KR102184007B1 - Method for predicting content of residual monomer and preparation method of polycarbonate resin - Google Patents

Abstract

The present invention provides a method for producing a polycarbonate product, the method comprising the steps of: inputting basic information of the product, an objective function based on the underproduction amount of the product and the price of the product, and constraints for the objective function ; Generating storage information indicating a storage amount of raw materials of the product; Storing basic information of the product, an objective function, a constraint condition, and storage information; Performing mathematical optimization using basic product information, constraint conditions, and storage information so that the objective function is minimized; Using the results of mathematical optimization, it includes the step of creating and displaying a production plan for a product, the shortage of the product is the difference between the production target and the actual production of the product, and the basic information is the product's, unit price, and total output. , Information on the total price, production target, production volume and production capacity of the line that produces the product.

Description

Polycarbonate production method and polycarbonate production equipment {METHOD FOR PREDICTING CONTENT OF RESIDUAL MONOMER AND PREPARATION METHOD OF POLYCARBONATE RESIN}

The present invention relates to a polycarbonate production method in consideration of product limitations and a polycarbonate production apparatus using the same in a continuous production process of a polycarbonate resin.

Polycarbonate resin is manufactured by condensation polymerization of an aromatic diol such as bisphenol A and a carbonate precursor such as phosgene, and has excellent impact strength, numerical stability, heat resistance and transparency, and has exterior materials for electrical and electronic products, automobile parts, construction materials, and optics. It is applied to a wide range of fields such as parts.

More specifically, such a polycarbonate resin may be prepared by reacting the aromatic diol with a proton acceptor such as sodium hydroxide or an aqueous solution thereof to change the aromatic diol into a reactive active species, and then polymerizing it with phosgene.

In the conventional production of polycarbonate, a production schedule manager manually created a schedule table for a polymerization device and an extrusion device, taking into account the limitations of the product, and established a production plan, thereby producing a product.

However, as the number of polycarbonate products currently produced on limited production lines increases, the number of considerations increases. Accordingly, a problem arises in that the conventional polycarbonate production method in which the production schedule manager manually plans directly by the person in charge of the production schedule due to an increase in decision-making factors in planning the production of a product causes a loss of sales.

The present invention is to provide a polycarbonate production method and a polycarbonate production apparatus using the same.

In addition, the present invention is to provide a polycarbonate production method capable of minimizing sales loss and a polycarbonate production apparatus using the same.

In addition, the present invention is to provide a polycarbonate production method and a polycarbonate production apparatus using the same that can minimize the loss of sales by using the type and quantity of demand.

In addition, the present invention is to provide a polycarbonate production method and a polycarbonate production apparatus using the same, which simplifies the decision factor used to establish a production plan.

The present invention provides a method of producing a polycarbonate product, the method comprising: an objective function based on the basic information of the product, the underproduction amount of the product, and the price of the product, and constraints on the objective function Entering a condition; Generating storage information indicating a storage amount of raw materials of the product; Storing the basic information of the product, the objective function, the constraint condition, and the storage information; Performing mathematical optimization using the basic information of the product, the constraint condition, and the storage information so that the objective function is minimized; And creating and displaying a production plan of the product by using the result of the mathematical optimization, wherein the underage amount of the product is a difference between the production target amount and the actual production amount of the product, and the basic information is the product This is information on the unit price, total production amount, total price, production target amount, production capacity and production capacity of the line that produces the product.

Further, in the method of producing a polycarbonate product according to the present invention, the constraint condition includes the storage amount of the product, the product storage amount is equal to a predetermined initial product storage amount at a first time point, and at a second time point, It is calculated by adding the number of products produced at the previous time to the amount of storage at a time before the second time point, and at a third time by subtracting the amount of demand for the product from the product storage at the second time point.

In addition, in the method of producing a polycarbonate product according to the present invention, the amount of insufficient production of the product is, the amount of production of the product at the second time point is subtracted from the amount of storage of the product at the third time point, and the amount of demand for the product is It is calculated by adding

Further, in the method of producing a polycarbonate product according to the present invention, the constraint condition includes the storage amount of the raw material, the raw material storage amount is equal to a predetermined initial raw material storage amount at a first time point, and at a second time point, It is calculated as adding the number of raw materials produced at the time before the second time point to the amount of raw materials stored at the time point before the second time point, and subtracting the number of raw materials used in the product at the time point before the second time point. In, it is calculated as adding the number of raw materials produced at the second time point to the product storage amount at the second time point, and subtracting the number of raw materials used in the product at the second time point, and the product at the second time point The number of raw materials used in takes into account the blending ratio of the raw materials.

In addition, in the method for producing a polycarbonate product according to the present invention, the constraint includes whether or not the polymerization reactor that produces the raw material produces raw materials, and whether or not the raw material is produced is the above at any time in any polymerization reactor. It is determined by the sum of the first discrete variables, which becomes 1 when raw materials are produced and 0 when not produced, and the sum of the first discrete variables is 1 or less.

