[0023] 4) Duration of listing

[0024] The third step is to determine the criteria.

[0025] The life cycle is divided into four stages: entry, growth, stability, and decline, which correspond to the four stages of the specification entering the market, rapid expansion, saturation, and gradual decline, respectively. There are three methods for judging the various indicators in the previous step: quadrant positioning method, index plotting method, and curve fitting method.

[0026] Step 4: Integrate the conclusions

[0027] 1) Multi-method consistency verification: Statistically analyze the judgment results of the three methods and calculate the consistency ratio;

[0028] 2) Voting on controversial samples: If the results of the three methods conflict, the Delphi method is used to implement multiple rounds of anonymous voting to correct the model results;

[0029] 3) Dynamic learning optimization: Record each amendment example and regularly update the weight coefficients in the life index method or the fitting parameters of the RGOmpertz function in the curve fitting method to improve the model's performance in special scenarios;

[0030] Step 5: Output and Verification

[0031] The final output shows the lifecycle stage of the cigarette specification, along with the criteria and correction instructions for each method. The model's accuracy can be verified through historical data backtesting, allowing for continuous parameter optimization.

[0032] Furthermore,

[0033] In the quadrant positioning method, by using the relative growth rate and relative market share of specifications, the four stages of the life cycle are correlated with two indicators, resulting in the following:

[0034] Entry stage: Relative growth rate > 0, relative market share < 0;

[0035] Upward trend: Relative growth rate > 0, relative market share > 0;

[0036] Downturn: Relative growth rate < 0, relative market share < 0;

[0037] Stable period: relative growth rate < 0, relative market share > 0.

[0038] In the index plotting method, based on relevant indicators, the life cycle index is constructed as a composite function related to sales volume, sales revenue, penetration rate, and time on the market, which is called the life index. According to the development law of products, the sales volume, sales revenue, and penetration rate of products show a trend of first rising and then falling as the time on the market increases.

[0039] The trend of the life index is directly proportional to the changes in sales volume, sales revenue, and penetration rate, but inversely proportional to the length of time on the market.

[0040] The growth rate or market share of sales volume and sales revenue also changes as the time on the market increases, first rising and then falling.

[0041] In curve fitting,

[0042] First, the relative growth rates of sales volume and sales revenue are combined to generate a comprehensive growth indicator, the formula of which is as follows:

[0043] Subsequently, the relationship between the comprehensive growth index and time t was fitted using the nonlinear least squares method to solve for the relevant parameters and calculate the inflection point;

[0044] Finally, based on the relationship between time and inflection point, determine the life cycle stage.

[0045] Furthermore,

[0046] The final growth rate ratio is determined by the weighted sum of the growth rate ratios under each category.

[0047] The weight coefficients of each category are determined using the information entropy method, and then the sum of the weights of each category is regarded as the final share contribution.

[0048] Through the above steps, the degree of influence of different classifications on this specification can be quantified, and the growth rate factor and scale factor can be derived, thereby obtaining the life index.

[0049] Once the life index is obtained, it is plotted as a scatter plot according to the time series. A multinomial function is used to fit the data to draw the trend curve between the points. The slope of each stage of the curve is used as the basis for judgment, and the life cycle stage within that time period is described by rules.

[0050] For the slope k of each stage i Calculate the average of the absolute values ​​of the slopes. Subsequent judgment:

[0051] ① If the slope of the i-th segment is less than or equal to the average of the absolute values ​​of the slopes, that is... Therefore, this stage of the life cycle is a stable period;

[0052] ② If the slope of the i-th segment is greater than the average absolute value of the slope, but the slope is negative, then the life cycle of this segment is a downward phase;

[0053] ③ If the slope of the i-th segment is greater than the average absolute value of the slopes, but the slope is positive, or if the slope of the i-th segment is less than the slope of the (i+1)-th segment, it indicates that the slope has an upward trend, and the life cycle of this stage is the entry stage; otherwise, it is the upward stage.

[0054] ④ When i = n, i.e., when judging the life cycle of the last stage, if the first two steps do not yield results, the slope value of the (i+1)th segment cannot be obtained. Therefore, based on k... i-1To assist in the judgment; if k i-1 <0,k i If the value is greater than 0, then this segment is the entry period; otherwise, this segment continues the derivation result of the previous segment.

