JP2007164580A - Production control system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve productivity/efficiency comprehensively by making a proper work instruction to each processing equipment in a production line adopting a job-shop production system. <P>SOLUTION: A flexible production control system having high overall efficiency is provided, which calculates an overall index that can weight a main index on the basis of a device state and a lot state for individual optimization but for improving the overall efficiency of a production line about items such as lead time, a device operating ratio, device efficiency and punctuality which are main efficiency indexes in a production line, and prepares a lot processing sequence corresponding to production status and index importance at that time and a process processing pattern. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a production control system for a manufacturing factory or the like that takes a production form of a job shop type in a variety of small quantities.

  In general, in every production line, complying with the delivery date of each lot and shortening the production lead time as much as possible are important items for efficient production. In order to operate the production line efficiently, various production forms such as a flow shop type, a job shop type, and an open shop type are practiced according to the process of the target product to be produced.

  In the semiconductor production line, there are many varieties to produce and the production process is complicated, so it is difficult to produce efficiently with a simple flow shop type. The job shop type is used for process processing. Among the production forms taking the job shop form, especially in the semiconductor production line, the manufacturing equipment that is more expensive than the production line of other products such as sputtering and stepper equipment is used as the processing equipment. In addition to an evaluation index such as time reduction, an evaluation index representing the operation rate of the apparatus is a major factor in evaluating the efficiency of the production line. Therefore, in the semiconductor production line, the operation rate of the apparatus is a main evaluation index that is indispensable when considering the overall efficiency of the production line.

  Thus, the weighting of the evaluation index in the production line may differ depending on factors such as the production target and production equipment. In addition, the constituent elements are different for each evaluation index.

  For example, there is a method for maximizing the throughput of the apparatus in order to improve the operating rate of the apparatus. For this, it is necessary to supply lots according to the processing method of each device. Generally, by continuously supplying lots that can be processed under the same recipe (conditions), time loss caused by recipe switching is reduced. In the reduction or batch knitting apparatus, processing is performed in a full batch to improve throughput.

  In addition, various evaluation index improvement methods have been devised and practiced by analyzing components of various evaluation indices. However, as mentioned above, there are many restrictions and factors to be considered, such as semiconductor production lines that produce a variety of products in small quantities, such as the weighting of the evaluation index varies depending on the production line, and various operating conditions and delivery times of the production equipment that operates. In addition, it is said that it is very difficult to improve the efficiency of the production line comprehensively because the evaluation indicators are not independent but interact with each other.

  Under these circumstances, many production control systems and simulation methods for improving the efficiency of production lines have been proposed, and examples thereof can be found in the following documents.

For example, in Patent Document 1, as a method for performing full batch processing, a schedule for processing in a full batch is created by combining a processing waiting lot in the device and a real-time scheduling device that predicts the arrival time of an unarrived lot in the device. There is a way to do it. Further, in Patent Document 2, a database of various states is created in order to appropriately set the input timing of the lot to be processed into the apparatus, and on this basis, the scheduling of the lot input into the apparatus is simulated, and the schedule efficiency The thing etc. which aimed at the improvement of are proposed.
JP-A-8-24115 JP-A-8-31709

  As shown in FIG. 14, in the method of Patent Document 1, the batch knitting process determines the arrival of the batch knitted lot by the latest start time of the batch knitting waiting lot, the scheduled arrival time of the batch knitted lot, and the current time. This mechanism is used to determine whether or not to start process processing. This mechanism is effective in increasing the number of batch formations while keeping delivery times, but the scheduled arrival time of batch-formable lots is calculated in advance by the scheduler. Therefore, it is insufficient that the possibility of advancing the estimated arrival time of the batch knitted lot by a method such as advancing the processing order of the batch knitted lot is advanced.

  In addition, such a method is intended to increase apparatus efficiency, which is one element of the evaluation index, and does not take into consideration improvement or improvement of other evaluation indices. Since Patent Document 2 also focuses on improving the efficiency of the apparatus, it cannot be said that the improvement of the efficiency of the entire production line is taken into consideration.

