Inventory constraint-oriented dynamic pricing collaborative optimization method and system

Abstract

The invention relates to the technical field of data processing, and discloses an inventory constraint-oriented dynamic pricing collaborative optimization method and system. The method comprises the steps of obtaining a historical sales data set and inventory parameters, and calculating an inventory health degree index; fitting to obtain an initial price elastic coefficient, and performing hyperbolic tangent transformation and modulation operation on the inventory health degree index to obtain a dynamic price elastic coefficient; demand prediction is carried out based on the dynamic price elasticity coefficient; and a multi-cycle income optimization model is established and solved, and a pricing strategy and a replenishment scheme are obtained. According to the invention, the technical problem that the demand prediction model cannot reflect the influence of the inventory state on the price sensitivity of the consumer in the prior art is solved, and the demand prediction precision and the controllability of the inventory evolution trajectory are improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a dynamic pricing collaborative optimization method and system oriented towards inventory constraints. Background Technology

[0002] In the field of inventory management and pricing decisions, existing technologies typically separate pricing optimization from inventory management. This involves first establishing a demand forecasting model with fixed parameters based on historical sales data, and then formulating pricing strategies and inventory replenishment plans based on this model. Key parameters such as the price elasticity coefficient in the demand forecasting model remain unchanged after fitting. Pricing decisions are mainly adjusted based on market demand fluctuations and cost structures, while inventory management focuses on setting safety stock thresholds and replenishment cycles. There is a lack of real-time information feedback and collaborative adjustment mechanisms between the two.

[0003] The main shortcoming of existing technologies lies in the static nature of demand forecasting models, which makes it impossible to accurately reflect the impact of inventory status on consumer purchasing behavior. When inventory levels change significantly, consumers’ price sensitivity will change accordingly. When inventory is abundant, consumers have a lower tolerance for price increases and tend to wait for price reductions and promotions. When inventory is tight, consumers are more accepting of high prices, worry about shortages, and accelerate their purchasing decisions. However, a fixed price elasticity coefficient cannot capture this modulating effect of inventory status on price sensitivity, causing demand forecasts to deviate from reality. Consequently, it is difficult for pricing strategies and inventory decisions based on this forecast to achieve true synergistic optimization. Summary of the Invention

[0004] This application provides a dynamic pricing collaborative optimization method and system oriented towards inventory constraints. By constructing a dynamic price elasticity coefficient modulation mechanism driven by inventory health indicators, it solves the technical problem that demand forecasting models in the prior art cannot reflect the impact of inventory status on consumer price sensitivity, thereby improving the accuracy of demand forecasting and the controllability of inventory evolution trajectory.

[0005] Firstly, this application provides a dynamic pricing collaborative optimization method oriented towards inventory constraints, the method comprising:

[0006] Step S1: Obtain historical sales dataset, current inventory level, safety stock threshold, and maximum inventory capacity. Perform a division operation using the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. Step S2: Based on the price data and sales volume data in the historical sales dataset, perform nonlinear regression fitting to obtain the initial price elasticity coefficient. Input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value. Multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor. Multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. Step S3: Substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to predict the demand quantity and obtain the demand forecast result related to the inventory status. Step S4: Establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain the pricing strategy and replenishment plan.

[0007] The acquisition module is used to acquire historical sales datasets, current inventory levels, safety stock thresholds, and maximum inventory capacity. It performs a division operation by taking the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. The fitting module is used to perform nonlinear regression fitting based on the price data and sales volume data in the historical sales dataset to obtain the initial price elasticity coefficient, input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value, multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor, and multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. The forecasting module is used to substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to forecast the demand quantity and obtain the demand forecast result related to the inventory status. The solution module is used to establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain pricing strategies and replenishment plans.

[0008] The technical solution provided in this application establishes a relative measurement system for inventory status by dividing the difference between the current inventory level and the safety stock threshold (as the numerator) and the difference between the maximum inventory capacity and the safety stock threshold (as the denominator). This indicator not only reflects the absolute quantity of inventory but also the relative positional relationship between inventory and the safety boundary and capacity limit, providing standardized input parameters for the dynamic adjustment of subsequent demand forecasting models. It overcomes the problem of incomparability between different scales of goods caused by directly using absolute inventory levels in existing technologies. Furthermore, by inputting the inventory health index into a hyperbolic tangent function for nonlinear transformation to obtain a transformed value, the bounded mapping property of the hyperbolic tangent function is used to compress extreme values ​​of inventory status. Within the range of -1 to +1, the excessive impact of abnormal inventory fluctuations on the price elasticity coefficient is avoided. The modulation factor is obtained by multiplying the transformed value and the elasticity modulation strength coefficient and adding 1. The modulation factor is then multiplied with the initial price elasticity coefficient, realizing the dynamic adjustment of the price elasticity coefficient according to the inventory health. When there is excess inventory, the modulation factor is greater than 1, which increases the price elasticity coefficient and reflects that consumers are more sensitive to prices. When there is tight inventory, the modulation factor is less than 1, which decreases the price elasticity coefficient and reflects that consumers are more accepting of higher prices. This dynamic modulation mechanism establishes a quantitative correlation between inventory status and consumer price sensitivity, enabling demand forecasting to accurately reflect the impact of inventory constraints on purchasing behavior and significantly improving the accuracy of demand forecasting. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a schematic diagram of an embodiment of the dynamic pricing collaborative optimization method for inventory constraints in this application. Figure 2 This is a schematic diagram comparing the performance indicators of the present invention with those of the prior art in the embodiments of this application; Figure 3 This is a schematic diagram illustrating the dynamic adjustment process of the pricing strategy in the embodiments of this application. Detailed Implementation

