An efficient key factor screening method for multi-echelon supply chain inventory system

Abstract

The application provides a high-efficiency key factor screening method for a multi-level supply chain inventory system, extracts controllable factors of the multi-level supply chain inventory system, performs key factor screening, and stores into a FIFO screening queue; extracts a current group factor G from the FIFO screening queue, determines a required increased design point, and collects corresponding system performance response observation values; uses a Bootstrap method to expand a sample size of the response observation values, and tests effect significance of the current group factor; if the effect is significant, judges a number of elements contained in the current group factor; if the number of elements contained in the current group factor is greater than 1, branches the current group factor into two subgroups, and sequentially puts the two subgroups into the FIFO screening queue; if the current group factor only contains 1 element, puts the element into an important factor set I, otherwise, deletes the current group factor. The application can screen important factors in a large-scale factor screening problem by using only a small amount of samples, and has good robustness.

Description

Technical Field

[0001] This invention belongs to the field of factor screening technology, specifically relating to an efficient key factor screening method for multi-level supply chain inventory systems. Background Technology

[0002] Inventory management is a crucial component of supply chain management, acting as a buffer between supply and demand and eliminating the time lag between production and demand. Simply put, inventory management considers when and how much replenishment to order at each node in the supply chain, as well as issues such as safety stock settings, average inventory levels, service levels, and costs. Its goal is to find the optimal balance between inventory investment and service levels. While single-stage inventory management strategies are classic and fundamental, supply chain problems often involve multi-stage inventory management. Multi-stage inventory management involves a large number of controllable factors, and the complexity of inventory, transportation, and the internal relationships between each node makes it difficult for classic analytical methods to identify bottlenecks in multi-level supply chain inventory management.

[0003] In fact, key factor screening, as the first step in experimental design, has been widely used in the identification of key factors in simulation systems. It can effectively simplify the system and extract controllable factors that can truly affect system performance. However, for complex multi-level supply chain inventory systems, how to minimize experimental costs and improve screening efficiency is a significant challenge. Furthermore, the data heterogeneity caused by system heterogeneity results in a small sample size for factor screening, placing higher demands on its efficiency. Therefore, this invention uses a sequential branching method to address the factor screening problem in multi-level supply chain systems, specifically overcoming the following two technical difficulties: First, classical factor screening methods are based on the fundamental assumption that the response follows a normal distribution. In real-world cases, a small sample size makes it difficult to verify the distribution type, thus rendering the assumption of a normal distribution in classical factor screening methods unreasonable. Second, classical factor screening methods are not applicable to situations where the distribution type is unknown, making it difficult to obtain factor effect estimates and construct corresponding hypothesis testing processes. Summary of the Invention

[0004] The purpose of this invention is to provide a key factor screening method for multi-level supply chain inventory systems, in order to solve the problem of how to infer overall characteristics using small samples and effectively test the significance of factor effects.

[0005] The technical solution to achieve the purpose of this invention is as follows: Expanding the sample size using the bootstrap method and combining it with nonparametric estimation to infer the overall distribution characteristics; improving the utility of factor effect testing by correcting the bias of the statistics; specifically including the following steps:

[0006] Step 1: Extract controllable factors from the multi-level supply chain inventory system, perform key factor screening, and store them in the FIFO screening queue.

[0007] Step 2: Extract the current group factor G from the FIFO screening queue, determine the design points to be added, and collect the corresponding system performance response observations, such as average profit and service level within the period.

[0008] Step 3: Use the Bootstrap method to expand the original sample size (i.e., response observations) and test the significance of the effect of the current group factor. If the effect is significant, proceed to step 4; if the effect is not significant, proceed to step 5.

[0009] Step 4: Determine the number of elements contained in the current group factor. If the number of elements contained in the current group factor is greater than 1, then branch it into two subgroups and put the two subgroups into the FIFO filtering queue in order. If the current group factor contains only 1 element, then put it into the set I of important factors and go to step 6.

[0010] Step 5: Delete the current group factor and proceed to step 6;

[0011] Step 6: Determine if the FIFO filtering queue is not empty. If the FIFO filtering queue is not empty, proceed to step 2 for the next loop. If the FIFO filtering queue is empty, terminate the filtering process. The elements contained in set I are the obtained important factors.