  In order to improve overall production line efficiency, it is not sufficient to optimally adjust each evaluation index individually. Important factors such as longer lead times, lower operating rates, lower equipment efficiency, and delayed delivery are important. Focusing on the elements, these evaluation indicators should be considered simultaneously and evaluated from a comprehensive perspective. In other words, it is important to optimize a plurality of evaluation indices in a comprehensive manner after balancing each other. On the other hand, in an actual production line, the importance of various evaluation indices in the production line changes according to inventory and market trends, so the importance of these production line evaluation indices is always constant. However, since the importance varies depending on the situation, it is desirable to be able to respond flexibly.

  The present invention relates to an evaluation index for evaluating various productivity / efficiency in a production line, and balances each evaluation index without biasing to one, so that lot processing that improves productivity / efficiency comprehensively is achieved. An object of the present invention is to provide a production control system capable of flexibly responding to a production situation while selecting an order and a process processing pattern based on the order.

  In order to achieve the above object, the present invention obtains the status data of each lot and the status data of each device of the process in a production line that takes a form of a job shop that processes a plurality of processes and a plurality of lots. Create a combination of lot processing order that can be taken, combine the processing order of lots of each process, configure all process processing patterns of all processes, state data of each lot, and status data of each device Based on the evaluation points obtained based on the process processing pattern, the process processing pattern with the best evaluation point is selected, and each device in the processing order of the lots of each process constituting the process processing pattern with the best evaluation point It is characterized by controlling.

  Also, for example, in a production line that takes the form of a job shop that processes a plurality of processes and a plurality of lots, the status data of each lot and the status data of each device of the process are acquired, and the processing order of lots that each process can take From the evaluation points obtained based on the status data of each lot and the status data of each device, all the process processing patterns of all the processes are configured by combining the lot processing order of each process. A first computing device that selects a process processing pattern with the best evaluation score from among the process processing patterns, and a lot of each process that makes up the best process processing pattern with the evaluation score obtained from the first computing device. It is good also as providing the 2nd calculation apparatus which controls each apparatus based on these processing orders and supplies a lot to each apparatus.

  Further, for example, the evaluation score may be calculated based on a lot processing lead time evaluation index, an apparatus operation rate evaluation index, an apparatus efficiency evaluation index, and a lot delivery date delay rate evaluation index. Good.

  Further, for example, the evaluation score may be calculated based on each evaluation index constituting the evaluation score multiplied by a weighting coefficient.

  For example, the weighting coefficient of the evaluation point may be variable.

  According to the configuration of the present invention, in a production line that takes a form of a job shop that processes a plurality of processes and a plurality of lots, the status data of each lot and the status data of each device in the process can be acquired, and each process can take Create a combination of lot processing order, combine lot processing order of each process, configure all process processing patterns of all processes, and obtain based on the status data of each lot and the status data of each device The process processing pattern with the best evaluation point is selected from the process processing patterns from the evaluation points to be controlled, and each device is controlled in the processing order of the lots of the respective processes constituting the process processing pattern with the best evaluation point. It was decided.

  By configuring in this way, from the data of both the state of the lot and the state of the device, the best evaluation point showing a comprehensive evaluation based on various evaluation indexes, the process processing pattern of all processes is extracted, Based on this, the lot processing order can be instructed to each device on the production line, and production control taking into account the various conditions obtained at the time of scheduling is performed to increase the efficiency of the production line comprehensively. It becomes possible.

  Also, in a production line that takes the form of a job shop that processes multiple processes and multiple lots, the status data of each lot and the status data of each device in the process are acquired, and combinations of lot processing orders that each process can take The process order of lots in each process is combined to form all process process patterns for all processes, and process processing is performed from the evaluation data obtained based on the status data of each lot and the status data of each device. A first computing device that selects a process processing pattern with the best evaluation point from among the patterns, and a lot processing for each process that makes up the best process processing pattern with the evaluation point obtained from the first computing device Based on the order, each apparatus is controlled, and a second calculation apparatus that supplies a lot to each apparatus is provided.

  By comprising in this way, the 1st calculation apparatus WHEREIN: From the data of both the state of a lot, and the state of an apparatus, the evaluation point which shows the comprehensive evaluation based on various evaluation indexes is the best process of all processes The processing pattern is extracted, and the second calculation device acquires this result, and based on this, performs control of each device and supply of lots, so information acquisition of equipment and the like, schedule calculation and production control are performed. By sharing, the addition of computers can be dispersed, and since it is divided by function, it is possible to improve the efficiency of the production line comprehensively while facilitating troubleshooting and maintenance.