[0011] This application provides a dynamic pricing collaborative optimization method and system oriented towards inventory constraints. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0012] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the dynamic pricing collaborative optimization method for inventory constraints in this application includes: Step S1: Obtain historical sales data, current inventory level, safety stock threshold, and maximum inventory capacity. Divide the current inventory level and the safety stock threshold as the numerator and the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. Specifically, the safety stock threshold is subtracted from the current inventory level to obtain the safety margin. A positive value indicates that the inventory is above the safety level, while a negative value indicates that the inventory is in the stockout risk zone. The maximum inventory capacity is subtracted from the safety stock threshold to obtain the inventory capacity range. This range defines the adjustable range of inventory from the safety boundary to the capacity limit. Dividing the two values ​​completes the normalization process, making the inventory status of goods of different sizes comparable. When the value of this indicator approaches 1, it reflects excess inventory. When the value approaches 0, it reflects that the inventory is at the safety boundary. When the value is negative, it reflects that the inventory is below the safety level.

[0013] Step S2: Based on the price data and sales volume data in the historical sales dataset, perform nonlinear regression fitting to obtain the initial price elasticity coefficient. Input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value. Multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor. Multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. Specifically, the initial price elasticity coefficient is obtained by performing a power function-based nonlinear regression on historical price and sales volume data. This coefficient reflects the average response strength of consumers to price changes when inventory status is not considered. The hyperbolic tangent function maps the inventory health index to a bounded interval from -1 to +1. The steepness of the mapping curve is controlled by the inventory response sensitivity parameter. The transformed value after mapping is multiplied by the elasticity modulation intensity coefficient to obtain the elasticity modulation amount. This modulation amount is added to the value 1 to form the modulation factor. When the inventory health index is positive, the modulation factor is greater than 1, which increases the price elasticity coefficient. When the inventory health index is negative, the modulation factor is less than 1, which decreases the price elasticity coefficient. The modulation factor is multiplied by the initial price elasticity coefficient to complete the dynamic adjustment of the elasticity parameter.

[0014] Step S3: Substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to predict the demand quantity and obtain the demand forecast results related to the inventory status. Specifically, the demand calculation formula models the inverse relationship between price and quantity demanded by raising the price variable to a negative power. The absolute value of the exponent of the negative power is the price elasticity coefficient. The larger the coefficient, the steeper the demand curve, indicating that consumers are more sensitive to price. After substituting the price elasticity coefficient obtained in step S2, which changes dynamically with inventory health, into the demand calculation formula, different elasticity parameters are used for demand forecasting under different inventory states. The price variable is multiplied by the basic demand scale parameter after exponentiation to obtain the predicted demand value. This predicted value is associated with the current inventory health index to form the demand forecast result associated with the inventory state. This result includes both the numerical prediction of demand and the corresponding inventory state information.

[0015] Step S4: Establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain the pricing strategy and replenishment plan.

[0016] Specifically, the multi-period revenue optimization model is constructed based on the discrete-time inventory dynamic evolution equation. This equation describes that the inventory level in each decision period is equal to the inventory level of the previous period minus the demand forecast plus the replenishment quantity. The net revenue of a single period is obtained by multiplying the price variable by the demand forecast. The net revenue of a single period is obtained by subtracting the procurement cost, inventory holding cost, stockout penalty cost, and inventory overflow cost from the sales revenue. The objective function of the multi-period revenue optimization model is the sum of the net revenue of a single period across all decision periods. The mixed-integer linear programming algorithm solves the objective function under the constraints of upper and lower limits of inventory level and upper limit of replenishment quantity. The solution process traverses the discrete decision space through a branch and bound strategy to obtain the pricing strategy and replenishment plan for each decision period that maximizes the cumulative revenue of the multi-period cycle.

