Adaptive inventory control method and device based on bayesian composite risk measure

Abstract

This application discloses an adaptive inventory control method and apparatus based on Bayesian composite risk measurement, relating to the fields of warehousing and supply chain management technology. Based on historical demand sequences, a hyperparameter vector representing the posterior probability distribution of unknown demand parameters is obtained. For each ordering action in the candidate ordering action set, based on current inventory data and the hyperparameter vector, combined with preset inventory state transition rules and cost functions, a two-layer risk measurement system is used to obtain the risk measurement value after executing each ordering action. The ordering action with the smallest risk measurement value in the candidate ordering action set is selected and output as the optimal ordering strategy and executed. The historical demand sequence is updated based on newly generated demand observation data in the next cycle, and the above steps are repeated to form a closed-loop adaptive control. This solves the problem that existing methods struggle to achieve an optimal balance between cost and risk in complex and volatile market environments.

Description

Technical Field

[0001] This application relates to the field of warehousing and supply chain management technology, and in particular to an adaptive inventory control method and apparatus based on Bayesian composite risk measurement. Background Technology

[0002] In modern supply chain and inventory management, a core challenge lies in balancing inventory holding costs with stockout losses, especially in the face of fluctuating demand. Traditional inventory control models, such as those based on economic order quantity (EOQ) or pricing models, typically rely on precisely known assumptions about demand distribution and its parameters. However, in real-world scenarios, particularly for new products or goods with rapidly changing demand patterns, the actual demand parameters are often unknown, requiring continuous learning through historical sales data.

[0003] While existing Bayesian adaptive MDP frameworks can learn demand parameters online through posterior distributions, their optimization objectives are usually still risk-neutral expected costs, failing to explicitly and quantitatively couple and manage the cognitive uncertainty in the parameter learning process with the decision-maker's risk preferences.

[0004] Therefore, existing methods struggle to simultaneously characterize and manage inherent randomness and cognitive uncertainty, making it difficult to achieve an optimal balance between cost and risk in complex and ever-changing market environments. Summary of the Invention

[0005] In this embodiment of the application, an adaptive inventory control method based on Bayesian composite risk measurement is provided, which solves the problem that existing methods are difficult to simultaneously characterize and manage inherent randomness and cognitive uncertainty, and are difficult to achieve the optimal balance between cost and risk in complex and ever-changing market environments.

[0006] In a first aspect, embodiments of this application provide an adaptive inventory control method based on Bayesian composite risk measurement. The method includes: step 101, acquiring current inventory data and historical demand sequences from the inventory system; step 102, based on the historical demand sequences, using Bayesian update rules to calculate and update the posterior probability distribution of unknown demand parameters, obtaining a hyperparameter vector characterizing the posterior probability distribution of unknown demand parameters; step 103, for each ordering action in the candidate ordering action set, based on the current inventory data and the hyperparameter vector, combined with preset inventory state transition rules and cost functions, obtaining a hyperparameter vector through a two-layer risk measurement system. Take the risk metric value after executing each ordering action; in the two-layer risk metric system, the inner layer risk metric is based on the unknown demand parameters corresponding to the hyperparameter vector, which characterizes the inherent randomness caused by demand fluctuations, and the outer layer risk metric is based on the posterior probability distribution represented by the hyperparameter vector, which characterizes the cognitive uncertainty caused by the estimation error of the demand parameters; in step 104, obtain the ordering action with the smallest risk metric value in the candidate ordering action set, output it as the optimal ordering strategy and execute it; after execution, enter the next cycle, update the historical demand sequence based on the newly generated demand observation data in this cycle, and repeat steps 102 to 104 to form a closed-loop adaptive control.