  Further, for example, the evaluation score is calculated based on a lot processing lead time evaluation index, an apparatus operation rate evaluation index, an apparatus efficiency evaluation index, and a lot delivery date delay rate evaluation index.

  By being configured in this way, the evaluation points are the main evaluation indexes for production line efficiency, such as lead time evaluation index, equipment operation rate evaluation index, equipment efficiency evaluation index, and delivery delay rate evaluation index. Therefore, the obtained evaluation points always reflect all these evaluation indexes. And since the process processing pattern of all the processes with the best evaluation score is extracted from these evaluation scores, the processing order of lots is instructed to each device of the production line based on this, and the production control is performed. It is possible to improve the efficiency of the production line.

  In addition, the evaluation score is calculated based on each evaluation index constituting the evaluation score multiplied by a weighting coefficient.

  By configuring in this way, the weight of each evaluation index of the lead time evaluation index, the device operation rate evaluation index, the device efficiency evaluation index, and the lot delivery date delay rate evaluation index evaluation index can be adjusted as necessary. As a result, it is possible to increase the overall efficiency of each production line by instructing the processing order of lots to each device on the production line with emphasis on highly important evaluation indexes in each production line. .

  In addition, the weighting coefficient of the evaluation score is variable.

  By configuring in this way, the main evaluation indicators such as lead time evaluation index, equipment utilization rate evaluation index, equipment efficiency evaluation index, and delivery delay rate evaluation index are changed to the production status and the importance of the evaluation index at that time. Accordingly, the weighting is flexibly adjusted to comprehensively evaluate the production line efficiency, and based on this, the lot processing order is created. Therefore, comprehensively optimized production control is performed while paying attention to important evaluation indexes. Can be done.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS. First, a block diagram showing an overall configuration of a production control system according to an embodiment of the present invention will be described with reference to FIG. The production control system includes a production management computer 1 that is a first computing device, a device control computer 2 that is a second computing device, a transport facility 3, a recording device 4, and production facilities S1 to SN that are processes for processing a lot. Consists of.

  The production management computer 1 as a first computing device is a computer that manages each device of production equipment S1 to production equipment SN (hereinafter referred to as production equipment (S1 to SN)) of a production line, and each production equipment (S1 to S1). (SN) status data of the device representing the operating status, processing capability, etc. is acquired, and recorded in the recording device 4 and stored. The production management computer 1 also acquires lot status data indicating the processing status or delivery date of each lot scheduled for processing or being processed, and records / stores it in the recording device 4.

  Then, the production management computer 1 creates a lot processing order for each device based on the device status data and the lot status data, and transmits the lot processing order to the device control computer 2 as a second computing device. Based on this processing order, the apparatus control computer 2 controls the apparatus of each production facility (S1 to SN) to process each lot. Moreover, the apparatus control computer 2 controls each lot to be conveyed to each production facility (S1 to SN) by the conveyance facility 3 based on this processing order. In this way, each lot is sequentially processed in a plurality of steps in accordance with the corresponding model (product) to reach a finished product.

  Next, the flow of lot processing sequence and process processing pattern creation of each apparatus will be described with reference to FIGS. FIG. 2 is a creation flowchart showing a flow from creation of a lot processing order of each process to determination of the best process processing pattern. FIG. 3 is a process flow chart showing a process flow. FIG. 4 is a diagram showing a combination of lot processing orders in step 1. FIG. 5 is a diagram showing total evaluation points as evaluation points indicating the total efficiency of the production line of each process processing pattern.

  The flow of lot processing order and process processing pattern creation for each device is as follows. First, a candidate for a process pattern is created as << Procedure 1 >>.

<< Procedure 1-1 >> Lot Processing Order Combination Creation for Each Process A lot processing order combination creation for each process is created from a production facility that processes process 1 as the first process. The production management computer 1 calculates all combinations of the processing order of the processing waiting lots of the production facility that processes the process 1 recorded in the recording device 4 and holds them in the memory in the production management computer 1.

