JP2013254329A - Raw material purchase/use plan creation apparatus, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To formulate, even when a constraint equation and an objective function are given in a nonlinear form, it into a mathematical programming problem of a linear form.SOLUTION: A raw material purchase/use plan creation apparatus creates a raw material purchase/use plan that observes restrictions relating to properties of products (pig irons, sintered ores, and slug) and a capacity of manufacturing facilities and minimizes costs required for purchasing and manufacturing the raw materials (iron ores, coke, coal, and auxiliary materials). In that occasion, the raw material purchase/use plan creation apparatus formulates the constraint equation relating to the properties of the products and the capacity of the manufacturing facilities and the objective function representing the cost into the mathematical programming problem of the linear form, with the purchase quantities and use quantities of the coke and coal defined as fixed values, optimizes the mathematical programming problem, and calculates the purchase quantities and use quantities of the raw materials minimizing the objective function, and the properties and the production quantity of the products.

Description

  The present invention complies with restrictions on the properties of pig iron, sintered ore and slag and the capacity of production equipment, and minimizes the cost of purchasing and manufacturing raw iron ore, coke, coal and auxiliary materials. The present invention relates to a raw material purchase and use plan creation apparatus, method and program for creating a purchase and use plan.

  In the steel industry, stable production of pig iron is an essential condition for operation. In addition, the quality of pig iron must be in a predetermined condition for stable operation after the next process. In order to meet these conditions and stably produce pig iron, purchase plans for raw materials such as iron ore, coke, coal, and auxiliary materials (serpentine, meteorite, lime, etc.) and use plans for purchased raw materials It is desirable to appropriately reduce the cost for purchasing and manufacturing as much as possible.

Iron ore has components (Fe, SiO ₂ , MgO, etc.) that differ greatly depending on the land to be produced, and is classified as a brand depending on the difference, but the number of iron ore is over 100 types. The properties of pig iron vary greatly depending on the composition of this brand. In addition, when making pig iron, powder iron ore is baked and compacted into a porous sintered ore to improve air flow in the blast furnace. However, in addition to chemical properties, it is necessary to consider properties such as physical difficulty of collapsing. Also, slag that appears as scrap when making pig iron needs to be within a range that has properties for reuse or disposal.

As mentioned above, when preparing a purchase and use plan for raw materials, there are a large number of iron ore brands that have very many restrictions on the properties to be considered with respect to pig iron, sintered ore, and slag as products. It is also necessary to consider the capacity constraints of manufacturing equipment. In addition, the purchase cost of raw materials includes not only the payment amount to the supplier but also the transport cost, and the use of gas processing costs such as COG, CO ₂ and BFG, which are by-products, and the use of manufacturing equipment. It is a very complicated problem that it is necessary to consider the manufacturing cost including the processing cost. It is not easy to solve these problems and create a purchase and use plan for raw materials that protects the constraints on the properties of the product and the capacity of the manufacturing equipment, and minimizes the cost of purchasing and manufacturing the raw materials.

  For example, Patent Document 1 discloses a method for optimizing the operation of a steel production factory including a steelmaking factory and a steelmaking factory, which includes a calculation model of the steelmaking factory and a calculation model of the steelmaking factory with the output amount and the hot metal component. It is disclosed that a condition that becomes a cost minimum of the entire steel production plant is calculated while being connected as a variable and changing an input parameter group including a crude steel production amount, a raw material, a hot metal ratio, and the like.

  In addition, Patent Document 2 includes a simulator for calculating the supply and demand state of mixed raw materials and the properties after mixing, and a supply and demand balance constraint of mixed raw materials in order to create a mixing plan for receiving and mixing multiple types of mixed raw materials. Using the formula model that expresses the formula model and the formula model that expresses the property constraint after mixing, and the formula model that is built by the model build unit, the objective function constructed for the purchase cost and the shipping cost of the compounded raw materials And a planning unit that performs an optimization calculation based on the calculation and calculates an instruction to the simulator.

  Further, in Patent Document 3, when creating a blending plan as described in Patent Document 2, in view of the fact that a mathematical model representing a property constraint after mixing may include a nonlinear mathematical formula, When the mathematical model representing the property constraint includes a nonlinear mathematical formula, a linear mathematical formula is introduced in place of the nonlinear mathematical formula to formulate the mathematical model, and a solution result using the mathematical model including the linear mathematical formula is the nonlinear It is disclosed that whether or not a mathematical model including the mathematical formula is satisfied is confirmed.

JP 2005-55997 A JP 2010-92188 A JP 2009-175804 A

When producing pig iron, iron ore and lump coke are alternately inserted into the blast furnace, and hot air and pulverized coal (finely pulverized coal) are blown from the blower tuyeres at the bottom of the blast furnace. Gasification generates high-temperature gas such as carbon monoxide and hydrogen. This gas becomes a reducing material, and pig iron is produced.
In addition, when producing sintered ore, coke and anthracite (high carbonization charcoal) are used as a coagulant for the raw material containing fine ore and fired to produce a sintered ore in the porous chamber. Is done.
The above-described combustion, gas generation amount, heat amount, etc. in the gasification phenomenon include complicated nonlinear elements in the calculation.
The properties required for pig iron, sintered ore and slag, and the cost required to be cheap, are related to the above-mentioned combustion and gasification phenomenon, and therefore include complex nonlinear elements, such as iron ore, coke, coal In addition, it is not possible to describe the purchase amount and usage amount of secondary raw materials in a linear format. For this reason, the production of sintered ore and the properties of pig iron, sinter and slag cannot be calculated by simple stacking of iron ore, coke, coal and auxiliary materials to be blended. It is given by a non-linear formula that combines the coefficient of the physical formula from the actual data.
Further, regarding the cost, the gas processing cost and the processing cost for using the manufacturing equipment are given by a non-linear expression.
Thus, the conditions (constraint equations) that must be observed and the index (objective function) to be minimized cannot be expressed in a linear format.

