A data-driven calculation method for the inventory quantity of electronic product parts in after-sales service

Abstract

The present invention discloses a data-driven calculation method for the inventory quantity of electronic product parts in after-sales service. A simple and efficient optimization method is proposed for the prediction of electronic product spare parts and the optimization of inventory costs. By making full use of historical data and combining the chance-constrained method to establish a prediction model, a robust optimization solution is obtained through the efficient solution of the prediction model. The prediction model obtained by solving can give the spare parts purchase decision plan for the subsequent time period, guiding the actual after-sales service manufacturers to make corresponding decisions, optimizing the relevant costs under the condition of meeting the spare parts replacement needs of users. Compared with the existing spare parts demand prediction methods, it makes more full use of data and has better optimization performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of spare part demand calculation, and particularly relates to a method for calculating the stock quantity of spare parts for after-sales service electronic products driven by data. Background Art

[0002] At present, with the continuous development of information technology, people's daily work and life rely more and more on electronic products. Electronic products such as laptops, mobile phones, and printers have become very popular. In particular, mobile phones, as a communication tool, have become an essential part of everyone's daily life. High-intensity use has accelerated the aging of electronic product components, and the demand for after-sales repair services for electronic products by consumers has increased significantly. When users need to repair electronic products and replace spare parts during the warranty period but cannot be satisfied, they will be dissatisfied with related brand products, which will affect the brand reputation and have a negative impact on the sales of subsequent products. Therefore, after-sales service providers of electronic products need to manufacture required repair parts during the warranty period to meet the needs of users for after-sales service. On the other hand, the rapid replacement of electronic product models has led to the inability of parts suppliers to maintain specific spare part production lines for a long time. Generally, the warranty period of electronic products is about one to three years, and relevant parts manufacturers will not continuously maintain specific spare part production lines for specific models, and cannot guarantee the continuous supply of spare parts during the warranty period.

[0003] To ensure consumers' trust in the brand and guarantee the quality of after-sales service, after-sales service providers need to prepare sufficient spare parts before the relevant products leave the production line to ensure that consumers' repair and replacement needs are met. Therefore, after-sales service providers need to decide the purchase quantity of relevant spare parts according to consumers' demands, and then replenish the inventory. At the same time, the ordering of spare parts will bring acquisition, inventory, and disposal costs. When the purchase quantity of spare parts is much larger than the demand, it will greatly increase the cost of after-sales service. Therefore, it is very necessary to accurately predict the demand for spare parts. Traditional spare part prediction methods often consider large-scale equipment, such as expensive equipment with a long warranty period, such as airplanes and manufacturing equipment (Capital Goods). The purchasers of such equipment are determined, and the maintenance period is long. Once the product is damaged, it is necessary to repair or replace the spare parts. However, electronic products such as mobile phones, laptops, and printers are user-type products (Customer Goods) with large sales volumes. Their sales volumes are large, and whether they are under warranty is affected by factors such as cost, user experience, usage duration, and whether new products are launched. The uncertainty is strong, and relevant research is relatively scarce. Therefore, the problem of predicting the demand for spare parts of electronic products and optimizing their inventory management has academic research value and application prospects.

[0004] For the above objectives, relevant research includes that Kim T.Y. et al. in <Spare part demand forecasting for consumer goods using installed base information> used the installed base (IB) of electronic product spare parts to forecast the demand quantity of spare parts. This work classified the installed base into: the number of devices currently remaining in the market calculated according to the expected service life (Lifetime IB, IBL); the number of devices currently remaining in the market calculated according to the warranty period (Warranty IB, IBW); the number of devices currently remaining in the market considering that products with uneconomical repairs are discarded (Economic IB, IBE); the number of devices currently remaining in the market considering the repair costs and benefits of consumers (Mixed IB, IBM). Based on the above concepts, this work used the survival probability distribution to simulate the damage situation of electronic products, fitted the functional relationship between the demand quantity D and IB, and predicted the demand quantity of mobile phones in the subsequent time period.

