JPH06161512A - Optimum operation schedule planning method - Google Patents

Abstract

PURPOSE:To provide an optimum operation schedule planning method which is suitable for the planning of an optimum operation schedule by determining the optimum combination of an operating device and the output. CONSTITUTION:The production of a device is determined based on the schedule condition of an object device by using an input device 201 inputting the schedule conditions of plural object devices, a storage device 202 storing the processing procedures of the schedule planning of the plural object devices and the characteristic data of the object devices, a computer 203 having a central arithmetic processing unit 204 performing a processing in accordance with a prescribed processing procedure based on the information from the input device 201 and the storage device 202, and an output device 205 outputting a processing result. Further, based on this condition, the production of other device to be optimum is determined. Based on the production of each device, the operation order of the device is determined, the combination of the devices to operated based on this operation order is determined, and the optimum operation schedule of the device is planned by evaluating the operation schedule.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optimum operation plan planning method for preparing operation plans for a plurality of devices, such as chemical and iron and steel devices.

[0002]

2. Description of the Related Art As a conventional technique, the document "Dynamic Programming"
As described in (Nikki Giren, Shohei Sugiyama, pp. 1, 2), in the conditional extreme value problem, a certain amount of raw material can be optimally distributed to a plurality of devices by Lagrange's undetermined multiplier method.
The allocation problem here is to determine the amount to be allocated to the i-th factory when a fixed amount x of resources is allocated to the N factory to maximize profit. gi (xi): Profit of factory i with resource xi xi: Resource amount allocated to factory i where Lagrange function with new variable λ added , And N equations ∂φ / ∂xi = 0 (i = 1, 2, 3, ..., N) and constraints can be used to determine xi and λ, and the distribution at this time is optimal. It is shown.

[0003]

The above prior art is optimally distributed when it is assumed to be distributed to all devices. When it is 0, it becomes 2 ⁵⁰ (> 10 ¹⁵ ), so there is a problem that it is difficult to determine the optimum combination of the devices to be operated. An object of the present invention is to provide an optimum operation plan planning method suitable for determining an optimum combination of devices to be operated and its output and making an optimum operation plan of the devices.

[0004]

In order to achieve the above object, after determining the optimum production amount of each device, the device to be operated is determined according to the order of the amount of profit per unit production of each device. , Determine the combination of operating devices and the production volume.

[0005]

In the process of determining the production amount, the production amount of a certain device is determined based on the planned condition of the target device, and the optimal production amount of the other device under this condition is determined and the operation is performed. In the process of determining the order, the operating order of the device is determined based on the distribution of the production amount of each device, and in the process of determining the operating device, the combination of the devices to be operated is determined based on the operating order, and the operation is performed. In the process of evaluating the plan, the operation plan is evaluated and the optimum operation plan is determined, so that the optimum operation plan of the device can be drafted.

[0006]

EXAMPLES Examples of the present invention will be described below. A first embodiment of the present invention will be described with reference to FIGS. 1 to 6 and Tables 1 to 5. FIG. 1 is a flow chart showing the procedure of the optimal operation planning method of the present invention, FIG. 2 shows the configuration of the planning device, and FIG. 3 shows the input and output of the device to be planned. The flow of planning in FIG. 1 is as follows.
Block 2, which inputs the production amount of one device, block 2
Block 3 for determining the production amount of another device to be operated based on the production amount of the device, Block 4 for determining the operating order of the device based on the production amount of each device, and the device to be operated based on the order of the operating device 5, a block 5 for determining a combination satisfying a constraint condition, a block 6 for determining a device satisfying a constraint condition, a block 7 for adjusting a production amount based on a combination of operating devices, and an operation plan of the device based on the adjusted production amount are evaluated. It is composed of a block 8 and a block 9 for outputting an optimum operation plan. In FIG. 2, the input device 201 inputs the planning condition of block 1 and the production amount of block 2. The storage device 202 stores the characteristic data of the device and the processes of blocks 3 to 8. The computer 203 uses the input from the input device 201 and the storage device 202.
The central processing unit performs actual processing based on the characteristic data of the apparatus and processing procedure. The output device 205 is block 9
The result of the computer 203 is output. The target problem is
This is to optimize the objective function of Expression (1) under the constraint condition of Expression (2). Here, a case will be described in which the cost is minimized by considering the objective function as the cost. The objective function C of the device is represented by an input function hi (ui), and the output characteristic gi (ui) of the device and the input characteristic fi of the device are shown in FIG.
The input / output relationship of (ui) is shown. Here, the operation amount u of the device i
i indicates the production amount. For example, input fi (ui)
Is the iron ore, the output of the steel production of output gi (ui) is output by the device i, and the total production of the steel of each device i is output.