[0012] Further, step 1 is specifically implemented as follows: Initialize key factor screening for the extracted multiple controllable factors: ① Extract controllable factors from the multi-level supply chain inventory system, determine the value range of all controllable factors, and encode the experimental levels of all controllable factors so that the low and high levels of the coded controllable factors are 0 and 1 respectively; ② Determine the direction and magnitude of the system performance change when each controllable factor is adjusted from a low level to a high level; ③ Adjust the experimental levels of the controllable factors so that when each controllable factor individually switches from a low level to a high level, the system response increases; ④ Arrange all controllable factors in order of effect value from smallest to largest or from largest to smallest to obtain the initialized group factors {x1,…,x}. k} and put it into the first-in-first-out (FIFO) filtering queue.

[0013] Furthermore, step 2 is specifically implemented as follows: Determine the required additional design points based on the current group factors, and collect the corresponding response observations. ① Assume the current group factors are represented as... Then, two new design points x(k0-1) and x(k1) need to be added. x(k0-1) represents the first k0-1 factors set to a high level, and the remaining factors set to a low level. Similarly, x(k1) represents the first k1 factors set to a high level, and the remaining factors set to a low level. ② Collect n response observations (i.e., original samples) at the two design points x(k0-1) and x(k1), respectively, denoted as y. i (k0-1) and y i (k1), where i = 1, ..., n.

[0014] Furthermore, step 3 is performed as follows: The Bootstrap method is used to expand the original sample size, and the significance of the current group factor is tested. ① Using the original sample y i (k0-1) and y i (k1) Construct two empirical distribution functions respectively, expressed as follows: and ②From two empirical distribution functions and A Bootstrap sample of size n is drawn from each sample, and the mean is calculated as the location parameter estimate, denoted as . and ③ Repeat the resampling parameter estimation process in ② B times to obtain the group factor location parameter estimates for the two groups based on the Bootstrap samples. and Where r = 1, ..., B; ④ Based on the group factor position effect estimates obtained above, a test statistic is constructed by combining robust statistics and bias correction ideas to test the significance of the current group factor; ⑤ Since the test statistic T in ④ R Multiplying by a constant, the response asymptotically follows a standard normal distribution. The statistic T is then calculated using the observed response data. R Then compare it with the quantile of the standard normal distribution, or calculate its p-value and compare it with the significance level to determine the significance of the current group factor.

[0015] Bootstrap Hypothesis Testing (RBT) Based on Robust Statistics

[0016] The position parameter estimates for the Bootstrap samples are corrected separately. The deviation correction is expressed as:

[0017]

[0018] in,

[0019]

[0020] and Similarly, location parameter estimators The deviation correction is expressed as:

[0021]

[0022] in,

[0023]

[0024] and Then, the two sets of corrected statistics are subtracted in pairs, and the classic student t-statistic is improved using robust statistics such as the median and the absolute deviation of the median:

[0025]

[0026] in,

[0027]

[0028] and

[0029]

[0030] because

[0031]

[0032] That is, using T R The asymptoticity of the statistic tests the difference in the distribution of the system response at two design points, where the constant is used.

[0033] Further, step 4 is implemented as follows: For the current group factors with significant effects in step 3, determine whether a branching step is needed and process its subgroups by judging the number of elements contained in the important current group factors. ① Calculate the number of factors contained in the current group factors, expressed as m = k1 - k0 + 1; ② If m > 1, divide the current group factors into two subgroups and put the two subgroups into the FIFO screening queue in order. The specific grouping rule is: put the first m1 factors into the first subgroup in the current order, and the remaining m-m1 factors into the second subgroup; where m1 is the largest integer power of 2 less than m. For example, when m = 18, m1 = 16; when m = 16, m1 = 8; ③ If m = 1, put the current group into the set I of important factors.

[0034] Furthermore, step 5 is performed as follows: For factors in the current group whose effects are not significant in step 3, the deletion operation is performed directly, saving a lot of experimental costs.

