JP7183754B2 - Production allocation determination device, production allocation determination system, and production allocation determination method - Google Patents

Description

The present invention relates to a production allocation determination device, a production allocation determination system, and a production allocation determination method.

Determining the optimal cost when allocating products (for example, various resources such as electricity, gas, and steam) produced by multiple producers (for example, various facilities or equipment such as power generation facilities, gas production facilities, boilers, etc.) and a method of determining the optimum cost when allocating the production amount of the products produced on the production line.

For example, a method of performing optimal control by solving a quadratic programming problem by parallel computing (Patent Document 1), a method of solving a quadratic programming problem by utilizing a calculation history (Non-Patent Document 2), etc. are known. .

Also, in order to facilitate online optimization calculations, a method of analyzing optimization problems off-line is known.

For example, there is known a method of generating an optimal control rule offline and substituting numerical values online to achieve optimal control (Patent Document 3, Non-Patent Document 1). Also known is a technique for easily realizing online optimization calculations by applying mathematical formula manipulation techniques offline (Patent Document 4, Patent Document 5, Non-Patent Document 2, Non-Patent Document 3).

For example, in the method described in Patent Document 4, the conditional expressions that must be satisfied when obtaining an optimal solution are used to reduce the scale of simultaneous equations that must be solved online for optimal control. In addition, in the methods described in Patent Document 5 and Non-Patent Documents 2 and 3, from the conditional expression that must be satisfied when the optimal solution is obtained, the total supply amount and the optimal marginal cost (optimal price) A method is described in which the relational expression to be satisfied is calculated off-line by numerical manipulation, and the optimum price and the optimum solution are calculated on-line by binary search.

In addition, in the methods described in Patent Document 5 and Non-Patent Documents 2 and 3, a method (Non-Patent Document 4) is used in which a problem is formulated by a first-order predicate logic formula and optimization is achieved by elimination of quantifiers. ing. Specifically, the quantifier represented by the universal quantifier (∀) and the existential symbol (∃), and the logical symbol represented by the product (∧) and sum (∨) of polynomial equations and inequalities of multiple variables. Combine the combined logical expressions using to obtain the first-order predicate logical expression. Among the variables that appear in a logical expression, those bound by quantifiers are called bound variables, and those that are not bound by quantifiers are called free variables. Optimization is achieved by eliminating the bound variables in the first-order predicate formula and deriving a formula to be satisfied by the free variables.

In addition, the interior point method described in Non-Patent Document 6 is known as one of the techniques for solving the quadratic programming problem.

JP 2012-138069 A JP-A-2004-288161 JP 2010-12890 A JP 2012-194960 A WO2016/075805

Alberto Bemporad, Manfred Morari, Vivek Dua, Efstratios N. Pistikopoulos "The explicit linear quadratic regulator for constrained systems" Automatica, Vol.38, pp.3-20 Yoshio Tange, Satoshi Kiryu, Tetsuro Matsui, "High-speed optimal distribution control for energy saving by optimality condition and mathematical formula processing", The Institute of Electrical Engineers of Japan Transaction C, Vol. 136, No. 9, pp. 1359-1366 Satoshi Kiryu, Yoshio Tange, Tatsuya Iizaka, Tetsuro Matsui, "Formula Processing Type High-speed Optimal Distribution Control Considering Demand Forecast and Change Rate Constraints", Proceedings of the 2018 Annual Conference of the Institute of Electrical Engineers of Japan, No.3, pp44-45 Hirokazu Anai, Kazuhiro Yokoyama, "QE Calculation Algorithm and Its Application Optimization by Numerical Manipulation", University of Tokyo Press, 2011, pp. 214-221 Hirokazu Anai, "Mathematical Optimization Solid Line Guide", Kodansha, 2013, pp. 63-68

In general, the amount of demand for a product changes from moment to moment due to various circumstances. Therefore, in order to procure necessary and sufficient products while suppressing the overall procurement cost, it is necessary to appropriately distribute the supply of each producer according to the demand. In particular, for example, when applying to targets with a short control cycle, it is necessary to quickly obtain an optimum solution (that is, optimum distribution of the amount of supply supplied by each producer to the consumer).

However, in the conventional methods described in Patent Document 1 and Patent Document 2, for example, an optimum solution is obtained by solving a quadratic programming problem. For this reason, repeated calculations are required to find the optimum solution, and sometimes no solution is found, making it difficult to achieve high-speed optimum control.

Further, in the conventional method described in Patent Document 3, for example, the optimum control rule is generated off-line, so the off-line calculation load increases. For this reason, it is sometimes difficult to apply the method to a large-scale optimization problem.

In addition, for example, in the conventional method described in Patent Document 4, it is necessary to solve simultaneous equations when performing online optimization, and high speed is not possible in environments with limited computational resources such as PLCs (Programmable Logic Controllers). could have been damaged. Moreover, in this conventional method, approximation of constraint conditions is also performed, so a strict optimal solution cannot be obtained.

Furthermore, the conventional methods described in Patent Document 5, Non-Patent Documents 2 and 3 use binary search in the process of calculating the optimum solution, and therefore speed may be impaired in an environment with limited computational resources. rice field.

SUMMARY OF THE INVENTION The present invention has been made in view of the above points, and it is an object of the present invention to quickly obtain a precise optimal solution in optimal control even in an environment where computational resources are limited.

In order to achieve the above object, a production allocation determination device according to one embodiment of the present invention is a production allocation determination device that determines the optimum allocation of supply volumes produced and supplied by a plurality of producers, a total supply curve calculating means for calculating a total supply curve model representing the relationship between the total supply volume of the plurality of producers and the marginal cost from the supply curve model representing the relationship between the supply volume and the marginal cost; and the total supply curve. Optimal price table creation means for creating an optimal price table for calculating an optimal price showing the optimal marginal cost according to the demand amount based on the model; Based on the given demand amount and the optimal price table an optimum price calculation means for calculating an optimum price according to the given amount of demand; and an optimum supply amount of each of the producers based on the supply curve model of each of the producers and the optimum price. and a supply amount calculation means for calculating an optimum supply amount that indicates an appropriate distribution.

Even in an environment with limited computational resources, it is possible to quickly obtain a precise optimal solution for optimal control.

BRIEF DESCRIPTION OF THE DRAWINGS It is a figure which shows an example of the whole structure of the production allocation determination apparatus which concerns on 1st embodiment. It is a figure which shows an example of the hardware constitutions of the production allocation determination apparatus which concerns on 1st embodiment. It is a figure showing an example of functional composition of a production allocation deciding device concerning a first embodiment. 4 is a flowchart showing an example of offline processing according to the first embodiment; FIG. 4 is a diagram for explaining an example of dividing a total supply curve model φ(λ, L) at breakpoints; It is a figure which shows an example of the optimal price table which concerns on 1st embodiment. 4 is a flowchart showing an example of online processing according to the first embodiment; 4 is a flow chart showing an example of calculation processing of an optimum supply amount P[k] according to the first embodiment; It is a figure (Example 1) which shows an example of a supply and demand system. It is a figure (Example 1) which shows an example of the supply curve model of each generator. FIG. 4 is a diagram (Example 1) showing an example of a total supply curve model φ(λ, L); It is a figure (Example 1) which shows an example of an optimal price table. FIG. 4 is a diagram for explaining an example of calculating the optimum supply amount of each generator (Example 1); It is a figure (Example 1) which shows the comparison result with a prior art. It is a figure which shows an example of a functional structure of the production allocation determination apparatus which concerns on 2nd embodiment. 10 is a flowchart (1/2) showing an example of offline processing according to the second embodiment; 10 is a flowchart (2/2) showing an example of offline processing according to the second embodiment; It is a figure which shows an example of the optimal price table which concerns on 2nd embodiment. 9 is a flowchart showing an example of online processing according to the second embodiment; 7 is a flow chart showing an example of calculation processing of the supply upper limit and the supply lower limit at the cross section s=T. FIG. 4 is a diagram for explaining an example of a supply range of a producer k at a cross section s=T; FIG. 11 is a flow chart showing an example of calculation processing of the optimum price λ[s] according to the second embodiment; FIG. 9 is a flow chart showing an example of calculation processing of the optimum supply amount P[k][s] according to the second embodiment. 7 is a flow chart showing an example of calculation processing of the supply upper limit and the supply lower limit in cross section s (<T). FIG. 4 is a diagram for explaining an example of a supply range of a producer k on a cross section s (<T); It is a figure (Example 2) which shows an example of demand. It is a figure (Example 2) which shows an example of an optimal price table. FIG. 11 is a diagram (embodiment 2) for explaining an example of calculating the optimum supply amount of each generator at cross section s=20; FIG. 11 is a diagram (embodiment 2) for explaining an example of calculating the optimum supply amount of each generator at cross section s=19; It is a figure (Example 2) which shows an example of the optimal supply amount of each generator. It is a figure (Example 2) which shows the comparison result with a prior art. It is a figure which shows an example of the whole structure of the production allocation determination system which concerns on 3rd embodiment.

Hereinafter, each embodiment of the present invention will be described with reference to the drawings. In each of the following embodiments, even for devices, devices, or systems (hereinafter also referred to as “edge devices”) with limited computational resources such as PLCs and DCSs (Distributed Control Systems), strict control in optimal control will be described. A case will be described where the optimum solution (that is, the optimum distribution of the supply amount supplied by each producer to the consumer) is obtained at high speed.

Note that the producers are various facilities or devices that produce and supply products. Specific examples include power generation facilities that produce and supply electric power as products, gas production facilities that produce and supply gas, boilers that produce and supply steam, and the like. Further, consumers are various facilities or devices that demand products produced by producers. Specifically, for example, there are various electric facilities that require electric power, power generation facilities that require gas, and turbines that require steam. However, products are not limited to resources such as electricity, gas, and steam. The product may be, for example, a work-in-progress product, a semi-finished product, or a finished product produced by processing raw materials by a producer.