Next, the processing contents of each block will be described. In the data input / read block 1, the number of devices is n, and the function hi (u) which is the input / output characteristic of the devices 1 to n.
i), gi (ui), fi (ui) and the requested amount U are input device 20
1 input or read from the storage device 202. Here, if the input / output characteristic of the device i is a polynomial expression of the manipulated variable ui, u
The coefficient of each degree of i will be read. Here, for simplification of explanation, hi (ui) = fi (ui) fi (ui) = ai (ui) ² + bi (ui) + ci (3) (function fi (ui) outputs It is assumed to increase monotonically in the range.) Ai, bi, and ci are coefficients of each order gi (ui) = ui (4) And In block 2, a plurality of production amounts of the device are set within the output range. Here, as an example, one of the set production amounts is u1j0 (the production amount set to the jth of the component value 1,
The last 0 will be described as a suffix indicating that it is set externally). According to the data read in block 1,
Assuming that the production amount uij0 (2 ≦ i) of the other device is determined as a function of u1j0, the production amount of the other device is calculated by equation (6) in block 3. uij = x (u1j) (6) The relationship between the production amount of the device 1 of the equation (6) and the production amount of other devices is read in the process of block 1. In FIG. 4, when the number of devices is specifically three, the device 1 represented by the formula (6) and another device 2,
The relationship with the device 3 is shown. When the production amount of the device 1 is u1, the production amounts of the device 2 and the device 3 are u2 and u3, respectively. In block 4, when the production amount uij0 is determined, the value of the cost per unit production amount fi (uij) is calculated from the equation (3).
0) / uij0 is calculated. FIG. 5 shows the production amount (u1, u2, u3) and cost (c1j0, c2j0, etc.) of each device.
c3j0). In FIG. 5, the slope of the straight line drawn from the origin indicates the value cij0 of the cost per unit production amount. Fi (uij), which is the cost per unit production
0) / uij0 is determined in descending order as the operating order of the apparatus. When the production amount uj10 of the device 1 is determined, the cost can be minimized when the devices are operated in order of the slope of the straight line in FIG. 5, and in the example of FIG. Becomes When maximizing the objective function, the order in which the equipment is run is reversed. Block 5
Then, on the basis of the order of operation of the devices determined in block 4, the combination of devices when operating from one to n devices is determined. Table 1 shows the combinations of the devices to be operated and the production amounts when the production amount u1 = u1j0 of the device 1 in the cases of FIGS. 4 and 5.

[Table 1] In Table 1, when the production volume is zero, it does not hold as a plan, so there is no problem even if it is omitted. Similarly,
A table is created when the production amount u1 is changed from u110 to u1k0 by Δu10. When the production amount is u1j0, the target device to be operated is the device 1, and the production amount is u1j0.
When 0 + u2j0, the target devices to be operated are the devices 1 and 2, and when the production amount is u1j0 + u2j0 + u3j0, the target devices to be operated are the devices 1, 2 and 3. This is called a production amount table and is shown in Table 2.