[0035] Furthermore, step 6 is performed as follows: The decision to terminate the factor selection process depends on whether the FIFO queue is not empty. If the FIFO queue is not empty, proceed to step 2 for the next iteration; if the FIFO queue is empty, terminate the selection process. At this point, the elements contained in set I are the obtained key factors.

[0036] Compared with existing technologies, the present invention has the following significant advantages: 1) It weakens the assumption of normal distribution of response in the classic sequential branching factor screening method, and enhances the applicability of the sequential branching factor screening method; 2) It adopts a bootstrap method to expand the sample size and integrates it into the effect significance test of group factors, so that the improved factor screening method is widely applicable to key factor screening problems with small sample sizes; 3) It can effectively distinguish between unimportant factors and important factors, effectively and efficiently identify important factors, and has good robustness to uncertain response distributions. Attached Figure Description

[0037] Figure 1 Overall Flowchart of the Implementation of this Invention

[0038] Figure 2 Trends in non-zero factor screening results of four factor screening methods Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0040] This invention targets multi-level supply chain inventory systems and employs a sequential branching method. By combining the Bootstrap method to expand the sample size, it integrates bias correction and robust statistical techniques for the significance testing of factor effects. This enables the screening of key factors in multi-level supply chain inventory systems under conditions of small samples and uncertain response distribution types.

[0041] This invention assumes that the supply chain inventory system contains a large number of factors, and only a small portion of them truly have a significant impact on system performance (sparse effect). Specifically, it is generally assumed that the relationship between inventory system performance (e.g., revenue) and controllable factors can be described by the following first-order polynomial:

[0042]

[0043] Where y represents the response variable (i.e., the system performance of interest, such as average periodic revenue, service level, etc.), x j (j = 1, ..., k_ represents the encoding level of the j-th controllable factor, taking values ​​of 0 or 1; β)j (j=1,…,k) represents the position effect coefficient of the j-th controllable factor, and satisfies β j ≥0; ε is the error term, representing a random variable with an unknown distribution and a mean of 0, and k represents the number of all controllable factors in the system.

[0044] Based on this, the present invention provides a factor effect testing method that combines robust statistics and bias correction for screening key factors in multi-level supply chain inventory systems. The implementation process is as follows: Figure 1 As shown, the specific steps are as follows:

[0045] Step 1: Extract controllable factors from the multi-level supply chain inventory system and initialize key factor screening. The specific steps are as follows:

[0046] ① Based on the characteristics of the inventory system, extract all controllable factors that can be set by the experimenter. For example, based on the selected (s,S) inventory strategy, the lower and upper limits of inventory at each level of the supply chain system, as well as the initial inventory level; the lead time for each type (unit) of customer; the maximum capacity and number of employees of the distribution center; and transportation-related parameters such as the number and speed of transportation vehicles. Let k represent the number of extracted controllable factors. Determine the value range of all controllable factors based on existing resource allocation information. For example, the existing scheme can generally be used as a reference, and the design value of the controllable factors can be varied by 20% above and below as the test area. Assume that the value range of the controllable factors is represented as [x l ,x u To determine the range of values ​​for all controllable factors, the controllable factors need to be standardized (encoded) so that the standardized values ​​are within the range of [0,1]. Therefore, the low and high levels of the coded controllable factors are 0 and 1, respectively.

[0047] ② Based on prior knowledge or previous experimental data, the testers determine the direction and magnitude of the system response value change when each controllable factor is adjusted from a low level to a high level. For example, the initial inventory of a distribution center generally has a small impact on the profit level of the entire cycle; raising the lower limit of the distribution center's inventory helps reduce losses caused by stockouts, thereby helping to increase profits, while raising the upper limit of inventory may increase inventory costs, leading to a decrease in profits.

[0048] ③ Adjust the low and high levels of the controllable factors so that the system response increases when each controllable factor individually switches from a low level to a high level. Furthermore, for controllable factors that bring a response gain when switched from 0 to 1, there is no need to change the encoding level; for example, the lower limit of inventory in the distribution center. Conversely, for controllable factors that cause a decrease in response value when switched from 0 to 1, the correspondence between the original level and the encoding level needs to be changed; for example, the upper limit of inventory in the distribution center. This part of the operation is to ensure that in the first-order polynomial model established by the encoded controllable factors and the response, the effect coefficient of each controllable factor is non-negative (i.e., β). j ≥0, j=1,…,k), thereby avoiding the effect cancellation caused by grouping and group effect estimation during the factor screening process.