[0007] In one possible implementation, the step of calculating and updating the posterior probability distribution of the unknown demand parameter based on the historical demand sequence and using Bayesian update rules to obtain a hyperparameter vector representing the posterior probability distribution of the unknown demand parameter includes: defining the unknown demand parameter as the average demand rate. Its prior distribution is set to the Gamma distribution: ;in, This is the initial demand. Let be the initial observation period; assume that each demand quantity in the historical demand sequence... It satisfies conditional independence, and in Under the condition that it follows a Poisson distribution: ;in, For the first Actual demand in the period; based on the Gamma-Poisson conjugate property, after observing the historical demand sequence, The posterior probability distribution remains a Gamma distribution, and the hyperparameter vector representing the posterior probability distribution of the unknown demand parameters is: The update rule for the hyperparameter vector is: ;in, For the first The hyperparameter vector of the period, For the first The cumulative demand over the period For the first The number of observation periods in a given period For the first The updated hyperparameter vector after the period, For the first The cumulative demand over the period For the first The number of observation periods; the mean of the posterior probability distribution satisfies: ;in, For expectation operator, For the first At the start of the period The posterior probability distribution is given by the hyperparameter vector. Characterize it.

[0008] In one possible implementation, the cost function is expressed as: ;in, This is a single-period total cost function, representing the total cost at the current inventory level. The order quantity for this period is The actual demand is In the case of inventory system, the total cost incurred in the current period, Unit ordering cost Cost of holding per unit Denotes the positive part function, The cost of stockout is determined by the unit cost; the order quantity is used as the specific value for the ordering action.

[0009] In one possible implementation, the inventory state transition rule is as follows: ;in, For the first Inventory levels at the start of the period This is the inventory state transition function. For the first Inventory levels at the start of the period For the first Order volume for the period For the first Actual demand during the period.

[0010] In one possible implementation, the two-layer risk measurement system includes: inner layer risk measurement. As the first condition in the value at risk ;in, For the inner layer risk level, Inner layer confidence level The first condition is the risk value; strategy The inner layer risk value satisfies: In the formula For strategy Total cost of discounts As a discount factor, For strategy The inner-layer risk value is the result of applying the inner-layer risk measure to the total cost of conditional discounts. For strategy The total cost of the discount is a random variable. For the first The time discount factor for periodic costs For the first The single-period total cost function at the time of application; outer layer risk measurement For the second condition in the value at risk ;in, For the outer layer risk level, outer layer confidence level The second condition is the risk value; strategy The Bayesian compound risk value under the following conditions satisfies: The risk metric used for ordering strategy decisions is the Bayesian composite risk value, specifically the strategy... Bayesian compound risk value The measurement result corresponding to the minimum value; where, for The initial posterior probability distribution, For strategy Bayesian compound risk value; different strategies for different ordering actions. This results in different Bayesian compound risk values.

[0011] In one possible implementation, when the inner risk measurement for At that time, the inner-layer risk estimation process includes: for the single-step total cost sample Sort by numerical value from smallest to largest; among them... , For the first Under the sample of demand parameters, the first... The cost per period corresponding to each demand sample As a discount factor, For the state value function of the next period, For the first Under the sample of demand parameters, the first... The next period's inventory level corresponding to each demand sample. For the first Under the sample of demand parameters, the first... The hyperparameter vector for the next period corresponding to each demand sample. and Determined by current ordering activity; based on inner confidence level Determine its quantile index, and select the tail portion following the quantile index. A portion of the sample; the arithmetic mean of the selected tail samples is taken to obtain a given result. The inner layer risk value; among which, To obtain unknown demand parameters The first random sample drawn from the posterior probability distribution One sample value; the same Different ordering actions generate different To obtain different inner layer risk values.

[0012] In one possible implementation, when the outer risk measurement for The outer layer risk estimation process includes: collecting inner layer risk values ​​corresponding to each parameter sample; different inner layer risk value sets corresponding to different ordering actions; sorting the inner layer risk values ​​from smallest to largest, and then applying the results based on the outer layer confidence level. Determine its quantile index, and select the tail portion following the quantile index. A subset of samples; the arithmetic mean of the selected tail samples is used to obtain the outer risk value.

[0013] In one possible implementation, the candidate order action set is constructed by selecting the maximum order quantity. Order Step Construct action set : The candidate order action set is either a subset or the entire set of actions. Each element in the set corresponds to a specific order quantity.