In Patent Documents 1 and 2 described above, the case where the constraint equation and the objective function are given by a nonlinear equation is not considered.
Further, in Patent Document 3 described above, a case where the mathematical model representing the property constraint after mixing includes a nonlinear mathematical formula is described, but the case where the objective function is given by a nonlinear formula is not considered.
Here, the production information, properties, costs, etc. calculated by the above physical formulas are accumulated and accumulated as a result of actual measurement of various production information, properties, costs, etc. that are close to the blending state. A device has been devised to further improve the accuracy by performing correction using correction calculation obtained by analyzing past performance data. However, the production information, properties, costs, etc. obtained are corrected using actual data, and as a result, the production information, properties, and costs calculated using the above physical formulas must be observed. Even if the calculation is performed while satisfying the (constraint equation), there is a case where the above condition is not satisfied or an index (objective function) to be minimized is not minimized by adding this correction calculation.
In the above-mentioned Patent Documents 1, 2, and 3, no consideration is given to the correction calculation based on the above-mentioned actual data and the above-mentioned problem that may be caused by the correction calculation.

The present invention has been made in view of the above points, and observes the restrictions on the properties of the product and the capacity of the manufacturing equipment, and purchases and uses the raw materials that minimize the cost of purchasing and manufacturing the raw materials. Even when a constraint equation and an objective function are given as nonlinear equations when creating a plan, the object is to formulate them into a mathematical programming problem in a linear form.
In addition, even when corrections are made using correction calculations obtained by analyzing accumulated past performance data, the restrictions on product properties and production equipment capabilities are observed, and raw materials are purchased and manufactured. The purpose is to minimize the cost.

The raw material purchasing and use plan creation apparatus of the present invention observes the restrictions on the properties of pig iron, sintered ore and slag, which are products, and the capacity of the manufacturing equipment, and the raw materials of iron ore, coke, coal and auxiliary materials. A raw material purchasing and usage plan creation device for creating a purchasing and usage plan for the raw material that minimizes the cost of purchasing and manufacturing, and data that captures plan information for formulating the purchasing and usage plan for the raw material Based on the plan information fetched by the data fetching means, and the cost and the cost of the coke and coal, the constraint formula regarding the property of the product and the capacity of the manufacturing equipment, and the cost Mathematical programming problem constructing means for formulating into a mathematical programming problem in which the objective function representing the function is linear, and the mathematical programming problem constructed by the mathematical programming problem constructing means Optimizing calculation execution means for calculating the purchase amount and usage amount of the raw material that optimizes and minimizes the objective function, the property and production amount of the product, and the raw material calculated by the optimization calculation execution means Correction calculation execution means for correcting the purchase amount and use amount, the property and production amount of the product based on actual results, the purchase amount and use amount of the raw material corrected by the correction calculation execution means, A correction calculation convergence determination unit that determines whether or not the property and the production amount have converged with respect to the result before correction, and a determination that the convergence has been made by the correction calculation convergence determination unit. With respect to coke and coal contained in the purchased and used amount of raw materials, calculate the amount of fluctuation that reduces the objective function in a form where the purchased and used amount of coke and coal are not fixed values. Fluctuation amount calculation means, and the mathematical programming problem construction means and the optimization calculation execution again with fixed values of the purchased and used amounts of coke and coal that have been fluctuated based on the fluctuation amount calculated by the fluctuation amount calculation means Cost comparison means for executing the processing of the correction calculation execution means and the correction calculation convergence determination means, and determining whether or not the cost obtained as a result has converged with respect to the previously calculated cost It is characterized by comprising.
Another feature of the raw material purchasing and use plan creation apparatus according to the present invention is that the data capturing means captures actual information, and based on the actual information captured by the data capturing means, provisional coke and Computation means for calculating the purchase amount and use amount of coal is provided, and when the mathematical programming problem construction means first constructs the mathematical programming problem, the provisional coke and the purchase amount and use of coal calculated by the computation means The amount is used as a fixed value.
Further, the raw material purchase and use plan creation apparatus according to the present invention is characterized in that the purchase and production costs are the purchase cost of the raw material, the transport cost of the raw material, and the treatment of gas as a by-product. Including the cost and the processing cost of using the manufacturing equipment.
Another feature of the apparatus for purchasing and using raw materials according to the present invention is that, when it is not determined that the correction calculation convergence determination means has converged, the purchase of the raw material corrected by the correction calculation execution means. The purchase amount of coke and coal included in the amount and the usage amount is set as a fixed value, and the mathematical programming problem construction unit, the optimization calculation execution unit, the correction calculation execution unit, and the correction calculation convergence determination unit are executed again. There is in point to do.
In addition, another feature of the raw material purchase and use plan creation apparatus according to the present invention is that the correction calculation convergence determination means includes the purchase amount and use amount of the raw material corrected by the correction calculation execution means, and the product. As an item for determining whether or not the property and the production amount have converged with respect to the result before correction, all items are targeted or some items are selected and narrowed down.
Another feature of the raw material purchasing and use plan creation apparatus according to the present invention is that the fluctuation amount calculating means calculates the fluctuation amount by a steepest descent method. In this case, the fluctuation amount calculation means, when the fluctuation range of the objective function in a form in which the purchased amount and usage amount of the coke and coal are not fixed values becomes smaller than a predetermined fluctuation range, the coke and coal You may make it add the fluctuation | variation which does not follow the steepest descent method to the purchase amount and usage-amount of. Furthermore, random fluctuations using random numbers may be given as fluctuations that do not conform to the steepest descent method.
The raw material purchase and use plan creation method of the present invention observes restrictions on the properties of pig iron, sintered ore and slag as products and the capacity of manufacturing equipment, and the raw materials of iron ore, coke, coal, and auxiliary materials. A raw material purchasing and usage plan creation method for creating a purchasing and usage plan for the raw material that minimizes the cost of purchasing and manufacturing, wherein the data capturing means is for formulating the purchasing and usage plan for the raw material. The step of capturing plan information, and the mathematical planning problem construction means, with the purchase amount and use amount of coke and coal as fixed values, based on the plan information captured by the data capture means, the properties of the product and the manufacturing equipment A step of formulating a constraint equation relating to the ability of the above and a mathematical programming problem in which the objective function representing the cost is linear, and an optimization calculation execution means, Optimize the mathematical programming problem constructed by the mathematical programming problem construction means, calculate the purchase amount and usage amount of the raw material that minimizes the objective function, the property and production amount of the product, and execute correction calculation Means for correcting the purchase amount and usage amount of the raw material calculated by the optimization calculation execution means, the properties and the production amount of the product based on actual results, respectively, and a correction calculation convergence determination means includes the correction A step of determining whether the purchase amount and usage amount of the raw material corrected by the calculation execution means, the property and production amount of the product have converged with respect to the result before correction, and a fluctuation amount calculation means, When it is determined that the correction calculation convergence determination means has converged, the coke and stone included in the purchased amount and the usage amount of the raw materials determined to have converged are coke and stone. A step of calculating a fluctuation amount that reduces the objective function in a form in which the purchase amount and the usage amount of the product are not fixed values, and a coke changed by the cost comparison means based on the fluctuation amount calculated by the fluctuation amount calculation means and The coal purchase amount and the consumption amount are fixed values, and the mathematical programming problem construction means, the optimization calculation execution means, the correction calculation execution means, and the correction calculation convergence determination means are executed again, and the result is obtained. And determining whether the cost has converged with respect to the previously calculated cost.
The program of the present invention observes the restrictions on the properties of pig iron, sintered ore and slag, which are products, and the capacity of production equipment, and purchases and costs of raw iron ore, coke, coal and auxiliary materials. A program for causing a computer to execute a process for creating a purchase and use plan for the raw material to minimize the data, a data fetching means for fetching plan information for creating the purchase and use plan for the raw material, coke, and Based on the plan information fetched by the data fetching means, the purchase amount and the usage amount of coal are fixed values, and a constraint equation regarding the properties of the product and the capacity of the manufacturing equipment, and an objective function representing the cost are plotted. Mathematical programming problem construction means formulated into formal mathematical programming problems, and mathematical programming problems constructed by the mathematical programming problem construction means are optimized A purchase amount and a use amount of the raw material that minimizes the objective function, an optimization calculation execution means for calculating a property and a production amount of the product, and a purchase amount of the raw material calculated by the optimization calculation execution means. Correction amount calculation means for correcting the usage amount, the property of the product and the production amount based on the actual results, the purchase amount and the usage amount of the raw material corrected by the correction calculation execution means, the property of the product, and When it is determined that the production amount has converged by the correction calculation convergence determination means for determining whether or not the production amount has converged with respect to the result before correction, and the correction calculation convergence determination means, it is determined that the production has converged. For coke and coal included in the purchased and used amount of raw materials, the amount of change that calculates the amount of change that reduces the objective function in a form where the purchased and used amount of coke and coal are not fixed values. The calculation means, and the purchase amount and use amount of coke and coal that have been changed based on the fluctuation amount calculated by the fluctuation amount calculation means as fixed values, again, the mathematical programming problem construction means, the optimization calculation execution means, A computer as a cost comparison unit that executes the processes of the correction calculation execution unit and the correction calculation convergence determination unit and determines whether the cost obtained as a result of the calculation has converged with respect to the previously calculated cost. To work.

