CN116307053A

CN116307053A - Method for optimizing stock layout and grouping orders based on square piece characteristics and Pearson correlation coefficients

Info

Publication number: CN116307053A
Application number: CN202211681689.XA
Authority: CN
Inventors: 王纪元; 张智冠; 宋效才; 周徐斌; 王伟; 赵万良; 张淼; 汪自军; 李东禹; 李绍良
Original assignee: Harbin Institute of Technology
Current assignee: Harbin Institute of Technology
Priority date: 2022-12-26
Filing date: 2022-12-26
Publication date: 2023-06-23

Abstract

A stock layout optimization and order batching method based on square part characteristics and Pearson correlation coefficients relates to a stock layout optimization and order batching method applied to the field of intelligent manufacturing. The cutting device solves the optimal cutting problem of square parts in the current personalized industrial products. The method comprises the following steps: 1. determining similar conditions, and establishing a one-dimensional array of required materials for each order; 2. determining similarity of each order by using Pearson correlation coefficients, and combining similar orders into a batch; 3. cutting materials in the same batch, and preprocessing square piece data of the same materials; 4. cutting is started by a large product item cutting method with the width of the original sheet as a resolution standard; 5. and arranging the rest small product items by using a small product item dense paving method. The invention fully utilizes order information and product information, combines production practice, provides a two-stage cutting method, effectively improves the utilization rate of the plate, and is suitable for batch cutting of a large number of various personalized custom square pieces.

Description

Method for optimizing stock layout and grouping orders based on square piece characteristics and Pearson correlation coefficients

Technical Field

The invention relates to a method in the field of intelligent manufacturing, in particular to a stock layout optimization and order batching method based on square part characteristics and Pearson correlation coefficients, which is used for optimal cutting of square parts in personalized industrial products.

Background

Aiming at the characteristics of more personalized customization varieties and huge order quantity, the current production organization mostly adopts an order group batch, mass production and order sorting mode for production. In this production mode, order batching and layout optimization is important.

The order group batch is to combine different orders into a certain number of batches under the limit of actual productivity, and the contradiction between individuation and production efficiency is solved during the batch group; the layout optimization essence is the blanking problem, optimizes the layout of square parts on the original sheet of the sheet material, reduces the waste of the sheet material in the blanking process, and simplifies the cutting process.

When orders are batched, the similar orders are generally formed into a plurality of batches according to the similarity of different orders, so that batch processing is facilitated, production efficiency is improved, and delivery period is shortened.

When cutting is performed, the cutting process can be divided into a head-trimming cutting mode and a non-head-trimming cutting mode according to different cutting processes, wherein the head-trimming cutting mode refers to that one edge perpendicular to a square piece is subjected to linear cutting, and each cutting divides the square piece into two pieces; the non-flush head cutting does not require that the square piece be divided into two pieces each time it is cut. Compared with the two methods, the cutting process of the headcut is simpler, and the blanking modes of the non-headcut are more various.

The butt cut may in turn subdivide precise and non-precise ways. The precision mode may result in all products after a specific cutting stage, whereas a part of the products cut in a non-precision mode may require one more cutting stage than the other products. After the cutting stages are determined, the precise manner can result in all the products after all the cutting stages are completed, whereas the non-precise manner can increase the cutting effort upon completion of all the cutting stages.

The above-mentioned cutting stage is proposed in the course of cutting due to the different cutting directions each time, the same cutting direction at the same stage. Too few stages may not result in the desired product, and too many stages may increase the cutting effort, so that a suitable cutting stage is selected to achieve maximum efficiency in completing the cutting task. The number of cutting stages is usually at most 3-4. Taking 3-stage cutting as an example, the modules generated by 1-stage cutting are called as strips, such as strip 1 and strip 2; the module generated by the stage 2 cutting is called Stack in the invention, such as the strip 1 is continuously cut into Stack1, stack2 and the like; the third stage cuts the resulting module, which is referred to herein as Item (product Item), such as Stack1 continues to be cut into items 1, 2, etc.

The main aim of order group batch and stock layout optimization is to maximize the utilization rate of the plate, namely, the method meets the following conditions:

wherein, gamma is the utilization rate of the plate, S _i Is the area of each product item, n is the total number of product items, n _{Original source} Is the number of original sheets S _{Original source} Is the original area of the sheet.