In addition, in the method for producing a polycarbonate product according to the present invention, the constraint condition includes whether or not the product is produced by extrusion that produces the product, and whether or not the product is produced is the product at any time in an arbitrary extruder. It is determined by the sum of the second discrete variables, which is 1 when produced and 0 when not produced, the sum of the second discrete variables is 1 or less, and the polymerizer produces only one raw material at a time.

In addition, in the method for producing a polycarbonate product according to the present invention, the constraint condition includes the production amount of the raw material, and the production amount of the raw material is the production amount produced by the raw material at a certain point in time in an arbitrary polymerization reactor. It is determined by the product of the unit yield of the raw material in the polymerization reactor.

In addition, in the method for producing a polycarbonate product according to the present invention, the constraint condition includes the product production amount of the product, and the product production amount is, if the product is produced at a certain point in time in the extruder producing the product, the The production amount of the product at any point in time corresponds to the unit production amount.

In addition, an embodiment of the present invention provides an apparatus for producing a polycarbonate product, the apparatus comprising: an objective function based on the basic information of the product, the underproduction amount of the product, and the price of the product, and the object An information input/output device configured to input a constraint condition for a function; A storage tank device configured to generate storage information indicating a storage amount of the raw material of the product; A storage device configured to store the basic information of the product, the objective function, the constraint condition, and the storage information; To minimize the objective function, mathematical optimization is performed using the basic information of the product, the constraint conditions, and the storage information, and a production plan of the product is created and displayed using the result of the mathematical optimization. And a control device configured to include a control device configured to, wherein the product shortage is a difference between a production target amount and an actual production amount of the product, and the basic information includes the product, unit price, total production amount, total price, production target amount, and the product. It is information on the production volume and capacity of the production line.

Further, in the apparatus for producing a polycarbonate product according to the present invention, the constraint condition includes a storage amount of the product, and the product storage amount is equal to a predetermined initial product storage amount at a first time point, and at a second time point, It is calculated by adding the number of products produced at the previous time to the amount of storage at a time before the second time point, and at a third time by subtracting the amount of demand for the product from the product storage at the second time point.

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the amount of insufficient production of the product is determined by subtracting the production amount of the product at the second time point from the storage amount of the product at the third time point, and It is calculated by adding

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the constraint condition includes the storage amount of the raw material, and the raw material storage amount is,

At a first time point, it is equal to a predetermined initial raw material storage amount, and at a second time point, the number of raw materials produced at a time before the second time point is added to the amount of raw material stocks at a time point before the second time point, and at a time point before the second time point. It is calculated as subtracting the number of raw materials used in the product at, and at a third time point, the number of raw materials produced at the second time point is added to the product storage amount at the second time point, and the product at the second time point It is calculated by subtracting the number of raw materials used, and the number of raw materials used in the product at the second time point takes into account the blending ratio of the raw materials.

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the constraint condition includes whether or not raw materials are produced by a polymerization reactor that produces the raw materials, and whether or not the raw materials are produced is the above at any time in an arbitrary polymerization reactor. It is determined by the sum of the first discrete variables, which becomes 1 when raw materials are produced and 0 when not produced, and the sum of the first discrete variables is 1 or less.

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the constraint includes whether or not the product is produced by extrusion that produces the product, and whether or not the product is produced is the product at any time in an arbitrary extruder. It is determined by the sum of the second discrete variables, which is 1 when produced and 0 when not produced, the sum of the second discrete variables is 1 or less, and the polymerizer produces only one raw material at a time.

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the constraint condition includes the production amount of the raw material, and the production amount of the raw material is the production amount of the raw material produced at a certain point in time in an arbitrary polymerization reactor. It is determined by multiplying the unit production amount of the raw material in the polymerization reactor.

In addition, in the apparatus for producing a polycarbonate product according to the present invention, the constraint condition includes the product production amount of the product, and the product production amount is, if the product is produced at a certain point in time in the extruder producing the product, the The product output at any point in time corresponds to the unit output.

According to the present invention, a polycarbonate production method and a polycarbonate production apparatus using the same are provided.

In addition, according to the present invention, a polycarbonate production method capable of minimizing sales loss and a polycarbonate production apparatus using the same are provided.

In addition, according to the present invention, there is provided a polycarbonate production method capable of minimizing sales loss by using the type and quantity of a product and a polycarbonate production apparatus using the same.

Further, according to the present invention, there is provided a polycarbonate production method and a polycarbonate production apparatus using the same, which simplifies the decision-making factor used to establish a production plan.