[0017] In this application, the dynamic price elasticity coefficient is substituted as a variable parameter into the demand calculation formula to obtain the demand forecast result related to inventory status. This allows different elasticity parameters to be used for calculating demand forecasts under different inventory health conditions. Based on the demand forecast result, a multi-period revenue optimization model is established and solved to obtain the pricing strategy and replenishment plan. This achieves true synergy between pricing decisions and inventory management. The optimization model considers sales revenue, inventory holding costs, stockout penalty costs, and inventory overflow costs in the objective function. The mixed-integer linear programming algorithm is used to ensure that the cumulative revenue of multiple periods is maximized while satisfying inventory constraints. Since the demand forecast has incorporated inventory status information, the optimized pricing strategy can effectively consume inventory through price reductions when there is excess inventory, and protect scarce resources and increase unit revenue by maintaining high prices when inventory is tight. This avoids the inventory control problem caused by the disconnect between pricing strategy and inventory status in the prior art. At the same time, the multi-period optimization framework enables the replenishment plan to respond to future demand changes in a predictive manner, reducing the frequency of stockouts and inventory overflows. The smooth adjustment of the pricing strategy reduces price fluctuations and increases market acceptance. The overall solution improves the profitability while enhancing the stability and controllability of inventory management.

[0018] In one specific embodiment, step S1 includes: Extract sales records from the sales system database within a preset historical time window. The sales records include time series labels, price series at the corresponding time, actual sales volume series, and inventory level series. Obtain the current real-time inventory level from the inventory management system, the safety stock threshold preset based on the physical storage space and product shelf life, and the maximum inventory capacity of the storage system. The inventory safety margin is obtained by subtracting the real-time inventory level from the safety stock threshold, and the inventory capacity range is obtained by subtracting the maximum inventory capacity from the safety stock threshold. The inventory health index is obtained by dividing the inventory safety margin as the numerator and the inventory capacity range as the denominator.

[0019] Specifically, when retrieving sales records from the sales system database, the length of the preset historical time window is determined based on the characteristics of the product sales cycle. The time window for fast-moving consumer goods is set to 30 to 90 days, and for durable goods, it is set to 180 to 365 days. Time series labels are sampled at fixed time intervals: the sampling interval for daily sales data is 1 day, and the sampling interval for hourly sales data is 1 hour. The price series records the product sales price corresponding to each time label, the actual sales volume series records the actual transaction quantity corresponding to each time label, and the inventory level series records the ending inventory quantity corresponding to each time label. These four types of data maintain a one-to-one correspondence in the time dimension, forming a complete set of historical sales records. The real-time inventory quantity obtained from the inventory management system is the available inventory quantity at the current decision-making moment. The safety stock threshold is calculated based on a combination of physical space constraints and product shelf-life constraints. Physical space constraints limit the minimum storage area, while product shelf-life constraints ensure that the safety stock quantity can be consumed within the shelf life. The maximum inventory capacity is the maximum inventory quantity that the warehousing system can accommodate under space and management capacity constraints.

[0020] The safety margin is obtained by subtracting the real-time inventory level from the safety stock threshold. When the real-time inventory level is greater than the safety stock threshold, the safety margin is positive, indicating that the inventory is in a safe state and has a certain degree of redundancy. When the real-time inventory level is less than the safety stock threshold, the safety margin is negative, indicating that the inventory is below the safe level and there is a risk of stockout. The inventory capacity range is obtained by subtracting the maximum inventory capacity from the safety stock boundary and the maximum capacity limit. This range quantifies the adjustable inventory space from the safety stock boundary to the maximum capacity limit. The inventory health index is obtained by dividing the safety margin by the inventory capacity range. This index maps the inventory status of different absolute sizes to a unified relative measurement scale. When the safety margin equals the inventory capacity range, the inventory health index equals 1, indicating that the inventory has reached the maximum capacity. When the safety margin equals 0, the inventory health index equals 0, indicating that the inventory is just at the safety boundary. When the safety margin is negative, the inventory health index is negative, indicating that the inventory is in a stockout risk area. The normalization characteristic of this index makes the inventory status of different product categories and different warehouse sizes comparable.

[0021] In one specific embodiment, step S2, which involves obtaining the initial price elasticity coefficient through nonlinear regression fitting based on price and sales volume data from a historical sales dataset, includes: Extract price sequences and actual sales volume sequences from historical sales datasets as training sample pairs; Construct a basic demand expression in the form of a power function. The basic demand expression is calculated by multiplying the price variable by a negative power by the basic demand size parameter. The absolute value of the exponent of the negative power is the initial price elasticity coefficient. Substitute the price series and the actual sales volume series into the basic demand expression to calculate the squared error between the predicted sales volume and the actual sales volume. By iteratively adjusting the basic demand scale parameter and the initial price elasticity coefficient using the least squares method, the sum of squared errors is minimized, thus obtaining the initial price elasticity coefficient.