In each of the following embodiments, it is assumed that all products produced by a plurality of producers are supplied to consumers. Let k be an index representing a producer, let each of a plurality of producers be denoted as "producer k", and let the total number of producers k be N (where N is an integer equal to or greater than 2).

Here, producer k needs a marginal cost corresponding to the amount of supply when producing a product. Marginal cost is the cost required to produce one additional unit of product. Let P[k] be the supply amount of producer k.

The relationship between the supply amount P[k] of producer k and the marginal cost is represented by a supply curve model C'[k]. That is, the marginal cost at a given supply P[k] is represented by C'[k](P[k]).

In the following embodiments, it is assumed that the supply curve model C'[k] of each producer k is given in advance. Also, the curve represented by each supply curve model C′[k] is assumed to be linear or piecewise linear (hereinafter referred to as “piecewise linear” including the case where it is linear).

[First embodiment]
In the first embodiment, a production distribution determination device 10 that determines the optimum distribution of the supply amount of each producer k when supplying products produced by each of a plurality of producers k to consumers. explain. Note that the production allocation determination device 10 according to the present embodiment is assumed to be an information processing device realized by, for example, a PC (personal computer) or the like.

<Overall composition>
First, the overall configuration of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 1 is a diagram showing an example of the overall configuration of a production allocation determination device 10 according to the first embodiment.

As shown in FIG. 1 , the production allocation determination device 10 according to this embodiment has an offline processing section 110 and an online processing section 120 .

As offline processing (hereinafter also referred to as “offline processing”), the offline processing unit 110 calculates the total supply amount (that is, , total production) and the marginal cost, and then use this total supply curve model φ to calculate the marginal cost (optimal price) λ for the amount L demanded by the customer. Create an optimal price table for Since the total supply curve model φ is expressed as a relational expression between the total supply (which is equal to the demand of the customer) L and the marginal cost λ, it is also expressed as φ(λ, L).

As online processing (hereinafter also referred to as “online processing”), the online processing unit 120 calculates the optimal price λ, which is the marginal cost for supplying a given amount of demand L, from the optimal price table, Using this optimum price λ, the supply amount (that is, production amount) P[k] of each producer k is calculated. This supply amount P[k] is the optimum allocation of the supply amount to be supplied by the producer k (that is, the optimum supply amount). As a result, the optimum supply amount for each producer k (that is, the optimum solution in optimum control) is determined.

Here, online processing is, for example, processing executed during control of a control target (that is, a supply and demand system to be optimally controlled). On the other hand, offline processing is, for example, processing that is executed irrespective of control of the controlled object (for example, processing that is executed when the controlled object is not being controlled). Therefore, the production allocation determination device 10 according to the present embodiment calculates the total supply curve model φ and creates the optimum price table offline, and calculates the optimum price λ using the optimum price table online. Calculation of the allocation P[k] can be performed. At this time, the calculation of the optimum price λ and the calculation of the optimum allocation P[k] using the optimum price table can be realized as processing with a relatively small calculation load, so that the calculation can be performed at high speed. In particular, even when only online processing is executed on an edge device with limited computational resources, high-speed computation is possible.

The off-line processing unit 110 described above is implemented by, for example, processing that one or more programs installed in the production allocation determination device 10 cause a CPU (Central Processing Unit) or the like to execute. Similarly, the above online processing unit 120 is realized by, for example, processing that one or more programs installed in the production allocation determination device 10 cause the CPU or the like to execute.

<Hardware configuration>
Next, the hardware configuration of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 2 is a diagram showing an example of the hardware configuration of the production allocation determination device 10 according to the first embodiment.

As shown in FIG. 2, the production allocation determination device 10 according to the present embodiment includes an input device 11, a display device 12, an external I/F 13, a communication I/F 14, a ROM (Read Only Memory) 15, It has a RAM (Random Access Memory) 16 , a CPU 17 and an auxiliary storage device 18 . These pieces of hardware are connected to each other via a bus 19 so as to be able to communicate with each other.

The input device 11 is, for example, various buttons, a touch panel, a keyboard, a mouse, etc., and is used to input various operations to the production allocation determination device 10 . The display device 12 is, for example, a display, and displays various processing results by the production allocation determination device 10 . Note that the production allocation determination device 10 may not have at least one of the input device 11 and the display device 12 .

The external I/F 13 is an interface with an external device. The external device includes a recording medium 13a and the like. The production allocation determination device 10 can perform reading and writing of the recording medium 13a via the external I/F 13. FIG. Examples of the recording medium 13a include an SD memory card, a USB memory, a CD (Compact Disk), a DVD (Digital Versatile Disk), and the like. One or more programs that implement the offline processing unit 110, one or more programs that implement the online processing unit 120, and the like may be recorded on the recording medium 13a.

The communication I/F 14 is an interface for the production allocation determining device 10 to perform data communication with other devices, equipment, facilities, and the like. One or more programs that implement the offline processing unit 110 and one or more programs that implement the online processing unit 120 may be acquired (downloaded) from a predetermined server or the like via the communication I/F 14 .

The ROM 15 is a non-volatile semiconductor memory that can retain data even when power is turned off. The RAM 16 is a volatile semiconductor memory that temporarily holds programs and data. The CPU 17 is an arithmetic device that reads programs and data from, for example, the auxiliary storage device 18 and the ROM 15 onto the RAM 16 and executes various processes.

The auxiliary storage device 18 is, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive), and is a non-volatile memory that stores programs and data. The programs and data stored in the auxiliary storage device 18 include, for example, one or more programs that implement the offline processing unit 110, one or more programs that implement the online processing unit 120, and an operating system (OS) that is basic software. , and various application programs that run on the OS.

The production allocation determination device 10 according to the present embodiment has the hardware configuration shown in FIG. 2, and thus can implement various processes described later. Although FIG. 2 shows a hardware configuration example in which the production allocation determination device 10 is realized by one computer, the configuration is not limited to this. The production allocation determination device 10 may be implemented by, for example, multiple computers.

<Functional configuration>
Next, the functional configuration of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 3 is a diagram showing an example of the functional configuration of the production allocation determination device 10 according to the first embodiment.

As shown in FIG. 3, the off-line processing section 110 of the production allocation determination device 10 according to this embodiment includes a total supply curve calculation section 111 and an optimum price table creation section 112 . The online processing unit 120 also includes an optimum price calculation unit 121 and an allocation calculation unit 122 .

The total supply curve calculator 111 calculates the total supply curve model φ(λ, L) from the supply curve model C′[k] of each producer k (k=1, . . . , N). A total supply curve model φ(λ, L) can be obtained by synthesizing supply curve models C′[k] of each producer k (k=1, . . . , N).

The optimum price table creation unit 112 creates an optimum price table using the total supply curve model φ(λ, L). The optimum price table is a table for calculating the optimum price λ for the quantity L demanded, as described above.

The optimum price calculator 121 calculates the optimum price λ for a given quantity of demand L using the optimum price table.

The allocation calculator 122 calculates the optimum supply amount P[k] for each producer k using the optimum price λ.

<Offline processing>
Next, offline processing of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 4 is a flowchart showing an example of offline processing according to the first embodiment. As described above, off-line processing involves the calculation of the aggregate supply curve model φ(λ,L) and the creation of the optimum price table. Note that step S101 in FIG. 4 is processing for calculating the total supply curve model φ(λ, L), and steps S102 to S114 are processing for creating the optimum price table.

First, the total supply curve calculator 111 calculates the total supply curve model φ(λ, L) from the supply curve model C′[k] of each producer k (k=1, . . . , N) (step S101).

That is, the total supply curve calculation unit 111 obtains the marginal cost λ and the total supply amount (that is, the demand amount) L of each producer k using the following equations.

そして、総供給曲線計算部１１１は、限界コストλと総供給量Ｌとが取り得る値を実行可能解（feasible solution）として計算することにより、総供給曲線モデルφ（λ，Ｌ）を得る。このような実行可能解は、各生産者ｋの供給曲線モデルＣ´［ｋ］を表す式と、上記の数１に示す限界コストλ及び総供給量Ｌと、論理記号とを用いて一階述語論理式を生成した上で、限定記号消去法により、この一階述語論理式の限定記号を消去することで得ることができる。これにより、総供給曲線モデルφ（λ，Ｌ）は、限界コストλと総供給量Ｌとの関係を示す論理式で表される。

Then, the total supply curve calculation unit 111 obtains the total supply curve model φ(λ, L) by calculating possible values of the marginal cost λ and the total supply amount L as a feasible solution. Such a feasible solution is first-order It can be obtained by generating a predicate logical formula and then eliminating the qualifier of this first-order predicate logical formula by the quantifier elimination method. Thus, the total supply curve model φ(λ,L) is represented by a logical expression showing the relationship between the marginal cost λ and the total supply L.

Next, the optimum price table creating unit 112 creates a mathematical formula (logical formula) in which the total supply curve model φ(λ, L) is arranged with respect to λ (step S102). Here, arranging a logical expression is also called "simplification of a logical expression" or "simplification of a logical expression", and refers to making a logical expression equivalent and simpler. Therefore, the rearranged formula (logical formula) is also expressed as "aggregate supply curve model φ(λ, L)". Arrangement of such logical expressions can be realized by, for example, mathematical formula manipulation software such as Mathematica.

Since the supply curve model C′[k] of each producer k is piecewise linear as described above, the total supply curve model φ(λ,L) is also piecewise linear.

Next, the optimum price table creation unit 112 divides the piecewise linear total supply curve model φ(λ, L) by the logical sum (∨) (step S103). This means dividing a graph (a graph composed of one or more straight lines) represented by the total supply curve model φ(λ, L) at breakpoints. Hereinafter, it is assumed that the total number of straight lines forming the graph represented by the total supply curve model φ(λ, L) is Q, and Q straight lines are obtained by dividing the graph at the breakpoints. That is, the total supply curve model φ(λ, L) is divided into Q mathematical formulas (logical formulas) each representing Q straight lines. Hereinafter, these Q mathematical expressions are referred to as "linear mathematical expressions".