1 is a block diagram showing the configuration of a polycarbonate production apparatus according to an embodiment of the present invention.
2 shows an example of the raw material combination ratio used in the production of the final product (P) according to an embodiment of the present invention.
3 is a flow chart showing a polycarbonate production method according to an embodiment of the present invention.
Figure 4a shows a mathematical optimization program and solver used in the polycarbonate production method according to an embodiment of the present invention.
4B is an example of inputting an objective function and a constraint condition to a solver used in a polycarbonate production method according to an embodiment of the present invention.
4C is an operation algorithm of a solver used in the polycarbonate production method according to the embodiment.
5A shows a production plan created by the prior art.
Figure 5b shows a production plan created using the polycarbonate production method according to an embodiment of the present invention.
6 shows a Gantt chart of a production plan created using a polycarbonate production method according to an embodiment of the present invention.

Hereinafter, a polycarbonate production method and a polycarbonate production apparatus according to the present invention will be described in more detail.

1 is a block diagram showing the configuration of a polycarbonate production apparatus according to an embodiment of the present invention.

2 shows an example of the raw material combination ratio used in the production of the final product (P) according to an embodiment of the present invention.

Hereinafter, an apparatus for producing polycarbonate according to the present invention will be described with reference to FIGS. 1 and 2.

Referring to FIG. 1, the polycarbonate production apparatus 1 according to the present invention includes an information input/output device 10, a storage device 20, a control device 30, a polymerization device 40, and a storage tank device 50. ), and an extrusion device 60.

In the information input/output device 10, basic information, an objective function, and a constraint condition for the objective function are input. The basic information includes basic product production information and factory/sales operation information. In addition, the information input / output device 10 is the result of the mathematical optimization performed by the polycarbonate production method according to the embodiment of the present invention according to the control information of the control device 30 and the polycarbonate production according to the embodiment of the present invention. The production plan created using the method can be displayed.

Specifically, the basic production information of the product includes the price (unit price) of the product, the total production volume by product, the total price of the product, weekly (for example, last week, this week, and next week) production product information, and weekly production target amount by product. /Order quantity, ratio of raw materials (e.g., flakes) for each product, production line information for each product, product production speed in each line, information such as production per unit time of each line and production capacity for each line May be included, but the present invention is not limited thereto.

In addition, the factory/business operation information may include information such as continuous production product information requiring continuous production, weekly shutdown schedule, and specific product safety stock, but the present invention is not limited thereto.

The storage device 20 stores basic information input to the information input device 10 and storage information (to be described later) of the storage tank device 50. The storage device 20 may be a database including, for example, a memory, a hard disk, and a flash memory capable of storing the above-described information, but the present invention is not limited thereto.

The control device 30 includes a program (see Fig. 6) required to perform the polycarbonate production method according to the embodiment of the present invention, and the polymerization device 40, the storage tank device 50, and the extrusion device 60 ), and control information for controlling the information input/output device 10, and based on the basic information and storage information stored in the database 20, mathematical optimization is performed using the solver of the above-described program. (Check point: Please review whether the expression in the underlined part is appropriate), and draw up a production plan for each product using the results of mathematical optimization. A specific method of preparing a production plan will be described later.

Hereinafter, a production process in which a polycarbonate (pc) product is produced by controlling the polymerization device 40, the storage tank device 50, and the extrusion device 60 according to the control information will be described.

The polymerization apparatus 40 is an apparatus for producing raw materials, for example, flakes, and the polymerization apparatus 40 includes a plurality of polymerization apparatuses 40 ₁ to 40 _p .

Raw materials (F ₁ to F _p ) produced in a plurality of polymerization reactors 40 ₁ to 40 _p are stored in the storage tank device 50 and can be used directly in the extrusion device 60 (production process in the present invention Is a continuous process). A description of a specific embodiment for producing raw materials in the polymerization apparatus 40 will be omitted.

The storage tank device 50 includes a plurality of storage tanks 50 ₁ to 50 _m , and each storage tank has a maximum storage amount for each type of raw material F, and one raw material is stored in one storage tank. The storage tank device 50 generates storage information including a real-time storage amount for each raw material.

The extrusion device 60 includes a plurality of extruders 60 ₁ to 60 _j , and each of the plurality of extruders 60 ₁ to 60 _j produces a corresponding product P ₁ to P _p . A plurality of extruders (60 ₁ to 60 _j ) can produce products (P ₁ to P _p ) using one or more raw materials.

Hereinafter, the combination ratio of raw materials used to produce products (P ₁ ~ P _p ) will be described.

Referring to FIG. 2, a final product P is produced by combining one or more raw materials, and each of the products P ₁ , P ₂ , ..., P _P has a combination ratio. For example, product (P ₁ ) is raw material (F ₁ ): raw material (F ₂ ) in combination ratio 2:8, product (P ₂ ) is raw material (F ₁ ): raw material (F _f ) in combination ratio 3:7 , The product (P _f ) is produced with the combination ratio of raw material (F ₁ ): raw material (F ₂ ): raw material (F _f ) in 3:3:4. Each combination ratio of these products (P ₁ , P ₂ , …, P _p ) is an example and the present invention is not limited thereto.