At present, most of the research on order batch adopts a clustering method, proper targets are selected according to the characteristics of different orders, and a clustering model is established under specific constraint. However, there are different constraints on the batching of product orders in different production areas, and there are also differences in the optimization goals. Square products have the problem of coupling order batching and stock layout optimization, so that the batching and stock layout optimization is needed. The current research on the problem of layout optimization is more in the theoretical level, the influence on the production efficiency caused by the fact that the cutting mode, the cutting stage and the like of the head-alignment cutting mode or the non-head-alignment cutting mode are not considered, and the square parts with special shapes such as the equal height blocks are optimized. Many methods are not universally applicable to a wide variety of product orders, a large number and variety of square product types.

Disclosure of Invention

The invention aims to provide a stock layout optimization and order grouping method based on square part characteristics and Pearson correlation coefficients, which solves the main problems that the current order grouping and stock layout optimization problem research does not consider the coupling problem between the square part characteristics and the Pearson correlation coefficients and the traditional stock layout optimization method cannot be universally applicable to square part orders with small batches and multiple types and is not suitable for actual production; the method has the advantages that the plate materials required by different orders are used as similar targets, and the Pearson correlation coefficient is used for grouping the orders, so that the same plate method is applied to the same group as much as possible, and the problem of collaborative optimization of grouping and discharging is solved; under the constraint of meeting the requirements of head-aligned cutting, 3-cutting stage and precise layout, a group of square piece data of the same type of plates are preprocessed by considering the characteristics of original plates and the characteristics of different square pieces, large product items and small product items are distinguished, and then square pieces are arranged, so that the arrangement method has higher cutting efficiency when cutting the square pieces and is universally applicable to various square pieces, is suitable for production practice of square piece production, and can better guide production work of enterprises.

The invention aims at realizing the following technical scheme: and establishing a one-dimensional array of the required materials for each order, normalizing the array, and applying the Pearson correlation coefficient to obtain the similarity between each order, wherein the orders with high similarity are combined into a batch according to the production constraint condition. In the same batch, all square pieces requiring the same raw sheet material are cut uniformly. Before cutting, preprocessing the data of the product items to separate large product items and small product items, then cutting the large product items, and finally densely paving the small product items to realize layout optimization.

The flow chart of the invention is shown in fig. 1, and the specific steps are as follows:

step one: similar conditions are determined.

The invention firstly counts all kinds of materials in all orders, and establishes a one-dimensional array of required materials for each order. If the order has the product item which needs a certain material, the corresponding position of the array is filled with the number of the product item which needs the material, if not, the corresponding position is filled with zero, and finally the array is normalized.

Step two: similar orders are combined into a batch using Pearson correlation coefficients.

The material array for each order may reflect the material demand for each order. Therefore, the invention can know whether the material requirements of each order are similar or not only by carrying out similarity comparison on the material arrays of each order. If the similarity is 1, then both orders require the same material. If the similarity is not greater than 0, then the materials required for the two orders are not the same. According to the invention, the correlation coefficient among the material arrays is calculated by applying the Pearson correlation coefficient formula, so that a correlation coefficient matrix among each order is obtained. The Pearson correlation coefficient formula is as follows:

wherein r is a correlation coefficient, and x and y are two variables.

The correlation coefficient matrix is shown in fig. 2. After the correlation coefficient matrix among each order is obtained, different orders are selected to form the same group according to the sequence from the big correlation coefficient to the small correlation coefficient.

Step three: in the same batch, the square piece data of the same material are preprocessed by cutting the materials separately.

The length of the long side of each product item is taken as the length of the product item, and the length of the short side of each product item is taken as the width of the product item, and the original specification is 2440 x 1220 (mm) for example. Data with the length between 1220mm and 2440mm in the product item are extracted to form a set A.

Step four: cutting is started by a large product item cutting method taking the width of an original sheet as a resolution standard.