According to the present invention, the costs associated with the purchase and production of raw materials (iron ore, coke, coal, and auxiliary materials) are observed while obeying restrictions on the properties of the products (pig iron, sintered ore and slag) and the capacity of the production equipment. Even when a constraint equation and an objective function are given by a non-linear expression when creating a purchase and use plan of raw materials that minimizes the above, it can be formulated into a mathematical programming problem in a linear form. This is because coke and coal are the factors that cannot express the constraint equation and the objective function in a linear format, and the purchase amount and the usage amount are fixed values. The objective function is formulated into a mathematical programming problem with a linear form.
In addition, even when corrections are made using correction calculations obtained by analyzing accumulated past performance data, the restrictions on product properties and production equipment capabilities are observed, and raw materials are purchased and manufactured. Can be minimized.

It is a figure which shows the structure of the purchasing and use plan preparation apparatus of the raw material which concerns on embodiment. It is a flowchart which shows the processing operation | movement of the purchasing and use plan preparation apparatus of the raw material which concerns on embodiment. It is a figure which shows the example of track record information. It is a figure which shows the example of track record information. It is a figure which shows the example of track record information. It is a figure which shows the example of plan information. It is a figure which shows the example of plan information. It is a figure which shows the example of plan information. It is a figure which shows the example of plan information. It is a figure which shows the example of plan information. It is a figure which shows the example of plan information. It is a figure which shows the example of the purchase amount of the raw material obtained by optimization calculation. It is a figure which shows the example of the property of the product obtained by optimization calculation. It is a figure which shows the example of the production information obtained by optimization calculation. It is a figure which shows the example of the purchase amount of the raw material obtained by correction | amendment calculation. It is a figure which shows the example of the property of the product obtained by correction | amendment calculation. It is a figure which shows the example of the production information obtained by correction | amendment calculation.

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
FIG. 1 shows a configuration of a raw material purchase and use plan creation apparatus 100 according to the present embodiment. The raw material purchase and use plan creation apparatus 100 observes restrictions on the properties of pig iron, sintered ore and slag as products and the capacity of manufacturing equipment, and purchases of raw iron ore, coke, coal, and auxiliary materials, In addition, a purchase and use plan for raw materials that minimizes manufacturing costs (simply referred to as costs) is created.

  Reference numeral 101 denotes a data fetching unit that functions as a data fetching unit, which fetches record information and plan information for planning a purchase and use plan of raw materials. The record information and the plan information may be imported from a database (not shown) in the apparatus 100 or from an external database via a network, or may be input from the input device 110, for example.

  Reference numeral 102 denotes a coke / coal amount calculation unit functioning as a calculation unit, and calculates the purchase amount and the use amount of temporary coke and coal based on the record information acquired by the data acquisition unit 101.

Reference numeral 103 denotes a mathematical programming problem construction unit that functions as a mathematical programming problem construction unit. The purchase amount and the usage amount of coke and coal are fixed values, and based on the plan information captured by the data capture unit 101, We formulate a mathematical programming problem in which the constraint function related to the capacity of the manufacturing facility and the objective function representing the cost are expressed in a linear form. When constructing a mathematical programming problem for the first time, provisional coke and the purchase and use of coal calculated by the coke / coal amount calculation unit 102 are used as fixed values. Then, when the purchase amount of coke and coal is given by the processing of the correction calculation execution unit 105, the correction calculation convergence determination unit 106, the coke / coal fluctuation amount calculation unit 107, and the cost comparison unit 108 which will be described later, it is set as a fixed value. Used as
As already mentioned, combustion when producing pig iron and sintered ore, the amount of gas generated in the gasification phenomenon, the amount of heat, etc. include complicated nonlinear elements in the calculation, and the constraint equation and objective function are expressed in linear form It is a factor that can not. The main factors are coke (bulk coke and pulverized coke) and coal (pulverized coal and anthracite), but there are only a few brands of coke and coal. It is possible to linearize the calculation.
However, here, coal for making coke (coking coal) is not considered, and coke produced from coking coal is present.