Hereinafter, a method of producing polycarbonate will be described with reference to FIGS. 3 to 6. 3 is a flow chart showing a polycarbonate production method according to an embodiment of the present invention. 3, the polycarbonate production method according to the present invention includes the following steps.

S1. The basic information, the objective function, and the constraint condition for the objective function are input to the information input/output device 10 (specific, objective function, and constraint conditions for the objective function will be described later). A specific example of the basic information has been described above with reference to FIG. 1 and thus is omitted here, and a configuration in which a constraint condition for the objective function and the objective function are input will be described later.

S2. Basic information and storage information are stored in the storage device 20. A specific example of the stored information has been described above with reference to FIG. 1 and thus is omitted here.

S3. The control device 30 performs mathematical optimization using a solver based on the input basic information, the objective function, and the constraint condition and storage information for the objective function.

)는 이하의 수학식 1과 같다.Specifically, for such mathematical optimization, constraints on the input objective function and objective function are used. In this embodiment, the objective function is a function that minimizes the sum of the product of the product of underproduction of the product (P) and the price of the product, that is, the amount of lost sales (Z), and the objective function is It is calculated by multiplying the underproduction amount by the price of the product. Specifically, the objective function according to an embodiment of the present invention (

) Is the same as in Equation 1 below.

는 제품(P)의 생산 미달량이고 제품(P)의 생산 미달량은 제품(P)의 생산 목표량과 실제 생산량 사이 차이며,

는 제품(P)의 판매가격으로서 상수이다. 제품(P)의 생산 미달량을 산출하는 구체적인 예는 후술한다.From here,

Is the underproduction amount of product (P) and the underproduction amount of product (P) is the difference between the production target amount of product (P) and the actual production amount,

Is the selling price of the product (P) and is a constant. A specific example of calculating the amount of underproduction of the product P will be described later.

At the first point in the production plan, the product (for example, material balance) constraint of Equation 1, Inventory of the product, is as Equation 2 below.

는 p제품의 시점(d)에서의 저장량(Inventory)이고, d는 날자 또는 요일이며,

는 상수로서 제품(P)의 초기 저장량이다. 수학식 2는 p제품의 첫 시점(d=d¹) 에서의 저장량은, 소정의 초기 저장량(

)과 같다는 것을 의미한다.From here,

Is the inventory at the time (d) of the product p, d is the date or day of the week,

Is a constant and is the initial storage amount of product (P). Equation 2 shows that the storage amount at the first time point (d=d ¹ ) of the p product is a predetermined initial storage amount (

Means the same as ).

In addition, the product storage amount, which is a product constraint condition of Equation 1 after the first time point (d=d ¹ ) of the production plan, is as Equation 3 below.

는 p 제품이 d시점에 j장치(예를 들어 압출기)에서 생산되었을 때의 생산된 제품의 양이고, 수학식 3은 p제품의 시점(d>d¹)에서의 제품의 저장량이, 시점(d)의 이전 시점(d^-1)의 저장량에 이전 시점에 생산된 제품의 수를 더한 것과 같다는 의미이다. 이전 시점(d^-1)에 생산된 제품량(

)은, 그 제품을 생산한 j장치에 대해 생산량을 모두 합한 것이다.From here,

Is the amount of product produced when the p product is produced in the device j (for example, an extruder) at time d, and Equation 3 is the storage amount of the product at the time point (d>d ¹ ) of the product p, the time point ( This means that it is equal to the number of products produced at the previous time, plus the amount of storage at the previous time (d ^-1 ) of d). The amount of product produced at the previous time (d ^-1 ) (

) Is the sum of all outputs for the j device that produced the product.

In addition, the product storage amount, which is the product constraint condition of Equation 1 at the last time point d ^last of the production plan, is shown in Equation 4 below.

는 상수로서 제품(P)의 수요량(또는 오더)이고, 수학식 4는 마지막 시점(d=d^last) 에서, 제품 수요량(

)만큼 제품(P)의 수가 빠져나가고, 만약 제품 저장량이 충분하지 않을 경우, 시점(d=d^last) 에서의 저장량(

)에서 시점(d>d¹)에 생산된 제품량(

)을 빼고 제품 수요량(

)을 더한 값으로 제품 생산 미달량(

)이 계산된다는 것을 의미한다.From here,

Is the demand (or order) of the product (P) as a constant, and Equation 4 is the last time (d=d ^last ), the product demand (

), and if the product storage is not sufficient, the storage amount at the time (d=d ^last ) (

) At the time point (d>d ¹ )

) Minus the product demand (

) Plus the product production shortage (

Means) is calculated.

In addition, at the first time point of the production plan, the amount of storage of the raw material, which is the constraint condition of the raw material (f: flake) (eg, material resin) of Equation 1, is as Equation 5 below.