[0055] The beneficial effects of this invention are

[0056] 1. More comprehensive indicators. The product integrates three core data categories: sales volume and sales revenue (scale-based indicators), number of cities covered (spatial penetration indicators), and time-based indicators (time on the market). These are combined to construct derivative indicators such as market share, relative growth rate, and penetration rate, systematically depicting the product's market performance.

[0057] 2. The method is highly robust. It innovatively integrates three technical approaches: "quadrant positioning method", "life index method" and "Gompertz curve fitting method", and cross-validates from different logical dimensions to reduce the bias caused by a single method;

[0058] 3. The results are highly interpretable. Consistency-weighted calculations are performed using three methods to output the results, combined with expert voting to correct any discrepancies. This balances model objectivity with industry specificity, ensuring that the conclusions conform to both data patterns and market realities. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the workflow of the present invention;

[0060] Figure 2 The example figure (1) uses the Gompertz curve;

[0061] Figure 3 The example figure (2) uses the Gompertz curve. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0063] This invention is essentially a data analysis technique. Therefore, this section will explain the entire process of the model from "input to processing to output" step by step, and unfold according to the logical chain of "data preparation - core indicator construction - multi-method judgment - result fusion and correction - output conclusion".

[0064] Step 1, Data Collection

[0065] This model requires the collection of two types of core data: performance data of the specification itself (annual sales volume, annual sales revenue, and market launch duration of the target cigarette specification) and market environment data (total annual sales volume, total annual sales revenue, and number of cities covered by the target specification within the same category). Subsequently, data cleaning operations such as removing outliers are performed on the data.

[0066] The second step is to construct indicators.

[0067] Cigarette specifications can be further subdivided according to different classification methods. For example, they can be classified by price, by product category, or by tar content. Assume there are i classification methods, j specifications under each category, k sales regions for each specification, and t years on the market for each specification.

[0068] Based on the given input data, let Q represent sales volume, M represent sales revenue, T represent launch date, and C represent market coverage rate. The following derivation can then be made:

[0069] 1. Regarding sales volume.

[0070] (1) Increment and growth rate

[0071] Let the annual sales volume of cigarettes of type j under type i in region k in year t be denoted as . Then the annual cigarette sales volume in year t-1 is expressed as: Therefore, the increase in its sales volume is

[0072]

[0073] The annual sales growth rate of this specification can then be expressed as:

[0074]

[0075] Let the annual sales volume of cigarettes in region k of the i-th category in year t be denoted as . That is Similarly, the annual sales growth rate of this category can be expressed as:

[0076] (2) Sales growth rate

[0077] To illustrate the growth advantage of this specification within the same market segment from a sales volume perspective, we use the sales growth rate ratio. The sales growth rate ratio is defined as the ratio of the annual sales growth rate of cigarette specification j to that of cigarette category i within region k in year t. A higher ratio indicates faster sales growth for that specification within that category. The formula is shown below.

[0078]

[0079] (3) Sales share ratio

[0080] To describe the sales advantage of a particular specification in the same market segment from a sales volume perspective, the sales share ratio is used. The sales share ratio is defined as the ratio of the annual sales volume of cigarettes of specification j to the annual sales volume of cigarettes of category i in region k during year t. The higher this ratio, the greater the sales advantage of that specification within that category.

[0081] The formula is expressed as follows:

[0082]

[0083] (4) Relative growth rate

[0084] The difference between the sales growth rate of specification j under category i in region k in year t and the sales growth rate of category i is defined as the relative growth rate of specification j. This relative growth rate describes whether the sales growth rate of specification j is dominant within the same category, and reflects whether the sales growth of specification j outpaces the growth of its category. The formula is as follows:

[0085]

[0086] (5) Relative share

[0087] The relative share of a specification is defined as the difference between the sales volume of the j-th specification within the i-th category in region k during year t and the reciprocal of the number of specifications within that category. This relative share describes whether the specification holds a sales advantage within the same category, from a sales volume perspective. If we assume all specifications within that category share equally, then the share ratio of each specification is the reciprocal of the number of specifications. This can be expressed as the formula below.

[0088]

[0089] In practical applications, the number of specifications within the same category may change from year to year. This is because in the actual market, new specifications may enter the market every year, or old specifications may be phased out every year. Therefore, the number of specifications j in the above definition is not a constant.