Here, as an example, the case where the total supply curve model φ(λ, L) is divided at the break points when Q=6 will be described with reference to FIG. FIG. 5 is a diagram for explaining an example of dividing the total supply curve model φ(λ, L) at breakpoints.

As shown in FIG. 5, when the graph represented by the total supply curve model φ(λ, L) is composed of six straight lines 1 to 6, the graph has five breakpoints. Then, dividing the total supply curve model φ(λ, L) by the disjunction (∨) means dividing the graph at each of these breakpoints. Therefore, by dividing the graph at these five breakpoints, the graph is divided into six straight lines 1 to 6. FIG. At this time, each linear formula is a formula representing each of the straight lines 1 to 6. FIG.

As for steps S102 and S103, for example, step S103 may be executed first, and then step S102 may be executed for each divided formula.

Next, the optimal price table creation unit 112 sets the variable q to represent the index of the linear formula (that is, the formula representing the straight line) divided in step S103, and the variable q to represent the index of the record stored in the optimal price table. is set to m, q and m are each initialized to 1 (step S104).

Next, the optimum price table creating unit 112 selects one straight line formula (that is, selects one straight line) from the straight line formulas divided in step S103 (step S105). The linear formula selected in this step is expressed as "q-th linear formula".

Next, the optimum price table creation unit 112 determines whether or not the q-th linear formula includes an equation regarding λ (step S106). Here, when an equality regarding λ is not included (in other words, when an inequality regarding λ is included), it means that the straight line represented by the linear formula is parallel to the λ axis. In the example shown in FIG. 5, straight lines 1, 4, and 6 are straight lines represented by mathematical formulas that do not include an equation regarding λ. On the other hand, if an equation for λ is included, it means that the straight line represented by the linear equation is not parallel to the λ axis. In the example shown in FIG. 5, straight lines 2, 3, and 5 are straight lines represented by straight line formulas including an equation regarding λ. Hereinafter, the equation regarding λ included in the q-th linear equation will be expressed as "λ=θ[q](L)".

If it is determined in step S106 that the q-th linear formula includes an equation regarding λ, the optimum price table creation unit 112 divides the linear formula by logical product (∧) (step S107). This divides the linear formula into a formula for L and an equation for λ=θ[q](L). Here, the formula regarding L is a formula representing the range of demand L, so it is represented as "α[q]≦L≦β[q]". Therefore, the qth linear equation is split into α[q]≦L≦β[q] and λ=θ[q](L). α[q] and β[q] are the lower and upper limits of demand L in the q-th linear equation, respectively.

Next, the optimum price table creation unit 112 extracts the equation λ=θ[q](L) regarding λ from the q-th linear formula (step S108). Next, the optimum price table creating unit 112 extracts a mathematical formula α[q]≦L≦β[q] regarding L from the q-th linear mathematical formula (step S109). The order of steps S108 and S109 is random.

Next, the optimum price table creation unit 112 extracts the lower limit α[q] and the upper limit β[q] from the mathematical expression α[q]≦L≦β[q] regarding L (step S110). Note that step S110 may be executed after step S109, and may be executed before step S108, for example.

Next, the optimum price table creation unit 112 creates a record in which the lower limit α[q], the upper limit β[q], and the equation λ=θ[q](L) related to λ are associated with each other as the m-th record. is added to the optimum price table (step S111).

Subsequently, the optimum price table creation unit 112 updates m to m+1 (step S112). Next, the optimum price table creation unit 112 determines whether or not there is a straight line formula that has not been selected in step S105 from among the Q straight line formulas (step S113).

Then, if it is determined in step S113 that there is an unselected linear formula or if it is determined in step S106 that the equation regarding λ is not included in the q-th linear formula, the optimum price table creation unit 112 performs q is updated to q+1 (step S114), and the process returns to step S105.

On the other hand, if it is determined in step S113 that there is no unselected linear formula, the offline processing unit 110 ends the offline processing. As a result, a record of the optimum price table is created from a linear formula representing a straight line that is not parallel to the λ axis.

FIG. 6 shows an example of the optimum price table created by the off-line processing described above, where M is the number of linear equations representing straight lines that are not parallel to the λ-axis among the Q linear equations. FIG. 6 is a diagram showing an example of an optimum price table according to the first embodiment. Note that the example shown in FIG. 6 shows a case where q is appropriately renumbered so that q=m for each m.

As shown in FIG. 6, each record stored in the optimum price table includes the items L lower limit, L upper limit, and λ relational expression. For the m-th record, α [m] is set in the item “L lower limit”, β [m] is set in the item “L upper limit”, and λ=θ [m] (L) is set in the item “λ relational expression”. be done. Thus, the optimum price table according to the present embodiment contains the lower limit α[m] of the demand L, the upper limit β[m] of the demand L, and the equation λ=θ[m](L) regarding λ. A record associated with is stored.

Note that the optimum price table does not necessarily have to be in a table format as long as the L lower limit, the L upper limit, and the λ relational expression are associated with each other.

<Online processing>
Next, online processing of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 7 is a flowchart showing an example of online processing according to the first embodiment. As described above, in the online processing, for a given amount of demand L, calculation of the optimum price λ and calculation of the optimum supply amount P[k] are performed. Note that steps S201 to S204 in FIG. 7 are processing for calculating the optimum price λ, and steps S205 to S207 are processing for calculating the optimum supply amount P[k].

First, the optimum price calculation unit 121 sets m as a variable representing the index of a record stored in the optimum price table, and initializes m to 1 (step S201).

Next, the optimum price calculation unit 121 determines whether or not the given demand quantity L is equal to or greater than the L lower limit α[m] and the L upper limit β[m] or less included in the m-th record (step S202). That is, if it is determined in step S202 that the optimum price calculation unit 121 does not satisfy α[m] ≤ L ≤ β [m] , the optimum price calculation unit 121 updates m to m+1 (step S203) and returns to step S202. As a result, the above step S202 is repeatedly executed until a record that satisfies α[m]≦L≦β[m] is found. In this way, the optimum price calculation unit 121 searches for a record that satisfies α[m]≦L≦β[m] for the given demand quantity L. FIG.

If it is determined in step S202 that α[m]≦L≦β[m] is satisfied, the optimum price calculation unit 121 calculates the λ relational expression λ=θ[m ] (L) to calculate the optimum price λ (step S204). That is, the optimum price calculation unit 121 substitutes the given demand quantity L for the λ relational expression λ=θ[m] (L) corresponding to α[m] and β[m], Calculate the optimal price λ. This gives the optimum price λ.

In this way, the production allocation determination device 10 according to the present embodiment searches (or searches) the optimum price table using the given demand quantity L, and then inserts the λ relational expression included in the searched record into the relevant The optimum price λ can be calculated easily and quickly by simply substituting the quantity L demanded.

Next, the distribution calculation unit 122 initializes a variable k representing the index of the producer to 1 (step S205).

Next, the distribution calculation unit 122 calculates the optimum supply amount P[k] of the producer k (step S206). Details of the processing of this step will be described later.

Next, the allocation calculator 122 determines whether or not k=N (step S207). If it is not determined in step S207 that k=N, the distribution calculation unit 122 updates k to k+1 (step S208) and returns to step S206. As a result, the optimum supply amount P[1] of the producer 1 to the optimum supply amount P[N] of the producer N are repeatedly calculated.

Then, when it is determined that k=N in step S207, the online processing unit 120 terminates the online processing. Thus, the optimum supply amount P[k], k=1, . . . , N for each producer k is determined. Therefore, using these optimum supply amounts P[1] to P[N], optimum control of the controlled object is achieved.

Here, the process of calculating the optimum supply amount P[k] for a certain producer k in step S206 will be described with reference to FIG. FIG. 8 is a flowchart showing an example of calculation processing for the optimum supply amount P[k] according to the first embodiment.

First, the allocation calculator 122 compares the optimum price λ with the marginal cost of the producer k (step S301). The marginal cost of producer k is represented by the supply curve model C'[k].

If the comparison result in step S301 is "the lower limit of the marginal cost of producer k>λ", the distribution calculation unit 122 sets the optimum supply amount of producer k to P[k]=min[k] (step S302). where min[k] represents the lower bound of the marginal cost of producer k. This case corresponds to the case where the producer k cannot produce and supply at the optimum price λ.

If the comparison result in step S301 is "the upper limit of the marginal cost of producer k≧λ≧the lower limit of the marginal cost of producer k", the distribution calculation unit 122 calculates the optimum supply amount of producer k, and the marginal cost is λ (that is, P[k] satisfying λ=C′[k] (P[k])) (step S303). This case corresponds to the case where producer k can produce and supply products commensurate with the optimum price λ.

If the comparison result in step S301 is "the upper limit of the marginal cost of producer k < λ", the distribution calculation unit 122 sets the optimum supply amount of producer k to P[k] = max[k] (step S304). where max[k] represents the upper limit of the marginal cost of producer k. This case corresponds to the case where producer k cannot produce and supply the amount of products corresponding to the optimum price λ.

<Example 1>
Hereinafter, as Example 1, an example of the production allocation determination device 10 according to the present embodiment will be described. In the first embodiment, optimization of the supply amount in the supply and demand system shown in FIG. 9 will be described. In the supply and demand system shown in FIG. 9, three generators (generator No. 1, generator No. 2, and generator No. 3) use fuel, respectively, P[1], P[2], It generates power of P[3] (MW) and supplies power L (MW) to the electrical equipment. Generator no. 1, generator no. 2 and generator no. 3 is the producer, and the electrical equipment is the consumer.

