CN116307053A - Layout Optimization and Order Grouping Method Based on Square Parts Features and Pearson Correlation Coefficient - Google Patents

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

Layout optimization and order batching based on square piece features and Pearson correlation coefficient method

technical field

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

Background technique

In view of the characteristics of many varieties of personalized customization and huge orders, the current production organization mostly adopts the mode of "order batching + mass production + order sorting" for production. In this production mode, order batching and layout optimization are very important.

Order batching is to combine different orders into a certain number of batches under the limitation of actual production capacity. When grouping batches, the contradiction between individualization and production efficiency must be resolved; layout optimization is essentially a blanking problem, and square parts are optimized. Layout on the original sheet to reduce sheet waste during blanking and simplify the cutting process.

When batching orders, generally according to the similarity of different orders, similar orders are grouped into several batches, which is conducive to batch processing, improves production efficiency, and shortens the delivery cycle.

When cutting, according to different cutting processes, it can be divided into two methods: straight cutting and non-flat cutting. The straight cutting method refers to a straight line cutting perpendicular to one side of the square piece, and the square is cut every time. The square piece is divided into two pieces; the non-flush method does not need to divide the square piece into two pieces every time it is cut. Comparing the two methods, the cutting process of straight cutting is simpler, and the cutting methods of non-uniform cutting are more diverse.

It can be subdivided into precise mode and non-precise mode. The precise way can get all the products after a specific cutting stage, while some products cut in the non-precise way need one more cutting stage than other products. After determining the cutting stage, the precise method can get all the products after completing all the cutting stages, while the inaccurate method will increase the cutting workload on the basis of completing all the cutting stages.

The cutting stage mentioned above is proposed because the cutting direction is different each time during the cutting process, and the cutting direction is the same at the same stage. If there are too few stages, the desired product cannot be obtained, and if there are too many stages, the cutting workload will be increased. Therefore, it is necessary to select the appropriate cutting stage to complete the cutting task with maximum efficiency. Common cutting stages are 3-4 at most. Taking the 3-stage cutting as an example, the modules generated by the first-stage cutting are called stripes in the present invention, such as Stripe1 and Stripe2; the modules generated by the second-stage cutting are called stacks in the present invention, such as Stripe1 Continue to be divided into Stack1, Stack2, etc.; the module generated by the third stage cutting is called item (product item), for example, Stack1 is continuously divided into Item1, Item2, etc.

The main purpose of order batching and layout optimization is to maximize the utilization rate of plates, that is, to meet:

Among them, γ is the plate utilization rate, S _i is the area of each product item, n is the total number of product items, n _{is originally} the number of original sheets, and S _{is originally} the area of the original sheet.

At present, most of the research on order batching adopts the clustering method, selects the appropriate target according to the characteristics of different orders, and establishes the clustering model under specific constraints. However, the batching of product orders in different production fields will have different constraints, and the optimization goals will also be different. There is a problem of mutual coupling between order batching and layout optimization for square parts, so the collaborative optimization of batching and layout is required. However, the current research on the layout optimization problem is more at the theoretical level, without considering the impact of the actual situation on the production efficiency such as the way of cutting or not cutting and the cutting stage. Specially shaped square pieces are optimized. In the face of a variety of product orders, a large number and a variety of square products, many methods are not generally applicable.

Contents of the invention

The object of the present invention is to propose a kind of layout optimization based on square piece feature and Pearson correlation coefficient and order batching method, overcome current order batching and layout optimization problem research because do not consider the coupling problem between the two and traditional arranging The sample optimization method itself cannot be generally applied to the "small batch, many types" square piece orders, which is not suitable for the actual production. By taking the plate materials required by different orders as similar targets, the orders are grouped by applying the Pearson correlation coefficient , in order to make the same batch use the same plate method as much as possible, and solve the collaborative optimization problem of batch and layout; under the constraints of simultaneous cutting, 3-cutting stages and precise layout, by considering the characteristics and differences of the original plate The characteristics of square pieces are used to preprocess a group of square piece data that requires the same type of plate, distinguish large product items from small product items, and then arrange square pieces to make the cutting efficiency of this arrangement method when cutting square pieces Higher and generally applicable to all kinds of square parts, it adapts to the actual production of square parts and can better guide the production work of enterprises.

The purpose of the present invention is achieved through the following technical solutions: set up a one-dimensional array of required materials for each order, normalize the array, apply the Pearson correlation coefficient to obtain the similarity between each order, and combine the high similarity Orders are combined into a batch according to production constraints. In the same batch, all square pieces requiring the same original sheet material are cut uniformly. Before cutting, the product item data is preprocessed first to separate large product items and small product items, then the large product items are cut first, and finally the small product items are densely paved to achieve layout optimization.

Flow chart of the present invention is as shown in Figure 1, and concrete steps are as follows:

Step 1: Identify similar conditions.