[0090] 2. Regarding sales revenue

[0091] (1) Increment and growth rate

[0092] Let the annual sales volume of cigarettes of type j under type i in region k in year t be denoted as . Then the annual cigarette sales volume in year t-1 is expressed as: Therefore, the increase in its sales revenue is

[0093]

[0094] The annual sales growth rate of this specification can then be expressed as:

[0095]

[0096] Let the annual sales volume of cigarettes in region k in year t be represented as... That is Similarly, the annual sales growth rate of this category can be expressed as:

[0097]

[0098] (2) Sales growth rate from the perspective of sales volume

[0099] The sales growth rate ratio is defined as the ratio of the annual sales growth rate of cigarettes of type j to that of cigarettes of type i within region k in year t. This ratio describes the growth advantage of that type of cigarette in the same market segment (from a sales revenue perspective). The higher the ratio, the faster the sales growth of that type of cigarette within that category. The formula is shown below.

[0100]

[0101] (3) Sales share ratio from the perspective of sales revenue

[0102] In region k, year t, the ratio of annual sales revenue of cigarettes of type j to annual sales revenue of cigarettes of type i is defined as the sales share ratio. This ratio describes the sales advantage (in terms of sales revenue) of that type of cigarette within the same market segment. A higher ratio indicates a greater sales advantage for that type of cigarette within that category. The formula is shown below.

[0103]

[0104] (4) Relative growth rate in terms of sales revenue

[0105] The difference between the sales growth rate of specification j under category i in region k in year t and the sales growth rate of category i is defined as the relative sales growth rate of specification j. This rate describes whether the sales growth rate of specification j is dominant within the same category, and reflects whether the sales growth of specification j outpaces the growth of its category. The formula is as follows:

[0106]

[0107] (5) Relative share in terms of sales revenue

[0108] The relative share of a specification is defined as the difference between the sales revenue of the j-th specification within the i-th category in region k during year t and the reciprocal of the number of specifications within that category. This relative share describes whether the specification holds an advantage in the same market segment from a sales revenue perspective. If we assume that all specifications within the category share equally, then the share ratio of each specification is the reciprocal of the number of specifications. This can be expressed as the formula below.

[0109]

[0110] In practical applications, the number of specifications within the same category may change from year to year. This is because in the actual market, new specifications may enter the market every year, or old specifications may be withdrawn from the market every year. Therefore, the number of specifications j here is not a constant.

[0111] 3. Regarding the coverage rate of prefecture-level cities

[0112] Let the number of regions covered by the sales of the j-th specification under the i-th category in year t be expressed as: Therefore, the maximum number of areas that this specification can theoretically cover is... The ratio of the number of regions to the maximum number of regions is defined as the regional coverage rate, also known as the penetration rate, for that specification. The formula is as follows:

[0113]

[0114] It's important to note that the maximum number of regions varies depending on the scale of focus. When focusing on the lifecycle of this specification nationwide, the maximum number of regions represents the maximum number of regions nationwide. However, when focusing on the lifecycle of this specification within a specific city, because it is limited to that city, the maximum number of regions is 1, and the penetration rate is 100%.

[0115] 4. Duration of listing

[0116] The duration of the j-th specification under the i-th category in region k in year t is calculated by comparing the current year t with the year of listing in that region. The difference is represented as, i.e.

[0117]

[0118] Under real-world conditions, the time it takes for different specifications to be available in different regions may vary. For example, a certain specification might only be launched in East China and Central China in its first year of availability, while it might only be launched in Northwest China in its third year. Therefore, the time it takes for this specification to be available in different regions will be different.

[0119] The third step is to determine the criteria.

[0120] First, considering that different classification methods can categorize specifications into different classes, applying the same criteria to all categories can easily lead to distorted results. For example, a specification might be classified as high-priced, slim cigarettes, or low-tar cigarettes. The total sales volume or revenue differs across categories, thus affecting the same specification differently.

[0121] The life cycle of cigarettes, modeled after that of general commodities, is divided into four stages: entry, growth, stability, and decline. These correspond to the initial market entry, rapid expansion, market saturation, and gradual decline of the cigarette product. Based on the indicators derived in the previous step, there are three main methods for assessment: quadrant positioning, index plotting, and curve fitting.