Also, generator No. 1, generator no. 2 and generator no. 3 supply curve model C′[k] is shown in FIG. In FIG. 10, C'[1] is generator number. 1 supply curve model, C'[2] for generator No. 2 supply curve model, C'[3] for generator No. 3 shows a supply curve model. Note that the unit of the marginal cost is 1,000 yen/MW·h.

FIG. 11 shows the total supply curve model φ(λ, L) calculated in step S101 of FIG. 4 at this time. The aggregate supply curve model φ(λ,L) shown in FIG. 11 can be calculated as follows.

first,
f ₁ :=L=P[1]+P[2]+P[3]
f ₂ := f ₂₁ ∧ f ₂₂ ∧ f ₂₃
f ₂₁ :=(50≦P[1]≦300λ=2×0,0015×P[1]+2.5)
∨(50=P[1]∧λ=2×0.0015×50+2.5)
∨(300=P[1]∧λ≧2×0.0015×300+2.5)
f ₂₂ := (100≦P[2]≦400λ=2×0.0005×P[2]+3.2)
∨(100=P[2]∧λ≦2×0.0005×100+3.2)
∨(400=P[2]∧λ≧2×0.0005×400+3.2)
_f23 :=(200≦P[3]≦500λ=2×0.0010×P[3]+3.5)
∨(200=P[3]∧λ≦2×0.0010×200+3.5)
∨(500=P[3]∧λ≧2×0.0010×500+3.5)
and Here, _f1 indicates that the demand L of the electrical equipment is equal to the sum of the power generation of each generator (P[1], P[2], P[3]). In addition, _f2 is a formula obtained by connecting the formulas _f21 , _f22 , and _f23 relating to the marginal costs of all generators by AND. Each f _2k (k = 1, 2, 3) is a formula that describes the marginal cost if the supply is between its upper and lower bounds, and a formula that describes the marginal cost if the supply is above its upper bound. , and a formula that indicates the marginal cost when the supply is at its lower bound.

Next, for the logical product of f ₁ and f ₂ , the power generation amounts P[1], P[2] and P[3] of each generator are given an existence symbol (∃), and the first-order predicate logical expression Generate ψ:=∃P[1]∃P[2]∃P[3](f ₁ ∧f ₂ ). Then, the total supply curve model φ is generated by applying the quantifier elimination method to the first-order predicate formula ψ. That is, for example, if the function for performing quantifier elimination is QE(·), then φ:=QE(ψ).

When the total supply curve model φ(λ, L) is arranged with respect to λ in step S102 of FIG. 4, the present embodiment is as follows.

φ (λ, L) = (L = 350 λ ≤ 53/20)
∨(350<L≦1700/3∧λ=(1600+3L)/1000)
∨(1700/3<L≦700∧λ=(11500+3L)/4000)
∨(700<L<900∧λ=(2700+L)/1000)
∨ (L = 900 ∧ 18/5 ≤ λ ≤ 39/10)
∨(900<L<1200∧λ=(1050+L)/500)
∨(L=1200∧λ≧9/2)
Therefore, when φ(λ, L) is divided by the logical sum in step S103 above, the division formula including the equation regarding λ is "(350<L≦1700/3∧λ=(1600+3L)/1000) ”, “(1700/3<L≦700λ=(11500+3L)/4000)”, “(700<L<900λ=(2700+L)/1000)”, and “(900<L<1200 ∧λ=(1050+L)/500)”. Therefore, in this embodiment, the optimum price table created by offline processing is as shown in FIG. The optimum price table shown in FIG. 12 is composed of records containing the L lower limit, the L upper limit, and the λ relational expression obtained from the above four division formulas.

Here, in this embodiment, it is assumed that demand L=820 (MW) is given in online processing. In this case, since 700≦820≦900 in step S202 of FIG. 7, the No. 3 record of the optimum price table shown in FIG. 12 is searched. Therefore, the optimum price λ is calculated as λ=(2700+820)/1000=3.52 in step S204 of FIG.

Accordingly, in step S206 of FIG. 7, the optimum supply amount P[k] of each generator is calculated as P[1]=300, P[2]=320, and P[3]=200. As shown in FIG. 1, the optimum price λ is larger than the upper limit of the marginal cost (=3.4), and the generator No. 2, lower limit of marginal cost≦optimal price λ≦upper limit of marginal cost. 3, the optimal price λ is smaller than the lower limit of the marginal cost (=3.9).

<Comparison result with conventional technology>
Here, FIG. 14 shows the result of comparing the calculation time of the optimum solution between the interior point method and binary search, which are conventional techniques, and the above-described first embodiment. As shown in FIG. 14, in the production allocation determination device 10 according to the present embodiment, 740.6 times the conventional technology (interior point method) and 38.7 times the conventional technology (binary search) We were able to obtain the optimal solution at high speed. Note that the mathematical formula processing described in Patent Document 5 was also used for the binary search.

As described above, the production allocation determination device 10 according to the present embodiment can significantly speed up the processing for obtaining the optimum solution as compared with the conventional technology. At this time, in calculating this optimum solution, it is only necessary to search an optimum price table that has been created off-line in advance. Moreover, an exact solution can be obtained as an optimum solution instead of an approximate solution. Therefore, according to the production allocation determination device 10 according to the present embodiment, for example, it is possible to immediately determine whether there is a solution or not, and to easily estimate the maximum calculation time.

Note that the off-line processing (that is, calculation of the total supply curve model φ and creation of the optimum price table) does not need to be performed again as long as the supply curve model C'[k] of each producer k is not changed. That is, while the supply curve model C'[k] for each producer k is not changed, the off-line processing needs to be performed only once.

[Second embodiment]
Next, a second embodiment will be described. In the second embodiment, when products produced by each of a plurality of producers k on each cross section s (s=1, . . . , T) of the prediction horizon are supplied to consumers, each cross section The production allocation determination device 10 for determining the optimum allocation of the supply amount of each producer k in s will be described. Here, T is an integer of 1 or more.

In the following, for convenience, cross section s=0 is assumed to be the current time. Note that the time width Δ _s between the cross sections s (that is, the time width Δ _s between the cross section s+1 and the cross section s) is arbitrarily determined. The time width Δ _s may be constant, but may not be constant, for example, the time width Δ _s may be different for each s.

In each cross section s (s=1, . . . , T), all the products produced by a plurality of producers k are supplied to consumers.

Note that the overall configuration and hardware configuration of the production allocation determination device 10 according to the second embodiment are the same as those of the first embodiment, so description thereof will be omitted.

<Functional configuration>
Next, the functional configuration of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. 15 . FIG. 15 is a diagram showing an example of the functional configuration of the production allocation determination device 10 according to the second embodiment.

As shown in FIG. 15, the off-line processing section 110 of the production allocation determination device 10 according to this embodiment includes a total supply curve calculation section 111 and an optimum price table creation section 112 . The online processing unit 120 also includes an optimum price calculation unit 121 , a distribution calculation unit 122 , an initial upper/lower limit calculation unit 123 , and an upper/lower limit calculation unit 124 .

The total supply curve calculator 111 calculates the total supply curve model φ from the supply curve model C′[k] of each producer k (k=1, . . . , N). The total supply curve model φ according to the present embodiment includes the marginal cost λ, the total supply amount L, the supply upper limit max[k] indicating the upper limit of the supply amount of each producer k, and the supply amount of each producer k. It is represented by a relational expression showing the relationship with the supply lower limit min[k] that indicates the lower limit. Therefore, the aggregate supply curve model φ according to this embodiment is expressed as φ(λ, L, min[1], . . . , min[N], max[1], . be done.

The optimum price table creation unit 112 uses the total supply curve model φ (λ, L, min[1], ..., min[N], max[1], ..., max[N]) to Create a best price table. The optimum price table according to this embodiment is a table for calculating the optimum price λ[s] at the cross section s. Note that the optimum price λ[s] is the optimum price for each future cross section s, so it is also called an “optimum price prediction value”.

The initial upper/lower limit calculator 123 calculates the upper limit of supply max[k][s] and the lower limit of supply min[k][s] of each producer k at cross section s=T. At this time, the initial upper/lower limit calculator 123 calculates the change rate constraint δ[k] of each producer k, the upper limit ul[k] and lower limit ll[k] of each producer k, and the current supply amount P [k][0], the upper limit of supply max[k][s] and the lower limit of supply min[k][s] for each producer k at cross section s=T are calculated. Here, the current supply amount P[k][0] is the supply amount P[k] of each producer k at the current time (that is, s=0).

Note that the change rate constraint δ[k] is, for example, a constraint condition indicating the amount or rate at which the producer k can change the production amount of the product per unit time. The rate-of-change constraint δ[k] may have different values, for example, when the production volume is decreased and when the production volume is increased.

Also, the capacity upper limit ul[k] is the upper limit of the amount of products that the producer k can produce. Similarly, the capacity upper limit ll[k] is the lower limit of the amount of product that producer k can produce. For example, when the producer k is a power generation facility, the upper capacity limit ul[k] corresponds to the maximum power generation amount, and the lower capacity limit ll[k] corresponds to the minimum power generation amount. The upper capacity ul[k] and the lower capacity ll[k] are obtained as the upper and lower limits of the supply amount P[k] in the supply curve model C'[k] of producer k.

Using the optimum price table, the optimum price calculation unit 121 calculates the optimum price λ Calculate [s]. Here, the demand amount L[s] is the demand amount at each cross section s in the future, so it is also called a "demand amount forecast value".

The distribution calculation unit 122 calculates the optimum supply amount P[k][s] for each producer k in the section s using the optimum price λ[s]. Note that the optimum supply amount P[k][s] is the optimum supply amount for each future cross section s, so it is also referred to as the "optimum supply amount prediction value".