  An optimization calculation execution unit 104 functions as an optimization calculation execution unit. The mathematical programming problem constructed by the mathematical programming problem construction unit 103 is converted into linear programming, mixed integer programming, integer programming, or quadratic programming. Calculate the amount of raw materials purchased and used, the properties of the product and the amount of production to optimize and minimize the objective function.

  Reference numeral 105 denotes a correction calculation execution unit that functions as a correction calculation execution unit, and corrects the purchase amount and usage amount of raw materials, the properties of the product, and the production amount calculated by the optimization calculation execution unit 104 based on actual results.

  Reference numeral 106 denotes a correction calculation convergence determination unit that functions as a correction calculation convergence determination unit. The purchase amount and usage amount of raw materials corrected by the correction calculation execution unit 105, the property and production amount of the product are respectively compared with the results before correction. It is determined whether or not it has converged, that is, whether or not the difference between the two is within a preset range. When it is not determined that the correction calculation convergence determination unit 106 has converged, the mathematical calculation problem is again set with the purchase amount of coke and coal included in the purchase amount and the usage amount of the raw material corrected by the correction calculation execution unit 105 as fixed values. The processing of the construction unit 103, the optimization calculation execution unit 104, and the correction calculation execution unit 105 is executed.

Reference numeral 107 denotes a coke / coal fluctuation amount calculation unit that functions as a fluctuation amount calculation means. When it is determined that the correction calculation convergence determination unit 106 has converged, it is included in the purchase amount and the usage amount of the raw material determined to have converged. With respect to coke and coal, the amount of fluctuation in which the objective function in a form where the purchased and used amount of coke and coal is not fixed values is reduced is calculated by a gradient method such as the steepest descent method.
Since there are over 100 types of iron ore and auxiliary materials, it is very difficult to determine the optimal purchase and usage for constraints and objective functions including nonlinear terms. By setting the purchase amount and the usage amount to fixed values, the constraints and the objective function can be linearized. As a result of performing optimization calculations on the linearized mathematical programming problem, if the purchase and usage of iron ore and secondary raw materials are obtained, coke (lump coke and fine coke) and coal (pulverized coal and Since anthracite is a few brands at most, it is technically possible to obtain better results by minutely changing the amount of purchase and use.

  Reference numeral 108 denotes a cost comparison unit that functions as a cost comparison unit. The purchase amount and use amount of coke and coal changed based on the fluctuation amount calculated by the coke / coal fluctuation amount calculation unit 107 are set as fixed values, and mathematical operations are performed again. The process of the planning problem construction unit 103, the optimization calculation execution unit 104, the correction calculation execution unit 105, and the correction calculation convergence determination unit 106 is executed, and the resulting cost is converged with respect to the previously calculated cost. Whether or not the difference between them is within a preset range is determined.

  Reference numeral 109 denotes a result output unit, which outputs raw material purchase and use plans when the cost is converged by the cost comparison unit 108. For example, the result is displayed on the display 111, or the result is output to an internal or external computer device or database of the apparatus 100.

  Reference numeral 110 denotes an input device such as a pointing device or a keyboard. Reference numeral 111 denotes a display.

Next, a raw material purchase and use plan creation method by the raw material purchase and use plan creation apparatus 100 according to the present embodiment will be described. FIG. 2 is a flowchart showing the processing operation of the raw material purchase and use plan creation apparatus 100 according to the present embodiment.
In this embodiment, a plurality of factories are dispersed, and raw materials used in each factory are purchased together and transported to each factory.
Further, it is assumed that a purchase and use plan for raw materials is created every certain period (for example, one year), and a purchase and use plan for raw materials is to be created with the next period as a planning target period.
In the following description, for the sake of simplicity, the purchase amount and the usage amount are assumed to be the same. If the purchase amount and the usage amount do not match, it can be dealt with by increasing the corresponding variable. If the purchase amount and the usage amount do not match, the upper limit and lower limit amounts that can be purchased are imposed on the purchase amount, and the usage amount must be within the upper limit and lower limit of the purchase amount. However, the structure of the basic problem is not significantly different from that in which the purchase amount and the usage amount are the same.

  The data capturing unit 101 captures record information and plan information for making a purchase and use plan for raw materials (step S1).

3A to 3C show examples of performance information.
FIG. 3A shows the actual purchase amount of raw materials, and describes the actual purchase amount (t) of iron ore, coke, coal, and auxiliary materials at each factory in a certain past period. In the illustrated example, coke and coal are described as being handled together, but they may be handled independently. As described above, iron ore is classified by brand and the number thereof is more than 100 types. In addition, there are about several tens of types of auxiliary materials. On the other hand, the category of coke and coal is about several brands at most.
FIG. 3B shows the performance characteristics of the product, and the performance characteristics of pig iron, sintered ore and slag at each factory over a certain period in the past, specifically the amount of Fe (kg / t) contained in pig iron, firing The FeO ratio (%) contained in the ore, basicity of slag, and the like are described. These properties are measured by an actual component inspection or the like.
FIG. 3C shows the actual production information of the product, which describes the actual production (t) of pig iron, sintered ore and slag at each factory in a certain past period. In addition, the generation amounts of BFG gas, COG gas, and the like, which are by-products, are also described.