[0122] 1. Quadrant positioning method

[0123] From the indicators derived in the previous step, four indicators were selected as key indicators for evaluating the life cycle of cigarettes: relative growth rate of sales volume, relative market share of sales volume, relative growth rate of sales revenue, and relative market share of sales revenue. A weighted average was then used to combine sales volume and sales revenue into a single dimension, resulting in a comprehensive relative growth rate. and relative share The formula is expressed as follows:

[0124]

[0125] Where ω and δ are the weighted average coefficients under the growth rate and the weighted average coefficients under the share, respectively, and are calculated by the ratio of each share to the sum of each share.

[0126] By using the relative growth rate and relative market share of specifications, the four stages of cigarette production are correlated with two indicators, resulting in the table shown below.

[0127]

[0128] During the entry phase, the product has just been launched, market awareness is low, customer acceptance is limited, and sales growth is slow. This is characterized by the growth rate of a particular specification exceeding the growth rate of its category, but its market share being lower than the average market share of its category, exhibiting a strong growth advantage. These specifications are generally new specifications launched that year and have good development potential. At this stage, the customer base is typically composed of early adopters or price-sensitive users. New customer acquisition relies on basic channel distribution, and brand loyalty is low. In special circumstances, this situation may also occur for certain older specifications due to policy relaxation or competitor contraction.

[0129] During the upward phase, the product is validated by the market, demand rises rapidly, customers flock in, and sales grow at a high speed, entering a golden period of "growth and market share" growth. This is characterized by the growth rate of the specification exceeding the growth rate of the category, and the market share exceeding the average market share of the category. These specifications of cigarettes are in an expansion or development phase. The consumer group expands from "early adopters" to "mainstream users," new customer acquisition is mainly through "word-of-mouth marketing + proactive selection," and brand loyalty is rapidly established.

[0130] During the stable period, the market tends to be saturated, demand growth slows, acquiring new customers becomes more difficult, and sales growth slows or stagnates. Cigarette products in this stage either maintain a stable overall market share, meaning their sales volume keeps pace with the expansion of the market at the same price point, and their brand advantages remain solid; or their sales growth slows, but cigarette products still maintain an upward trend, showing a situation where market share declines while sales volume continues to increase.

[0131] During a downturn, market demand shrinks, substitutes emerge, customers are lost, and sales continue to decline. This may be the beginning of a new product launch or the end for some older models. The consumer base is primarily composed of price-sensitive long-term customers, new customers are almost nonexistent, and brand loyalty further declines. From an external perspective, policy restrictions, the pressure from substitutes, and economic downturns can all negatively impact sales. Internally, product aging, declining channel profits, and reduced resource allocation can all lead to a contraction phase for certain product categories.

[0132] Besides the four scenarios mentioned above, when the relative growth rate or relative share is zero, it is considered a special case. This corresponds to situations where the growth rate of specifications is equal to the growth rate of market share, or where the market share is exactly evenly distributed among all market shares.

[0133] 2. Index plotting method

[0134] Based on the relevant indicators derived in the previous step, the life cycle index of cigarettes is constructed as a composite function related to sales volume, sales revenue, market penetration rate, and market duration, which is called the life index. According to the general development pattern of commodities, sales volume, sales revenue, and market penetration rate tend to increase first and then decrease as market duration increases. Therefore, the trend of the cigarette life index should be similar to, or directly proportional to, the changes in sales volume, sales revenue, and market penetration rate, and inversely proportional to market duration.

[0135] Similarly, the growth rate or market share of sales volume and sales revenue should also show a trend of first rising and then falling as the time on the market increases. Therefore, in order to construct a life index, we should consider both growth rate and market share, and supplement them with penetration rate and time on the market for adjustment.

[0136] (1) Growth factor

[0137] From a growth rate perspective, we consider both the sales volume growth rate ratio and the sales revenue growth rate ratio. For different categories, since the growth rate ratio for each specification is the same, the difference in growth rate ratios primarily stems from the denominator, i.e., the growth rate of total sales volume or total sales revenue under that category. To reduce the differences in growth rate ratios caused by different categories and to avoid distortion in the assessment due to different categories, we use the weighted sum of the growth rate ratios under each category as the final growth rate ratio. The sales volume growth rate and sales revenue growth rate are expressed as follows:

[0138]

[0139] Where the weighting coefficient ω i The information entropy method is used to determine the weight of a category. If the number of goods in a category is small and competition is not intense, the growth rate of specifications within that category better reflects the true contribution of the goods. Conversely, if the number of goods in a category is large and competition is more intense, the contribution of the growth rate of specifications within that category is relatively small. The information entropy method quantifies the "competitive disorder" of a category; the lower the entropy value (reflecting less intense competition among goods in that category), the higher the weight.