[0014] Secondly, embodiments of this application provide an adaptive inventory control device based on Bayesian composite risk measurement. The device includes: an acquisition module for acquiring current inventory data and historical demand sequences from the inventory system; an update module for calculating and updating the posterior probability distribution of unknown demand parameters based on the historical demand sequence and using Bayesian update rules, to obtain a hyperparameter vector representing the posterior probability distribution of the unknown demand parameters; and an execution module for executing each ordering action in the candidate ordering action set, based on the current inventory data and the hyperparameter vector, combined with preset inventory state transition rules and a cost function, through a two-layer risk measurement system. Obtain the risk metric value after executing each ordering action; in the two-layer risk metric system, the inner layer risk metric is based on the unknown demand parameters corresponding to the hyperparameter vector, characterizing the inherent randomness caused by demand fluctuations, and the outer layer risk metric is based on the posterior probability distribution represented by the hyperparameter vector, characterizing the cognitive uncertainty caused by the estimation error of the demand parameters; the output module is used to obtain the ordering action with the smallest risk metric value in the candidate ordering action set, output it as the optimal ordering strategy and execute it; after execution, enter the next cycle, update the historical demand sequence based on the newly generated demand observation data in this cycle, and repeat steps 102 to 104 to form a closed-loop adaptive control.

[0015] The one or more technical solutions provided in this application embodiment have at least the following technical effects: This application embodiment provides an adaptive inventory control method based on Bayesian composite risk measurement. This method uses a two-layer risk measurement system to characterize the inherent randomness caused by demand fluctuations using the inner layer risk measurement and to characterize the cognitive uncertainty caused by the estimation error of demand parameters using the outer layer risk measurement. It can simultaneously quantify and distinguish the two types of uncertainty within a unified framework, avoiding the strategy bias caused by existing technologies that only consider a single source of risk. Based on historical demand sequences, Bayesian updates are performed in real time, dynamically adjusting the posterior distribution and hyperparameter vector of unknown demand parameters, enabling inventory decisions to continuously learn and iteratively optimize with actual demand data. It is particularly suitable for scenarios where demand parameters are unknown and demand patterns are constantly changing, and has strong adaptive capabilities. For each candidate ordering action, the corresponding risk measurement value is calculated, and the optimal ordering strategy is selected with the goal of minimizing risk. This ensures that order quantity decisions directly serve the goal of balancing cost and risk, avoiding blind ordering, overly conservative ordering, or extreme stockout risks. It solves the problem that existing inventory control methods are unable to simultaneously characterize and manage inherent randomness and cognitive uncertainty, and are unable to achieve the optimal balance between cost and risk in complex and ever-changing market environments. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of an adaptive inventory control method based on Bayesian composite risk measurement provided in this application embodiment.

[0018] Figure 2 This is a schematic diagram of an adaptive inventory control device based on Bayesian composite risk measurement, provided as an embodiment of this application.

[0019] Figure 3 This is a schematic diagram of an adaptive inventory control server based on Bayesian composite risk measurement, provided as an embodiment of this application. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0021] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0022] This application provides an adaptive inventory control method based on Bayesian composite risk measurement, such as... Figure 1 As shown, the method includes steps 101 to 104. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order for an adaptive inventory control method based on Bayesian composite risk measurement. Where the final result can be achieved, Figure 1 The steps shown can be performed in parallel or in reverse order.

[0023] Step 101: Obtain the current inventory data and historical demand sequence of the inventory system.

[0024] Specifically, the current inventory data is the amount of product inventory available for sale at the beginning of period t (i.e., physical inventory status), and the historical demand sequence is the set of actual observed demand in previous periods, used to support Bayesian updates of unknown demand parameters.

[0025] Step 102: Based on the historical demand sequence, the posterior probability distribution of the unknown demand parameters is calculated and updated using the Bayesian update rule to obtain the hyperparameter vector representing the posterior probability distribution of the unknown demand parameters.