4A to 4F show examples of plan information.
FIG. 4A shows the amount of raw material that can be purchased. For each of iron ore, coke, coal, and secondary raw materials, an upper limit amount and a lower limit amount that represent the take-up target amount are described. Take-up of raw materials Each Yamamoto has contracts for each brand, for example, how much is taken up per year, and it is necessary to purchase raw materials so as to keep this take-up target amount.
Fig. 4B shows the purchasing unit price and transportation unit cost of raw materials. Purchasing cost per ton (yen / t) for iron ore, coke, coal, and auxiliary materials, and transportation cost per ton to each factory (yen) / T).
FIG. 4C shows the property information of the raw material, describing the properties of iron ore, coke, coal, and auxiliary materials, specifically the Fe ratio (%), FeO ratio (%), etc. contained in each. .
FIG. 4D shows the production information of the product, which specifies the production amount (t) of pig iron to be produced at each factory in the planning target period.
FIG. 4E shows facility capacity constraint information (target value), in which facility capacity constraints at each factory are described. In this example, it is set as a facility capacity constraint on the total amount for ore crushing and sintering production within the planning target period.
FIG. 4F shows product constraint information (target value), which describes information related to constraints to be satisfied by the plan created result. For example, pig iron-Fe (kg / t) in the factory 1 needs to satisfy the constraint that it is 950.1 (kg / t) or more. In addition, although the constraint of “above” is described, it is also possible to handle the constraints of “equivalent” and “below”.

Next, the coke / coal amount calculation unit 102 calculates the provisional coke and coal purchase amount based on the record information acquired in step S1 (step S2).
Here, the amount of coke and coal (t / tp) required to produce pig iron 1 (t) is provisionally determined (tp: the amount of pig iron pig iron). In this example, assuming that the actual result and the operation condition of the planning target period have not changed significantly, the same value as the actual result is set as a provisional value. That is, using the results information of FIGS. 3A and 3C,
Factory 1 coke amount (t / tp) = 450/1200
Factory 2 coke amount (t / tp) = 400/1050
Factory n coke amount (t / tp) = 400/1070
Is a provisional value.

Next, the mathematical programming problem constructing unit 103 sets the purchased amount and the used amount of coke and coal as fixed values, and based on the plan information captured by the data capturing unit 101, restrictions on the properties of the product and the capacity of the manufacturing equipment The formula and the objective function representing the cost are formulated into a mathematical programming problem in a linear form. In the first loop, the provisional coke and the purchase amount of coal calculated in step S2 are used as fixed values. Moreover, when the purchase amount of coke and coal is given by step S7, S10 mentioned later, it is used as a fixed value.
Here, the objective function is defined by the following expression (1), the constraint expression is defined by the following expression (2), and the variables corresponding to the variable x _i are defined by the following expressions (3) and (4). Then, the formulation according to the formulation of the linear programming problem as shown in the following equation (5) is performed.

  The objective function represented by the above equation (1) is a function that represents the cost of purchasing raw materials, the cost of transporting raw materials to each factory, the cost of gas processing, and the processing cost of using the manufacturing equipment. I want to minimize. Specifically, the following equations (6) to (9) are given.

Here, the processing cost is the cost for processing gas (COG, CO ₂ , BFG, etc.), and the processing cost is the cost for using manufacturing equipment (ore crushing equipment, etc.). Is given by a complex nonlinear equation.
In this case, if the coke / coal purchase quantity buy_coke brand and factory are considered as fixed values, the above formulas (8) and (9) are described in simple iron ore / sub-material purchase quantity buy_ore brand and factory line format. can do.
Therefore, in order to linearize the objective function, the buy_coke brand, the temporary coke obtained in step S2 as a factory, and the purchase amount of coal are used as fixed values, and the above equations (8) and (9) are converted into the following equations (10 ), As shown in (11).

The constraint equation represented by Formula (2) is a formula that represents constraints on pig iron, sintered ore and slag properties, production facility capability, and production information.
Describing the restrictions on the properties of pig iron, sintered ore, and slag, the constraint equation for the characteristics of pig iron is given by the following equation (12), for example. For example, the target value of factory 1 is given as 950.1 (kg / t) using the plan information in FIG. 4F.

  The constraint equation for the properties of sintered ore and slag is given by a complex nonlinear equation with the purchase quantity as a variable, for example, as in the following equations (13) and (14).

In this case, if the coke / coal purchase amount buy_coke brand and factory are considered as fixed values, the above formulas (13) and (14) are described in simple iron ore / sub-material purchase quantity buy_ore brand and factory line format. can do.
Therefore, in order to linearize the constraint equation, the buy_coke brand, the temporary coke obtained in step S2 as a factory, and the purchase amount of coal are used as fixed values, and the above equations (13) and (14) are converted into the following equations (15 ), As shown in (16).

The above equation (15) can be rewritten into the following equation (15 ′) in accordance with the formulation of the linear programming problem by performing operations such as transfer, and is used as a constraint equation.
Also, the above equation (16) can be rewritten into the following equation (16 ′) in accordance with the formulation of the linear programming problem by performing an operation such as a transfer term, and is used as a constraint equation.

  Further, the capacity constraint of the manufacturing facility will be described. The constraint equation is given by the following equations (17) and (18), for example. The iron ore in the following formula (17) is an unselected ore (a mixture of lump and powdered iron ore) that needs to be crushed among iron ores. For example, the target value of the factory 1 is given as 980 (kg / t) using the plan information of FIG. 4E. Further, the iron ore, auxiliary material, and coke in the following formula (18) are obtained by selecting iron ore, auxiliary material, and coke that are materials for making sintering. For example, the target value of the factory 1 is given as the sum of 480 (t) and 500 (t) using the plan information of FIG. 4E.

  Further, the constraints on production information will be described. The constraint equations for the amount of sintered ore and the BFG generation basic unit are given by the following equations (19) and (20).

In this case, if the purchase quantity of coke / coal buy_coke brand and factory are considered as fixed values, the above formulas (19) and (20) are the simple purchase quantities of iron ore and auxiliary materials according to the formulation of the linear programming problem. The buy_ore brand can be described in a factory line format.
Therefore, in order to linearize the constraint equation, the buy_coke brand, the temporary coke obtained in step S2 as a factory, and the purchase amount of coal are used as fixed values, and the above equations (19) and (20) ) And (22) as shown in FIG.