[0049] ④ Based on prior knowledge or previous relevant research, arrange all controllable factors in order of effect size from smallest to largest or from largest to smallest, to obtain the initial group factors {x1,…,x}. k} and place them into a first-in, first-out (FIFO) screening queue. Controllable factors can be classified according to the structure and function of the inventory system, and factors of the same type should be grouped together as much as possible. For example, it is generally believed that controllable factors related to transportation have a lower impact on profits than controllable factors related to inventory strategies.

[0050] Step 2: According to the FIFO rule, extract a group from the screening queue as the current group factor G, select the corresponding design point, and collect response observations. The specific steps are as follows:

[0051] Determine the required additional design points based on the current group factors and collect the corresponding response observations. ① Assume the current group factors are expressed as follows: Then two new design points x(k0-1) and x(k1) need to be added. Here, x(k0-1) represents the first k0-1 factors set to high level (after encoding), and the remaining factors set to low level (after encoding). Similarly, x(k1) represents the first k1 factors set to high level (after encoding), and the remaining factors set to low level (after encoding). ② Collect n original sample points at the two design points x(k0-1) and x(k1) respectively, denoted as y. i (k0-1) and y i (k1), where i = 1, ..., n.

[0052] Step 3: Test the significance of the factor effect in the current group. If the effect is significant, proceed to step 4; otherwise, proceed to step 5. This is a judgmental step, which can lead to two different steps depending on the significance test results; therefore, it is the core step of this invention. First, the Bootstrap method is used to expand the sample size. Then, bias correction and robust statistical methods are combined to construct a statistic for testing the factor effect. The specific steps are as follows:

[0053] ① Using the original sample y i (k0-1) and y i (k1) Construct two empirical distribution functions respectively, expressed as follows: and

[0054] ②From two empirical distribution functions and A Bootstrap sample of size n is drawn from each sample, and the mean is calculated as the location parameter estimate, denoted as . and

[0055] ③ Repeat the resampling parameter estimation process in ② B times to obtain the group factor location parameter estimates for the two groups based on the Bootstrap samples. and Where r = 1, ..., B;

[0056] ④ Based on the group factor position effect estimates obtained above, a test statistic is constructed by combining robust statistics and bias correction techniques to test the significance of the current group factor. The specific method is as follows:

[0057] The position parameter estimates for the Bootstrap samples are corrected separately. First, the position parameter estimates are corrected. The deviation correction is expressed as:

[0058]

[0059] in,

[0060]

[0061] and Similarly, for position parameter estimators The deviation correction is expressed as:

[0062]

[0063] in,

[0064]

[0065] and Then, the two sets of corrected statistics are subtracted in pairs, and the classic student t-statistic is improved using robust statistics such as the median and the absolute deviation of the median:

[0066]

[0067] in,

[0068]

[0069] and

[0070]

[0071] because

[0072]

[0073] That is, using T R The asymptoticity of the statistic tests the difference in the distribution of the system response at two design points, where the constant is used.

[0074] ⑤ Based on the test statistic constructed in ④, calculate the value based on the resampled sample, and then compare it with the quantiles of the normal distribution, or calculate the p-value corresponding to the statistic, to determine the significance of the current group factor. First, calculate the value of the statistic and select the significance level α (generally 0.01, 0.005, etc.). It should be noted that the smaller the significance level, the fewer important factors will be screened. Therefore, one approach to testing the significance of group factors is to compare C·T... R With z 1-α The value of C·T R >z 1-α If the effect of the current group factor is significant, then the effect of the current group factor is significant (go to step 4); conversely, if C·T R ≤z 1-α If the effect of the factor in the current group is not significant, proceed to step 5. Another approach to testing the significance of a factor is to calculate C·T under the assumption of a normal distribution. R The p-value, i.e.