<< Procedure 1-2 >> Expected calculation of process start time and process end time for each lot processing order combination For each lot processing order combination calculated in <Procedure 1-1 >>, the processing order for each lot The processing time of step 1 based on the above can be calculated, and the expected process start time and expected process completion time in each lot can be obtained. By adding the transport time to the next process to this, the lot arrival time at each of the next processes (process 2-1 and process 2-2 in FIG. 3) is calculated.

  Subsequently, for each of the steps 2-1 and 2-2, a combination of lot processing orders is created for all lots in the same manner as in <Procedure 1-1>. Then, according to the flow of << Procedure 1-2 >>, the arrival time at each next process is calculated for each of the processes 2-1 and 2-2. Thereafter, by repeating this operation until the final process, it is possible to calculate the combination of lot processing orders in all processes and calculate the expected process start time, expected process completion time, and lot arrival time in each process of each lot.

  << Procedure 1-3 >> Deletion of Process Process Patterns with Inconsistency between Process Process Pattern Combination Creation and Process Process Flow

  Next, the lot processing order of each process calculated above is combined for each process to create all combinations of process processing patterns in all processes. Then, the production management computer 1 takes out the process processing flow from the recording device 4 and is compared with all the process processing patterns created above, and there is a temporal contradiction or is described in the process processing flow. An invalid process pattern that does not match the existing process order is excluded.

  << Procedure 2 >> Calculation of overall evaluation points for process pattern

  As the lead time evaluation index for each lot constituting this process processing pattern, from the above result, lot state data, apparatus state data, etc. in each effective process processing pattern created in << Procedure 1 >> The lead time evaluation point / delivery time delay rate evaluation index, and the equipment efficiency as the equipment non-working time / efficiency evaluation index as the operation rate evaluation index for each device that constitutes this process processing pattern are calculated. Based on this, a predetermined calculation is performed to calculate a comprehensive evaluation score.

  << Procedure 2-1 >> Calculation of Lead Time Evaluation Score

  The lead time, which is the difference between the actual process start time of the first process and the scheduled completion time of the final process, is obtained for all lots. Then, the difference between the processing start time and the processing completion time, which is the processing time of each process, is obtained as the sum of all processes, and this is used as the lead time evaluation point for each lot.

《手順２−２》納期遅延率評価点の算出 Formula 1. Lead time evaluation point calculation formula

<< Procedure 2-2 >> Calculation of delay rate evaluation point for delivery

  The difference between the delivery date set for each lot and the scheduled delivery date is obtained, and the ratio of the number of lots expected to be shipped by the delivery date in the shipment lot is set as the delivery delay evaluation point.

  Formula 2. Delivery delay rate evaluation point calculation formula

《手順２−３》装置非稼働時間の算出
各装置におけるロット処理見込時間（処理開始見込時刻−処理完了見込時刻）の総和を求め（稼働見込時間）、それを生産ライン稼働時間から減じて、装置非稼働時間を算出する。

<< Procedure 2-3 >> Calculation of equipment non-operation time Obtain the total of lot processing expected time (processing start expected time-processing completion expected time) in each device (operation expected time) and subtract it from the production line operating time. The device non-operation time is calculated.

《手順２−４》装置効率の算出 Formula 3. Equipment non-operation time calculation formula

<< Procedure 2-4 >> Calculation of apparatus efficiency

  The expected operating time and the number of expected processing lots in each device are obtained, and the device efficiency is obtained by dividing the expected operating time by the number of expected processing lots. In other words, it can be said that the lower the value, the higher the processing amount per unit time and the higher the processing efficiency.

Formula 4. Equipment efficiency calculation formula

  Then, based on the respective process processing patterns from the four evaluation points (indexes) calculated in << Procedure 2-1 >> to << Procedure 2-4 >>, the sum of the lead time evaluation points of all lots of this process processing pattern, Total process date for all lots, total operation rate of all devices, and device efficiency of all devices are calculated and multiplied by weighting parameters as weighting factors. The overall evaluation score of the pattern is calculated.

但し、α・β・δ・εは重み付けパラメータとする。
《手順３》総合評価点が最良となる工程処理パターンの決定 Formula 5. Comprehensive score calculation formula

However, α, β, δ, and ε are weighting parameters.
<< Procedure 3 >> Determination of process treatment pattern with the best overall evaluation score

  Comparing the overall evaluation points of all effective process processing patterns calculated in << Procedure 1 >> to << Procedure 2 >>, extracting the process processing pattern that satisfies this as the best score that minimizes the overall evaluation score, and adopting it To do.