Next, the optimization calculation execution unit 104 optimizes the mathematical programming problem constructed in step S3 using linear programming, mixed integer programming, integer programming, or quadratic programming to minimize the objective function. The purchase amount of raw materials to be processed, the properties of the product, and the production information are calculated (step S4). Note that these linear programming, mixed integer programming, integer programming, or quadratic programming are general techniques, and thus description thereof is omitted here.
FIG. 5A shows the purchase amount of raw materials obtained by the optimization calculation. The calculated purchase quantity (t) of iron ore, coke, coal, and auxiliary materials at each factory is described. The coke and coal have fixed values given in step S2 or steps S7 and S10 described later.
FIG. 5B shows the properties of the product obtained by the optimization calculation. Describes the calculation characteristics of pig iron, sintered ore and slag at each factory, specifically Fe amount (kg / t) contained in pig iron, FeO ratio (%) contained in sintered ore, basicity of slag, etc. Has been.
FIG. 5C shows production information obtained by optimization calculation. The calculated production (t) of pig iron, sintered ore and slag at each factory is described. In addition, the generation amounts of BFG gas, COG gas, and the like, which are by-products, are also described. The pig iron amount (t), which is the target product, is assumed to be given by the plan information in FIG. 4D.

Here, in general programming methods such as linear programming, mixed integer programming, integer programming, and quadratic programming, the objective function is expressed by a function of a quadratic term and the constraint expression is expressed by a linear constraint. There is a need. When both the objective function and the constraint equation are composed of nonlinear equations, the Lagrange undetermined multiplier method is generally known. In order to solve the Lagrangian multiplier method, it is necessary to subtract the linear sum of each constraint condition from the objective function and solve the partial differential with variables as simultaneous equations. Since these simultaneous equations are non-linear simultaneous equations, there is a problem that a convergence calculation based on numerical analysis is required, and it takes time to solve.
On the other hand, in this embodiment, since the coke and coal purchase amounts are handled as fixed values, both the objective function and the constraint equation are configured in a linear format, so linear programming, mixed integer programming, integer programming or It becomes possible to optimize by a normal solution method using quadratic programming.
In addition, the amount of coke and coal purchased temporarily fixed here is slightly changed in the direction of cost reduction using a gradient method such as steepest descent, and based on the changed value, the above linear programming method, By repeating the procedure of repeated optimization using mixed integer programming, integer programming, or quadratic programming, it is possible to calculate the optimal amount of coke and coal purchases, while significantly reducing the solution time. Is possible.

Next, the correction calculation execution unit 105 corrects the raw material purchase amount, the product properties, and the production information (excluding the pig iron amount given by the plan information in FIG. 4D) calculated in step S4 based on the actual results. (Step S5).
In step S4, a solution satisfying the constraint is obtained. However, the properties shown in the equations (15 ′) and (16 ′), the equipment capacities shown in the equations (17) and (18), and (21) , (22) Expression related to production information shown in Expression (22), and the expression used for the objective function calculation of Expression (6), (7), (10), and (11) as the cost It is a combination of physical formula coefficients. The calculated value of the solution obtained using these equations takes a value that deviates from the measured values of pig iron, sintered ore and slag generated from the actual blending.
Therefore, as a device to further increase the accuracy, the solution shown in FIGS. 5A to 5C obtained in Step 4 and the blending state are close to each other, using actual data in which various properties and costs are actually measured, and from the difference from this actual data. Correct the calculated value.
For example, the purchase amount of raw materials is corrected as shown in the following equation (23). Moreover, about the property of a product, it correct | amends like the following Formula (23). Further, the production information is corrected as shown in the following equation (25). X property represents pig iron-Fe, sintered ore-FeO, etc. Y information represents pig iron amount, sintered ore amount, and the like.

  Other than the above, pig iron-Fe, slag basicity, BFG generation basic unit, and the like are also corrected.

As a result, there is a case where a value satisfying the constraint condition causes a constraint violation in the value before correction that is a calculated value by the optimization calculation. For example, if the sintered ore-FeO (%) is constrained to be 7.0 or more before correction, 6.9 or the like is generated by the correction calculation.
Such a correction calculation includes a very complicated calculation and includes a calculation that can be calculated only from the calculation result, and thus cannot be incorporated into the optimization calculation.

Next, the correction calculation convergence determination unit 106 determines whether or not the raw material purchase amount, the product properties, and the production information corrected in step S5 have converged with respect to the result before each correction, that is, the difference between the two. It is determined whether or not it is within a preset range (step S6).
When the purchase amount of raw materials after correction, the properties of the product, and the production information are significantly different from the values before correction, there is a high possibility that the constraints that are observed in the optimization calculation are broken after correction. Therefore, it is determined whether or not the difference between the corrected raw material purchase amount, product properties and production information and the value before each correction is within a preset range. The items for judging whether or not the difference between the corrected purchase amount of raw materials, the properties of the product and the production information and the values before each correction are within a preset range are applicable to all items. It is also possible to narrow down by selecting items that are considered important.
For example, since iron-related constraints are the most important indicators, whether pig iron-Fe, which is the iron content in pig iron, and sinter-FeO, which is the iron component of the sinter, are within a preset range. Is selected as an item for judging. On the other hand, the BFG generation unit, which is the amount of gas generated from a blast furnace per ton of pig iron, is used for power generation, and since it is less important with respect to the quality of pig iron, it does not matter even if there is a slight fluctuation. Therefore, it may not be selected as an item for determining whether or not it is within a preset range. By narrowing down the above item selection, it is possible to create a usage plan that strictly observes restrictions for important indicators, and at the same time, for indicators that are not very important, it is not necessary to make convergence judgment, so iterative calculation due to convergence judgment violations. This makes it possible to create a high-speed plan.

As a result, if the result before the correction is not converged, the purchased quantity of coke and coal included in the purchased quantity of raw material corrected in step S5 is set as a fixed value (step S7), and the mathematical programming problem (step S3), optimization calculation (step S4), correction calculation (step S5), and convergence determination (step S6) are executed. This is repeated until it is determined that the corrected raw material purchase amount, product properties and production information and the values before each correction are within a preset range. Here, the corrected raw material purchase amount, product properties, and production information are corrected with the values calculated by the optimization calculation, and have values that are almost close to the actual measured values. . Therefore, paying attention to the fact that the accuracy of the production information, properties, and costs after the correction calculation is comparable to the actual data, it is possible to consider the corrected data as a new actual result. . For this reason, in the correction calculation (step S5), the corrected raw material purchase amount, product properties, and production information obtained in the previous correction calculation (step S5) are regarded as actual data in the current loop. Execute correction calculation. By this operation, there is no difference between the purchase amount of raw material before correction, the properties of the product and the production information, and the purchase amount of raw material after correction, the properties of the product and the production information, and convergence is achieved.
On the other hand, when it converges with respect to the result before correction | amendment, it transfers to step S8.