[0005] The above prediction method uses historical data for linear fitting to obtain corresponding coefficients. However, due to its simple assumptions, in actual application scenarios, it generally can only predict the trend of spare part demand, and cannot give precise suggestions for spare part purchase decisions. It also does not consider factors such as acquisition, storage, and destruction costs. Therefore, the obtained prediction results are not accurate enough. Summary of the Invention

[0006] In view of this, the present invention provides a data-driven calculation method for the inventory quantity of after-sales service electronic product parts, realizing the quantitative calculation of the inventory quantity of electronic product parts based on historical data.

[0007] A data-driven calculation method for the inventory quantity of after-sales service electronic product parts provided by the present invention includes the following steps:

[0008] Step 1: Determine the preprocessing method of input variables and construct an input sample set for electronic products;

[0009] Step 2: Construct a mixed-integer programming model based on a data-driven chance-constrained method to establish a prediction model for the inventory quantity of electronic product parts, as shown in the following formula:

[0010]

[0011]

[0012]

[0013] Among them, Q(i) is the quantity of spare parts purchased from the supplier in the i-th month, r is the decision variable, X(i) is the input data in the i-th month, and c p is the purchase cost of a single spare part, and c b is the cost per unit time of backlogging a single spare part, and c h is the cost per unit time of shortage of a single spare part. b(i) is the backlog quantity of spare parts in the i-th month, and h(i) is the shortage quantity of spare parts in the i-th month;

[0014] Step 3: Input the input sample set of the electronic product into the prediction model of the electronic product parts stock preparation quantity, and use a solver to solve to obtain a determined prediction model of the electronic product parts stock preparation quantity;

[0015] Step 4: In actual use, according to the input variable preprocessing method in Step 1, obtain the actual historical data occurring before the prediction time period as the actual input variables, and input the actual input variables into the prediction model of the electronic product parts stock preparation quantity obtained in Step 3 to obtain the quantity of electronic product parts to be purchased required for the prediction time period.

[0016] Further, the input variable preprocessing method in Step 1 is to obtain the sales volume in the W months before the prediction time period and establish an input variable X(i) of W + 3 dimensions:

[0017] X(i) = {B(i - W), B(i - W + 1),..., B(i - 1), 1, D(i - 1), i}

[0018] Among them, B(i - W) is the sales volume of the electronic product in the (i - W)-th month, B(i - W + 1) is the sales volume of the electronic product in the (i - W + 1)-th month, B(i - 1) is the sales volume of the electronic product in the (i - 1)-th month, and D(i - 1) is the demand for specific spare parts in the (i - 1)-th month.

[0019] Further, the data-driven chance-constrained inequality constructed based on the sample average method in the prediction model of the electronic product parts stock preparation quantity is:

[0020]

[0021]

[0022] Among them, M is a very large integer, S(i) is the inventory quantity of spare parts in the i-th month; γ(i) is an integer variable, which represents that the spare parts demand in the i-th month is not met when taking the value of 1, and represents that the spare parts demand in the i-th month is met when taking the value of 0; α is the chance-constrained threshold.

[0023] Further, the value of the chance-constrained threshold is 0.01.

[0024] Beneficial effects:

[0025] The present invention proposes a simple and efficient optimization method for the prediction of spare parts of electronic products and the optimization of inventory costs. It makes full use of historical data, combines the chance-constrained method to establish a prediction model, obtains a robust optimization solution through the efficient solution of the prediction model, and uses the obtained prediction model to give a spare parts purchase decision plan for the subsequent time period, guiding the actual after-sales service manufacturers to make corresponding decisions. Under the condition of meeting the spare parts replacement needs of users, the relevant costs are optimized. Compared with the existing spare parts demand prediction methods, it makes more full use of data and has better optimization performance. Brief Description of the Drawings

[0026] Figure 1 It is a schematic diagram of the inventory optimization problem of spare parts of electronic products in the after-sales stage.