는 상수로서, 원재료(f)의 초기 저장량이다. 수학식 5는, 원재료(f)의 첫 시점(d=d¹) 에서의 저장량은, 소정의 초기 저장량(

)과 같다는 것을 의미한다.Here, f is the kind of raw material (f) for the production of product (P), p is the kind of product to be produced, d is the date or day of the week, and j is the polymerizer and extruder.

Is a constant and is the initial storage amount of the raw material f. In Equation 5, the storage amount at the first time point (d=d ¹ ) of the raw material f is a predetermined initial storage amount (

Means the same as ).

In addition, the raw material storage amount, which is the raw material constraint condition of Equation 1 after the first point in time (d=d ¹ ) of the production plan, is as Equation 6 below.

는 f 원재료가 d 시점에 j 장치에서 생산되었을 때, 생산된 원재료의 양이고,

는 p 제품이 d 시점에 j 장치에서 생산되었을 때의 생산된 제품의 양이며,

은 제품(P)을 생산하기 위해 배합해야 하는 원재료(f)의 배합비율이고, 수학식 6은 원재료(f)의 시점(d>d¹) 에서의 저장량은, 시점(d)의 이전 시점(d^-1)의 원재료 저장량에 이전 시점에 생산된 원재료의 양을 더하고, p 제품에 사용된 원재료(f)의 양을 뺀 것과 같다는 의미이다. 이전 시점(d^-1)에 생산된 원재료의 생산 량(

)은 그 원재료를 생산한 j장치에 대해 생산량을 모두 합한 것이다. 이전 시점(d^-1)에 제품(P)의 생산에 사용된 원재료의 양(

)은 배합 비율(

)을 고려한다.From here,

F is the amount of raw material produced when the raw material is produced in the device j at time d,

Is the amount of product produced when product p was produced in device j at time d,

It is the mixing ratio of the raw material (f) that must be blended to produce the silver product (P), and Equation 6 shows the amount of storage at the time point (d>d ¹ ) of the raw material (f) is the previous time point ( This means that it is equal to the amount of raw material stored in d ^-1 ) plus the amount of raw material produced at the previous time, and subtracting the amount of raw material (f) used in p product. The amount of raw material produced at the previous point in time (d ^-1 ) (

) Is the sum of all outputs for the device j that produced the raw material. The amount of raw materials used in the production of the product (P) at the previous time (d ^-1 ) (

) Is the blending ratio (

).

In addition, the raw material storage amount, which is the raw material constraint condition of Equation 1 at the last time point d ^last of the production plan, is shown in Equation 7 below.

Of the raw material produced in the expression (7) is the last point in (d = d ^last), storage amount of the last point of the raw material ^{(f) (d = d last} ) it is, prior to the previous point (d) the storage amount of time (d) It means that it is equal to adding the amount and subtracting the amount of raw materials used in the product.

In addition, whether or not the polymerization reactor produces raw materials, which is the limiting condition of the polymerization reactor in Equation 1, means that only one raw material (f) is produced at a time in the predetermined polymerization reactor (j), and whether or not the polymerization reactor produces raw materials It is as shown in Equation 8 below.

는 이산 변수로서, 원재료(f)를 중합기(j)에서 시점(d)에 생산하면 1이고 생산하지 않으면 0이다.From here,

Is a discrete variable, and it is 1 if the raw material f is produced at the time point d in the polymerization reactor j and 0 if it is not produced.

In Equation 8, an arbitrary polymerization reactor (j) can produce only one raw material (f) at an arbitrary time point (d). Therefore, Equation 8 means that the sum of all discrete variables at an arbitrary polymerization reactor j and an arbitrary time point d is 1 or less.

In addition, whether or not the extruder produces a product, which is the extruder constraint of Equation 1, means that only one product (P) is produced at a time in a predetermined extruder (j), and whether or not the product is produced by the extruder is Equation 9 below. Same as

는 이산 변수로서, 제품(P)을 압출기(j)에서 시점(d)에 생산하면 1이고 생산하지 않으면 0이다.From here,

Is a discrete variable, which is 1 if the product (P) is produced from the extruder (j) at the time point (d) and 0 if it is not produced.

In Equation 9, an arbitrary extruder (j) can produce only one product (P) at a specific time point (d). Therefore, Equation 9 means that the sum of all discrete variables at any extruder (j) and any time point (d) is 1 or less.

In addition, the raw material production amount which is the raw material production amount constraint condition of Equation 1 is calculated by the following Equation 10.

는 변수로서, 원재료(f)가 중합기(j)에서 시점(d)에서 생산된 생산량이고,

는 중합기(j)에서의 원재료(f)의 단위 생산량이다. 수학식 10은 원재료(f)가 임의의 시점(d)에서 임의의 중합기(j)에 의해 생산되면(

), 그 시점에서 생산되는 원재료(f)의 양은 단위 생산량(b)만큼 생산된다는 것을 의미한다.From here,

Is a variable, where the raw material (f) is the production amount produced at the time point (d) in the polymerization reactor (j),

Is the unit production amount of the raw material f in the polymerization reactor j. Equation 10 shows that when the raw material (f) is produced by an arbitrary polymerization reactor (j) at an arbitrary time point (d) (

), means that the amount of raw material (f) produced at that point is produced as much as the unit production amount (b).