  The above is the flow of calculation of the optimum process processing pattern in the present invention. The process processing patterns of all the processes extracted in this way are evaluated by comprehensive evaluation points based on the evaluation indices related to lead time, equipment availability, equipment efficiency, and delivery delay, which are the main evaluation indices of the production line. Among them, since the overall evaluation score is the best, the main evaluation index is always reflected, and all the evaluation indexes are comprehensively excellent.

  Based on this process processing pattern, by instructing each device on the production line about the lot processing order, it is possible to control the production line with high efficiency in consideration of various conditions obtained at the time of scheduling. Can be performed.

  Further, with this configuration, the production management computer 1 has the best evaluation score indicating the comprehensive evaluation based on various evaluation indexes from the data of both the lot state and the device state. The process control pattern 2 is calculated / extracted, and the apparatus control computer 2 acquires this result, controls each apparatus and supplies a lot based on this result, and acquires information on equipment, etc., schedule calculation and production control. Since it is shared, the addition of computers can be distributed, and since it is divided by function, it is possible to improve the efficiency of the production line comprehensively while facilitating troubleshooting and maintenance.

  Also, in Equation 5 for calculating the overall evaluation score, each term on the right side is multiplied by a weighting parameter of α, β, δ, and ε. For example, when emphasizing on delivery date, β is replaced with other parameters. By having such a weighting parameter, the main evaluation indicators such as lead time evaluation point, equipment non-operation time, equipment efficiency, and delivery time delay rate evaluation point can be adjusted. In accordance with the importance of the evaluation index at that time, the weighting is flexibly adjusted to comprehensively evaluate the production line efficiency, and based on this, the production control can be comprehensively optimized.

  In the present embodiment, various types of data processing are performed using the production management computer 1 and the apparatus control computer 2, but these data processing can be performed by any computer in a batch or distributed manner.

  Next, the embodiment described so far will be described with reference to FIGS. 6 to 13 by showing more specific examples.

  Here, as a specific example, a flow of determining process process patterns of LOT01 and LOT03 of the model (product) A and LOT02 of the model (product) B in the factory of the three processes and five apparatuses as shown in FIG.

  The model A and the model B have the same processing apparatus for the process 1, and the processes 2 and 3 are processed using different apparatuses. The apparatus 2 is a batch knitting apparatus and can process a maximum of 2 lots simultaneously. Other devices are devices that process one lot at a time. The processing times of steps 1, 2, and 3 are 60 minutes, 120 minutes, and 60 minutes, respectively. For the sake of explanation, the current time is assumed to be 0:00. It is assumed that LOT03 has already completed the process of step 1 at the time of 0:00 and is already in process 2. In addition, a delivery date as shown in FIG. 7 is set for each lot.

  Under the above circumstances, all process processing pattern combinations include a combination of lot processing orders of LOT01 and LOT02 in process 1, and two lots are processed simultaneously in LOT01, LOT02 and LOT03 in process 2-1. There are a combination of lot processing orders and a combination of lot processing orders to be processed separately. Further, there are combinations of lot processing orders of LOT01, LOT02, and LOT03 in step 2-2, step 3-1 and step 3-2, respectively.

  From the combination of the processing order of lots in each of these processes, it is applied according to the process processing flow of model A (process 1 → process 2-1 → process 3-1), and all process processing patterns for model A are created. . For the model B as well, as with the model A, all process processing patterns are created. Then, the process process flow (FIG. 6) and all process process patterns for the created models A and B are collated, and the process process flow has a different processing order or does not exist in the flow (for example, process 2- 2), a process pattern including a process for processing LOT01 is excluded.

  In this manner, effective process processing patterns that match the process processing flow are extracted, and a comprehensive evaluation score is calculated for each of these process processing patterns using Equations 1 to 5.

  Here, for the sake of simplicity, the conveyance time is omitted, and four patterns shown in FIG. Patterns 1 and 2 are for the case where the process 2-1 is made to flow alone, and patterns 3 and 4 are cases where the process 2-1 is made to flow in two batches.