In step S8, the cost comparison unit 108 determines whether or not the cost obtained by the mathematical programming problem (step S3) and the optimization calculation (step S4) has converged with respect to the previously calculated cost. It is determined whether or not the difference is within a preset range.
When the first loop (the cost calculated last time does not exist) and when the cost has not converged with respect to the cost calculated last time, the process proceeds to step S9. In step S9, the coke / coal fluctuation amount calculation unit 107 relates to the coke and coal included in the purchase amount of the raw materials determined to have converged in step S6, that is, the original objective function, that is, the above formulas (6) to (9). The amount of fluctuation of the coke / coal purchase amount buy_coke brand and the objective function in a form that does not use the factory as a fixed value is calculated by a gradient method such as the steepest descent method (step S9). The buy_coke brand and factory changed based on the amount of change are given by the following equation (26).

Then, the purchased amount of coke and coal after the change is set as a fixed value for the purchased amount of coke and coal (step S10), and again, a mathematical programming problem (step S3), an optimization calculation (step S4), and a correction calculation (step S5) Convergence determination (step S6) and cost comparison (step S8) are executed. This is repeated until it is determined that the difference between the currently calculated cost and the previously calculated cost is within a preset range.
Here, since this problem includes nonlinear items in the constraint condition and the objective function, there is a possibility that the convergence calculation by the steepest descent method falls into a local optimal solution. Therefore, in order to prevent the solution from falling into the local optimal solution, when the fluctuation range of the objective function becomes smaller than the predetermined fluctuation range, a fluctuation that does not conform to the steepest descent method is added to the purchase amount of coke and coal. It is also possible to get out of the local optimal solution. For example, when the fluctuation range of the objective function is 0.1% or less with respect to the value of the latest objective function, a random number is generated, and the random fluctuation using the random number is used as the purchase amount of coke and coal. It is also possible to give. Or, when the gradient vector is x, orthogonal to the gradient vector, and y is the same length vector as the gradient vector, as shown in the following equation (27), z is a vector located between them, and this z It is also possible to give the amount of coke and coal purchased as a variable amount.

The process of adding fluctuations that do not comply with the steepest descent method can be terminated when a predetermined number of times is executed.
On the other hand, when it converges with respect to the cost calculated last time, it transfers to step S11.

  In step S11, the result output unit 109 outputs the purchase and use plan of raw materials. As the purchase and use plan of raw materials, specifically, the cost (objective function value) determined to have converged with respect to the previously calculated cost, or finally obtained as shown in FIGS. 6A to 6C. Output the purchased amount of raw materials, properties of products and production information.

As mentioned above, the cost of purchasing and manufacturing raw materials (iron ore, coke, coal, and auxiliary materials) should be observed while obeying restrictions on the properties of the products (pig iron, sintered ore and slag) and the capacity of the production equipment. Even when a constraint equation and an objective function are given by a non-linear expression when creating a purchase and use plan of raw materials that minimizes the above, it can be formulated into a mathematical programming problem in a linear form. This is because coke and coal are the factors that cannot express the constraint equation and the objective function in a linear format, and the purchase amount and the usage amount are fixed values. The objective function is formulated into a mathematical programming problem with a linear form.
In addition, it is necessary to protect the accuracy of the production information, properties, costs, etc. by using the actual data that has been actually measured and making correction calculations for the values of production information, properties, costs, etc. Even if there is a problem that the index (objective function) that satisfies the condition (constraint expression) that cannot be minimized is not minimized, the calculation result is considered as new actual data, and the convergence calculation is performed. Can be
This is because the production information, properties, and costs after the correction calculation are focused on the fact that the accuracy has improved to the same extent as the actual data, and by considering the corrected data as new actual data, Based on this new performance data, the result of optimization calculation is repeatedly subjected to correction calculation, so that the value after correction calculation satisfies the condition to be protected.
As a result, it is possible to make a purchase and use plan of raw materials mathematically and at high speed with a simple algorithm.

The units 101 to 109 of the raw material purchase and use plan creation apparatus 100 to which the present invention is applied are realized by a computer device including a CPU, a ROM, a RAM, and the like, for example.
As mentioned above, although this invention was demonstrated with various embodiment, this invention is not limited only to these embodiment, A change etc. are possible within the scope of the present invention.
The present invention also provides software (program) that implements the functions of the present invention to a system or apparatus via a network or various storage media, and the system or apparatus computer reads out and executes the program. It is feasible.

DESCRIPTION OF SYMBOLS 100: Raw material purchase and use plan preparation apparatus 101: Data acquisition part 102: Coke / coal amount calculation part 103: Mathematical programming problem construction part 104: Optimization calculation execution part 105: Correction calculation execution part 106: Correction calculation convergence determination part 107: Coke / coal fluctuation amount calculation unit 108: Cost comparison unit 109: Result output unit

Claims (10)