[0026] Based on historical demand sequences, the posterior probability distribution of unknown demand parameters is calculated and updated using Bayesian update rules to obtain a hyperparameter vector representing the posterior probability distribution of unknown demand parameters, including the following:

[0027] Define the unknown demand parameter as the average demand rate. Its prior distribution is set to the Gamma distribution: .in, This is the initial demand. This represents the initial observation period.

[0028] Specifically, the initial demand corresponds to the shape parameter of the Gamma prior distribution, and the initial number of observation periods corresponds to the scale parameter of the Gamma prior distribution, used to quantify the initial decision-making process. The initial cognitive state.

[0029] Assuming each demand quantity in the historical demand sequence It satisfies conditional independence, and in Under the condition that it follows a Poisson distribution: .in, For the first Actual demand during the period.

[0030] Specifically, It is a non-negative integer random variable.

[0031] Based on the Gamma-Poisson conjugation property, after observing the historical demand sequence... The posterior probability distribution remains a Gamma distribution, and the hyperparameter vector representing the posterior probability distribution of the unknown demand parameters is: The update rule for the hyperparameter vector is: .in, For the first The hyperparameter vector of the period, For the first The cumulative demand over the period For the first The number of observation periods in a given period For the first The updated hyperparameter vector after the period, For the first The cumulative demand over the period For the first The number of observation periods.

[0032] Specifically, due to The posterior probability distribution remains a Gamma distribution, allowing for efficient updates without changing the distribution type. This posterior probability distribution is uniquely characterized by the hyperparameter vector. Cumulative demand over the period For the initial demand and the previous The sum of actual demand in each period corresponds to the shape parameter of the posterior Gamma distribution. Number of observation periods The initial observation period and the previous The sum of the actual number of observation periods corresponds to the scale parameter of the posterior Gamma distribution.

[0033] Based on the statistical properties of the Gamma distribution, the mean of the posterior probability distribution satisfies: .in, For expectation operator, For the first At the start of the period The posterior probability distribution is given by the hyperparameter vector. This is represented. Specifically, the mean is the value of the current cognitive state regarding... The optimal estimate.

[0034] Step 103: For each ordering action in the candidate ordering action set, based on the current inventory data and hyperparameter vector, and combined with preset inventory state transition rules and cost functions, obtain the risk measurement value after executing each ordering action through a two-layer risk measurement system. In the two-layer risk measurement system, the inner layer risk measurement is based on the unknown demand parameters corresponding to the hyperparameter vector, characterizing the inherent randomness caused by demand fluctuations; the outer layer risk measurement is based on the posterior probability distribution represented by the hyperparameter vector, characterizing the cognitive uncertainty caused by the estimation error of demand parameters.

[0035] The expression for the cost function is: .in, This is a single-period total cost function, representing the total cost at the current inventory level. The order quantity for this period is The actual demand is In the case of inventory system, the total cost incurred in the current period, Unit ordering cost Cost of holding per unit Denotes the positive part function, Penalty cost for stockouts per unit.

[0036] The order quantity is used as the specific value for the ordering action.

[0037] Specifically, A value greater than 0 indicates the unit cost related to ordering, purchasing, and transportation; it represents the fixed or amortized cost incurred for each product ordered. The quantity of products ordered from suppliers is determined during the decision-making stage, which directly affects the current ordering cost and subsequent inventory levels. A value greater than 0 covers unit cycle costs arising from inventory occupancy, working capital, and the risk of obsolescence and loss; this cost is only charged on remaining inventory at the end of the period. Positive part function. Equivalent to This is used to filter non-negative values ​​to avoid interference from negative inventory or negative stockouts in cost calculations.

[0038] The inventory status transfer rules are as follows: .in, For the first Inventory levels at the start of the period This is the inventory state transition function. For the first Inventory levels at the start of the period For the first Order volume for the period For the first Actual demand during the period.

[0039] The specific implementation of the two-tier risk measurement system includes the following:

[0040] Inner layer risk measurement As the first condition in the value at risk .in, For the inner layer risk level, Inner layer confidence level The first condition is the risk value.