Further, the product production amount, which is the product production amount constraint condition of Equation 1, is calculated by the following Equation 11.

는 변수로서, 제품(P)이 압출기(j)에서 시점(d)에 생산된 생산량 이고,

는 압출기(j)에서의 제품(P)의 단위 생산량이다. 수학식 11은 제품(P)이 임의의 시점(d)에서 임의의 압출기(j)에 의해 생산되면(

), 그 시점에서 생산되는 제품(P)의 양은 단위 생산량(c)만큼 생산된다는 것을 의미한다.From here,

Is the variable, the product (P) is the production amount produced at the time point (d) in the extruder (j),

Is the unit output of product (P) in extruder (j). Equation 11 shows that if the product (P) is produced by an arbitrary extruder (j) at a certain point in time (d) (

), it means that the amount of product (P) produced at that point is produced by the unit production amount (c).

Equations 1 to 11 described above are input to a solver used in the polycarbonate production method according to an embodiment of the present invention through the information input/output device 10. Hereinafter, a specific example of the mathematical modeling used in the method for producing polycarbonate according to the embodiment of the present invention for mathematical optimization will be described with reference to FIGS. 4A to 4C.

4A shows an example of a mathematical modeling program and solver used in a method for producing polycarbonate according to an embodiment of the present invention.

4B is an example of inputting an objective function and a constraint condition to a solver used in a polycarbonate production method according to an embodiment of the present invention.

4A and 4B, programs for finding optimal solutions to Equations 1 to 11 described above, for example, GAMS, MATLAB, etc. are input, and such programs are equipped with a commercial optimization solver. The polycarbonate production method according to an embodiment of the present invention uses an integer programming method (MILP) using discrete variables, and there is a solver including various optimal algorithms such as CLPEX, XPRESS, CBC, GUROBI, etc. . The selection of the optimization solver may be selected according to the characteristics of the problem, for example, the presence or absence of a discrete variable, the presence or absence of a quadratic equation, or a linear problem, but the present invention is not limited thereto.

A screen in which an objective function (Equation 1) is input to GAMS used in the polycarbonate production method according to an embodiment of the present invention is shown, and the constraint conditions of Equations 2 to 11 described above can be entered using this program code. However, the present invention is not limited thereto.

4C is an operation algorithm of a solver used in the polycarbonate production method according to the embodiment.

The operation algorithm of the solver used in the polycarbonate production method according to the embodiment is basically a structure that searches for an optimal solution based on a method called branch-and-bound. This branch-and-bound method is a method of comparing the values of the objective function while expanding each discrete variable and finding an appropriate discrete variable value. This branch-and-bound method is included in the optimization solver.

Referring to FIG. 4C, when the value of Value is the value of the objective function, and X1, X2, and X3 are 0 or 1, the value of the objective function is calculated. As a result, X1, X2, and X3 all have integer values and the node with a large objective function is the P3 node, and this is the optimal solution, and the mathematical optimization result is generated by finding this optimal solution.

S4. The control device 30 creates a production plan based on the result of mathematical optimization.

5A shows a production plan created by the prior art.

Figure 5b shows a production plan created using the polycarbonate production method according to an embodiment of the present invention.

Hereinafter, with reference to Figures 5a and 5b, a production plan using optimization according to an embodiment of the present invention will be described.

In FIGS. 5A and 5B, T1 and T2 denote raw material F, and A, B, C, D, E, and F denote product P, respectively. N1 to N5 are the types of the raw material F, and the time length of each period is 6h in the planned period of one week (t1, t2, ..., t28). Here, the types and demands of the product P are shown in the following table.

Production product (P) Demand (ton) Price (million won/ton) 1201W 240 2.78 1337T 240 2.7 1303N 180 2.36 1310N 480 2.1 1315N 990 2.24 1322N 870 2.38 1330N 90 2.21 1302T 420 2.64 133CT 240 2.44 1201AW 120 2.45 1301W 120 2.98 1301V 360 2.4 1080CN 70 2.4 1208W 120 2.7 1210T 240 2.6 1080N 210 2.23 total 4330

The optimization results using the product type and demand in Table 1 are shown in Table 2 below.