The upper/lower limit calculation unit 124 calculates the upper limit max[k][s] and Calculate the lower supply limit min[k][s]. At this time, the upper/lower limit calculator 124 calculates the change rate constraint δ[k] of each producer k, the upper limit ul[k] and lower limit ll[k] of each producer k, the current supply amount P[ k][0], an upper supply limit max[k][s] and a lower supply limit min[k][s] are calculated.

Here, the online processing unit 120 according to the present embodiment sequentially calculates the upper supply limit max[k][s] and the lower supply limit min[k][s] from the cross section s=T to s=1, and calculates the optimum price By repeating the calculation of λ [s] and the calculation of the optimum supply amount P [k] [s], the optimum supply amount P for each producer k at each cross section s (s = 1, ..., T) Determine [k][s].

<Offline processing>
Next, offline processing of the production allocation determination device 10 according to this embodiment will be described with reference to FIGS. 16A and 16B. 16A and 16B are flowcharts showing an example of offline processing according to the second embodiment. Note that step S401 in FIGS. 16A and 16B generates the aggregate supply curve model φ(λ, L, min[1], . . . , min[N], max[1], . 16A and 16B are processing for creating the optimum price table.

First, the total supply curve calculator 111 calculates the total supply curve model φ(λ, L, min[1], , min[N], max[1], . . . , max[N]) are calculated (step S401).

That is, the total supply curve calculation unit 111 obtains the marginal cost λ and the total supply amount (that is, the demand amount) L of each producer k using the following equations.

そして、総供給曲線計算部１１１は、限界コストλと総供給量Ｌと供給下限［ｋ］と供給上限ｍａｘ［ｋ］とが取り得る値を実行可能解（feasible solution）として計算することにより、総供給曲線モデルφ（λ，Ｌ，ｍｉｎ［１］，・・・，ｍｉｎ［Ｎ］，ｍａｘ［１］，・・・，ｍａｘ［Ｎ］）を得る。このような実行可能解は、各生産者ｋの供給曲線モデルＣ´［ｋ］を表す式と、上記の数２に示す限界コストλ及び総供給量Ｌと、論理記号とを用いて一階述語論理式を生成した上で、限定記号消去法により、この一階述語論理式の限定記号を消去することで得ることができる。これにより、総供給曲線モデルφ（λ，Ｌ，ｍｉｎ［１］，・・・，ｍｉｎ［Ｎ］，ｍａｘ［１］，・・・，ｍａｘ［Ｎ］）は、限界コストλと、総供給量Ｌと、各生産者ｋの供給下限ｍｉｎ［ｋ］及び供給上限ｍａｘ［ｋ］との関係を示す論理式で表される。

Then, the total supply curve calculation unit 111 calculates possible values of the marginal cost λ, the total supply amount L, the lower limit of supply [k], and the upper limit of supply max[k] as a feasible solution, Obtain the aggregate supply curve model φ(λ, L, min[1], . . . , min[N], max[1], . Such a feasible solution is first-order It can be obtained by generating a predicate logical formula and then eliminating the qualifier of this first-order predicate logical formula by the quantifier elimination method. Thus, the aggregate supply curve model φ(λ, L, min[1], . . . , min[N], max[1], . It is represented by a logical expression showing the relationship between the quantity L and the minimum supply min[k] and the maximum supply max[k] of each producer k.

In the following, to simplify the notation, the aggregate supply curve model φ(λ, L, min[1], . . . , min[N], max[1], . is also expressed as "aggregate supply curve model φ(λ, L, min[k], max[k])".

Next, the optimum price table creating unit 112 creates a formula (logical formula) in which the total supply curve model φ(λ, L, min[k], max[k]) is arranged with respect to λ (step S402). As described above, since the supply curve model C′[k] for each producer k is piecewise linear, the total supply curve model φ(λ, L, min[k], max[k]) is also piecewise linear. Become.

Next, the optimum price table creation unit 112 divides the piecewise linear total supply curve model φ(λ, L, min[k], max[k]) by logical sum (step S403). As in the first embodiment, hereinafter, assuming that the formula is divided into Q mathematical formulas (logical formulas), these Q mathematical formulas are referred to as "linear formulas".

As for steps S402 and S403, for example, step S403 may be executed first, and then step S402 may be executed for each divided formula.

Next, the optimum price table creation unit 112 initializes to 1 the variable q representing the index of the linear formula divided in step S403 and the variable m representing the index of the record stored in the optimal price table. (step S404).

Next, the optimum price table creation unit 112 selects one linear formula from among the linear formulas divided in step S403 (step S405). The linear formula selected in this step is expressed as "q-th linear formula".

Next, the optimum price table creation unit 112 determines whether or not the q-th linear formula includes an equation regarding λ (step S406).

If it is determined in step S406 that the equation regarding λ is not included in the q-th linear formula, the optimum price table creation unit 112 updates q to q+1 (step S407) and returns to step S405.

If it is determined in step S406 that the q-th linear formula includes an equation regarding λ, the optimum price table creation unit 112 divides the linear formula by logical product (step S408). Thus, the linear equation is the equation λ=θ[q](L, min[1], . . . , min[N], max[1], . , and a conditional expression F other than the equality with respect to λ. Conditional expression F is a conditional expression expressed by a formula (logical expression) other than the equation λ=θ[q] regarding λ.

In the following, for simplicity of notation, the equation λ=θ[q](L, min[1], . . . , min[N], max[1], . N]) is also denoted as “the equation for λ=θ[q](L, min[k], max[k])”.

Next, the optimum price table creation unit 112 extracts a conditional expression F other than the equation regarding λ from the q-th linear expression (step S409). Next, the optimum price table creation unit 112 extracts an equation λ=θ[q] (L, min[k], max[k]) regarding λ from the q-th linear formula (step S410). The order of steps S409 and S410 is random. Also, step S410 may be executed at any point, for example, before the determination of step S421, which will be described later, is performed.

Next, the optimum price table creation unit 112 creates a mathematical formula in which the conditional expression F other than the equation regarding λ is rearranged for L (step S411). Next, the optimum price table creating unit 112 divides the rearranged formula (that is, the formula obtained by rearranging the conditional expression F with respect to L) by logical sum (step S412). Here, hereinafter, let the conditional expressions (formulas) obtained by this division be H[i], i=1, . . . Note that I is an integer of 1 or more, but since the specific value is determined by the q-th linear formula, I=I[q].

Next, the optimum price table creation unit 112 initializes the variable i representing the index of the conditional expression H[i] to 1 (step S413).

Next, the optimum price table creating unit 112 selects one conditional expression H[i] from the conditional expressions H[i] divided in step S412 (step S414). In this embodiment, as an example, conditional expressions H[i] are selected in order from i=1 to I in this step. However, the conditional expression H[i] may be arbitrarily selected.

Next, the optimum price table creation unit 112 calculates a group of formulas α[q][j ₁ ], j ₁ =1, . J _i1 is extracted (step S415).

Next, the optimum price table creating unit 112 creates a group of formulas β[q][j ₂ ], j ₂ =1, . . . J _i2 is extracted (step S416).

Next, the optimum price table creation unit 112 creates a group of formulas γ[q][j ₃ ], j ₃ =1, . . . J _i3 is extracted (step S417).

Note that the above steps S415 to S417 are in no particular order.

Then, the optimum price table creation unit 112 creates a group of formulas α[j ₁ ] related to the lower limit of L, a group of formulas β[j ₂ ] related to the upper limit of L, a group of formulas γ[j ₃ ] unrelated to L, λ is added to the optimum price table as the m-th record (step S418).

Subsequently, the optimum price table creation unit 112 updates m to m+1 (step S419). Next, the optimum price table creation unit 112 determines whether or not there is a conditional expression H[i] that has not been selected in step S414 among the I conditional expressions H[i] (step S420).

If it is determined in step S420 that there is an unselected conditional expression H[i], the optimum price table creation unit 112 updates i to i+1 (step S421) and returns to step S414.

If it is determined in step S420 that there is no unselected conditional expression H[i], the optimum price table creation unit 112 determines whether there is an unselected linear formula (step S422).

Then, if it is determined in step S420 that there is an unselected linear formula, the optimum price table creation unit 112 updates q to q+1 (step S407) and returns to step S405. On the other hand, if it is determined in step S420 that there is no unselected linear formula, the optimum price table creation unit 112 terminates the offline processing. This creates a record in the best price table from a linear equation containing the equation λ=θ[q](L, min[k], max[k]) on λ.

Here, among _the Q linear _equations , the index _of the linear equation containing the equation for λ is q ₁ , . ], an example of the optimum price table created by the offline processing is shown in FIG. FIG. 17 is a diagram showing an example of an optimum price table according to the second embodiment. Note that the example shown in FIG. 17 shows a case where q is appropriately renumbered so that q=m for each m.

As shown in FIG. 17, each record stored in the optimum price table includes, as items, L lower limit, L upper limit, conditions other than L and λ, and λ relational expression. For the m-th record, {α[m][ _{j 1} ], j ₁ = ₁ , . _] , _{j 2 =} 1, _. λ=θ[m] (L, min[k], max[k]) is set in the “λ relational expression”. As described above, the optimum price table according to the present embodiment includes a group of formulas relating to the lower limit of the demand quantity L, a group of formulas relating to the upper limit of the demand quantity L, a conditional expression unrelated to L and λ, and an equation relating to λ = θ[m] (L, min[k], max[k]) are associated with each other.

The optimum price table does not necessarily have to be in a table format as long as it associates the L lower limit, the L upper limit, the conditions other than L and λ, and the λ relational expression.

<Online processing>
Next, online processing of the production allocation determination device 10 according to this embodiment will be described with reference to FIG. FIG. 18 is a flowchart showing an example of online processing according to the second embodiment. Here, in the online processing according to the present embodiment, the demand amount L[s], s=1, . . . , T and the supply amount current value P[k][0] are given.