[0022] Specifically, the basic demand expression uses a power function to establish a nonlinear mapping relationship between price and quantity demanded. The design of using negative powers for the price variable reflects the inverse relationship between price and quantity demanded. The absolute value of the negative power is the initial price elasticity coefficient. The larger the value of this coefficient, the higher the sensitivity of demand to price changes. The basic demand scale parameter controls the overall horizontal position of the demand curve. The price variable, after being raised to a negative power, is multiplied by the basic demand scale parameter to obtain the predicted sales volume. The price series in the historical sales dataset is substituted into this expression one by one to calculate the corresponding predicted sales volume series. The difference between the predicted sales volume and the actual sales volume is squared to eliminate the positive and negative offsetting effects. The squared errors at all time points are summed to obtain the overall fitting error.

[0023] The least squares method finds the parameter combination that minimizes the sum of squared errors through an iterative optimization process. During the iteration, two parameters to be fitted are simultaneously adjusted: the basic demand scale parameter and the initial price elasticity coefficient. In each iteration, the sum of squared errors under the current parameter combination is calculated, and the parameter values ​​are updated through gradient descent. When the change in the sum of squared errors after several consecutive iterations is less than a preset convergence threshold, the optimization process is considered to have converged. The initial price elasticity coefficient obtained at this time is the parameter value with the best fit on the historical sales dataset. This parameter reflects the average response strength of consumers to price changes without considering the impact of inventory status. The magnitude of the initial price elasticity coefficient directly determines the baseline level of the subsequent inventory status adjustment process. A larger initial price elasticity coefficient indicates that consumers are more sensitive to prices, while a smaller initial price elasticity coefficient indicates that consumers are less sensitive to price changes.

[0024] In one specific embodiment, step S2 involves inputting the inventory health index into a hyperbolic tangent function for nonlinear transformation to obtain a transformed value, including: The inventory health index is multiplied by the preset inventory response sensitivity parameter to obtain the sensitivity-adjusted inventory status value. The inventory status value is input into the hyperbolic tangent function for nonlinear mapping calculation. The hyperbolic tangent function maps the input value to a numerical range from negative 1 to positive 1. Numerical extraction is performed on the output of the hyperbolic tangent function to obtain a transformation value ranging from -1 to +1.

[0025] Specifically, the inventory response sensitivity parameter controls the sensitivity of the inventory health index to price elasticity modulation. When this parameter is large, small changes in the inventory status will cause a large elasticity modulation amplitude. When this parameter is small, a large change in the inventory status is required to produce a significant elasticity modulation effect. The inventory health index and the inventory response sensitivity parameter are multiplied to obtain the sensitivity-adjusted inventory status value. This multiplication operation realizes the scaling of the original inventory health index. When the inventory response sensitivity parameter is greater than 1, the numerical range of the inventory status value is expanded. When the inventory response sensitivity parameter is less than 1, the numerical range of the inventory status value is compressed. The sensitivity-adjusted inventory status value is used as the input parameter of the hyperbolic tangent function. The value of this parameter directly affects the mapping result of the hyperbolic tangent function.

[0026] The hyperbolic tangent function maps any real number input to a bounded interval from -1 to +1 through exponential and division operations. When the input value is positive, the hyperbolic tangent function outputs a positive value, which approaches 1 as the input value increases. When the input value is negative, the hyperbolic tangent function outputs a negative value, which approaches -1 as the input value decreases. When the input value is 0, the hyperbolic tangent function outputs 0. This function has an approximately linear mapping characteristic in the region where the input value is close to 0. In the region where the absolute value of the input value is large, the mapping curve tends to saturate. The nonlinear mapping characteristic of the hyperbolic tangent function compresses the extreme values ​​of inventory status to a bounded range, avoiding excessive influence of abnormal fluctuations in inventory status on the price elasticity coefficient. The numerical extraction process of the hyperbolic tangent function output results in a transformed value with a range of -1 to +1. This transformed value retains the positive and negative sign information and relative magnitude relationship of the inventory status, while limiting the numerical range to a fixed interval.

[0027] In one specific embodiment, step S2 involves multiplying the transformed value by the elastic modulation intensity coefficient and then adding 1 to obtain the modulation factor. Multiplying the modulation factor by the initial price elasticity coefficient includes: The transformed value is multiplied by the preset elastic modulation intensity coefficient to obtain the elastic modulation amount; The modulation factor is obtained by adding the elastic modulation amount to the value 1. The modulation factor is multiplied by the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with inventory health.