[Table 2] In Table 2, the operating device Wjd sets the production amount u1 to u1j0.
Then, a set of devices to be operated up to d is shown,
ujd is the sum of the production volumes of up to d-th operating equipment. For example, when u1 = u110, the sum of production u1
When 1 is requested, it indicates that the device to be operated is the device W11, that is, one device. Similarly, when the sum of production u1n is requested, the device to be operated indicates to operate the device W1n, that is, all units. In the above, the output function of equation (2) is quadratic,
When the formula (6) is a first-order case and the input / output function is a high-order polynomial in the processing of blocks 3 and 4, the production amount table can be similarly created. In block 6, a combination that minimizes the absolute value of the difference between the right side and the left side, which is represented by the equation (2) that is the constraint condition, is determined. This means that it is necessary to extract the combination of devices that satisfy the formula (2), that is, the demand amount and the production amount match, but satisfy the formula (2) when the production amount u1j0 of the device 1 is satisfied. Is generally not. The results at this time are shown in Table 3. For example, when the production amount of the device 1 is u110 and the total production amount is u1, it means that one of the operating devices W11 to W1n shown in Table 2 is selected as one of the cost-appropriate devices W1. The same applies when the production amount of the device 1 is u120 to u1k and the total production amount is u2 to uk. Generally, each production amount of the device 1 is u1.
The total production amount at j0 is Ud (d = 1, 2, 3, ...
k), Wd (d = 1, 2, 3, ...
It is shown by k). The above processing is determined for each production amount of the device 1 input in block 2.

[Table 3] In block 7, in the combination of devices determined in block 6 for each production amount of the device 1, the device 1 is calculated by the formula (6).
The production amount of each device is changed, and the production amount of each device is adjusted so as to satisfy the equation (2). In block 8, the objective function of the formula (1) is calculated using the formula (3) for the combination of the devices determined for each production amount of the device 1. In block 9, the operation plan of the device having the smallest objective function among the combinations of the devices is output. Output example Table 4
Shown in. In Table 4, when the required amount, that is, the production amount is U,
The number of devices to operate is the number of devices 1, 2, and n, and the sum of costs f1 (u1d), f2 (u2d), and fn (und) of each device is Cd.

[Table 4] In the above, when the production amount of the device 1 was determined, the production amount of the other device was determined, but the Lagrange's undetermined multiplier λ is introduced to determine the production amount of the other device, and the block 3, Block 7 can also be processed as follows. Minimizing the objective function is the same as minimizing Eq. (7). In Expression (7), the first term corresponds to the cost and the second term corresponds to the constraint condition. By the way, the necessary condition for the objective function to be the minimum is ∂φ / ∂ui = 0, and from this, λ = 2ai · ui + bi (8) The method of determining the amount can be as follows. The production amount u1j0 of the device 1 is substituted into the equation (8) to obtain λ. The production amount uij0 of another device is calculated using this λ. In FIG.
The solid line indicates the amount of increase in cost when the unit production amount of the device 1, the device 2, and the device 3 is increased.
And the production amount u of the other devices 2 and 3 from this λj
2. Calculate u3. In this case, in block 7, the Lagrange's undetermined multiplier λ is corrected according to the equation (9) to adjust the production amounts of the other devices. Further, in the block 6, the combination of the devices is determined from the condition that the constraint condition (2) is satisfied.
The combination of devices may be determined from among the conditions satisfying the constraint condition (0). The following constraint condition is taken into consideration in order to make a plan that can cope even when the demand amount changes and reaches the predicted maximum demand amount Umax. The maximum value of the total production amount can be determined from the sum of the maximum production amounts of the respective devices of the formula (5) when the combination of operating devices is determined. Table 5 is a table in which the item of the maximum production amount, which is additionally determined when the combination of the devices is determined, is added to the production amount table of Table 1. In addition, Table 5 is an example in the case of FIG. 3 and FIG. 4, and the maximum production amount satisfies the expression (10).

[Table 5] As described above, according to the first embodiment, a plurality of production amounts of one device are set, the production amount of another device is determined from the production amount, and the production amount of each device and the device at this time are determined. The operating order of the equipment is determined from the cost ratio of the operating equipment, the operating equipment combination that satisfies the constraint conditions for the operating equipment combination is determined, and the production amount of each equipment is adjusted in the determined operating equipment combination. It is possible to optimize the operation plan of the equipment by matching the required quantity with the production quantity, calculating the cost in the adjusted production quantity, and outputting the combination of the equipment that minimizes the cost and the production quantity of each equipment. .