[0140] Then the growth factor of specification j in region k in year t. This can be expressed as the weighted average of the sales growth rate ratio and the sales revenue growth rate ratio, i.e.

[0141]

[0142] Where ω Q and ω m These are the weighted coefficients of the sales growth rate ratio and the sales revenue growth rate ratio, respectively, which are derived from the share of each part's growth rate ratio in the sum of all growth rate ratios.

[0143] (2) Share factor

[0144] Similarly, we consider sales volume share and sales revenue share from a market share perspective. Since total sales volume or total sales revenue differs across categories, the share ratio will vary significantly for the same specification across different categories. Therefore, similar to the growth rate method, we use the information entropy method to determine the weight coefficients of each category, and then consider the sum of these weights as the final share contribution. Expressed as formulas, sales volume share and sales revenue share can be represented as follows:

[0145]

[0146] Similarly, the weighting coefficient δ iThe information entropy method is used to determine the proportion of products in a category (see appendix for details). If the number of products in a category is small and the competition is not intense, the proportion of product specifications in that category will better reflect the true contribution of the products. Conversely, if the number of products in a category is large and the competition is more intense, the contribution of the proportion of product specifications in that category will be relatively small.

[0147] Then the scale factor of specification j in region k in year t. This can be expressed as a weighted average of sales volume share and sales revenue share, i.e.

[0148]

[0149] Where δ Q and δ M These are the weighted coefficients of the sales volume ratio and the sales revenue ratio, respectively, which are derived from the share of each part's scale ratio in the sum of the total scale ratios.

[0150] (3) Vital Index

[0151] Through the above steps, the impact of different classifications on this specification can be quantified, and expressions for the growth rate factor and scale factor can be derived. Considering that the life cycle of a specific specification is influenced not only by growth rate and scale, but also by the penetration rate reflecting its life cycle stage when the scope is expanded nationwide; furthermore, theoretically, the time to market for a specification is also a direct factor affecting its life cycle. Therefore, after comprehensive consideration, the life index is expressed as the following formula.

[0152]

[0153] α and β are the weighting coefficients of the growth rate factor and the scale factor, respectively, reflecting the degree of influence of growth rate and scale on the life cycle. They are determined using the coefficient of variation weighting method (see Appendix for details).

[0154] (4) Slope method judgment

[0155] After obtaining the life index, it is plotted as a scatter plot according to the time series. However, it is not easy to judge the trend of the value change in the scatter plot. Therefore, a polynomial function fitting method is used to draw the trend curve between points, and the slope of each stage of the curve is used as the basis for judgment. The life cycle stage within the time period is described by certain rules.

[0156] For the slope k of each stage i The average of the absolute values ​​of the slopes can be obtained. Subsequent judgment:

[0157] ① If the slope of the i-th segment is less than or equal to the average of the absolute values ​​of the slopes, that is... Therefore, this stage of the life cycle is a stable period;

[0158] ② If the slope of the i-th segment is greater than the average absolute value of the slope, but the slope is negative, then the life cycle of this segment is a downward phase;

[0159] ③ If the slope of the i-th segment is greater than the average absolute value of the slopes, but the slope is positive, or if the slope of the i-th segment is less than the slope of the (i+1)-th segment, it indicates that the slope has an upward trend, and the life cycle of this stage is the entry stage; otherwise, it is the upward stage.

[0160] ④ When i = n, i.e., when judging the life cycle of the last stage, if the first two steps do not yield results, the slope value of the (i+1)th segment cannot be obtained. Therefore, based on k... i-1 Use it to assist in the judgment. If k i-1 <0,k i If the value is greater than 0, then this segment is the entry period; otherwise, this segment continues the derivation result of the previous segment.

[0161] The above judgment process can be simply represented as in d). Figure 1 As shown:

[0162] 3. Curve fitting method

[0163] The Gompertz curve is commonly used to describe changes in the size of biological communities, such as in population growth models. This curve is characterized by slow growth in the early and late stages, followed by rapid growth in the middle. The function is time-dependent, and its formula is as follows:

[0164]

[0165] Here, K is the limit of the function, and a and b are curve shape parameters that determine the steepness of the curve and the location of inflection points. If we take the first derivative of f(t) and maximize it, we get t0 = ln(b) / a, which is the inflection point of the curve. Figure 2 As shown.