[0041] Specifically, Used to measure the tail extreme cost risk caused by random fluctuations in demand when given demand parameters.

[0042] Strategy The inner layer risk value satisfies: In the formula For strategy Total cost of discounts As a discount factor, For strategy The inner-layer risk value is the result of applying the inner-layer risk measure to the total cost of conditional discounts. For strategy The total cost of the discount is a random variable. For the first The time discount factor for periodic costs For the first The total cost function for a single period.

[0043] Specifically, the discount factor is used to assign time weights to costs in different periods. The closer it is to 1, the more emphasis is placed on long-term costs.

[0044] Outer risk measurement For the second condition in the value at risk .in, For the outer layer risk level, outer layer confidence level The second condition is the risk value.

[0045] Strategy The Bayesian compound risk value under the following conditions satisfies: The risk metric used for ordering strategy decisions is the Bayesian composite risk value, specifically the strategy... Bayesian compound risk value The measurement result corresponding to the minimum value. Wherein, for The initial posterior probability distribution, For strategy The Bayesian compound risk value.

[0046] Different ordering actions require different strategies. This results in different Bayesian compound risk values.

[0047] Specifically, strategy Bayesian compound risk value The minimum value corresponds to the optimal inventory strategy.

[0048] When inner layer risk measurement for The inner-layer risk estimation process includes the following:

[0049] For single-step total cost samples Sort by numerical value from smallest to largest. , For the first Under the sample of demand parameters, the first... The cost per period corresponding to each demand sample As a discount factor, For the state value function of the next period, For the first Under the sample of demand parameters, the first... The next period's inventory level corresponding to each demand sample. For the first Under the sample of demand parameters, the first... The hyperparameter vector for the next period corresponding to each demand sample. and Determined by the current ordering action.

[0050] Specifically, It is determined by the cost function. It is determined by the inventory status transfer rules.

[0051] Based on inner layer confidence level Determine its quantile index, and select the tail portion following the quantile index. Partial sample.

[0052] Specifically, statistics The total number of inner-layer requirement samples generated under each requirement parameter sample is denoted as . That is, the total number of samples of total cost per step, based on the inner confidence level. The quantile index is determined by rounding down to the nearest integer. Specifically, a "partial sample" can refer to all samples from the next quantile index to the last quantile index.

[0053] Take the arithmetic mean of the selected tail samples to obtain the given... The inner layer risk value. Among them, To obtain unknown demand parameters The first random sample drawn from the posterior probability distribution Each sample value.

[0054] same Different ordering actions generate different To obtain different inner layer risk values.

[0055] When outer layer risk measurement for At that time, the outer layer risk estimation process includes the following:

[0056] Collect the inner-layer risk values ​​corresponding to each parameter sample. Different ordering actions correspond to different sets of inner-layer risk values.

[0057] The inner layer risk values ​​are sorted from smallest to largest, based on the outer layer confidence level. Determine its quantile index, and select the tail portion following the quantile index. Partial sample.

[0058] The outer risk value is obtained by taking the arithmetic mean of the selected tail samples.

[0059] Step 104: Obtain the ordering action with the lowest risk metric value from the candidate ordering action set, output it as the optimal ordering strategy, and execute it. After execution, proceed to the next cycle, update the historical demand sequence based on the newly generated demand observation data in this cycle, and repeat steps 102 to 104 to form a closed-loop adaptive control.

[0060] The candidate order action set is constructed by selecting the largest order quantity. Order Step Construct action set : .

[0061] Specifically, the maximum order quantity can be determined based on actual scenarios such as inventory system storage capacity and capital constraints.

[0062] The candidate order action set can be a subset or the entire action set. Each element in the set corresponds to a specific order quantity.

[0063] This application also includes a comparison method, as detailed below.

[0064] Bayesian Composite Risk Measure (BCR-MDP)

[0065] Risk-neutral Bayesian MDP (B-MDP): , This refers to the traditional Bayesian adaptive MDP. Among them, For expectation operators.