  FIG. 8 shows the expected processing start time and the expected completion time for each pattern. For these four patterns, the results of calculating the lead time evaluation point, the delivery delay evaluation point, the device non-operation time, and the device efficiency using Equations 1 to 4 are shown in FIGS. And based on Formula 5, what totaled the comprehensive evaluation score of each 4 patterns is FIG. (Here, the weighting parameters α, β, δ, and ε are all set to 1.)

  Of the four overall evaluation points obtained in this way, the pattern 2 having the minimum value is extracted as the process processing pattern that provides the best overall production efficiency, and the lots of each process constituting the process processing pattern. Adopt as processing order.

  In such a case, in the prior art, when deciding whether to start from LOT01 or LOT02 in step 1, LOT01 whose delivery date is approaching is often selected. In that case, the cases of patterns 1, 3, and 4 are obtained, and the total lead time evaluation score is 3.25 or 3.50.

  Or, since emphasis is placed on increasing the number of batch lots of the apparatus 2, if the patterns 3 and 4 are employed, the total lead time evaluation score is 3.50.

  However, according to the production control system of the present invention, when all the weighting parameters are 1, the lead time evaluation points of each pattern are as shown in FIG. 9, and the lead time evaluation point of pattern 2 is 3.00, which is the most. It can be seen that the pattern 2 is the best in the overall evaluation point of FIG.

  In other words, even with a pattern such as Pattern 2, which was not selected by the conventional method, a pattern in which LOT02 processing with sufficient time for delivery is started first, the overall production efficiency is high, and the lead time evaluation score is also high. The results are high, and when emphasizing the overall production efficiency and emphasizing the shortening of the lead time, it can be seen that the pattern 2 is most suitable, and the effectiveness of this production control system is clear.

  Although the embodiments of the present invention have been described above, the scope of the present invention is not limited to these embodiments, and various modifications can be made without departing from the spirit of the invention.

Production control system configuration diagram of the present invention Creation flow diagram showing the flow of creating lot processing sequence for each process Process processing flow diagram showing process flow The figure which shows the combination of the lot processing order in process 1 The figure showing the evaluation point (total evaluation point) of each process processing pattern Example of specific configuration based on the present invention (embodiment) Table showing delivery date by lot in the embodiment Table showing the relationship between lots and process patterns in the embodiment Table showing lead time evaluation points in the embodiment Table showing delivery point delay evaluation points in the embodiment Table showing apparatus non-operation time in the embodiment Table showing apparatus efficiency in the embodiment Table showing overall evaluation points in the embodiment Conventional batch knitting process

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Production management computer 2 Apparatus control computer 3 Conveying equipment 4 Recording apparatus S1-SN Production equipment

Claims (5)

In a production line that takes the form of a job shop that processes a plurality of processes and a plurality of lots, obtain the status data of each lot and the status data of each device of the process,
Create a combination of the processing order of the lot that each process can take, combine the processing order of the lot of each process, configure all the process processing pattern of all processes,
Based on the status data of each lot and the evaluation points obtained based on the status data of each device, the process processing pattern with the best evaluation score is selected from the process processing patterns, and the evaluation score is A production control system for controlling the respective devices in the processing order of the lots of the respective steps constituting the best process processing pattern. In a production line that takes the form of a job shop that processes a plurality of processes and a plurality of lots, obtain the status data of each lot and the status data of each device of the process,
Create a combination of the processing order of the lot that each process can take, combine the processing order of the lot of each process, configure all the process processing pattern of all processes,
A first calculation device that selects the process processing pattern with the best evaluation point from the process processing patterns based on the state data of each lot and the evaluation points obtained based on the state data of each device. When,
Based on the processing order of the lots of the respective steps that constitute the process processing pattern having the best evaluation score obtained from the first calculation device, the respective devices are controlled, and the lots are assigned to the respective devices. A production control system comprising a second computing device for supply.   The evaluation score is calculated based on the lot processing lead time evaluation index, the operation rate evaluation index of the device, the efficiency evaluation index of the device, and the delivery date delay rate evaluation index of the lot, The production control system according to claim 1 or 2.   The production control system according to claim 4, wherein the evaluation score is calculated based on a value obtained by multiplying each evaluation index constituting the evaluation score by a weighting coefficient.   The production control system according to claim 4, wherein the weighting coefficient is variable.

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