Next, a second embodiment of the present invention will be described with reference to FIG. 7 and Table 6. FIG. 7 shows a flow chart of the operation plan formulation of the device of the second embodiment, and the processing of blocks 12 and 13 is different from the flow chart of the operation plan formulation of the device of the first embodiment of FIG. In block 12, the Lagrange's undetermined multiplier λ of equation (8) is equal and the objective function fi (ui) / ui per unit production amount is equal for each combination of all two devices, and the undetermined multiplier λ is calculated. Before and after this undetermined multiplier λ, the order of operation of the two devices changes. For example, when the combination of the device 1 and the device 2 is selected, the following equation may be solved. λ = 2a1 · u1 + b1 = 2a2 · u2 + b2 f1 (u1) / u1 = f2 (u2) / u2 When the function fi (ui) has a higher degree than the second order, the undetermined multiplier λ is calculated using the convergence calculation. However, the production amounts of the devices 1 and 2 need to satisfy the constraint condition of the equation (5). If you are not satisfied, there is no solution. Function fi (u
When i) is quadratic, the combination of two arbitrary devices is n (n + 1) / 2, and when the objective function is a quadratic equation, the number of intervals of the undetermined multiplier λ is It is at most n (n + 1) +1. In block 13, the values of the undetermined multiplier λ when the driving order changes calculated in block 12 are sorted in ascending order. After sorting, the cost per unit production amount of each device at the average value for every two adjacent λ (change points) is calculated, and the order in which the cost is smaller is the operating order of the devices between the adjacent change points. Becomes The production range of each device is λ
Is calculated by the equation (8). Table 6 shows Lagrange's undetermined multipliers λj and λj + 1 (j = 1, 2, 3, ...
., K-1), the set Wjd (d) of the driving devices in the section
= 1, 2, 3, ..., N).

[Table 6] In this second embodiment, the λ in which the order of operation is unchanged
Since the number of production tables to be prepared can be reduced because the number of production tables is sufficient within the range of 1 and the number of tables is one, the processing time can be shortened.

Next, a third embodiment of the present invention will be described with reference to FIGS.
It will be described using 0. In the third embodiment, while the first embodiment prepares an operation plan only for a certain time, it plans a continuous time of the apparatus. In other words, depending on the target device, a plan for a certain time may limit a plan for another time. For example, if the device is operated at a certain time, it is necessary to continue the operation for a certain fixed time or longer. FIG. 8 shows a flow chart of operation planning of the device of the third embodiment. FIG. 9 shows the change over time in the required amount. The planning procedure will be described below. In block 1 of FIG. 8, in the input of the planning conditions shown in block 1 of FIG. 1, the planning target time T, the production amount of each target time, the number N of planning candidates at each time, and the like are further input or read. In the flow of FIG. 8, blocks 12 to 28 make a plan for the cross section at each time.
Note that the constraint conditions of block 6 are the conditions at each time, such as the above-described agreement between the requested amount and the production amount, the maximum production amount being equal to or greater than the maximum required amount, as described above. In block 28, the operation plan is evaluated and the evaluation ranking is determined. At this time, the top N evaluation ranks are stored in the storage device 202 as plan candidates. The above processing is repeated for the set planning time T. At block 38, the plan during the planning time T is evaluated. The detailed processing of the block 38 is shown in FIG. However, for simplicity, the target time is 3 times (T =
3) The candidate for the plan to be stored is N. Block 107
Where C (t, i) is the value of the objective function of the evaluation order i-th plan at time t, and C (t, i; t + 1, j) is the time (t + 1) from the evaluation order i-th plan state at time t. The evaluation order is the cost when changing to the j-th planned state. In the blocks 101 and 102, when changing from the i-th planned state of the evaluation order at the time t to the j-th planned state of the time (t + 1) and the constraint condition in continuous time is not satisfied, the blocks 103 and 104 are shown. Like C
(T, i; t + 1, j) is a sufficiently large cost value α,
If it is satisfied, the actual cost (0 here) is set as in blocks 105 and 106. Block 107
, The objective function of time i is the i-th plan, time 2 is the j-th plan, and time 3 is the k-th plan of C (i, j,
k). In this block 107, the costs for all the paths (j ≦ N, k ≦ N, i ≦ N) are calculated. In this way, in block 28, the cost of all the routes, that is, the planned time for all the combinations of the plans at each time are evaluated. It should be noted that instead of calculating the costs for all the routes, it is possible to determine the plan with the minimum cost by using the dynamic programming method shown in equation (11). F (m, i) = min {C (m, i) + C (m, i; m + 1, j) + F (m, j)} (11) where F (m, i) Is the minimum cost from the last time T to time m. In block 29, the optimum operation plan is output from the operation plans for the planned target time. As described above, in the third embodiment, it is possible to draw up a plan that satisfies the constraint condition in continuous time of the device.