[0066] Static CVaR-MDP: Assumptions are known Using a single layer The conditional value at risk (with a single-layer confidence level of 0.7) is used as the objective for optimization, while parameter learning is ignored.

[0067] Strategy: A classic heuristic strategy, when inventory is below... Restocking Here and The inventory quantity is estimated using historical data.

[0068] Evaluation metrics: long-term average cost per period, 95th percentile of cost distribution (reflecting tail risk), and cumulative number of stockouts.

[0069] Results after the experiment: After averaging 100 independent simulations, the results are shown in Table 1.

[0070] Table 1 Comparison of results after averaging 100 independent simulation runs

[0071]

[0072] Analysis of the data comparison results in Table 1 shows that the Bayesian composite risk measure BCR-MDP of this application achieved the lowest average cost, indicating that Bayesian learning accurately approximates the real needs, and its risk-averse optimization objective effectively avoids high-cost events, resulting in the best overall benefits in the long run.

[0073] The cost 95th percentile of this application is significantly lower than that of the risk-neutral Bayesian B-MDP, indicating that it successfully controls tail risk. Although it is slightly higher than the static CVaR-MDP (theoretical lower limit) with known true parameters, this is a necessary and controllable cost for learning unknown parameters.

[0074] and Compared with other strategies, this application demonstrates significant advantages in all metrics, reflecting the superiority of model-based optimization methods.

[0075] In summary, this application successfully achieved adaptive inventory control based on risk perception in an environment with unknown demand parameters through a Bayesian composite risk measurement framework. While ensuring long-term average performance, it effectively manages extreme risks and has good practical value.

[0076] This application also provides an adaptive inventory control device 200 based on Bayesian composite risk measurement, such as... Figure 2 As shown, the device includes: an acquisition module 201, an update module 202, an execution module 203, and an output module 204.

[0077] The acquisition module 201 is used to acquire the current inventory data of the inventory system, as well as the historical demand sequence.

[0078] The update module 202 is used to calculate and update the posterior probability distribution of unknown demand parameters based on historical demand sequences and using Bayesian update rules, so as to obtain a hyperparameter vector representing the posterior probability distribution of unknown demand parameters.

[0079] The execution module 203 is used to obtain the risk measurement value after executing each ordering action in the candidate ordering action set, based on the current inventory data and hyperparameter vector, combined with preset inventory state transition rules and cost functions, through a two-layer risk measurement system. In the two-layer risk measurement system, the inner layer risk measurement is based on the unknown demand parameters corresponding to the hyperparameter vector, characterizing the inherent randomness caused by demand fluctuations, while the outer layer risk measurement is based on the posterior probability distribution represented by the hyperparameter vector, characterizing the cognitive uncertainty caused by the estimation error of demand parameters.

[0080] Output module 204 is used to obtain the ordering action with the smallest risk metric value from the candidate ordering action set, output it as the optimal ordering strategy and execute it. After execution, the next cycle begins, and the historical demand sequence is updated based on the newly generated demand observation data in this cycle. Steps 102 to 104 are repeated to form a closed-loop adaptive control.

[0081] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0082] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0083] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, for example, as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module implementing the method or a structure within a hardware component.

[0084] like Figure 3 As shown in the figure, this application embodiment also provides an adaptive inventory control server based on Bayesian composite risk measurement, including a memory 301 and a processor 302; the memory 301 is used to store computer-executable instructions; the processor 302 is used to execute computer-executable instructions to implement the adaptive inventory control method based on Bayesian composite risk measurement described above in this application embodiment.

[0085] This application also provides a computer-readable storage medium storing executable instructions. When a computer executes the executable instructions, it can implement the adaptive inventory control method based on Bayesian composite risk measurement described above in this application.

[0086] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the embodiments of this application.

[0087] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations.