[0028] Specifically, the elasticity modulation strength coefficient controls the maximum modulation magnitude of the price elasticity coefficient by the inventory status. The value of this coefficient ranges from 0.2 to 0.8. When the elasticity modulation strength coefficient is 0.5, it means that the inventory status causes a maximum relative change of 50% in the price elasticity coefficient. The elasticity modulation amount is obtained by multiplying the transformation value and the elasticity modulation strength coefficient. Since the transformation value ranges from -1 to +1, the elasticity modulation amount ranges from the negative elasticity modulation strength coefficient to the positive elasticity modulation strength coefficient. When the transformation value is positive, the elasticity modulation amount is positive, indicating that the price elasticity needs to be enhanced. When the transformation value is negative, the elasticity modulation amount is negative, indicating that the price elasticity needs to be weakened. The modulation factor is obtained by adding the elasticity modulation amount to the value 1. This addition operation converts the elasticity modulation amount from an incremental form to a proportional form. The value of the modulation factor ranges from 1 minus the elasticity modulation strength coefficient to 1 plus the elasticity modulation strength coefficient. The modulation factor is always positive to ensure that subsequent multiplication operations will not change the sign of the price elasticity coefficient.

[0029] The multiplication of the modulation factor and the initial price elasticity coefficient enables dynamic adjustment of the price elasticity coefficient. When the modulation factor is greater than 1, the multiplication increases the price elasticity coefficient, indicating that consumers are more sensitive to prices under the current inventory state. When the modulation factor is less than 1, the multiplication decreases the price elasticity coefficient, indicating that consumers are less sensitive to prices under the current inventory state. When the modulation factor equals 1, the price elasticity coefficient remains unchanged from its initial value, indicating that the current inventory state is at a neutral level and does not produce a modulation effect. The price elasticity coefficient, which changes dynamically with the inventory health level, incorporates inventory status information into the demand forecasting model. Different inventory health indicators correspond to different price elasticity coefficient values. When the inventory health indicator increases, the price elasticity coefficient increases accordingly, and when the inventory health indicator decreases, the price elasticity coefficient decreases accordingly. This dynamic adjustment mechanism enables demand forecasting to reflect the impact of inventory constraints on consumer purchasing behavior.

[0030] In one specific embodiment, step S3 involves substituting the price elasticity coefficient as a variable parameter into the demand calculation formula to predict the quantity demanded, including: The demand calculation formula is constructed by multiplying the price variable by a negative power by the basic demand scale parameter. The absolute value of the negative power is the price elasticity coefficient. The price elasticity coefficient, which changes dynamically with inventory health, is used as the current value of the price elasticity coefficient and substituted into the demand calculation formula. Substitute the price variable to be optimized into the demand calculation formula, and calculate the predicted demand value through exponentiation and multiplication operations. By associating demand forecasts with inventory health indicators, we can obtain demand forecast results that are correlated with inventory status.

[0031] Specifically, the design of using negative powers of the price variable in the demand calculation formula ensures that price and quantity demanded move in opposite directions. When the price increases, the result of the negative power operation decreases, leading to a decrease in quantity demanded; when the price decreases, the result of the negative power operation increases, leading to an increase in quantity demanded. The absolute value of the negative power is the price elasticity coefficient, which controls the strength of the response of quantity demanded to price changes. The larger the price elasticity coefficient, the greater the magnitude of the change in quantity demanded due to price changes. By substituting the price elasticity coefficient, which dynamically changes with inventory health, into the demand calculation formula instead of a fixed price elasticity coefficient, the parameters of the demand calculation formula are adjusted in real time according to the inventory status. Different price elasticity coefficients are used to calculate the demand under different inventory health indicators. A larger price elasticity coefficient is used when inventory is excessive, making demand forecasts more sensitive to price declines. A smaller price elasticity coefficient is used when inventory is tight, weakening the inhibitory effect of demand forecasts on price increases.

[0032] The price variable to be optimized serves as the input parameter for the demand calculation formula. During the optimization process, this price variable is used as a decision variable for iterative adjustment. The price variable is raised to a negative power to calculate the price's impact factor on demand based on the current price elasticity coefficient. This impact factor is multiplied by the basic demand scale parameter to obtain the predicted demand value. The magnitude of the predicted demand value is affected by both the price variable and the price elasticity coefficient. The process of associating the predicted demand value with the inventory health index establishes a correspondence between the demand forecast result and the inventory status. Each predicted demand value is attached with the label information of the current inventory health index. The demand forecast result associated with the inventory status includes two parts: the numerical prediction of the demand and the corresponding inventory status. This association and labeling mechanism allows the subsequent optimization process to trace the inventory status background when each demand forecast result is generated, ensuring the synergy between pricing decisions and inventory constraints.