[0166] As we can see, the Gompertz curve focuses more on growth, but often fails to accurately reflect the end of the lifecycle, i.e., the decline phase. Therefore, the Gompertz function is modified to include a decay term, which is named the RGompertz function, where R stands for Reduced. Its formula is as follows:

[0167]

[0168] Where K is the limit of the function, γ is the growth coefficient, controlling the steepness of the growth in the first half of the S-curve, α is the decay coefficient, controlling the rate of decline; t0 is the point in time with the fastest growth rate, generally the center point of the first half of the S-curve; t p The point in time when the function reaches its maximum value is also known as the peak time. For example... Figure 3 As shown.

[0169] Based on the indicators derived above, we can take the relative growth rate of different specifications under different categories and fit a Gompertz curve. For example, for a certain brand, we can calculate the relative growth rate of that specification under the three categories of slim cigarettes, high-priced cigarettes, and low-tar cigarettes. After fitting with Gompertz curve, we can obtain the life cycle stage of that specification under different categories, which can reflect the impact of different categories on the specification.

[0170] First, the relative growth rates of sales volume and sales revenue from the previous step are combined to generate a comprehensive growth indicator G, the formula of which is as follows:

[0171]

[0172] Where ω is the weighting coefficient, which is obtained by the coefficient of variation method. For specific steps, please refer to the appendix.

[0173] Subsequently, the relationship between the comprehensive growth index G and t was fitted using the nonlinear least squares method to solve for the relevant parameters, and the inflection points t0 and tt were calculated. p .

[0174] Finally, the life cycle stage is determined based on the relationship between time t and the inflection point.

[0175] Life cycle stage Judgment Logic Curve characteristics Entry period <![CDATA[t < t0 / 2 and G < K / 3]]> G rises slowly and remains below one-third of the maturity level. Upward period <![CDATA[t0 / 2 < t < t0, and G rises from K / 3 to the maximum value]]> <![CDATA[The slope of G gradually increases, and the growth becomes faster and faster. When t = t0, the growth rate is the fastest.]]> Stable period <![CDATA[t0<t<t p And G > 0 The slope of G gradually decreases, its growth becomes increasingly full, and it approaches K. Downward period <![CDATA[t>t p or G<0]]> The slope of G becomes negative, continues to decrease, and even falls below 0.

[0176] Step 4: Integrate the conclusions

[0177] 1. Multi-method consistency verification: Statistically analyze the judgment results of three methods and calculate the consistency ratio;

[0178] 2. Expert voting on controversial samples: If the results of the three methods conflict, industry experts will be organized to conduct multiple rounds of anonymous voting using the Delphi method to correct the model results;

[0179] 3. Dynamic learning and optimization: Record each expert amendment example and regularly update the weight coefficients in the life index method or the fitting parameters of the RGompertz function in the curve fitting method to improve the model's adaptability to special scenarios (such as new product categories or policy changes).

[0180] Step 5: Output and Verification

[0181] The final output shows the life cycle stage of the cigarette specification (entry stage / upward stage / stable stage / downward stage), along with the judgment criteria for each method (such as quadrant chart coordinates, life index value, Gompertz curve inflection point time) and expert correction explanations. Companies can use historical data to backtest the model's accuracy (e.g., compare it with actual sales turning points) and continuously optimize the parameters.

[0182] I. Information Entropy

[0183] The core of information entropy is: the greater the data difference, the smaller the entropy value, the more "information" that dimension has, and the higher its weight should be.

[0184] The first step is to standardize the objective quantity for which we want to solve for the weights into relative importance, denoted as P. i This refers to the proportion of the target quantity to the total target quantity. The purpose is to avoid interference caused by differences in the denominator of the target quantity ratio. Taking the sales growth rate ratio as an example, it can be expressed by the following formula:

[0185]

[0186] Similarly, taking sales share ratio as an example, the formula is as follows:

[0187]

[0188] P i The larger the value, the more prominent the sales volume of the specified specification is relative to other categories under that category, and the stronger the "correlation" of that category with the specified specification.