[0088] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application 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 or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. An adaptive inventory control method based on Bayesian composite risk measurement, characterized in that, include: Step 101: Obtain the current inventory data and historical demand sequence from the inventory system; Step 102: Based on the historical demand sequence, the posterior probability distribution of the unknown demand parameters is calculated and updated using the Bayesian update rule to obtain the hyperparameter vector representing the posterior probability distribution of the unknown demand parameters. Step 103: For each ordering action in the candidate ordering action set, based on the current inventory data and hyperparameter vector, and combined with the preset inventory status transition rules and cost function, obtain the risk measurement value after executing each ordering action through a two-layer risk measurement system. In the two-layer risk measurement system, the inner layer risk measurement is based on the unknown demand parameters corresponding to the hyperparameter vector, which characterizes the inherent randomness caused by demand fluctuations, while the outer layer risk measurement is based on the posterior probability distribution represented by the hyperparameter vector, which characterizes the cognitive uncertainty caused by the estimation error of the demand parameters. Step 104: Obtain the ordering action with the smallest risk metric value from the candidate ordering action set, output it as the optimal ordering strategy and execute it; after execution, enter the next cycle, update the historical demand sequence based on the newly generated demand observation data in this cycle, and repeat steps 102 to 104 to form a closed-loop adaptive control. The specific implementation of the two-tier risk measurement system includes: Inner layer risk measurement As the first condition in the value at risk ;in, For the inner layer risk level, Inner layer confidence level The first condition is the value at risk; Strategy The inner layer risk value satisfies: In the formula For strategy Total cost of discounts As a discount factor, For strategy The inner-layer risk value is the result of applying the inner-layer risk measure to the total cost of conditional discounts. For strategy The total cost of the discount is a random variable. For the first The time discount factor for periodic costs For the first The total cost function for a single period at that time; Outer risk measurement For the second condition in the value at risk ;in, For the outer layer risk level, outer layer confidence level The second condition is the value at risk; Strategy The Bayesian compound risk value under the following conditions satisfies: The risk metric used for ordering strategy decisions is the Bayesian composite risk value, specifically the strategy... Bayesian compound risk value The measurement result corresponding to the minimum value; where, for The initial posterior probability distribution, For strategy Bayesian compound risk value; Different ordering actions correspond to different strategies , resulting in different Bayesian composite risk values.

2. The Bayesian composite risk metric based adaptive inventory control method of claim 1, wherein, The process involves calculating and updating the posterior probability distribution of unknown demand parameters based on historical demand sequences and using Bayesian update rules to obtain a hyperparameter vector representing the posterior probability distribution of the unknown demand parameters, including: Define the unknown demand parameter as the average demand rate. Its prior distribution is set to the Gamma distribution: ;in, This is the initial demand. This represents the initial observation period. Assuming each demand quantity in the historical demand sequence It satisfies conditional independence, and in Under the condition that it follows a Poisson distribution: ;in, For the first Actual demand during the period; Based on the Gamma-Poisson conjugation property, after observing the historical demand sequence... The posterior probability distribution remains a Gamma distribution, and the hyperparameter vector representing the posterior probability distribution of the unknown demand parameters is: The update rule for the hyperparameter vector is as follows: ;in, For the first The hyperparameter vector of the period, For the first The cumulative demand over the period For the first The number of observation periods in a given period For the first The updated hyperparameter vector after the period, For the first The cumulative demand over the period For the first The number of observation periods; The mean of the posterior probability distribution satisfies: ;in, For expectation operator, For the first At the start of the period The posterior probability distribution is given by the hyperparameter vector. Characterize it.

3. The Bayesian composite risk metric based adaptive inventory control method of claim 2, wherein, The expression for the cost function is: ;in, This is a single-period total cost function, representing the total cost at the current inventory level. The order quantity for this period is The actual demand is In the case of inventory system, the total cost incurred in the current period, Unit ordering cost Cost of holding per unit Denotes the positive part function, Penalty cost for stockouts per unit; The order quantity is used as the specific value for the ordering action.

4. The Bayesian composite risk metric based adaptive inventory control method of claim 3, wherein, The inventory status transfer rules are as follows: ;in, For the first Inventory levels at the start of the period This is the inventory state transition function. For the first Inventory levels at the start of the period For the first Order volume for the period For the first Actual demand during the period.