The above raw materials that meet the restrictions on the properties of pig iron, sintered ore and slag, which are the products, and the capacity of the production equipment, and minimize the costs of purchasing and manufacturing iron ore, coke, coal and auxiliary materials. A raw material purchasing and usage plan creation device for creating a purchasing and usage plan for
Data capturing means for capturing planning information for planning the purchase and use of the raw materials;
Based on the plan information captured by the data capturing means, with the purchased and used amounts of coke and coal as fixed values, a constraint equation regarding the properties of the product and the capacity of the manufacturing facility, and an objective function representing the cost A mathematical programming problem construction means for formulating a mathematical programming problem into a linear form,
Optimization calculation execution means for optimizing the mathematical programming problem constructed by the mathematical programming problem construction means and calculating the purchase amount and usage amount of the raw material, the property of the product and the production amount to minimize the objective function; ,
Correction calculation execution means for correcting the purchase amount and use amount of the raw material calculated by the optimization calculation execution means, the properties and production amount of the product, respectively, based on actual results;
Correction calculation convergence determination means for determining whether the purchase amount and usage amount of the raw material corrected by the correction calculation execution means, the properties of the product and the production amount have converged with respect to the result before correction, respectively. ,
When it is determined that the correction calculation convergence determination unit has converged, regarding the coke and coal included in the purchase amount and the use amount of the raw materials determined to have converged, the purchase amount and the use amount of coke and coal are set to a fixed value. A fluctuation amount calculating means for calculating a fluctuation amount that reduces the objective function in a form that does not,
Based on the fluctuation amount calculated by the fluctuation amount calculation means, the purchased quantity and usage amount of coke and coal are fixed values, and again the mathematical programming problem construction means, the optimization calculation execution means, and the correction calculation execution And a cost comparison means for determining whether or not the cost obtained as a result has converged with respect to the previously calculated cost. Characteristic raw material purchase and use plan creation device. The data capturing means captures performance information,
Based on the results information captured by the data capturing means, comprising a calculation means for calculating the purchase amount and usage of temporary coke and coal,
2. The mathematical programming problem constructing means, when constructing a mathematical programming problem for the first time, uses the provisional coke and the purchased amount and the used amount of coal as fixed values calculated by the computing means. Equipment for purchasing and using the listed raw materials.   The purchase and production costs include a purchase cost of the raw material, a transport cost of the raw material, a processing cost of gas as a by-product, and a processing cost in using the production facility. Or the raw material purchase and use plan preparation apparatus of 2 description.   When it is not determined that the correction calculation convergence determination means has converged, the purchase quantity of the coke and coal included in the purchase amount and the use amount of the raw material corrected by the correction calculation execution means is set as a fixed value, and the mathematical calculation is performed again. The purchase of raw materials according to any one of claims 1 to 3, wherein processing of a planning problem construction unit, the optimization calculation execution unit, the correction calculation execution unit, and the correction calculation convergence determination unit is executed. And use plan creation device.   The correction calculation convergence determination means determines whether the purchase amount and usage amount of the raw material corrected by the correction calculation execution means, the property of the product and the production amount have converged with respect to the result before correction, respectively. The raw material purchasing and use plan creation device according to any one of claims 1 to 4, wherein all items are selected as items to be determined, or some items are selected and narrowed down.   6. The raw material purchase and use plan creation device according to claim 1, wherein the fluctuation amount calculation means calculates the fluctuation amount by a steepest descent method.   The fluctuation amount calculation means, when the fluctuation range of the objective function in a form in which the purchase amount and usage amount of the coke and coal are not fixed values becomes smaller than a predetermined fluctuation range, the purchase amount of coke and coal and The raw material purchase and use plan creation device according to claim 6, wherein fluctuations not in accordance with the steepest descent method are added to the usage amount.   The raw material purchase and use plan creation apparatus according to claim 7, wherein random fluctuations using random numbers are given as fluctuations not conforming to the steepest descent method. The above raw materials that meet the restrictions on the properties of pig iron, sintered ore and slag, which are the products, and the capacity of the production equipment, and minimize the costs of purchasing and manufacturing iron ore, coke, coal and auxiliary materials. A raw material purchasing and usage plan creation method for creating a purchasing and usage plan for
A step of fetching plan information for making a plan for purchasing and using the raw material, the data fetching means;
Mathematical programming problem structuring means, with a fixed amount of coke and coal purchased and used, based on the plan information captured by the data capturing means, a constraint equation regarding the properties of the product and the capacity of the manufacturing equipment, And formulating the objective function representing the cost into a mathematical programming problem in a linear form,
The optimization calculation execution means optimizes the mathematical programming problem constructed by the mathematical programming problem construction means, and calculates the purchase amount and usage amount of the raw material that minimizes the objective function, the property and the production amount of the product. And steps to
Correction calculation execution means, the amount of purchase and usage of the raw material calculated by the optimization calculation execution means, the property and production amount of the product, respectively, based on the actual results,
The correction calculation convergence determination means determines whether the purchase amount and usage amount of the raw material corrected by the correction calculation execution means, the property of the product and the production amount have converged with respect to the result before correction, respectively. And steps to
When the fluctuation amount calculation means is determined to have converged by the correction calculation convergence determination means, regarding the coke and coal included in the purchase amount and the usage amount of the raw materials determined to have converged, the purchase amount of coke and coal and Calculating a fluctuation amount that reduces the objective function in a form in which the usage amount is not a fixed value;
The cost comparison means uses, as fixed values, the purchased quantity and the used quantity of coke and coal that have been changed based on the fluctuation amount calculated by the fluctuation amount calculation means, and again the mathematical programming problem construction means, the optimization calculation execution means , Executing the processes of the correction calculation execution means and the correction calculation convergence determination means, and determining whether or not the cost obtained as a result has converged with respect to the previously calculated cost. A method for purchasing and using raw materials. The above raw materials that meet the restrictions on the properties of pig iron, sintered ore and slag, which are the products, and the capacity of the production equipment, and minimize the costs of purchasing and manufacturing iron ore, coke, coal and auxiliary materials. A program for causing a computer to execute a process for creating a purchase and use plan for
Data capturing means for capturing planning information for planning the purchase and use of the raw materials;
Based on the plan information captured by the data capturing means, with the purchased and used amounts of coke and coal as fixed values, a constraint equation regarding the properties of the product and the capacity of the manufacturing facility, and an objective function representing the cost A mathematical programming problem construction means for formulating a mathematical programming problem into a linear form,
Optimization calculation execution means for optimizing the mathematical programming problem constructed by the mathematical programming problem construction means and calculating the purchase amount and usage amount of the raw material, the property of the product and the production amount to minimize the objective function; ,
Correction calculation execution means for correcting the purchase amount and use amount of the raw material calculated by the optimization calculation execution means, the properties and production amount of the product, respectively, based on actual results;
Correction calculation convergence determination means for determining whether the purchase amount and usage amount of the raw material corrected by the correction calculation execution means, the properties of the product and the production amount have converged with respect to the result before correction, respectively. ,
When it is determined that the correction calculation convergence determination unit has converged, regarding the coke and coal included in the purchase amount and the use amount of the raw materials determined to have converged, the purchase amount and the use amount of coke and coal are set to a fixed value. A fluctuation amount calculating means for calculating a fluctuation amount that reduces the objective function in a form that does not,
Based on the fluctuation amount calculated by the fluctuation amount calculation means, the purchased quantity and usage amount of coke and coal are fixed values, and again the mathematical programming problem construction means, the optimization calculation execution means, and the correction calculation execution And the correction calculation convergence determination means are executed, and the computer functions as a cost comparison means for determining whether or not the cost obtained as a result has converged with respect to the previously calculated cost. Program.

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