[0027] Figure 2 It is a schematic diagram of the actual sales data of a certain model of mobile phone in a certain place.

[0028] Figure 3 It is a schematic diagram of the monthly spare parts purchase quantity and the inventory quantity under the actual demand obtained by using a data-driven calculation method for the stock quantity of spare parts of after-sales service electronic products provided by the present invention.

[0029] Figure 4 It is a schematic diagram of the monthly spare parts purchase quantity and the inventory quantity under the actual demand obtained by using the method of Kim T.Y. et al. Detailed Embodiment

[0030] The following are embodiments given in conjunction with the drawings to describe the present invention in detail.

[0031] The technical problem addressed by the present invention is the inventory optimization problem of spare parts of electronic products (such as batteries, cameras, motherboards, etc.) in the after-sales stage. The problem schematic diagram is as shown in the appendix Figure 1 shown. Specifically, taking a mobile phone as an example, as Figure 1As shown in the upper part, the important time nodes after the mobile phone is launched include: the start of sales, the selling period, the daily purchase period of spare parts, the end of sales, and the final purchase from the manufacturer; for users, after purchasing the mobile phone, it enters the mobile phone warranty period (set as W). If there are problems that cannot be solved during the warranty period, they will seek help from the after-sales service provider for repair and replacement of spare parts; after the given mobile phone starts to be sold, due to reasons such as the mobile phone's own failures, users' requests to the after-sales party for replacing parts and repairing the mobile phone will bring corresponding demands for parts. The present invention helps the after-sales service party to decide the monthly purchase quantity of given parts after the electronic product is launched, thereby minimizing the absolute value of the difference between the inventory and the actual demand within a given time period. Among them, taking months as the unit, considering m time periods from the start of selling the electronic product until all sold products are out of the warranty period, for a given spare part, the monthly sales volume of the electronic product is B(i), and the demand for the specific spare part to be calculated is D(i).

[0032] Therefore, the key technical problems to be solved by the present invention include: how to select appropriate data as the input data for predicting future spare part demands; how to establish a data-driven chance-constrained optimization mixed-integer programming model, make full use of historical data, and effectively obtain decision coefficients through its solution; for a given N, how to control the constraint strength by adjusting the chance-constraint threshold, the smaller the chance-constraint threshold, the less the model can tolerate the inventory value in the historical data not meeting the demand requirements, and vice versa, the optimization model can be appropriately relaxed. In the application process, how to balance the computational complexity of solving the optimization model and the degree of constraint satisfaction through the chance-constraint threshold.

[0033] A data-driven calculation method for the spare part stock quantity of after-sales service electronic products provided by the present invention specifically includes the following steps:

[0034] Step 1, determine the preprocessing method of input variables and construct an input sample set for electronic products.

[0035] In the present invention, the input sample data X is W + 3-dimensional data, and its format is as follows:

[0036] X(i) = {B(i - W), B(i - W + 1),..., B(i - 1), 1, D(i - 1), i}

[0037] Among them, the first W-dimensional data represents the sales volume in the W months before time point i, that is, the sales data of the mobile phones currently within the warranty period; the (W + 1)-th dimensional data is a constant. Since the purchase quantity is determined by Q(i) = r T ·X(i), the (W + 1)-th dimension represents the constant in the purchase quantity that has nothing to do with other data. Q(i) is the quantity of spare parts purchased from the supplier in the i-th month, and r is the decision variable; the (W + 2)-th dimension is the demand in the previous month, such as 0 at this position when i = 1; the (W + 3)-th dimension represents the number of months from the start of sales to the current time.

[0038] Step 2: Construct a mixed-integer programming model based on the data-driven chance-constrained method to establish a prediction model for the stock quantity of electronic product parts.