The present invention first counts all types of materials in all orders, and establishes a one-dimensional array of required materials for each order. If there is a product item that requires a certain material in the order, fill in the number of product items that require the material in the corresponding position of the array, if not, fill in zero in the corresponding position, and finally normalize the array.

Step 2: Apply the Pearson correlation coefficient to combine similar orders into a batch.

The material array of each order can reflect the material requirements of each order. In this way, the present invention can know whether the material requirements of each order are similar as long as the similarity comparison is performed on the material arrays of each order. If the similarity is 1, the two orders require the same material. If the similarity is not greater than 0, the materials required by the two orders are not the same. The present invention calculates the correlation coefficient between each material array by applying the Pearson correlation coefficient formula, and then obtains the correlation coefficient matrix between each order. The Pearson correlation coefficient formula is as follows:

Among them, r is the correlation coefficient, and x and y are two variables.

The correlation coefficient matrix is shown in Figure 2. After obtaining the correlation coefficient matrix between each order, select different orders to form the same batch according to the order of correlation coefficient from large to small.

Step 3: In the same group of batches, cut by material, and preprocess the square piece data of the same material.

First, 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. Take the original film size of 2440*1220 (mm) as an example. Extract the data whose length is between 1220mm-2440mm in the product item to form set A.

Step 4: Use the large product item cutting method based on the original film width to start cutting.

The first piece of original film is cut with the maximum length L _a1 of the product item in A, and the space on the left side is arranged first. The length L _b1 obtained by subtracting L _a1 from the long side of the original film is used as the corresponding data classification criterion of the first original film, and all data whose length is less than 1220mm and width is less than or equal to L _b1 form the corresponding data group B1 of the first original film. If the data in the corresponding data set is empty, the short boards obtained after the first cutting are all waste. If the data of the corresponding data set is not empty, after the first stage of cutting, start from L _a1 on the long board in order from long to short, and continue cutting the boards in set A with the width as the constraint, until the remaining width of the original board cannot be arranged. A product item, at this time the remaining boards are temporarily included in scrap collection C. This is the first stage cut on the left, as shown in Figure 3.

When performing the second stage cutting on the left side, look for unarranged product items whose width is smaller than the remaining width of the current original film. If the length of the product item is less than La1, it can be put into the temporary waste collection C, and the waste can be reused. This method is beneficial to reduce the waste output rate. However, within the remaining width of the current original film, only one product can be arranged in the length direction, otherwise the fourth stage of cutting will occur. The schematic diagram of the second stage cutting on the left is shown in Figure 4.

There are two cases of the third-stage cutting on the left side, one such as item2 shown in Figure 5, where the production of the product item is completed directly by means of the third-stage cutting. The second type, such as item4 shown in Figure 5, needs to use the second-stage cutting to cut off the remaining width because the width is not fully occupied, so that the third-stage cutting can be used to complete the production of the product item.

When there is no layout space on the left side, start to arrange the right side. As shown in Figure 6, the product items on the right are arranged vertically. First, select the product items whose width is less than the current maximum remaining length and whose length is less than 1220mm, and arrange them in the lower left corner of the original film on the right. Select a product item whose width is smaller than the previous product item and whose length is smaller than the remaining width of the original film after placing the previous product item, and arrange it on the upper side of the previous product item, left-aligned. When the remaining width cannot arrange the next product item, open another A column is rearranged from the bottom, and when the length of the right side is full, arrange the next original piece.

At this time, the cutting in the first stage on the right will produce three pieces of temporary waste, item10, item11 and item12. Find product items that match the size from the unarranged product items and discharge them into these wastes. This solution can further increase the material utilization rate. The vertical row on the right side has certain advantages. It can use the first-stage cutting to first cut the original sheet into vertical strips, as shown in Figure 7.

Carry out the second-stage cutting of the vertical strips to obtain the plate as shown in Figure 8.

The third stage of cutting on the right is shown in Figure 9. So far, the whole process of the large product item cutting method based on the original film width is completed, and the remaining product items will continue to be arranged by the small product item intensive paving method.

Step 5: Apply the dense paving method of small product items to arrange the remaining small product items.

Sort all remaining product items in descending order of width, and arrange them in order from the lower left corner of the original film. When the length sum exceeds 2440mm, the next board starts to line up, opening the second row. When the width exceeds 1220mm, the next product item is arranged from the lower left corner of the next original piece. Arrange the product items on the original sheet according to the above arrangement method until all the product items are arranged. Through this method, product items with similar widths can be arranged in a row, so that the scrap rate is reduced. This method will produce the same temporary waste of the length and width of the original film as the cutting method of large product items based on the width of the original film. Using the same method, first find the product item with the largest area in the waste size and discharge it into the waste. Material utilization can be increased.

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

1) The present invention combines actual production and overcomes the shortcomings of ignoring practical limitations such as cutting methods in the current research. Under the constraints that need to be faced during actual cutting such as head-to-head cutting and three-stage cutting, the length of the product item and the original film, Width information, a two-stage method such as the cutting method of large product items and the dense paving method of small product items based on the original sheet width is proposed, which greatly improves the utilization rate of the board while meeting the order requirements and related constraints. The production of waste is reduced and can be used to guide actual production.