First, the online processing unit 120 initializes the cross section s to T (that is, initializes the cross section s to s=T, which is the final cross section of the predicted horizon) (step S501). Next, the initial upper/lower limit calculator 123 calculates the supply upper limit max[k][s] and the supply lower limit min[k][s] of each producer k at the cross section s=T (step S502). Details of the processing of this step will be described later.

Next, the optimum price calculation unit 121 uses the optimum price table to calculate the following for the demand quantity L[s], the supply upper limit max[k][s], and the supply lower limit min[k][s]: Calculate the optimum price λ[s] (step S503). Details of the processing of this step will be described later.

Next, the distribution calculation unit 122 calculates the optimum supply amount P[k][s] for each producer k in the section s using the optimum price λ[s] (step S504). Details of the processing of this step will be described later.

Next, the online processing unit 120 updates the cross section s to s−1 (step S505). Next, the online processing unit 120 determines whether or not the cross section s is 1 or more (step S506).

If it is determined in step S506 that the cross section s is equal to or greater than 1, the upper/lower limit calculator 124 calculates the upper limit max[k][s] and the lower limit min[k ][s] is calculated (step S507). Details of the processing of this step will be described later. Then, the online processing unit 120 returns to step S503.

On the other hand, if it is not determined in step S506 that the cross section s is 1 or more, the online processing unit 120 terminates the online processing. As a result, the optimum supply amount P[k][s] for each producer k at each cross section s is determined. Therefore, using these optimum supply amounts P[k][s], optimum control of the controlled object is realized.

Here, the process of calculating the supply upper limit max[k][s] and the supply lower limit min[k][s] of each producer k at the cross section s=T in step S502 will be described with reference to FIG. do. FIG. 19 is a flowchart showing an example of calculation processing of the supply upper limit and the supply lower limit at the cross section s=T.

First, the initial upper/lower limit calculator 123 initializes the variable k representing the index of the producer to 1 (step S601).

Next, the initial upper/lower limit calculation unit 123 calculates the following based on the change rate constraint δ[k] of the producer k, the upper capacity limit ul[k] of the producer k, and the current supply amount P[k][0]. Then, the supply upper limit max[k][s] at the cross section s=T is calculated (step S602).

The initial upper/lower limit calculator 123 sets max1[k][s]=P[k][0]+s×δ[k], and then max[k][s]=MIN(ul[k], max1 [k][s]) to calculate the supply upper limit max[k][s]. That is, the initial upper/lower limit calculator 123 sets the smaller one of ul[k] and max1[k][s] as the supply upper limit max[k][s]. This means that the supply amount is changed from the current supply amount P[k][0] in consideration of the upper limit of the amount that the producer k can produce (the upper limit of capacity ul[k]) and the change rate constraint δ[k]. This means that the supply upper limit max[k][s] is set to the upper limit (max1[k][s]) that the producer k can produce at the cross section s when it is

Next, the initial upper/lower limit calculation unit 123 calculates based on the change rate constraint δ[k] of the producer k, the lower capacity limit ll[k] of the producer k, and the current supply amount P[k][0]. Then, the lower supply limit min[k][s] at the cross section s=T is calculated (step S603).

The initial upper/lower limit calculator 123 sets min1[k][s]=P[k][0]−s×δ[k], and then min[k][s]=MAX(ll[k], min1[k][s]) to calculate the lower supply limit min[k][s]. That is, the initial upper/lower limit calculator 123 sets the larger one of ll[k] and min1[k][s] as the supply lower limit min[k][s]. This means that the supply amount is changed from the current supply amount P[k][0] in consideration of the lower limit amount (capacity lower limit ll[k]) that the producer k can produce and the change rate constraint δ[k]. This means that the lower limit of supply min [k] [s] is set to the lower limit (min1 [k] [s]) that producer k can produce at cross section s when the supply is increased.

Note that the above steps S602 and S603 are in no particular order.

Next, the initial upper/lower limit calculator 123 updates the variable k representing the index of the producer to k+1 (step S604).

Next, the initial upper/lower limit calculator 123 determines whether or not k≦N (step S605).

If it is determined in step S605 that k≦N, the initial upper/lower limit calculator 123 returns to step S602. On the other hand, if it is not determined that k≦N in step S605, the initial upper/lower limit calculator 123 terminates the process. As a result, the supply upper limit max[k][s] and the supply lower limit min[k][s] of each producer k at the cross section s=T are obtained.

Here, the possible supply range of the producer k at the cross section s=T is represented by the upper limit of supply max[k][s] and the lower limit of supply min[k][s]. FIG. 20 shows the supply range of a certain producer k. In the example shown in FIG. 20, max1[k][s]>ul[k] and min1[k][s]>ll[k]. In this case, the supply upper limit max[k][s]=ul[k] and the supply lower limit min[k][s]=min1[k][s]. At this time, in the cross section s=T, the range of the supply amount P[k][s] that the producer k can supply (supplyable range) is min[k][s]≤P[k][s]≤ max[k][s].

Next, the process of calculating the optimum price λ[s] at a certain cross section s in step S503 will be described with reference to FIG. FIG. 21 is a flowchart showing an example of calculation processing of the optimum price λ[s] according to the second embodiment.

First, the optimum price calculation unit 121 initializes to 1 a variable m representing the index of a record stored in the optimum price table (step S701).

Next, the optimum price calculation unit 121 determines whether the given demand L[s] is equal to or greater than the maximum value of the L lower limit formula group and less than or equal to the minimum L upper limit formula group included in the m-th record. Determine (step S702).

That _{is ,} first, for each producer _k ( After substituting the supply upper limit max[k][s] and the supply lower limit min[k][s] of k=1, . That is, α[m][s]=MAX{α[m][j ₁ ](min[1][s], . , max[N][s]), j ₁ =1, . . . , J _i1 }.

Similarly _, for _each producer k( _k = 1, . That is, β[m][s]=MIN{β[m][j ₂ ](min[1][s],...,min[N][s],max[1][s],. , max[N][s]), j ₂ =1, . . . , J _i2 }.

Then, the optimum price calculation unit 121 determines whether α[m][s]≦L[s]≦β[m][s] is satisfied.

If it is determined in step S702 that α[m][s]≦L[s]≦β[m][s] is satisfied, the optimum price calculation unit 121 calculates conditions other than L and λ (that is, {γ[ m][j ₃ ], j ₃ =1, . . . , J _i3 }) is satisfied (step S703). Here, satisfying conditions other than L and _λ means that for {γ[m][j ₃ ], j ₃ =1, . 1, . . . , N). In other words _{, γ[m][j 3 ]} (min[1][s], . . . , min[N][s], max[1][s], . , max[N][s]) is True.

If it is determined in step S703 that the conditions other than L and λ are satisfied, the optimum price calculation unit 121 calculates {α[m][j ₁ ], j ₁ =1, . . . , J _i1 }, {β. [m][j ₂ ], j ₂ =1, . . . , J _i2 } and {γ[m][j ₃ ], j ₃ = ₁ , . = θ[m] (L, min[k], max[k]) to calculate the optimum price λ[s] (step S704). That is, the optimum price calculation unit 121 calculates the demand amount L[s] at the cross section s and each producer k Substituting the upper supply limit max [k] [s] and the lower supply limit min [k] [s] of (k = 1, ..., N), λ [s] = θ [m] (L [s ], min[1][s], . . . , min[N][s], max[1][s], . This gives the optimum price λ[s] at the cross section s.

If it is determined in step S702 that α[m][s]≤L[s]≤β[m][s] is not satisfied, or if it is determined in step S703 that conditions other than L and λ are not satisfied, The optimum price calculator 121 updates m to m+1 (step S705) and returns to step S702.

In this way, the production allocation determination device 10 according to the present embodiment uses the demand quantity L[s], the upper limit of supply max[k][s] and the lower limit of supply min[k][s] to obtain the optimal price table is searched (or searched), and the demand quantity L [s] and the supply upper limit max [k] [s] and the supply lower limit min [k] [s] are substituted into the λ relational expression included in the searched record. , the optimum price λ[s] in the cross section s can be calculated easily and quickly.

Next, the process of calculating the optimum supply amount P for each producer k in step S504 will be described with reference to FIG. FIG. 22 is a flowchart showing an example of calculation processing of the optimum supply amount P[k][s] according to the second embodiment.

First, the allocation calculation unit 122 initializes a variable k representing a producer's index to 1 (step S801).

Next, the distribution calculation unit 122 compares the optimal price λ[s] in the section s with the marginal cost of the producer k in the section s (step S802). The marginal cost of producer k at cross section s is represented by the supply curve model C'[k].

If the result of the comparison in step S301 is “the lower limit of the marginal cost of producer k>λ[s]”, the distribution calculation unit 122 calculates the optimum supply amount of producer k at cross section s as P[k][s] =min[k][s] (step S803). In this case, the producer k cannot produce and supply the optimum price λ[s] at the cross section s.

If the comparison result in step S301 is "upper limit of marginal cost of producer k≧λ[s]≧lower limit of marginal cost of producer k", the distribution calculation unit 122 calculates the optimum supply amount of producer k in section s. be P[k][s] (that is, λ[s]=C′[k](P[k][s], min[k][s], max[k][ s]) is assumed to be P[k][s]) (step S804). In this case, the producer k can produce and supply the optimum price λ[s] at the cross section s.

If the comparison result in step S301 is "the upper limit of the marginal cost of producer k < λ [s]", the distribution calculation unit 122 calculates the optimum supply amount of producer k at cross section s as P [k] = max [ k][s] (step S805). This case corresponds to the case where producer k cannot produce and supply the amount of product corresponding to optimal price λ[s] at cross section s.

Following step S803, step S804, or step S805, the distribution calculation unit 122 updates k to k+1 (step S806). Next, the distribution calculation unit 122 determines whether or not k≦N (step S807).