[0039] To enable the commercial solution software to solve the problem within a limited time, the present invention constructs a mixed-integer programming model for this problem based on the data-driven chance-constrained method. The specific construction process includes the following steps:

[0040] Step 2.1: Define the intermediate variables, decision variables, and other variables as shown in the following table:

[0041]

[0042] Step 2.2: According to the above problem description, define the problem optimization objective as shown in formula (1), which represents minimizing the sum of the shortage, overstock, and spare part acquisition costs at all data nodes using N sets of historical data nodes. Minimizing this value can achieve the fitting of spare part demand and the optimization of costs.

[0043]

[0044] Step 2.3: Define the inventory iteration relationship between adjacent time periods. The inventory of this month is determined by adding the inventory of last month, the purchase quantity of this month, and subtracting the demand quantity of this month, as shown in formula (2) specifically. Among them, S(-1)=0 is the critical condition, indicating that in the first month, the inventory is only related to the demand and purchase quantity of that month.

[0045]

[0046] Step 2.4: Based on the Sample Average Approach (SAA), construct data-driven chance-constrained inequalities as shown in formulas (4) and (5). Among them, formula (4) defines whether each data node meets the user demand. If the inventory and order quantity of that month meet the demand, the formula holds when r(i)=0; if the inventory and order quantity of that month do not meet the demand, the formula holds when r(i)=1. Therefore, the value of the intermediate variable r(i) can represent whether the demand of that month is met. r(i)=1 means that the spare part demand in the i-th month is not met. In formula (5), count the sum of r(i). Its sum represents the number of time periods among N data nodes that do not meet the demand of that month. According to the definition of chance-constrained optimization, its frequency needs to be less than the set threshold α, and then formula (5) is constructed.

[0047]

[0048]

[0049] Step 2.5. Let b(i) denote the number of spare parts backlogged in the i-th month period. b(i)≥0 in formulas (6-9) and (15) is a linear representation of b(i)=max(S(i),0). Formulas (6) and (15) ensure that b(i) is greater than or equal to S(i) and 0. Formula (9) represents u 1 (i) and u 2 (i), and at least one of the variables u

[0050]

[0051]

[0052]

[0053]

[0054] Step 2.6. Let h(i) denote the number of spare parts lacking in the i-th month period. Similar to Step 2.5, h(i)≥0 in formulas (10-13) and (15) is a linear representation of h(i)=max(-S(i),0).

[0055]

[0056]

[0057]

[0058]

[0059] Step 2.7. Formula (14) indicates that the purchase quantity in the i-th month has a linear relationship with the input variable X, where the input variable is the one obtained after data preprocessing in Step 1, and r is the decision variable.

[0060]

[0061]

[0062] Step 3. Input the electronic product input sample set constructed in Step 1 into the electronic product parts stock preparation quantity prediction model established in Step 2, and use a solver to solve the mixed-integer programming model, then the decision variables in the electronic product parts stock preparation quantity prediction model can be obtained, and further the opportunity constraint threshold can be obtained to complete the solution of the electronic product parts stock preparation quantity prediction model.

[0063] Step 4: In actual use, according to the input variable preprocessing method in Step 1, obtain the actual historical data occurring before the prediction time period as the actual input variable, and input the actual input variable into the electronic product parts stock preparation quantity prediction model obtained by solving in Step 3 to obtain the stock preparation quantity of electronic product parts required to be purchased during the prediction time period.