[0010]

According to the present invention, since the process for determining the production amount, the process for determining the operation order, the process for determining the operating device, and the process for evaluating the operation plan are used, the optimum operation plan for the device is prepared. can do. Moreover, since the production amount of the apparatus is determined by the Lagrange's undetermined multiplier method, the number of production amount tables to be created is reduced, and the processing time can be shortened. Further, since the plan is made in consideration of the time change of the device, it is possible to make a plan that satisfies the constraint condition in the continuous time of the device.

[Brief description of drawings]

FIG. 1 is a flow chart of a first embodiment of the present invention.

FIG. 2 is a diagram showing a configuration of a planning device.

FIG. 3 is a block diagram showing input / output of the device.

FIG. 4 is a diagram showing a method of determining the production amount of each device.

FIG. 5 is a diagram showing the relationship between the production amount and cost of each device.

FIG. 6 is a diagram showing a method of determining the production amount of each device.

FIG. 7 is a flowchart of a second embodiment of the present invention.

FIG. 8 is a flow chart of a third embodiment of the present invention.

FIG. 9 is a diagram showing a change with time of a required amount.

FIG. 10 is a chart for evaluating a planned time.

[Explanation of symbols]

4 Block for deciding the operating order of the device based on the production amount of each device 5 Block for determining a combination of the devices to be operated based on the operating order of the device 6 Block for deciding an operating device satisfying the constraint condition 7 Block 8 for determining the production amount based on the combination of operating devices 8 Block for evaluating the operation plan of the device based on the adjusted production amount 201 Input device 202 Storage device 203 Computer 204 Central processing unit 205 Output device

Claims (6)

[Claims] 1. An input device for inputting planning conditions for a plurality of target devices, a storage device for storing a planning procedure for the plurality of target devices and characteristic data of the target devices, the input device and the storage device. The following procedure is executed by using a computer having a central processing unit that performs processing according to a predetermined processing procedure based on information and an output device that outputs the processing result, and an optimal operation plan of the target apparatus is drafted. An optimal operation planning method characterized by the above. (1) Determining the production amount of each target device, (2) Determining the operation order of the device based on the determined production amount. 2. An input device for inputting planning conditions for a plurality of target devices, a storage device for storing a planning procedure for a plurality of target devices and characteristic data of the target devices, the input device and the storage device. The following procedure is executed by using a computer having a central processing unit that performs processing according to a predetermined processing procedure based on information and an output device that outputs the processing result, and an optimal operation plan of the target apparatus is drafted. An optimal operation planning method characterized by the above. (1) Determining the production amount of each target device, (2) Determining the operation order of the device based on the determined production amount. (3) To determine the combination of devices to be operated based on the operating order of the devices. (4) To determine the combination of operating devices that satisfy the constraint conditions with the items determined by the combination of the above devices. 3. The optimum operation plan planning method according to claim 1, wherein the production amount of the apparatus is determined by Lagrange's undetermined multiplier method. 4. The optimum operation planning method according to claim 2, wherein the constraint condition is that the required amount and the production amount match. 5. The optimum operation plan planning method according to claim 2, wherein the constraint condition is not less than the maximum required amount when the required amount changes. 6. An input device for inputting planning conditions for a plurality of target devices, a storage device for storing a procedure for planning a plurality of target devices and characteristic data of the target devices, the input device and the storage device. The following procedure is executed by using a computer having a central processing unit that performs processing according to a predetermined processing procedure based on information and an output device that outputs the processing result, and an optimal operation plan of the target apparatus is drafted. An optimal operation planning method characterized by the above. (1) To determine an undetermined multiplier in which the driving order of the target device changes according to Lagrange's undetermined multiplier method, (2) To determine the operation order of the device for each section of Lagrange's undetermined multiplier method in which the driving order does not change (3) Determine the combination of devices to be operated based on the operating order of the devices. (4) To determine the combination of operating devices that satisfy the constraint conditions with the items determined by the combination of the above devices.