[0075]

[0076] Then compare the p-value with the significance level α. If p < α, the effect of the current group factor is significant (go to step 4); otherwise, if p ≥ α, the effect of the current group factor is not significant (go to step 5).

[0077] Step 4: For the current group factors with significant effects in Step 3, determine whether a branching step is needed by judging the number of elements contained in the important current group factors, and process its subgroups accordingly. For example, if the current group factor contains more than 1 element, it is divided into two subgroups, and the two subgroups are placed into the FIFO screening queue in order; if the current group factor contains only 1 element, it is placed into the set I of important factors. The specific method is as follows:

[0078] ① Calculate the number of factors contained in the current subgroup, expressed as m = k1 - k0 + 1;

[0079] ② If m > 1, the current group of factors is divided into two subgroups, and the two subgroups are placed into the FIFO filtering queue in order. The grouping rule is as follows: the first m1 factors are placed into the first subgroup in the current order, and the remaining m-m1 factors are placed into the second subgroup; where m1 is the largest integer power of 2 less than m. For example, when m = 18, m1 = 16; when m = 16, m1 = 8.

[0080] ③ If m = 1, then place the current group into the set I of important factors.

[0081] Step 5: For factors in the current group whose effects are not significant in Step 3, delete them directly, which can save a lot of experimental costs.

[0082] Step 6: Determine whether the factor screening process terminates based on whether the FIFO queue is not empty. If the FIFO queue is not empty, proceed to Step 2 for the next iteration; if the FIFO queue is empty, terminate the screening process. At this point, the elements contained in set I are the obtained key factors.

[0083] Example

[0084] To verify the effectiveness of this invention in screening key quality factors in multi-level supply chain inventory systems, a Monte Carlo simulation experiment of a multi-level supply chain inventory system is conducted below. In this embodiment, the response distribution type, parameters, and factor effects are assumed. Then, statistical inferences are made on the overall distribution or response model parameters using only the response observations, and compared with the assumed actual parameters or response model parameters to illustrate the effectiveness of the invention. It should be understood that the examples described herein are merely illustrative of this application and are not intended to limit this application.

[0085] For ease of description, the factor selection method proposed in this invention will be denoted as SB-RBT, and the classic method based on the Student's t-test will be denoted as SB-TT. Assume that the multi-level supply chain inventory system contains 100 controllable factors, and the relationship between the controllable factors and the response variable satisfies the following first-order polynomial:

[0086]

[0087] Where y represents the response variable, x j (j=1,…,k) represents the coding level of the j-th controllable factor, taking values ​​of 0 or 1; β j (j=1,…,k) represents the position effect coefficient of the j-th controllable factor, and satisfies β j ≥0; ε is the error term, representing a random variable with an unknown distribution and a mean of 0, and k represents the number of all controllable factors in the system.

[0088] In this simulation case, it is assumed that the number of controllable factors k = 100, and based on the assumption of effect sparsity, only the coefficients of the first 8 factors are non-zero, while the effect coefficients of the remaining 92 factors are all equal to zero. The effect coefficients of the first 8 factors are expressed as β = (1.6, 2, 2.4, 2.8, 3.2, 3.6, 4, 4.4), the sample size for resampling is B = 200, and the unimportance threshold Δ = 2. Therefore, the key factor selection for this multi-level supply chain inventory system specifically includes the following steps:

[0089] Step 1: Extract k = 100 controllable factors, denoted as {x1, ..., x...} 100}, where each controllable factor is already standardized, and its encoded low and high levels are 0 and 1 respectively. Then, {x1,…,x 100 Add it to the FIFO filtering queue;

[0090] Step 2: Extract a group from the filtering queue according to the FIFO rule as the current group factor G. It's important to note that this step is iterative, and the extracted group factor may vary depending on the number of iterations and randomness. Specifically, when performing Step 2 for the first time, the group factor extracted from the FIFO queue is {x1,…,x}. 100 Generally, we assume that the extracted group factors are... This requires adding two new design points, x(k0-1) and x(k1). x(k0-1) represents the first k0-1 factors set to high levels (after encoding), and the remaining factors set to low levels (after encoding). Similarly, x(k1) represents the first k1 factors set to high levels (after encoding), and the remaining factors set to low levels (after encoding). At each of the two design points x(k0-1) and x(k1), collect n (n=5) original sample points, denoted as y. i (k0-1) and y i (k1), where i = 1, ..., n.