With the maximum value L of the product item length in A _a1 Cutting the first original piece, and firstly, arranging the left space. Subtracting L from the long side of the original sheet _a1 Length L obtained _b1 As the data classification standard corresponding to the first original piece, the length is less than 1220mm, and the width is less than or equal to L _b1 The data of which constitute the corresponding data set B1 of the first original piece. If the corresponding data set is empty, the short plates obtained after the first knife cutting are all waste materials. If the data of the corresponding data group is not empty, cutting in the first stage, and then forming a long plate with a pattern L _a1 And continuously cutting the plates in the set A by taking the width as a constraint according to the sequence from long to short until the remaining width of the original sheet cannot arrange the next product item, and temporarily counting the remaining plates into a waste set C. This is the first stage cut on the left as shown in fig. 3.

And when the left second stage cutting is carried out, searching for an unordered product item with the width smaller than the residual width of the current original piece, and if the length of the product item is smaller than La1, putting the product item into a temporary waste collection C, wherein the waste is reused. The method is beneficial to reducing the waste yield. However, only one product can be arranged in the length direction within the remaining width of the current original sheet, otherwise, the fourth-stage cutting can be generated. The second stage cutting on the left side is schematically illustrated in fig. 4.

There are two cases of third stage cutting on the left, one such as item2 shown in fig. 5, and the production of the product item is accomplished directly by means of the third stage cutting. The second type, item4 for example, shown in fig. 5, requires cutting the remaining width by means of a second stage cut to complete the production of the product item using a third stage cut, since the width is not full.

When there is no arrangement space on the left side, arrangement on the right side is started. As shown in FIG. 6, the right product items are vertically arranged, and first, the product items with the width smaller than the current maximum remaining length and the length smaller than 1220mm are selected and arranged at the left lower corner of the right original sheet. Selecting a product item with the width smaller than that of the previous product item and the length smaller than that of the original piece after the previous product item is placed, arranging the product item on the upper side of the previous product item, aligning left, when the next product item cannot be arranged in the residual width, starting to arrange the product item from the bottom again, and when the length of the right side is fully arranged, arranging the next original piece.

The right first stage cut at this time produces three pieces of temporary waste item10, item11 and item 12. Finding out the product items of the same size from the unordered product items is discharged into the waste materials, and the scheme can further increase the material utilization rate. The right vertical row has the advantage that the original sheet can be cut first into vertical strips using a first stage cut, as shown in fig. 7.

And cutting the vertical strip at the second stage to obtain the plate shown in fig. 8.

The third stage of cutting on the right side is shown in fig. 9, so that the whole process of the large product item cutting method taking the width of the original piece as a resolution standard is completed, and the rest product items are continuously arranged by a small product item dense paving method.

Step five: and arranging the rest small product items by using a small product item dense paving method.

And sequencing all the remaining product items from large to small according to the width, and sequentially arranging the product items from the left lower corner of the original sheet according to the sequence. When the sum exceeds 2440mm, the next plate starts to line up, opening the second row. When the sum of the widths exceeds 1220mm, the next product item is arranged starting from the lower left corner of the next original piece. And arranging the product items on the original sheet according to the arrangement method until all the product items are arranged. By this method, product items of similar width can be arranged in a row, so that the scrap rate becomes small. The method can generate the same primary sheet length temporary waste and width temporary waste as the large product item cutting method with the primary sheet width as the resolution standard, and the same method is used for preferentially searching the product item which accords with the largest area in the size of the waste and discharging the product item into the waste, so that the material utilization rate can be increased.

Compared with the prior art, the invention has the following advantages:

1) The invention combines production practice, overcomes the defect that the practical limitations of cutting modes and the like are ignored in the current research, utilizes the length and width information of the product item and the original sheet under the constraint that the practical cutting needs to be faced in the process of head-aligned cutting, three-stage cutting and the like, and provides a two-stage method of a large product item cutting method and a small product item intensive paving method which take the width of the original sheet as a resolution standard.

2) In the process of solving the problems, the invention fully utilizes the order information and the product information. When analyzing the order correlation, a correlation coefficient matrix is established based on the Pearson coefficient; and in the process of layout optimization, the length and width information of the product item and the original sheet are utilized. The use of this information greatly ensures the rationality and operability of product item scheduling and order batching.

Drawings

FIG. 1 is a flow chart of a stock layout optimization and order batching method based on square features and Pearson correlation coefficients.