[0189] The second step is to calculate the information entropy value for each category, denoted as E. i Its formula is expressed as follows:

[0190] E i =-P i ·log2(P i )

[0191] The third step is to calculate the difference coefficient for each category. According to the definition of information entropy, E... i The smaller the value, the stronger the P-value for that category. i The more unique something is, the more it needs to be amplified by a "difference coefficient," which can be expressed by the following formula:

[0192] D i =1-E i

[0193] The fourth step is to normalize the difference coefficients, which will give the final weight ω for each category. i The formula is as follows:

[0194]

[0195] By following the above four steps, the weight of the target quantity is obtained.

[0196] II. Coefficient of Variation Weighting Method

[0197] The coefficient of variation reflects the "information volatility" of an indicator. The greater the volatility, the stronger the indicator's ability to distinguish growth trends, and the higher its weight should be. The steps are as follows:

[0198] The first step is to calculate the mean.

[0199] The mean reflects the average growth level of an indicator and is the basis for calculating the coefficient of variation. Its calculation formula is as follows:

[0200]

[0201] Where X(t) is a time-related value, which can be replaced by the relative growth rate of sales volume or the relative growth rate of sales revenue; n is the period of the time series, that is, the time since the specification was launched.

[0202] The second step is to calculate the sample standard deviation.

[0203] Standard deviation reflects the dispersion of an indicator, that is, the magnitude of its fluctuation across different periods. Since historical data for a commodity is "sample data," the sample standard deviation (i.e., the denominator is the period number minus 1) needs to be used. Its calculation formula is as follows:

[0204]

[0205] Where X(t) is a time-related value, which can be replaced by the relative growth rate of sales volume or the relative growth rate of sales revenue; n is the period of the time series, i.e. the listing duration of the specification; and μ is the mean of the corresponding indicator.

[0206] The third step is to calculate the coefficient of variation.

[0207] The coefficient of variation (COP) is the ratio of the standard deviation to the absolute value of the mean, used to eliminate differences in the magnitude of an indicator. A larger COP indicates greater volatility and a higher information contribution. Its calculation formula is...

[0208]

[0209] The absolute value of the mean is used here to avoid a negative coefficient of variation due to a negative mean (such as when the growth rate of a commodity is lower than that of the category for a long period of time), thus ensuring the reasonableness of the fluctuation.

[0210] Step 4: Calculate the weights

[0211] The weight is determined by the proportion of the coefficient of variation of a single indicator to the sum of the coefficients of variation of all indicators, ensuring that the sum of the weights is 1, and that indicators with greater volatility have higher weights. The calculation formula is as follows:

[0212]

[0213] In summary, this invention solves the problems of subjectivity and one-sidedness in traditional cigarette life cycle assessment by mining multi-dimensional indicators, cross-validating multiple methods, and integrating expert experience. It provides enterprises with a more accurate and interpretable tool for determining product stages, and has significant practical value and technological innovation.

[0214] The above description is merely a preferred embodiment of the present invention and is used only to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A dynamic assessment method for the cigarette lifecycle based on the fusion of multi-dimensional indicators and multiple methods, characterized in that, include: 1) Construct a multi-dimensional indicator system, based on four dimensions: sales performance, competitiveness in different market categories, regional coverage, and time accumulation. Extract market share, relative growth rate, and penetration rate based on specifications to form a framework covering market position, expansion capability, and time cycle. 2) Cross-validation lifecycle determination: Using relative growth rate and relative market share, the four stages of the lifecycle are assigned to four quadrants, achieving a quadrant positioning method with growth rate as the vertical axis and market share as the horizontal axis; by combining sales volume, sales revenue, penetration rate, and time to market, a life index is constructed and thresholds are set to divide the stages; with time as the independent variable and relative growth rate as the dependent variable, the Gompertz function with added decay term is fitted, and the stage is identified by the curve inflection point; 3) Dynamic correction: Consistency verification of the output stage conclusions is performed. By voting on controversial samples, model bias is corrected to form the final judgment result.