[0091] Step 3: Test the significance of the factor effect in the current group. If the effect is significant, proceed to step 4; otherwise, proceed to step 5. First, the bootstrap method is used to expand the sample size. Then, bias correction and robust statistical methods are combined to construct a statistic for testing the factor effect. The specific steps are as follows:

[0092] ① Using the original sample y i (k0-1) and y i (k1) Construct two empirical distribution functions respectively, expressed as follows: and

[0093] ②From two empirical distribution functions and We extract n Bootstrap samples from each sample and calculate their mean as the location parameter estimate, denoted as . and

[0094] ③ Repeat the resampling parameter estimation process in ② B times to obtain the group factor position effect estimates for the two groups based on the Bootstrap samples. and Where r = 1, ..., B;

[0095] ④ Considering the significant deviation between the estimated values ​​obtained from the original samples and the location parameters of the overall response, this deviation is estimated first. A set of original sample points y at the design point x(k1) is used. i (k i Taking (i = 1, ..., n) as an example, the deviation between the original sample mean estimate and the population mean. It can be estimated using the following formula:

[0096]

[0097] Therefore, the original sample y i (k i The bias correction for the )(i=1,…,n)Boostrap statistic is expressed as:

[0098]

[0099] Similarly, the original sample y i The Bootstrap statistic bias correction for (k0-1) (i=1,…,n) is expressed as:

[0100]

[0101] Then, the two sets of corrected statistics are subtracted in pairs. Considering that the Bootstrap estimator may not strictly follow a normal distribution, the robust statistics of median and median absolute deviation are used to improve the classic Student's t-statistic:

[0102]

[0103] in,

[0104]

[0105] and

[0106]

[0107] Regarding T R The asymptoticity has the following properties:

[0108]

[0109] in,

[0110] ⑤ First, select the significance level α (0.01), and then calculate C·T. R and z 1-α Comparison: If C·T R >z 1-α If the effect of the current group factor is significant, then the effect of the current group factor is significant (go to step 4); conversely, if C·T R ≤z 1-α If the effect of the current group factor is not significant, proceed to step 5.

[0111] Step 4: For significant group factors, determine the number of elements in them. If the current group factor contains more than 1 element, divide it into two subgroups and put the two subgroups into the FIFO screening queue in order. If the current group factor contains only 1 element, put it into the set I of important factors.

[0112] Step 5: Delete the current group factor;

[0113] Step 6: If the FIFO filtering queue is not empty, proceed to step 2; if the FIFO is empty, the process terminates, and the filtered key factors are represented as set I.

[0114] As described above, the process involves iterations. Completing one screening step signifies the completion of one screening cycle, yielding the corresponding key factors. Due to the randomness of the response, a single screening result is insufficient to verify the effectiveness and robustness of the factor selection. Therefore, an N=1000 repetition of the screening process was performed, and the frequency at which each factor was identified as an important factor was calculated to measure the efficiency of the factor selection method, denoted as f. I (·)

[0115] Furthermore, the factor selection results were examined under two distribution types (normal and uniform distribution), seven process standard deviations (σ = 2, 2.5, 3, 3.5, 4, 4.5, 5), and six sample sizes (n = 5, 10, 15, 20, 25, 30). The obtained factor selection results are analyzed and explained below in two aspects (non-zero factor selection results and zero-effect factor selection results).