Fig. 2 is a correlation matrix.

Fig. 3 is a schematic view of the left side first stage cutting.

Fig. 4 is a schematic view of the left second stage cut.

Fig. 5 is a schematic view of the third stage cut on the left.

Fig. 6 is a right side cut schematic.

Fig. 7 is a schematic view of the first stage cutting on the right.

Fig. 8 is a right side second stage cut schematic.

Fig. 9 is a schematic view of the third stage cutting on the right.

FIG. 10 is a schematic diagram showing the cutting results of the large product item cutting method based on the original sheet width as a resolution standard in the implementation.

FIG. 11 is a schematic diagram of the results of small product item intensive tiling cutting in an embodiment.

Detailed Description

The following describes embodiments of the invention in connection with data set B2 in topic B of the study mathematics modeling large scale of 2022:

the B2 group data contains the information of the length, the width, the required materials, the belonged orders and the like of the product items, and totally relates to 146 original plate materials and 403 groups of orders.

Executing the first step: and determining similar conditions, and establishing a one-dimensional array according to the total number of required materials.

Counting all kinds of materials in all orders to obtain a kind number of 146, and establishing a one-dimensional array of required materials with the length of 146 for each order. If the order has the product item which needs a certain material, the corresponding position of the array is filled with the number of the product item which needs the material, if not, the corresponding position is filled with zero, and finally the array is normalized.

Executing the second step: similar orders are combined into a batch using Pearson correlation coefficients.

after the correlation coefficient matrix among each order is obtained, different orders are selected to form the same group according to the sequence from the big correlation coefficient to the small correlation coefficient. During batch, certain batch constraints exist according to practical production limits. In this case, the total number of product items in a single batch cannot be more than 1000, and the total area of product items in a single batch cannot be more than 250m due to capacity limitation ² All orders were eventually divided into 26 batches.

Executing the third step: the 26 batches were treated separately. In the same batch, the square piece data of the same material are preprocessed by cutting the materials separately.

All orders are processed batch by batch, in each batch, square pieces of the same material are put together for cutting. The length of the long side of each product item which needs the same material is taken as the length of the product item, the length of the short side of each product item is taken as the width of the product item, and the original sheet specification is 2440 x 1220 (mm). Data with the length of 1220mm-2440mm in the product item needing the same material is extracted to form a set, and different sets are formed according to different materials.

Executing the fourth step: and respectively applying a large product item cutting method taking the width of the original sheet as a resolution standard to start cutting on different sets of different batches.

The cutting is performed batch by batch, and in each batch, the cutting is performed separately according to the material. For example, in a first batch, 28 materials are required, with the product items of each material each making up a collection of 28 total collections. For each set, a large product item cutting method with the original sheet width as a resolution standard is applied to cut, and the large product item and part of small product items in each set are cut, as shown in fig. 10.

Executing the fifth step: and (3) respectively applying a small product item intensive paving method to different sets of different batches to arrange the rest small product items.

Cutting the rest small product items in each set of each batch, and arranging the rest small product items by using a small product item dense paving method. As shown in fig. 11. After the arrangement is finished, the product items in each set are cut. Still processing the batch by batch, cutting the next batch after all the sets of one batch are cut, and completing all the order tasks until all the batches are completed.

For the two-stage cutting method provided by the invention, namely the large product item cutting method and the small product item dense paving method which take the width of the original sheet as a resolution standard, four groups of data are used for testing, and good material utilization rate is obtained, as shown in table 1. The invention is applied to B2 data in the B problem of the 2022 study mathematics modeling large race, and the utilization rate of materials obtained by taking the first four batches is shown in table 2. As can be seen from a comparison of tables 1 and 2, in practical problems, the utilization of materials is reduced after the batching of orders is considered. Under the practical production constraint, the invention still has good material utilization rate and can be well applied to production practice.