[0033] In one specific embodiment, step S4, which involves establishing and solving a multi-period revenue optimization model based on demand forecast results, includes: The optimization time range is set as multiple consecutive decision cycles. Based on the demand forecast results, a discrete-time inventory dynamic evolution equation is constructed. The inventory dynamic evolution equation is calculated by subtracting the demand forecast value from the inventory of the previous cycle and adding the replenishment quantity to obtain the inventory of the current cycle. Sales revenue is calculated by multiplying the price variable by the demand forecast. The net profit for a single period is obtained by subtracting the purchase cost, inventory holding cost, stockout penalty cost, and inventory overflow cost from the sales revenue. The objective function of the multi-period return optimization model is constructed by summing the net returns of each single period across all decision-making periods. Under the constraints of upper and lower limits of inventory and upper limit of replenishment, the objective function is solved by a mixed integer linear programming algorithm to obtain the pricing strategy and replenishment plan for each decision cycle.

[0034] Specifically, the discrete-time inventory dynamic evolution equation describes the transfer pattern of inventory levels between consecutive decision-making cycles. The current cycle inventory level equals the previous cycle inventory level minus the demand forecast plus the replenishment quantity. This equation establishes a recursive relationship of inventory status in the time dimension. The demand forecast is deducted from the previous cycle inventory level as an inventory consumption item, and the replenishment quantity is added to the current cycle inventory level as an inventory replenishment item. The inventory level for each decision-making cycle is gradually derived from the initial inventory level through this recursive equation. Sales revenue is calculated by multiplying the price variable by the demand forecast. The procurement cost is the product of the demand forecast and the unit purchase price of the commodity. The inventory holding cost is the product of the current cycle inventory level and the unit inventory holding cost coefficient. The stockout penalty cost is generated when the inventory level is lower than the safety stock threshold. It is calculated by multiplying the difference between the safety stock threshold and the current inventory level by the stockout penalty cost coefficient. The inventory overflow cost is generated when the inventory level exceeds the maximum inventory capacity. It is calculated by multiplying the difference between the current inventory level and the maximum inventory capacity by the overflow handling cost coefficient. The net profit for a single cycle is the sales revenue minus the above four costs.

[0035] The objective function of the multi-period revenue optimization model is obtained by summing the net revenue of each single period across all decision periods. This objective function quantifies the overall economic benefit over the entire optimization timeframe. Inventory upper and lower bound constraints require that the inventory level in each decision period must be between the minimum inventory threshold and the maximum inventory capacity. The upper bound constraint for replenishment quantity limits the replenishment quantity in each decision period to not exceed the maximum replenishment capacity of the supply chain in a single period. The mixed-integer linear programming algorithm uses price and replenishment quantity as decision variables and traverses the discrete decision space using a branch-and-bound strategy to find the optimal solution. At each branch node, the algorithm solves a linear programming relaxation problem to obtain the upper bound of the objective function. When the upper bound of a branch is lower than the currently known optimal solution, that branch is pruned. After traversing the complete branch tree, a combination of decision variables that satisfies all constraints and maximizes the objective function is obtained. This combination corresponds to the pricing strategy and replenishment plan for each decision period. The pricing strategy includes the optimal selling price for each decision period, and the replenishment plan includes the optimal replenishment quantity for each decision period.

[0036] Figure 2This is a schematic diagram comparing the performance indicators of the present invention with those of the prior art in the embodiments of this application. This embodiment verifies the technical effectiveness of the method of the present invention through comparative experiments. Using existing technology performance indicators as a benchmark and normalized to 100, a comparative analysis is conducted from five dimensions: total revenue, inventory turnover rate, number of stockouts, number of inventory overflows, and price fluctuation amplitude. The present invention achieves a total revenue of 118.5, an improvement of 18.5% compared to existing technologies; an inventory turnover rate of 125.3, an improvement of 25.3% compared to existing technologies; a reduction in the number of stockouts to 35.2, a reduction of 64.8% compared to existing technologies; a reduction in the number of inventory overflows to 28.6, a reduction of 71.4% compared to existing technologies; and a reduction in price fluctuation amplitude to 62.4, a reduction of 37.6% compared to existing technologies. The improvement in total revenue and inventory turnover rate stems from the dynamic price elasticity coefficient's ability to adaptively adjust demand forecast accuracy based on inventory health indicators. The significant reduction in the number of stockouts and inventory overflows is due to the multi-period revenue optimization model introducing stockout penalty costs and overflow handling costs into the objective function to achieve precise control of inventory levels. The reduction in price fluctuation amplitude is due to the demand forecast results associated with inventory status, enabling pricing decisions to smoothly respond to inventory changes rather than drastic fluctuations.