Comparative example Example


Underproduction
product product name Underweight(ton) product name Underweight(ton) 1201W 120 1303N 150 1315N 150 1315N 300 1322N 195.6 1322N 512.4 1330N 90 1330N 73.2 1302T 120 1310V 360 Sum 6 pieces 1035.6 4 1035.6 Total sales loss
(one million won) 2514.828 2407.284

The comparative example of Table 2 is an example corresponding to FIG. 5A, which is a production plan written by hand by a person in charge in the prior art, and the embodiment corresponds to FIG. 4B, and shows a polycarbonate production method according to an embodiment of the present invention. It is a production plan created using. Using the polycarbonate production method according to an embodiment of the present invention, while reducing the production of low-cost products such as product 1322N, there is an effect that can additionally produce products such as 1301V, 1302T, which were not in the conventional production plan.

6 shows a Gantt chart of a production plan created using a polycarbonate production method according to an embodiment of the present invention.

Hereinafter, a production plan created using the polycarbonate production method according to an embodiment of the present invention will be described with reference to FIG. 6.

S5. The control device 30 creates a production plan for each product using the generated mathematical optimization result, and displays the created production plan on the information input/output device 10 (e.g., in a Gantt chart). Control to be displayed). Referring to FIG. 5, part a of the Gantt chart is a part that determines whether or not to perform a task in the second column of the heater equipment, and is calculated as 1 if the task is performed by applying a discrete variable, or 0 otherwise. In this Gantt chart, product No. 1 was heated by 52 tons, and the discrete variable value corresponding to the heater No. 1 product/2 time was calculated as 1.

Part a of the Gantt chart means that no work was performed in the 3rd time zone of the Still equipment, and correspondingly, the values of the discrete variables wvP of the Still/All Products/3rd time were all calculated as 0. In addition, the c and d parts of the Gantt chart mean that the work was performed on the product 5 in the 6th and 7th time zones on the still device, and in response to this, The discrete variable wvP was calculated as 1.

In addition, the user can view these Gantt charts, check and modify the production plan of the created product P.

1: production device
10: information input/output device
20: storage device
30: control device
40: polymerization device
50: storage tank device
60: extrusion device

Claims (16)