2) The present invention makes full use of order information and product information in the process of solving the problem. When analyzing the order correlation, a correlation coefficient matrix is established based on the Pearson coefficient; when optimizing the layout, the length and width information of the product item and the original film are used. The use of these information greatly guarantees the rationality and operability of product item layout and order batching.

Description of drawings

Fig. 1 is a flow chart of layout optimization and order batching method based on square piece features and Pearson correlation coefficient.

Figure 2 is the correlation matrix.

Figure 3 is a schematic diagram of the first stage cutting on the left.

Figure 4 is a schematic diagram of the second stage cutting on the left.

Figure 5 is a schematic diagram of the third stage cutting on the left.

Figure 6 is a schematic diagram of cutting on the right side.

Figure 7 is a schematic diagram of the first stage cutting on the right side.

Figure 8 is a schematic diagram of the second stage cutting on the right.

Figure 9 is a schematic diagram of the third stage cutting on the right side.

Fig. 10 is a schematic diagram of the cutting results of the large product item cutting method with the width of the original film as the resolution reference during specific implementation.

Fig. 11 is a schematic diagram of the cutting results of the small product item dense paving method during the specific implementation.

Detailed ways

The following describes the specific implementation of the present invention in conjunction with the B2 group data in the 2022 Postgraduate Mathematical Modeling Contest B question:

The data in group B2 includes information such as product item length, width, required materials, and orders, involving 146 original board materials and 403 groups of orders.

Execute Step 1: Determine similar conditions, and create a one-dimensional array based on the total number of required materials.

Count all types of materials in all orders, and get 146 types, and create a one-dimensional array of required materials with a length of 146 for each order. If there is a product item that requires a certain material in the order, fill in the number of product items that require the material in the corresponding position of the array, if not, fill in zero in the corresponding position, and finally normalize the array.

Execute Step 2: Apply Pearson correlation coefficient to combine similar orders into one batch.

The material array of each order can reflect the material requirements of each order. In this way, the present invention can know whether the material requirements of each order are similar as long as the similarity comparison is performed on the material arrays of each order. If the similarity is 1, the two orders require the same material. If the similarity is not greater than 0, the materials required by the two orders are not the same. The present invention calculates the correlation coefficient between each material array by applying the Pearson correlation coefficient formula, and then obtains the correlation coefficient matrix between each order. The Pearson correlation coefficient formula is as follows:

After obtaining the correlation coefficient matrix between each order, select different orders to form the same batch according to the order of correlation coefficient from large to small. When grouping batches, according to actual production constraints, there will be certain batch constraints. In this example, due to capacity constraints, the total number of product items in a single batch cannot exceed 1000, and the total area of product items in a single batch cannot exceed 250m ² . Finally, all orders are divided into 26 batches.

Execute Step 3: Process the 26 batches separately. In the same group of batches, the material is cut, and the data of square pieces of the same material is preprocessed.

All orders are processed in batches, and within each batch, square pieces requiring the same material are put together for cutting. Take the length of the long side of each product item requiring the same material as the length of the product item, and the length of the short side of each product item as the width of the product item. The original film size is 2440*1220 (mm). Extract the data whose length is between 1220mm-2440mm from the product items requiring the same material to form a collection, and form different collections according to different materials.

Execute Step 4: Apply the large product item cutting method based on the original film width to start cutting for different batches and different collections.

Cutting is performed batch by batch, and in each batch, cutting is performed separately according to the material. For example, in the first batch, 28 kinds of materials are required, and the product items of each material form a set, and there are 28 sets in total. For each set, the large product item cutting method based on the original film width is used for cutting, and the large product item and some small product items in each set are cut out, as shown in Figure 10.

Execute Step 5: Apply the small product item dense paving method to different batches and different sets to arrange the remaining small product items.

The remaining small product items in each set of each batch are cut, and the remaining small product items are arranged by applying the dense paving method of small product items. As shown in Figure 11. After the arrangement is complete, the product items in each set are cut. It is still processed batch by batch. After all the sets of a batch are cut, the next batch is cut until all batches are completed, that is, all order tasks are completed.

For the two-stage cutting method proposed by the present invention, the large product item cutting method and the small product item intensive paving method based on the original film width, the present invention uses four sets of data to test, and obtains a good material utilization rate. As shown in Table 1. Applying the present invention to the data of group B2 in question B of the 2022 Postgraduate Mathematical Modeling Contest, the material utilization rate obtained by taking the first four batches is shown in Table 2. By comparing Table 1 and Table 2, it can be seen that in practical problems, after considering the batching of orders, the utilization rate of materials will decrease. Under the constraints of actual production, the present invention still has good material utilization rate and can be well applied in production practice.

Table 1 4 groups of data material utilization rate

Table 2 B2 data material utilization rate

Claims (8)

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.

Images