[0037] Figure 3 This is a schematic diagram illustrating the dynamic adjustment process of the pricing strategy in this embodiment. This embodiment simulates and compares the execution process of the pricing strategy over 15 consecutive decision-making cycles. The horizontal axis represents the decision-making cycle number, and the vertical axis represents the sales price set in each cycle. The price curve of the method of this invention exhibits smooth fluctuations, with the price range concentrated between 85 and 95 yuan. The price curve of the prior art exhibits drastic fluctuations, with the price range distributed between 80 and 108 yuan. In the 4th to 5th decision-making cycles, the price of the prior art rose sharply from 80 yuan to 105 yuan, an increase of 31.25%. In the 8th to 9th decision-making cycles, the price of the prior art rose sharply from 85 yuan to 102 yuan, an increase of 20%. In contrast, the price change range of the method of this invention is controlled within 6 yuan and 7 yuan respectively in the same cycles. The reason for the smooth price fluctuations in the method of this invention is that the dynamic price elasticity coefficient achieves a gradual response of the pricing decision to changes in inventory status through continuous modulation of the inventory health index. This avoids the overreaction of the pricing strategy when inventory levels change abruptly due to the static elasticity coefficient in the prior art. The smooth price curve reduces consumers' negative perception of price instability and improves the market acceptance of the pricing strategy.

[0038] The above describes the dynamic pricing collaborative optimization method for inventory constraints in the embodiments of this application. The following describes the dynamic pricing collaborative optimization system for inventory constraints in the embodiments of this application. One embodiment of the dynamic pricing collaborative optimization system for inventory constraints in the embodiments of this application includes: The acquisition module is used to acquire historical sales datasets, current inventory levels, safety stock thresholds, and maximum inventory capacity. It performs a division operation by taking the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. The fitting module is used to perform nonlinear regression fitting based on the price data and sales volume data in the historical sales dataset to obtain the initial price elasticity coefficient, input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value, multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor, and multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. The forecasting module is used to substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to forecast the demand quantity and obtain the demand forecast result related to the inventory status. The solution module is used to establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain pricing strategies and replenishment plans.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic pricing collaborative optimization method oriented towards inventory constraints, characterized in that, The method includes: Step S1: Obtain historical sales dataset, current inventory level, safety stock threshold, and maximum inventory capacity. Perform a division operation using the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. Step S2: Based on the price data and sales volume data in the historical sales dataset, perform nonlinear regression fitting to obtain the initial price elasticity coefficient. Input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value. Multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor. Multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. Step S3: Substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to predict the demand quantity and obtain the demand forecast result related to the inventory status. Step S4: Establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain the pricing strategy and replenishment plan.

2. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 1, characterized in that, Step S1 includes: Extract sales records from the sales system database within a preset historical time window. The sales records include time series labels, price series at the corresponding time, actual sales volume series, and inventory level series. Obtain the current real-time inventory level from the inventory management system, the safety stock threshold preset based on the physical storage space and product shelf life, and the maximum inventory capacity of the storage system. The real-time inventory level is subtracted from the safety stock threshold to obtain the safety margin of inventory, and the maximum inventory capacity is subtracted from the safety stock threshold to obtain the inventory capacity range. The inventory health index is obtained by dividing the inventory safety margin as the numerator and the inventory capacity range as the denominator.

3. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 1, characterized in that, Step S2, which involves performing a nonlinear regression fitting based on the price and sales volume data in the historical sales dataset to obtain the initial price elasticity coefficient, includes: Extract price sequences and actual sales volume sequences from the historical sales dataset as training sample pairs; A power function form of the basic demand expression is constructed. The basic demand expression is calculated by multiplying the price variable by a negative power by the basic demand scale parameter. The absolute value of the exponent of the negative power is the initial price elasticity coefficient. Substitute the price series and the actual sales volume series into the basic demand expression to calculate the squared error between the predicted sales volume and the actual sales volume. The basic demand scale parameter and the initial price elasticity coefficient are iteratively adjusted using the least squares method to minimize the sum of the squared errors, thus obtaining the initial price elasticity coefficient.

4. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 3, characterized in that, In step S2, the inventory health index is input into a hyperbolic tangent function for nonlinear transformation to obtain the transformed value, including: The inventory health index is multiplied by a preset inventory response sensitivity parameter to obtain the sensitivity-adjusted inventory status value. The inventory status value is input into the hyperbolic tangent function for nonlinear mapping calculation, and the hyperbolic tangent function maps the input value to a numerical range from negative 1 to positive 1. The output of the hyperbolic tangent function is numerically extracted to obtain a transformation value ranging from -1 to +1.

5. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 4, characterized in that, In step S2, the transformation value is multiplied by the elastic modulation intensity coefficient, and then 1 is added to obtain the modulation factor. The modulation factor is then multiplied by the initial price elasticity coefficient, including: The transformed value is multiplied by a preset elastic modulation intensity coefficient to obtain the elastic modulation amount; The modulation factor is obtained by adding the elastic modulation amount to the value 1. The modulation factor is multiplied by the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with inventory health.

6. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 1, characterized in that, Step S3 involves substituting the price elasticity coefficient as a variable parameter into the demand calculation formula to predict the quantity demanded, including: A demand calculation formula is constructed, which is calculated by multiplying the price variable by a negative power and the basic demand scale parameter. The absolute value of the negative power is the price elasticity coefficient. The price elasticity coefficient that dynamically changes with inventory health is substituted into the demand calculation formula as the current value of the price elasticity coefficient; Substitute the price variable to be optimized into the demand calculation formula, and calculate the predicted demand value through exponentiation and multiplication operations. The demand forecast value is associated with the inventory health index to obtain the demand forecast result associated with the inventory status.

7. The dynamic pricing collaborative optimization method oriented towards inventory constraints according to claim 6, characterized in that, Step S4, which involves establishing and solving a multi-period revenue optimization model based on the demand forecast results, includes: The optimization time range is set as multiple continuous decision-making cycles. Based on the demand forecast results, a discrete-time inventory dynamic evolution equation is constructed. The inventory dynamic evolution equation is calculated by subtracting the demand forecast value from the inventory of the previous cycle and then adding the replenishment quantity to obtain the inventory of the current cycle. Based on the demand forecast results, the price variable is multiplied by the demand forecast value to calculate the sales revenue. The purchase cost, inventory holding cost, stockout penalty cost and inventory overflow cost are subtracted from the sales revenue to obtain the net profit for a single period. The objective function of the multi-period return optimization model is constructed by summing the net returns of each single period across all decision-making periods. Under the constraints of upper and lower limits of inventory and upper limit of replenishment, the objective function is solved by a mixed integer linear programming algorithm to obtain the pricing strategy and replenishment plan for each decision cycle.

8. A dynamic pricing collaborative optimization system oriented towards inventory constraints, characterized in that, For implementing the inventory-constrained dynamic pricing collaborative optimization method as described in any one of claims 1-7, the inventory-constrained dynamic pricing collaborative optimization system comprises: The acquisition module is used to acquire historical sales datasets, current inventory levels, safety stock thresholds, and maximum inventory capacity. It performs a division operation by taking the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain the inventory health index. The fitting module is used to perform nonlinear regression fitting based on the price data and sales volume data in the historical sales dataset to obtain the initial price elasticity coefficient, input the inventory health index into the hyperbolic tangent function for nonlinear transformation to obtain the transformation value, multiply the transformation value with the elasticity modulation intensity coefficient and add 1 to obtain the modulation factor, and multiply the modulation factor with the initial price elasticity coefficient to obtain the price elasticity coefficient that dynamically changes with the inventory health. The forecasting module is used to substitute the price elasticity coefficient as a variable parameter into the demand calculation formula to forecast the demand quantity and obtain the demand forecast result related to the inventory status. The solution module is used to establish and solve a multi-cycle revenue optimization model based on the demand forecast results to obtain pricing strategies and replenishment plans.

9. The system according to claim 8, characterized in that, Obtain historical sales data, current inventory level, safety stock threshold, and maximum inventory capacity. Perform a division operation using the difference between the current inventory level and the safety stock threshold as the numerator and the difference between the maximum inventory capacity and the safety stock threshold as the denominator to obtain inventory health indicators, including: Extract sales records from the sales system database within a preset historical time window. The sales records include time series labels, price series at the corresponding time, actual sales volume series, and inventory level series. Obtain the current real-time inventory level from the inventory management system, the safety stock threshold preset based on the physical storage space and product shelf life, and the maximum inventory capacity of the storage system. The real-time inventory level is subtracted from the safety stock threshold to obtain the safety margin of inventory, and the maximum inventory capacity is subtracted from the safety stock threshold to obtain the inventory capacity range. The inventory health index is obtained by dividing the inventory safety margin as the numerator and the inventory capacity range as the denominator.

10. The system according to claim 9, characterized in that, The initial price elasticity coefficient is obtained by performing nonlinear regression fitting based on the price data and sales volume data in the historical sales dataset, including: Extract price sequences and actual sales volume sequences from the historical sales dataset as training sample pairs; A power function form of the basic demand expression is constructed. The basic demand expression is calculated by multiplying the price variable by a negative power by the basic demand scale parameter. The absolute value of the exponent of the negative power is the initial price elasticity coefficient. Substitute the price series and the actual sales volume series into the basic demand expression to calculate the squared error between the predicted sales volume and the actual sales volume. The basic demand scale parameter and the initial price elasticity coefficient are iteratively adjusted using the least squares method to minimize the sum of the squared errors, thus obtaining the initial price elasticity coefficient.

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