Table 14 group data material utilization

Table 2B2 group data material utilization

Claims

1. A layout optimization and order batching method based on square features and Pearson correlation coefficients is characterized by comprising the following steps:

step one: firstly, counting all kinds of materials in all orders, and establishing a one-dimensional array of required materials for each order;

step two: the material array of each order can reflect the material requirement condition of each order, and the similar orders are combined into a batch by using the Pearson correlation coefficient;

step three: taking the length of the long side of each product item as the length of the product item, taking the length of the short side of each product item as the width of the product item, and screening out large product items by combining the original piece specification information;

step four: cutting is started by using a large product item cutting method with the width of the original sheet as a resolution standard, the large product item is firstly cut, and the rest part of the original sheet after the large product item is cut is used for cutting a proper small product item;

step five: and arranging the rest small product items by using a small product item dense paving method, and finally finishing cutting of all the products.

2. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the first step is:

if the order has the product item which needs a certain material, the corresponding position of the array is filled with the number of the product item which needs the material, if not, the corresponding position is filled with zero, and finally the array is normalized.

3. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the step two is:

1) Calculating correlation coefficients among the material arrays by applying a Pearson correlation coefficient formula, so as to obtain a correlation coefficient matrix among each order, wherein the Pearson correlation coefficient formula is as follows:

wherein r is a correlation coefficient, and x and y are two variables;

2) After the correlation coefficient matrix among each order is obtained, different orders are selected to form the same group according to the sequence from the big correlation coefficient to the small correlation coefficient.

4. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the fourth step is:

1) Cutting a first original piece by using the maximum value La1 of the length of a product item in A, firstly, arranging a left space, taking the length Lb1 obtained by subtracting La1 from the long side of the original piece as the corresponding data classification standard of the first original piece, forming a corresponding data group B1 of the first original piece by using data with the length smaller than 1220mm and the width smaller than or equal to Lb1, wherein if the corresponding data group data is empty, the short plates obtained after the first knife cutting are waste materials, if the corresponding data group data is not empty, continuously cutting plates in the set A on the long plates by taking the width as constraint from La1 in the order from long to short after the first stage cutting, until the rest width of the original piece cannot be used for arranging the next product item, and temporarily counting the rest plates into a waste material set C at the moment, wherein the first stage cutting on the left side;

2) When the left-side second-stage cutting is carried out, an unordered product item with the width smaller than the residual width of the current original sheet is searched, if the length of the product item is smaller than La1, the product item can be put into a temporary waste collection C, and waste is reused.

3) The third stage cutting on the left side has two cases, one is directly used for completing the production of the product item by the third stage cutting, and the second is used for completing the production of the product item by the second stage cutting, wherein the left side is used for completing the production of the product item by the third stage cutting because the width is not full.

5. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the fourth step is:

when the left side does not have a layout space, the right side is vertically arranged, firstly, the product items with the width smaller than the current maximum remaining length and the length smaller than 1220mm are selected and arranged at the left lower corner of the right original piece, the product items with the width smaller than the front product items and the length smaller than the remaining width of the original piece after the front product items are arranged at the upper side of the front product items, the left side is aligned, when the remaining width cannot arrange the next product item, a row is opened again, the arrangement is started from the bottom, and when the length of the right side is fully arranged, the next original piece is arranged.

6. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the fourth step is:

the first-stage cutting on the right side produces temporary scraps into which product items conforming to the size are discharged from the unordered product items, which can further increase the material utilization rate, and the vertical row on the right side has a certain advantage in that the original sheet can be cut into vertical strips by the first-stage cutting.

7. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the fourth step is:

after the whole process of the large product item cutting method taking the width of the original sheet as a resolution standard is completed, the rest product items are continuously arranged by a small product item dense paving method.

8. The method for optimizing stock layout and batching orders based on square features and Pearson correlation coefficients according to claim 1, wherein the fifth step is:

1) Sequencing all the remaining product items from large to small according to the width, sequentially arranging the product items from the left lower corner of the original sheet in sequence, starting to arrange the next sheet upwards when the length sum exceeds 2440mm, starting to arrange the next product item from the left lower corner of the original sheet when the width sum exceeds 1220mm, arranging the product items on the original sheet according to the arrangement method until all the product items are arranged, and arranging the product items with similar widths in one row by the method, so that the waste rate is reduced;

2) The method can generate the same primary sheet length temporary waste and width temporary waste as the large product item cutting method with the primary sheet width as the resolution standard, and the same method is used for preferentially searching the product item which accords with the largest area in the size of the waste and discharging the product item into the waste, so that the material utilization rate can be increased.