[0064] To verify the performance of the present invention, the algorithm is verified using the actual production and sales data of a certain brand. Among them, the present invention is programmed in Python language, calls the Gurobi 9.5.1 educational version solver, the computing environment is Intel(R)core(TM)i7-4790 CPU@3.6GHz / 16GB RAM, and the operating system is windows 10. The sales data of a certain mobile phone is as Figure 2 shown, where the blue trend line represents the sales quantity of mobile phones in that month, and the orange trend line represents the number of mobile phones within the warranty period in the market when the quantity is guaranteed for 1 year (12 months). Based on this data, take the first half of the data with N = 30 as historical data, and use the method of the present invention and the prediction method in the aforementioned literature to predict and optimize the subsequent data respectively, where the opportunity constraint threshold α of the present invention is 0.01. The results are as Figures 3-4 shown, Figure 3 is the prediction and optimization result of the present invention, Figure 4 is the prediction result of the literature. The blue data nodes in the figure are the actual mobile phone spare part demand quantities, the orange data nodes are the predicted results of the demand quantities, and the green nodes are the inventory situations under the actual demand quantities when making stock preparation decisions using this prediction method. It can be Figure 3 seen that under the spare part purchase decision of the present invention, the inventory level remains positive, there is no out-of-stock situation, and at the same time, the inventory water level line does not maintain a high level for a long time, and the inventory cost is low. And it can be Figure 4 seen that this method better predicts the spare part demand trend, but under the spare part purchase decision of the prediction method in this literature, the inventory is basically negative, continuously out of stock, and the needs of users cannot be met, making it difficult to guarantee the after-sales service reputation of the brand.

[0065] It can be seen from this that the present invention establishes a data-driven chance-constrained mixed-integer programming model, makes the most of the existing data, and can obtain the spare part purchase strategy through the solution of commercial software, which is applicable to actual engineering application problems.

[0066] In summary, the above is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A data-driven calculation method for the stock quantity of electronic product parts in after-sales service, characterized in that, it includes the following steps: Step 1: Determine the preprocessing method of input variables and construct an input sample set for electronic products; Step 2: Construct a mixed-integer programming model based on the data-driven chance-constrained method to establish a prediction model for the stock quantity of electronic product parts, as shown in the following formula: Where Q(i) is the number of spare parts purchased from suppliers in month i, r is the decision variable, X(i) is the input data in month i, c p is the purchase cost of a single spare part, c b is the cost per unit time of a single spare part backlog, c h is the cost per unit time of a single spare part out of stock, b(i) is the spare parts inventory backlog in the ith month, and h(i) is the spare parts out of stock in the ith month; Step 3: Input the input sample set of the electronic products into the prediction model for the stock quantity of electronic product parts and use a solver to solve it to obtain a determined prediction model for the stock quantity of electronic product parts; Step 4: In actual use, according to the preprocessing method of the input variables in Step 1, obtain the actual historical data occurring before the prediction time period as the actual input variables, and input the actual input variables into the prediction model for the stock quantity of electronic product parts obtained in Step 3 to obtain the stock quantity of electronic product parts to be purchased during the prediction time period; The data-driven chance-constrained inequality constructed based on the sample average method in the prediction model for the stock quantity of electronic product parts is: where M is a very large integer, S(i) is the spare part inventory at the i-th month; γ(i) is an integer variable, when taking the value of 1, it means that the spare part demand in the i-th month is not met, and when taking the value of 0, it means that the spare part demand in the i-th month is met; α is the chance-constrained threshold.

2. The calculation method for the stock quantity of electronic product parts in after-sales service according to claim 1, characterized in that, the preprocessing method of the input variables in Step 1 is to obtain the sales volume in the W months before the prediction time period and establish an input variable X(i) of dimension W + 3: X(i) = {B(i - W), B(i - W + 1),..., B(i - 1), 1, D(i - 1), i} where B(i - W) is the sales volume of electronic products in the (i - W)-th month, B(i - W + 1) is the sales volume of electronic products in the (i - W + 1)-th month, B(i - 1) is the sales volume of electronic products in the (i - 1)-th month, and D(i - 1) is the demand for specific spare parts in the (i - 1)-th month.

3. The calculation method for the stock quantity of electronic product parts in after-sales service according to claim 1, characterized in that, the value of the chance-constrained threshold is 0.01.

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