5. The Bayesian composite risk metric based adaptive inventory control method of claim 4, wherein, When the inner layer risk metric is , the inner layer risk estimation process comprises: For single-step total cost samples Sort by numerical value from smallest to largest; among them... , For the first Under the sample of demand parameters, the first... The cost per period corresponding to each demand sample As a discount factor, For the state value function of the next period, For the first Under the sample of demand parameters, the first... The next period's inventory level corresponding to each demand sample. For the first Under the sample of demand parameters, the first... The hyperparameter vector for the next period corresponding to each demand sample. and Determined by the current ordering action; Based on inner layer confidence level Determine its quantile index, and select the tail portion following the quantile index. Partial sample; Take the arithmetic mean of the selected tail samples to obtain the given... The inner layer risk value; among which, To obtain unknown demand parameters The first random sample drawn from the posterior probability distribution Each sample value; The same The different ordering actions generate different to obtain different inner layer risk values.

6. The Bayesian composite risk metric based adaptive inventory control method of claim 5, wherein, When the outer layer risk metric is , the outer layer risk estimation process comprises: Collect the inner-layer risk values ​​corresponding to each parameter sample; different ordering actions correspond to different sets of inner-layer risk values; The inner layer risk values ​​are sorted from smallest to largest, based on the outer layer confidence level. Determine its quantile index, and select the tail portion following the quantile index. Partial sample; The outer risk value is obtained by taking the arithmetic mean of the selected tail samples.

7. The adaptive inventory control method based on Bayesian composite risk measurement according to claim 6, characterized in that, The candidate order action set is constructed as follows: Select the maximum order quantity Order Step Construct action set : ; The candidate order action set can be a subset or the entire action set. Each element in the set corresponds to a specific order quantity.

8. An adaptive inventory control apparatus based on Bayesian composite risk measure, characterized by, The device performs the method as described in any one of claims 1 to 7, including: The acquisition module is used to acquire the current inventory data and historical demand sequences of the inventory system; The update module is used to calculate and update the posterior probability distribution of unknown demand parameters based on historical demand sequences and using Bayesian update rules, so as to obtain a hyperparameter vector representing the posterior probability distribution of unknown demand parameters. The execution module is used to obtain the risk measurement value after executing each ordering action in the candidate ordering action set, based on the current inventory data and hyperparameter vector, combined with the preset inventory state transition rules and cost function, through a two-layer risk measurement system. In the two-layer risk measurement system, the inner layer risk measurement is based on the unknown demand parameters corresponding to the hyperparameter vector to characterize the inherent randomness caused by demand fluctuations, and the outer layer risk measurement is based on the posterior probability distribution represented by the hyperparameter vector to characterize the cognitive uncertainty caused by the estimation error of demand parameters. The output module is used to obtain the ordering action with the smallest risk metric value in the candidate ordering action set, output it as the optimal ordering strategy and execute it; after execution, it enters the next cycle, updates the historical demand sequence based on the newly generated demand observation data in the cycle, and repeats steps 102 to 104 to form a closed-loop adaptive control. The specific implementation of the two-tier risk measurement system includes: Inner layer risk measurement As the first condition in the value at risk ;in, For the inner layer risk level, Inner layer confidence level The first condition is the value at risk; Strategy The inner layer risk value satisfies: In the formula For strategy Total cost of discounts As a discount factor, For strategy The inner-layer risk value is the result of applying the inner-layer risk measure to the total cost of conditional discounts. For strategy The total cost of the discount is a random variable. For the first The time discount factor for periodic costs For the first The total cost function for a single period at that time; Outer risk measurement For the second condition in the value at risk ;in, For the outer layer risk level, outer layer confidence level The second condition is the value at risk; Strategy The Bayesian compound risk value under the following conditions satisfies: The risk metric used for ordering strategy decisions is the Bayesian composite risk value, specifically the strategy... Bayesian compound risk value The measurement result corresponding to the minimum value; where, for The initial posterior probability distribution, For strategy Bayesian compound risk value; Different ordering actions require different strategies. This results in different Bayesian compound risk values.

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