[0116] (1) Results of non-zero factor screening

[0117] For the eight factors with non-zero factor effects, the frequency f of which a factor is significantly identified as an important factor is calculated. IThe screening results of the factor screening method SB-RBT of this invention and the classical factor screening method SB-TT are compared from two perspectives: the screening frequency growth rate γ and the screening results. First, the factor screening results of the simulation scheme (response standard deviation σ = 5, sample size n = 5) are examined (see...). Figure 2 The graphs, with the left and right subgraphs representing two distribution types respectively, show the factor effect on the horizontal axis. It can be observed that the factor screening results of the SB-RBT method of this invention exhibit a generally linear growth trend with increasing factor effect under both distribution types, demonstrating the robustness of SB-RBT across different distribution types. However, the classic factor screening method SB-TT shows slightly lower results under a uniform distribution compared to a normal distribution. Furthermore, with increasing factor effect, the SB-RBT screening results show a significant growth trend and a higher growth rate; in contrast, the SB-TT growth rate is lower. In fact, with increasing factor effect, a higher growth rate in the screening results indicates that the method is better at distinguishing factors with different effects; conversely, a low growth rate suggests that it easily mixes factors with different effects together.

[0118] Based on this, under the combined response standard deviation and sample size, the growth rate γ of the frequency of factors identified as significant factors as the factor effect increases was calculated for both factor screening methods, as shown in Tables 1 to 4.

[0119] Table 1. Growth rate γ of SB-TT factor screening results under normal distribution

[0120]

[0121] Table 2. Growth rate γ of SB-RBT factor screening results under normal distribution

[0122]

[0123]

[0124] Table 3. Growth rate γ of SB-TT factor screening results under uniform distribution

[0125]

[0126] Table 4. Growth rate γ of SB-RBT factor screening results under uniform distribution

[0127]

[0128] First, under the two assumed distribution types (normal distribution and uniform distribution), if the response standard deviation is small and the sample size is relatively large, the growth rate of the classic factor screening method SB-TT is greater than that of the proposed method SB-RBT. Conversely, when the response standard deviation is large and the sample size is relatively small, the growth rate of the proposed factor screening method SB-RBT is significantly greater than that of SB-TT. Furthermore, by comparing the growth rates of the two screening methods under normal and uniform distributions, it can be found that the growth rate of the proposed SB-RBT method is not significantly affected by the distribution type, verifying its good robustness.

[0129] (2) Analysis of Zero Factor Screening Results

[0130] Based on the fundamental assumptions of the simulation examples, among the 100 factors, 92 have zero effects (referred to as zero factors). Furthermore, for two distribution types (normal and uniform distributions) and 42 simulation schemes (7 response standard deviations and 6 sample sizes), the frequency with which the factor selection method identified zero factors as important factors in N (=1000) repeated selections was statistically analyzed, denoted as f. I 0 Statistical results show that, under 42 simulation schemes and two factor screening methods, a total of 7728 (92 × 42 × 2) zero-factor screening results f1 can be obtained. 0 Most of them are F1 0 =0. In other words, in most of the simulation scenarios examined, zero factors will not be mistakenly identified as important factors. Taking the SB-RSB method as an example, under the assumption of a normal distribution, f1 0 Results ≠ 0 occurred 92 times, accounting for 2.38% of the total screening results; while under the assumption of uniform distribution, f1... 0 Results with a value of ≠ 0 occurred 111 times, accounting for 2.87% of the total screening results.