As a method of producing polycarbonate products,
Inputting, by an information input/output device, an objective function based on basic information of the product, an underproduction amount of the product, and a price of the product, and a constraint condition for the objective function;
Generating, by the storage tank device, storage information indicating a storage amount of raw materials of the product;
Storing, by a storage device, basic information of the product, an objective function, the constraint condition, and the storage information;
Performing, by a control device, a mathematical optimization using the basic information of the product, the constraint condition, and the stored information so that the objective function is minimized;
The control device, using the result of the mathematical optimization, creating and displaying a production plan of the product,
The objective function is a function for minimizing the amount of lost sales, which is the sum of the product of the product of the product underproduction and the price of the product, and the underachievement of the product is a difference between the target production amount and the actual production amount of the product,
The basic information is information on a unit price, a total production amount, a total price, a production target amount, a production amount and production capacity of a line that produces the product. As a method of producing polycarbonate products,
Inputting, by an information input/output device, an objective function based on basic information of the product, an underproduction amount of the product, and a price of the product, and a constraint condition for the objective function;
Generating, by the storage tank device, storage information indicating a storage amount of raw materials of the product;
Storing, by a storage device, basic information of the product, an objective function, the constraint condition, and the storage information;
Performing, by a control device, a mathematical optimization using the basic information of the product, the constraint condition, and the stored information so that the objective function is minimized;
The control device, using the result of the mathematical optimization, creating and displaying a production plan of the product,
The shortage amount of the product is the difference between the production target amount and the actual production amount of the product,
The basic information is information on the unit price, total production amount, total price, production target amount, production amount and production capacity of the line that produces the product,
The constraint includes the amount of storage of the product,
The amount of storage of the product is,
At the first point, it is equal to the predetermined initial product storage amount,
At a second time point, it is calculated by adding the number of products produced at the previous time to the amount of storage at the time before the second time point,
At a third time point, calculated as subtracting the amount of demand for the product from the amount of product stored at the second time point. The method of claim 2,
The method of claim 1, wherein the underproduction amount of the product is calculated by subtracting the production amount of the product at the second time point from the storage amount of the product at the third time point and adding the demanded amount of the product. The method of claim 3,
The constraint condition includes the storage amount of the raw material,
The storage amount of the raw material is,
At the first time point, it is equal to the predetermined initial raw material storage amount,
At the second time point, it is calculated as adding the number of raw materials produced at the time before the second time point to the amount of raw materials stored at the time point before the second time point, and subtracting the number of raw materials used in the product at the time point before the second time point. And
At a third time point, it is calculated as adding the number of raw materials produced at the second time point to the product storage amount at the second time point, and subtracting the number of raw materials used for the product at the second time point,
The method, wherein the number of raw materials used in the product at the second time point takes into account the blending ratio of the raw materials. The method of claim 4,
The constraint includes whether or not the polymerization reactor that produces the raw materials produces raw materials,
Whether or not to produce the raw material is determined by the sum of the first discrete variables, which becomes 1 if the raw material is produced at a certain point in time in an arbitrary polymerization reactor, and 0 if it is not produced,
The sum of the first discrete variables is 1 or less. The method of claim 5,
The constraint includes whether the extruder that produces the product produces a product,
Whether or not to produce the product is determined by the sum of the second discrete variables, which becomes 1 if the product is produced at any time in an arbitrary extruder, and 0 if it is not produced,
The sum of the second discrete variables is 1 or less,
The method, wherein the polymerizer produces only one raw material at a time. The method of claim 6,
The constraint condition includes the production amount of the raw material,
The method of claim 1, wherein the production amount of the raw material is determined by a product of the production amount of the raw material produced at a certain point in time in an arbitrary polymerization reactor and a unit production amount of the raw material in the polymerization reactor. The method of claim 7,
The constraint includes the product yield of the product,
The product production amount, if the product is produced at a certain point in time in an extruder producing the product, the product production amount at the certain time point corresponds to a unit production amount. As a device for producing polycarbonate products,
An information input/output device configured to input basic information of the product, an objective function based on a production underproduction amount of the product, and a price of the product, and a constraint condition for the objective function;
A storage tank device configured to generate storage information indicating a storage amount of the raw material of the product;
A storage device configured to store the basic information of the product, the objective function, the constraint condition, and the storage information; And
To minimize the objective function, mathematical optimization is performed using the basic information of the product, the constraint conditions, and the storage information, and a production plan of the product is created and displayed using the result of the mathematical optimization. It includes a control device configured to,
The objective function is a function for minimizing the amount of lost sales, which is the sum of the product of the product of the product underproduction and the price of the product, and the underachievement of the product is a difference between the target production amount and the actual production amount of the product,
The basic information is information on a unit price, a total production amount, a total price, a production target amount, a production amount and production capacity of a line that produces the product. As a device for producing polycarbonate products,
An information input/output device configured to input basic information of the product, an objective function based on a production underproduction amount of the product, and a price of the product, and a constraint condition for the objective function;
A storage tank device configured to generate storage information indicating a storage amount of the raw material of the product;
A storage device configured to store the basic information of the product, the objective function, the constraint condition, and the storage information; And
To minimize the objective function, mathematical optimization is performed using the basic information of the product, the constraint conditions, and the storage information, and a production plan of the product is created and displayed using the result of the mathematical optimization. It includes a control device configured to,
The shortage amount of the product is the difference between the production target amount and the actual production amount of the product,
The basic information is information on the unit price, total production amount, total price, production target amount, production amount and production capacity of the line that produces the product,
The constraint includes the amount of storage of the product,
The amount of storage of the product is,
At the first point, it is equal to the predetermined initial product storage amount,
At a second time point, it is calculated by adding the number of products produced at the previous time to the amount of storage at the time before the second time point,
At a third point in time, calculated as subtracting the amount of demand for the product from the amount of product stored at the second point in time. The method of claim 10,
The apparatus, wherein the production underproduction amount of the product is calculated by subtracting the production amount of the product at the second time point from the storage amount of the product at the third time point and adding the demanded amount of the product. The method of claim 11,
The constraint condition includes the storage amount of the raw material,
The storage amount of the raw material is,
At the first time point, it is equal to the predetermined initial raw material storage amount,
At the second time point, it is calculated as adding the number of raw materials produced at the time before the second time point to the amount of raw materials stored at the time point before the second time point, and subtracting the number of raw materials used in the product at the time point before the second time point. And
At a third time point, it is calculated as adding the number of raw materials produced at the second time point to the product storage amount at the second time point, and subtracting the number of raw materials used for the product at the second time point,
The device, wherein the number of raw materials used in the product at the second point in time takes into account a blending ratio of the raw materials. The method of claim 12,
The constraint includes whether or not the polymerization reactor that produces the raw materials produces raw materials,
Whether or not to produce the raw material is determined by the sum of the first discrete variables, which becomes 1 if the raw material is produced at a certain point in time in an arbitrary polymerization reactor, and 0 if it is not produced,
Wherein the sum of the first discrete variables is equal to or less than one. The method of claim 13,
The constraint includes whether the extruder that produces the product produces a product,
Whether or not to produce the product is determined by the sum of the second discrete variables, which becomes 1 if the product is produced at any time in an arbitrary extruder, and 0 if it is not produced,
The sum of the second discrete variables is 1 or less,
The apparatus, wherein the polymerizer produces only one raw material at a time. The method of claim 14,
The constraint condition includes the production amount of the raw material,
The production amount of the raw material is determined by a product of the production amount of the raw material produced at a certain point in time in an arbitrary polymerization reactor and a unit production amount of the raw material in the polymerization reactor. The method of claim 15,
The constraint includes the product yield of the product,
The product production amount, if the product is produced at a certain point in time in an extruder that produces the product, the product production amount at the certain time point corresponds to a unit production amount.

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