Then, if it is not determined in step S807 that k≦N, the distribution calculation unit 122 returns to step S802. On the other hand, if it is determined in step S807 that k≦N, the distribution calculation unit 122 terminates the process. Thereby, the optimum supply amount P[k][s] for each producer k in the section s is calculated.

Next, refer to FIG. 23 for the process of calculating the upper limit of supply max[k][s] and the lower limit of supply min[k][s] for each producer k in cross section s (<T) in step S507 above. while explaining. FIG. 23 is a flowchart showing an example of calculation processing of the supply upper limit and the supply lower limit at the cross section s (<T).

First, the upper/lower limit calculator 124 initializes a variable k representing a producer's index to 1 (step S901).

Next, upper/lower limit calculator 124 calculates producer k's rate of change constraint δ[k], producer k's upper capacity limit ul[k], current supply amount P[k][0], section s+1 Based on the optimum supply amount P[k][s+1] of the producer k at , the upper supply limit max[k][s] at the cross section s (<T) is calculated (step S902).

The upper/lower limit calculator 124 sets max1[k][s]=P[k][0]+s×δ[k] and max2[k][s]=P[k][s+1]+δ[k]. Above, calculate the upper supply limit max[k][s] by max[k][s]=MIN(ul[k], max1[k][s], max2[k][s]). That is, the upper/lower limit calculator 124 sets the smallest of ul[k], max1[k][s], or max2[k][s] as the supply upper limit max[k][s]. This means that the upper/lower limit calculator 124 calculates the current supply amount P[k][ 0], the maximum amount that producer k can produce at cross section s (max1 [k] [s]) and the optimum supply amount P [ k] [s + 1] and the upper limit that producer k can produce at cross section s (max2 [k] [s]), the smallest of which is the upper limit of supply max [k] [ s].

Next, the upper/lower limit calculator 124 calculates producer k's change rate constraint δ[k], producer k's lower capacity limit ll[k], current supply amount P[k][0], section s+1 Based on the optimum supply amount P[k][s+1] of the producer k at , the lower limit supply min[k][s] at the cross section s (<T) is calculated (step S903).

Upper/lower limit calculator 124 calculates min1[k][s]=P[k][0]−s×δ[k], min2[k][s]=P[k][s+1]−δ[k] Then, the supply lower limit min[k][s] is calculated by min[k][s]=MAX(ll[k], min1[k][s], min2[k][s]). That is, the upper/lower limit calculator 124 sets the largest one of ll[k], min1[k][s], or min2[k][s] as the supply lower limit min[k][s]. This means that the upper/lower limit calculator 124 calculates the current supply amount P[k][ 0], the optimum supply amount P[ k] [s + 1] and the minimum amount (min2 [k] [s]) that producer k can produce at cross section s when the supply amount is changed from s].

Note that the above steps S902 and S903 are performed in no particular order.

Next, the upper/lower limit calculator 124 updates k to k+1 (step S904). Next, the upper/lower limit calculator 124 determines whether or not k≦N (step S905).

If it is determined in step S905 that k≦N, the upper/lower limit calculator 124 returns to step S902. On the other hand, if it is not determined in step S905 that k≦N, the upper/lower limit calculator 124 terminates the process.

Here, the possible supply range of producer k at cross section s (<T) is represented by upper supply limit max[k][s] and lower supply limit min[k][s]. FIG. 24 shows the supply range of a certain producer k. In the example shown in FIG. 24, max1[k][s]>ul[k]>max2[k][s] and min1[k][s]>min2[k][s]>ll[k] is. In this case, the supply upper limit max[k][s]=max2[k][s] and the supply lower limit min[k][s]=min1[k][s]. At this time, in the section s (<t), the range of the supply amount P [k] [s] that the producer k can supply (supplyable range) is min [k] [s] ≤ P [k] [s ]≦max[k][s].

In this way, at the cross section s (<T), the upper limit of supply max[k][s] and the lower limit of supply min[k ][s]. This makes it possible to determine the optimum supply upper limit max[k][s] and supply lower limit [k][s] for each cross section s (<T).

<Example 2>
Hereinafter, as Example 2, an example of the production allocation determination device 10 according to the present embodiment will be described. In Example 2, as in Example 1, optimization of the supply amount in the supply and demand system shown in FIG. 9 will be described.

At this time, T=20, and the time width between cross section s+1 and cross section s is Δ _s =5 (min).

Also, generator No. 1's upper capacity ul[1], lower capacity ll[1] and rate-of-change constraint of .delta.[1] are as follows.

- Capability upper limit ul[1] = 300 (MW)
- Capability lower limit ll [1] = 50 (MW)
・ Change rate constraint δ [1] = ±20 (MW/5 min)
Similarly, generator no. 2's upper capacity ul[2], lower capacity ll[2] and rate-of-change constraint of .delta.[2] are as follows.

- Capability upper limit ul[2] = 400 (MW)
- Capability lower limit ll [2] = 100 (MW)
・ Change rate constraint δ [2] = ±10 (MW/5 min)
Similarly, generator no. 3's upper capacity ul[3], lower capacity ll[3] and rate-of-change constraint of .delta.[3] are as follows.

- Capability upper limit ul[3] = 500 (MW)
- Capability lower limit ll [3] = 200 (MW)
・ Change rate constraint δ [3] = ±30 (MW/5 min)
FIG. 25 shows demand amounts L[s], s=1, . FIG. 25 shows the demand L[s] (that is, the power demand forecast value) from 9:35 (cross section s=1) to 11:10 (cross section s=20) with the current time being 9:30. ing.

Furthermore, the supply amount (that is, supply amount current value) P[1][0], P[2][0] and P[3][0] of each generator at the current time 9:30 is as follows.

・Generator No. 1 supply current value P[1][0]=100 (MW)
・Generator No. 2 supply current value P[2][0]=150 (MW)
・Generator No. 3 supply current value P[3][0]=250 (MW)
That is, the supply and demand system shown in FIG. 9 supplies power of P[1][0]+P[2][0]+P[3][0]=500 (MW) to the electrical equipment at the current time of 9:30. ing.

At this time, the total supply curve model φ (λ, L, min[1], min[2], min[3], max[1], max[2], max[3]) is calculated as follows. can be done.

first,
f ₁ :=L=P[1]+P[2]+P[3]
f ₂ := f ₂₁ ∧ f ₂₂ ∧ f ₂₃
f ₂₁ :=(min[1]≤P[1]≤max[1]λ=2×0,0015×P[1]+2.5)∨(min[1]=P[1]λ= 2×0.0015×min[1]+2.5)∨(max[1]=P[1]λ≧2×0.0015×max[1]+2.5)
f ₂₂ :=(min[2]≤P[2]≤max[2]λ=2×0.0005×P[2]+3.2)∨(min[2]=P[2]λ≤ 2×0.0005×min[2]+3.2)∨(max[2]=P[2]λ≧2×0.0005×max[2]+3.2)
f ₂₃ :=(min[3]≤P[3]≤max[3]λ=2×0.0010×P[3]+3.5)∨(min[3]=P[3]λ≤ 2×0.0010×min[3]+3.5)∨(max[3]=P[3]λ≧2×0.0010×max[3]+3.5)
and Here, _f1 indicates that the demand L of the electrical equipment is equal to the sum of the power generation of each generator (P[1], P[2], P[3]). In addition, _f2 is a formula obtained by connecting the formulas _f21 , _f22 , and _f23 relating to the marginal costs of all generators by AND. Each f _2k (k = 1, 2, 3) is a formula showing the marginal cost when the supply is between the upper supply limit and the lower supply limit, and a formula showing the marginal cost when the supply is at the upper supply limit. and a mathematical expression representing the marginal cost when the supply amount is the lower limit of supply.

Next, for the logical product of f ₁ and f ₂ , the power generation amounts P[1], P[2] and P[3] of each generator are given an existence symbol (∃), and the first-order predicate logical expression Generate ψ:=∃P[1]∃P[2]∃P[3](f ₁ ∧f ₂ ). Then, the total supply curve model φ is generated by applying the quantifier elimination method to the first-order predicate formula ψ. That is, for example, if the function for performing quantifier elimination is QE(·), then φ:=QE(ψ). As a result, the total supply curve model φ(λ, L, min[1], min[2], min[3], max[1], max[2], max[3]) in Example 2 is obtained. .

Therefore, the optimal price table shown in FIG. 26 is created by the offline processing of FIGS. 16A and 16B. The optimum price table shown in FIG. 26 is composed of records including L lower limit, L upper limit, conditions other than L and λ, and λ relational expressions.

Here, in the online processing of this embodiment, the following supply upper limit max[k][20] and supply lower limit min[k][20] are calculated in step S502.

・max[1][20]=300, min[1][20]=50
・max[2][20]=350, min[2][20]=100
・max[3][20]=500, min[3][20]=200
Also, at the cross section s=20, in the above step S503, from the given demand quantity L[20]=820 (MW), conditions other than the L lower limit, the L upper limit, and L and λ of the No. 6 record in the optimum price table is satisfied, the optimal price λ[20] is calculated as λ[20]=88/25=3.52.

Next, at the cross section s=20, in step S504, the optimum supply amount P[k][20] of each generator is P[1][20]=300, P[2][20]=320 , P[3][20]=200. As shown in FIG. 1, the optimum price λ[20] is larger than the upper limit of the marginal cost (=3.4), and the generator No. 2, lower limit of marginal cost≦optimum price λ[20]≦upper limit of marginal cost. 3, the optimal price λ[20] is smaller than the lower limit of the marginal cost (=3.9).

Next, at the cross section s=19, the following supply upper limit max[k][19] and supply lower limit min[k][19] are calculated in step S507.

・max[1][19]=300, min[1][19]=280
・max[2][19]=330, min[2][19]=310
・max[3][19]=230, min[3][19]=200
Also, in the section s=19, in the above step S503, from the given demand quantity L[19]=800 (MW), conditions other than L lower limit, L upper limit and L and λ of record No. 20 in the optimum price table is satisfied, the optimum price λ[19] is calculated as λ[19]=337/100=3.37.