[0131] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0132] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for selecting efficient key factors in a multi-level supply chain inventory system, characterized in that, Includes the following steps: Step 1: Extract controllable factors from the multi-level supply chain inventory system, perform key factor screening, and store them in the FIFO screening queue. Step 2: Extract the current group factor G from the FIFO screening queue, determine the required additional design points, and collect the corresponding system performance response observations; Step 3: Use the Bootstrap method to expand the sample size of the response observations and test the significance of the effect of the current group factor. If the effect is significant, proceed to step 4; if the effect is not significant, proceed to step 5. The specific method is as follows: Using response observations and Construct two empirical distribution functions, respectively, as follows: and ; From two empirical distribution functions and The sample size drawn from each is The Bootstrap samples are used to calculate the mean as an estimate of the location parameters, denoted as . and ; repeat The resampling parameter estimation process is repeated B times, resulting in two sets of group factor location parameter estimates based on the Bootstrap samples. and ,in ; Based on the obtained group factor position effect estimates, a test statistic is constructed by combining robust statistics and bias correction techniques to test the significance of the current group factor. The specific method is as follows: The position parameter estimates for the Bootstrap samples are corrected separately. The deviation correction is expressed as: ； in, ； and ; Similarly, location parameter estimators The deviation correction is expressed as: ； in, ； and ; Then, the two sets of corrected statistics are subtracted in pairs, and the classic student t-statistic is improved using robust statistics such as the median and the absolute deviation of the median: ； in, ； and ； because ； That is, using T R The asymptoticity of the statistic tests the difference in the distribution of the system response at two design points, where the constant is used. ; because The test statistic T R Multiplying by a constant, the response asymptotically follows a standard normal distribution. The statistic T is then calculated using the observed response data. R And compare it with the quantile of the standard normal distribution, or calculate its p-value and compare it with the significance level to determine the significance of the current group factor; Step 4: Determine the number of elements contained in the current group factor. If the number of elements contained in the current group factor is greater than 1, then branch it into two subgroups and put the two subgroups into the FIFO filtering queue in order. If the current group factor contains only 1 element, then put it into the set I of important factors and go to step 6. Step 5: Delete the current group factor and proceed to step 6; Step 6: Determine if the FIFO filtering queue is not empty. If the FIFO filtering queue is not empty, proceed to step 2 for the next loop. If the FIFO filtering queue is empty, terminate the filtering process. The elements contained in set I are the obtained important factors. The controllable factors include the lower and upper limits of inventory at each level of warehouses in the supply chain system, the initial inventory level, the lead time for each type / customer, the maximum capacity and number of employees of the distribution center, the number and speed of transportation vehicles, and the performance response observations include the average profit or service level within the period.

2. The key factor screening method for multi-level supply chain inventory systems according to claim 1, characterized in that, Step 1: Extract controllable factors from the multi-level supply chain inventory system and perform key factor screening. The specific method is as follows: Extract the controllable factors of the multi-level supply chain inventory system, determine the value range of all controllable factors, and encode the experimental levels of all controllable factors so that the low level and high level of the coded controllable factors are 0 and 1, respectively. Determine the direction and magnitude of the system performance change when each controllable factor is adjusted from a low level to a high level; Adjusting the experimental levels of controllable factors so that the system response increases when each controllable factor is switched from a low level to a high level individually; Arrange all controllable factors in ascending or descending order of effect size to obtain the initial group factors. And put it into the first-in-first-out (FIFO) filtering queue.

3. The key factor screening method for multi-level supply chain inventory systems according to claim 1, characterized in that, Step 2: Determine the required additional design points based on the current group factors and collect the corresponding response observations. The specific method is as follows: Assume the current group factor is represented as Then two additional design points are needed. and ,in, Indicates the preceding One factor is set to a high level, and the rest are set to a low level; similarly... Indicates the preceding One factor was set to a high level, and the rest of the factors were set to a low level. At two design points and Collect n response observations at each location, denoted as . and ,in .

4. The key factor screening method for multi-level supply chain inventory systems according to claim 1, characterized in that, Step 4: Determine the number of elements contained in the current group factor. If the current group factor contains more than 1 element, branch it into two subgroups and place the two subgroups into the FIFO screening queue in order. If the current group factor contains only 1 element, place it into the set I of important factors. The specific method is as follows: Calculate the number of factors contained in the current group, expressed as: ; if Then, the current group of factors is divided into two subgroups, and the two subgroups are placed into the FIFO filtering queue in order. The specific grouping rule is: the first m1 factors are placed into the first subgroup in the current order, and the remaining factors are placed into the second subgroup. Each factor enters the second subgroup; where m1 is the largest integer power of 2 less than m; if If so, the current group will be placed into the set I of important factors.

5. A key factor screening system for multi-level supply chain inventory systems, characterized in that, Based on the key factor screening method for multi-level supply chain inventory systems as described in any one of claims 1-4, key factor screening for multi-level supply chain inventory systems is achieved.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it performs key factor screening for a multi-level supply chain inventory system based on the key factor screening method for a multi-level supply chain inventory system as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it performs key factor screening for a multi-level supply chain inventory system based on the key factor screening method for a multi-level supply chain inventory system as described in any one of claims 1-4.

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