2. The method according to claim 1, characterized in that, The specific steps are as follows: Step 1, Data Collection Two types of core data were collected: performance data of the specifications themselves and market environment data, and then the data was cleaned. The second step is to construct indicators. 1) Regarding sales volume, including (1.1) Increment and growth rate (1.2) Sales growth rate ratio (1.3) Sales share ratio (1.4) Relative growth rate (1.5) Relative share; 2) Regarding sales revenue (2.1) Increment and growth rate (2.2) Sales growth rate ratio in terms of sales volume (2.3) Sales share ratio in terms of sales volume (2.4) Relative growth rate in terms of sales volume (2.5) Relative share in terms of sales volume; 3) Regarding the coverage rate of prefecture-level cities 4) Duration of listing The third step is to determine the criteria. The life cycle is divided into four stages: entry, growth, stability, and decline, which correspond to the four stages of the specification entering the market, rapid expansion, saturation, and gradual decline, respectively. There are three methods for judging the various indicators in the previous step: quadrant positioning method, index plotting method, and curve fitting method. Step 4: Integrate the conclusions 1) Multi-method consistency verification: Statistically analyze the judgment results of the three methods and calculate the consistency ratio; 2) Voting on controversial samples: If the results of the three methods conflict, the Delphi method is used to implement multiple rounds of anonymous voting to correct the model results; 3) Dynamic learning optimization: Record each amendment example and regularly update the weight coefficients in the life index method or the fitting parameters of the RGOmpertz function in the curve fitting method to improve the model's performance in special scenarios; Step 5: Output and Verification The final output shows the lifecycle stage of the cigarette specification, along with the judgment criteria and correction instructions for each method; the accuracy of the model is verified by backtesting historical data, and the parameters are continuously optimized.

3. The method according to claim 2, characterized in that, In the quadrant positioning method, by using the relative growth rate and relative market share of specifications, the four stages of the life cycle are correlated with two indicators, resulting in the following: Entry stage: Relative growth rate > 0, relative market share < 0; Upward trend: Relative growth rate > 0, relative market share > 0; Downturn: Relative growth rate < 0, relative market share < 0; Stable period: relative growth rate < 0, relative market share > 0.

4. The method according to claim 2, characterized in that, In the index plotting method, based on relevant indicators, the life cycle index is constructed as a composite function related to sales volume, sales revenue, penetration rate, and time on the market, which is called the life index. According to the development law of products, the sales volume, sales revenue, and penetration rate of products show a trend of first rising and then falling as the time on the market increases.

5. The method according to claim 4, characterized in that, The trend of the life index is directly proportional to the changes in sales volume, sales revenue, and penetration rate, but inversely proportional to the length of time on the market. The growth rate or market share of sales volume and sales revenue also changes as the time on the market increases, first rising and then falling.

6. The method according to claim 5, characterized in that, In curve fitting, First, the relative growth rates of sales volume and sales revenue are combined to generate a comprehensive growth indicator, the formula of which is as follows: Subsequently, the relationship between the comprehensive growth index and time t was fitted using the nonlinear least squares method to solve for the relevant parameters and calculate the inflection point; Finally, the life cycle stage is determined based on the relationship between time and inflection point.

7. The method according to claim 5, characterized in that, The final growth rate ratio is determined by the weighted sum of the growth rate ratios under each category. The weight coefficients of each category are determined using the information entropy method, and then the sum of the weights of each category is regarded as the final share contribution. Through the above steps, the degree of influence of different classifications on this specification can be quantified, and the growth rate factor and scale factor can be derived, thereby obtaining the life index; Once the life index is obtained, it is plotted as a scatter plot according to the time series. A multinomial function is used to fit the data to draw the trend curve between the points. The slope of each stage of the curve is used as the basis for judgment, and the life cycle stage within that time period is described by rules.

8. The method according to claim 7, characterized in that, For the slope k of each stage i Calculate the average of the absolute values ​​of the slopes. Subsequent judgment: ① If the slope of the i-th segment is less than or equal to the average of the absolute values ​​of the slopes, that is... Therefore, this stage of the life cycle is a stable period; ② If the slope of the i-th segment is greater than the average absolute value of the slope, but the slope is negative, then the life cycle of this segment is a downward phase; ③ If the slope of the i-th segment is greater than the average absolute value of the slopes, but the slope is positive, or if the slope of the i-th segment is less than the slope of the (i+1)-th segment, it indicates that the slope has an upward trend, and the life cycle of this stage is the entry stage; otherwise, it is the upward stage. ④ When i = n, i.e., when judging the life cycle of the last stage, if the first two steps do not yield results, the slope value of the (i+1)th segment cannot be obtained. Therefore, based on k... i-1 To assist in the judgment; if k i-1 <0,k i If the value is greater than 0, then this segment is the entry period; otherwise, this segment continues the derivation result of the previous segment.

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