Next, at the cross section s=19, in step S504, the optimum supply amount P[k][19] of each generator is P[1][19]=290, P[2][19]=310 , P[3][19]=200. As shown in FIG. 1, the upper limit of the marginal cost ≤ the optimum price λ[19] ≤ the lower limit of the marginal cost, and the generator No. 2, the optimum price λ[19] is smaller than the lower limit of the marginal cost (=3.51). 3, the optimal price λ[19] is smaller than the lower limit of the marginal cost (=3.9).

Thereafter, similarly, the optimum supply amount P[k][s] of each generator at each cross section s is calculated while shifting backward one cross section from cross section s=18 to cross section s=1.

FIG. 10 shows the result of calculating the optimum supply amount P[k][s] of the cross section s (s=1, . 29. FIG. 29 shows the optimum supply amount P[k][s] of each generator at each cross section s.

<Comparison result with conventional technology>
FIG. 30 shows the result of comparing the calculation time of the optimum solution between the conventional binary search and the second embodiment. As shown in FIG. 30, the production allocation determination device 10 according to this embodiment was able to obtain the optimum solution 16.9 times faster than the conventional technology (binary search). Note that the mathematical formula processing described in Patent Document 5 was also used for the binary search.

In this embodiment, the case of calculating the optimum supply amount P[k][s] for each cross section s (s=1, . . . , T) at a certain time t has been described. The optimum supply amount P[k][s] for each cross section s (s=1, . . . , T) may be calculated repeatedly every time t. That is, with t being an index representing a certain time interval (for example, a control cycle) and P _t [k] [s] being the optimum supply amount at time t, the optimum supply amount is P _t [k] at each time t. [s] (s=1, . . . , T) may be calculated.

[Third Embodiment]
Next, a third embodiment will be described. In the third embodiment, a case will be described in which the offline processing unit 110 and the online processing unit 120 are provided in different devices. As shown in FIG. 31, the production allocation determination system according to this embodiment includes an optimum price table creation device 20 having an offline processing section 110 and a production allocation determination device 30 having an online processing section 120 . Also, the optimum price table creation device 20 and the production allocation determination device 30 are communicably connected via a network.

In the case of such a configuration, in the off-line processing, the optimal price table creation device 20 should create the optimal price table, and the created optimal price table should be sent to the production allocation determination device 30 . Then, the production allocation determining device 30 may store the received optimum price table in an auxiliary storage device or the like. As a result, in online processing, the production distribution determination device 30 can calculate the optimum supply amount of the producers constituting the plant using the optimum price table stored in the auxiliary storage device or the like.

As a result, for example, the optimum price table creation device 20 that executes offline processing is realized by an information processing device (for example, a PC, etc.) with relatively large computational resources, while the production allocation determination device 30 that executes online processing is compared. It can be realized by an edge device (for example, a control device such as a PLC or DCS) that has few physical computational resources.

The invention is not limited to the specifically disclosed embodiments above, but various modifications and changes are possible without departing from the scope of the claims.

10 production allocation determination device 110 offline processing unit 111 total supply curve calculation unit 112 optimum price table creation unit 120 online processing unit 121 optimum price calculation unit 122 allocation calculation unit

Claims (15)

A production allocation determination device that determines the optimal allocation of supply volumes produced and supplied by a plurality of producers,
a total supply curve calculating means for calculating a total supply curve model representing the relationship between the total supply volume and the marginal cost of the plurality of producers from the supply curve model representing the relationship between the supply volume and the marginal cost of each producer;
Optimal price table creation means for creating an optimal price table for calculating an optimal price indicating the optimal marginal cost according to the quantity demanded, based on the aggregate supply curve model;
optimum price calculation means for calculating an optimum price corresponding to the given demand quantity based on the given demand quantity and the optimum price table;
a supply amount calculation means for calculating an optimum supply amount indicating an optimum distribution of the supply amount of each of the producers based on the supply curve model of each producer and the optimum price;
A production allocation determination device characterized by having: The optimal price table creation means includes:
2. The production allocation determination device according to claim 1, wherein the optimal price table is created by arranging the variables representing the marginal cost of the total supply curve model and dividing them by a logical sum or a logical product. . The optimal price table includes one or more records,
The record includes an upper limit and a lower limit of the demand amount and a calculation formula corresponding to the upper limit and the lower limit of the demand amount,
3. The production allocation determination device according to claim 1, wherein said calculation formula is a formula for calculating the optimum price according to the quantity demanded. The optimal price calculation means is
Searching one or more records included in the optimum price table for a record in which the given quantity of demand is within the range of the upper limit and the lower limit of the quantity of demand;
4. The production allocation determination device according to claim 3, wherein the optimal price is calculated by substituting the given demand quantity into the formula included in the searched record. The aggregate supply curve calculation means,
By using a quantifier elimination method for a first-order predicate logical expression using a variable representing the total supply, a variable representing the marginal cost, and a logical symbol, the variable representing the total supply and the 5. The production allocation determination device according to any one of claims 1 to 4, wherein an aggregate supply curve model representing a relationship with variables representing marginal costs is calculated. The production allocation determination device is a production allocation determination device that determines the optimum allocation of the supply amount produced and supplied by the plurality of producers at each time s (s = 1, ..., T),
At time s having upper and lower limit calculation means for calculating upper and lower supply limits respectively indicating the upper and lower limits of the supply amount of each producer in
The optimal price calculation means is
Calculate the optimum price at time s according to the given demand quantity based on the given demand quantity and the optimum price table,
The supply amount calculation means is
The optimum supply amount is calculated based on the upper and lower supply limits of each producer at the time s, the supply curve model of each producer, and the optimum price at the time s. Item 1. The production allocation determination device according to item 1. The optimal price table creation means includes:
The optimal price table is created by organizing the aggregate supply curve model with respect to variables representing the marginal cost and the variables representing the quantity demanded, and dividing them by a logical sum or a logical product. 7. The production allocation determination device according to 6. The optimal price table includes one or more records,
The record includes a first group of formulas and a second group of formulas respectively representing the upper limit and the lower limit of the demand amount, a third group of formulas not including variables representing the demand amount, and the first group of formulas. , calculation formulas corresponding to the second group of formulas and the third group of formulas,
8. The production allocation determination device according to claim 6, wherein said calculation formula is a formula for calculating the optimum price at time s according to the quantity demanded. The optimal price calculation means is
Among the one or more records included in the optimum price table, the given demand quantity falls within the range between the minimum value of the first formula group and the maximum value of the second formula group, and Search for records where the formula group of 3 is true,
9. The optimum price is calculated by substituting the given demand quantity, the upper supply limit and the lower supply limit into the formula included in the searched record. Production allocation decision device. The aggregate supply curve calculation means,
Eliminate quantifiers from the first-order predicate logic formula using the variable representing the total supply amount, the variable representing the marginal cost, the variables representing the upper supply limit and the lower supply limit of each producer, and logical symbols calculating an aggregate supply curve model representing the relationship between the variables representing the total supply, the variables representing the marginal costs, and the variables representing the upper and lower supply limits of each of the producers, respectively, by using the method of 10. The production allocation determination device according to any one of claims 6 to 9, characterized in that: Calculation of the upper and lower supply limits by the upper and lower limit calculation means, calculation of the optimum price by the optimum price calculation means, and calculation of the optimum supply amount by the supply amount calculation means are performed from time s=T to time 11. The production allocation determination device according to any one of claims 6 to 10, wherein the process is repeatedly executed until s=1. performing off-line calculation of the aggregate supply curve model by the aggregate supply curve calculation means and creation of the optimum price table by the optimum price table creation means;
12. The method according to any one of claims 1 to 11, wherein the calculation of said optimum price by said optimum price calculation means and the calculation of said optimum supply quantity by said supply quantity calculation means are executed online. Production allocation decision device. A production allocation determination system for determining the optimum allocation of supply volumes produced and supplied by a plurality of producers, the production allocation determination system including an information processing device and a control device,
The information processing device is
a total supply curve calculating means for calculating a total supply curve model representing the relationship between the total supply volume and the marginal cost of the plurality of producers from the supply curve model representing the relationship between the supply volume and the marginal cost of each producer;
an optimal price table creation means for creating an optimal price table for calculating an optimal price indicating the optimal marginal cost according to the quantity demanded, based on the aggregate supply curve model;
The control device is
optimum price calculation means for calculating an optimum price corresponding to the given demand quantity based on the given demand quantity and the optimum price table;
a supply amount calculation means for calculating an optimum supply amount indicating an optimum distribution of the supply amount of each of the producers based on the supply curve model of each producer and the optimum price;
A production allocation determination system characterized by having: the information processing device performs off-line calculation of the aggregate supply curve model by the aggregate supply curve calculation means and creation of the optimum price table by the optimum price table creation means;
14. The production allocation according to claim 13, wherein said control device executes the calculation of said optimum price by said optimum price calculation means and the calculation of said optimum supply quantity by said supply quantity calculation means on-line. decision system. A production allocation determination device that determines the optimal allocation of supply volumes produced and supplied by multiple producers,
a total supply curve calculation procedure for calculating a total supply curve model representing the relationship between the total supply volume and the marginal cost of the plurality of producers from the supply curve model representing the relationship between the supply volume and the marginal cost of each producer;
an optimum price table creation procedure for creating an optimum price table for calculating an optimum price indicating the optimum marginal cost according to the quantity demanded, based on the aggregate supply curve model;
an optimum price calculation procedure for calculating an optimum price corresponding to the given demand quantity based on the given demand quantity and the optimum price table;
a supply amount calculation procedure for calculating an optimum supply amount indicating an optimum allocation of the supply amount of each of the producers based on the supply curve model of each producer and the optimum price;
A production allocation determination method characterized by comprising:

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