Scheduling robust optimization method for slab yard crown blocks of iron and steel enterprises

Abstract

The invention discloses a robust optimization method for slab yard crown block scheduling of an iron and steel enterprise, relates to a method for optimizing a crown block operation process, and provides a robust optimization model for solving a slab yard crown block scheduling problem, so that the crown block operation process is effectively optimized, and the in-out warehouse efficiency of slabs is improved. According to the actual starting time of slab hoisting operation, a mathematical model is established by taking the minimum slab warehousing time as a target function. Establishing a deterministic crown block scheduling model under an ideal condition; due to the fact that many uncontrollable factors can occur in slab operation, crown block scheduling can be affected, an original operation plan is not feasible, and a robust optimization model of crown block scheduling under uncertain factors is established on the basis of a deterministic model. And solving the model by using LINGO, and verifying the correctness and feasibility of the model. And testing the influence of uncertain parameters on the crown block scheduling problem by using a sensitivity analysis method, and verifying the robustness of the model.

Description

Technical Field

[0001] The invention relates to an optimization method for overhead crane scheduling in a steel enterprise, and in particular to a robust optimization method for overhead crane scheduling in a slab warehouse of a steel enterprise. Background Art

[0002] With the rapid development of modern science and technology, steel enterprises are facing increasingly fierce market competition. Improving their own logistics efficiency has become an indispensable and effective means to enhance their competitiveness. However, in the actual steel production process, due to the time and space limitations of the slab warehouse hoist, the slab casting slow cooling link is restricted, which greatly affects the overall production efficiency. Therefore, it is of practical significance to conduct in-depth research on the optimization problem of slab warehouse crane scheduling.

[0003] The overhead crane scheduling problem is one of the typical multi-machine multi-task parallel scheduling problems. In the actual slab warehouse operation process, several overhead cranes need to perform several lifting tasks together within a time window, and there are complex interrelationships and constraints between these tasks. In addition, the overhead crane is also restricted by real constraints such as stack layout, process flow, and operation interference during the execution of tasks. The idea of ​​robust optimization scheduling provides an effective solution to this problem. It emphasizes that in an uncertain environment, a robust scheduling scheme should be designed to cope with various possible interferences and changes.

[0004] By combining the actual production and operation conditions of the steel group, the crane scheduling optimization plan is constructed and adjusted to effectively improve the efficiency of slab warehouse in and out, reduce the consumption of production resources and energy, and enable it to play the maximum benefit in actual production. At the same time, this will also help to enhance the comprehensive strength and status of steel enterprises in market competition. Summary of the invention

[0005] The purpose of the present invention is to provide a robust optimization method for the scheduling of overhead cranes in slab warehouses of steel enterprises. The method proposes a robust optimization model for the scheduling problem of overhead cranes in slab warehouses, which is a robust optimization algorithm for scheduling problems based on LINGO to obtain a better solution with both safety and robustness. The present invention achieves the goal of minimizing the penalty cost of slab storage, improves the working efficiency of overhead cranes in slab warehouses, and greatly improves the efficiency of slab storage and warehousing in and out of enterprises.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A robust optimization method for overhead crane scheduling of slab warehouses in steel enterprises is provided. The method is a robust optimization method for overhead crane scheduling of slab warehouses taking penalty costs into consideration, and comprises the following steps:

[0008] S1: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs;

[0009] S2: Model robustness

[0010] Taking the uncertainty of slab storage operation time into consideration, the S1 mathematical model is robustly optimized to transform the slab storage deterministic model into a robust model with uncertainty.

[0011] S3: LINGO solves the robust model

[0012] Define the set, decision variables and constants of the model established by S2, assign various types of data to the corresponding original set and derived set, and write the objective function and constraints according to the robust model in S2. After the LINGO code is written, it is operated and adjusted multiple times to obtain the result;

[0013] S4: Sensitivity analysis of uncertain parameters

[0014] A sensitivity analysis of the robust optimization results is conducted based on the three uncertain factors of slab task quantity change, storage time change, and adjustment parameter change.

[0015] S5: Data Analysis

[0016] The influence of different uncertain parameters on the S2 robust model is compared through line graphs, and the risk resistance of the S2 robust model in the face of different interferences is tested.

[0017] The above-mentioned robust optimization method for overhead crane scheduling of slab warehouse of steel enterprise, the specific implementation steps of step S1 are as follows:

[0018] S101: Establish a matrix for each variable that needs to be considered. Specifically, let i be the slab task, B be the penalty coefficient of the unit delayed lifting time of slab i, s i is the actual start time of slab i, a i is the expected storage time of slab i, f i is the actual completion time of the operation of slab i;

[0019] S102: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs:

[0020]

[0021]

[0022] Formula (1) is the objective function that takes into account the penalty cost of slab storage delay into account. Formula (2) and Formula (3) indicate that each slab storage task can only be performed by one overhead crane, and the slab storage task can only be performed once. Formula (4) indicates that the operating speed of the overhead crane when performing the slab storage task is subject to realistic constraints. Formula (5) indicates that the two overhead cranes must maintain a safe distance when performing the slab storage task. Formula (6) indicates that the actual start time of slab i is not earlier than the expected storage time. Formulas (7) and (8) indicate that the time window of each task is constrained. Formula (9) indicates that slab i is lifted before slab j is lifted. Formula (10) indicates that the sum of the number of working overhead cranes must not exceed the sum of the available overhead cranes in the slab warehouse. Formulas (11), (12) and (13) define the value range of the variables.

[0023] In the above-mentioned robust optimization method for overhead crane scheduling of slab warehouse of steel enterprise, the method for generating a robust model in step S2 is:

[0024] S201: taking into account the uncertainty of the slab storage operation time, the S1 mathematical model is robustly optimized;

[0025] According to the characteristics of the robust model, Bertsimas' robust optimization method is used. To obtain robustness, we first assume that the storage time is is the interval variation, and then a new parameter Γ is introduced to find the optimal value of the objective function when Γ data changes;

[0026] If Γ = 0, it means that the impact of the storage time deviation is completely ignored; as the value of Γ increases, the cost of robustness increases;

[0027] Finally, add the parameter Γ i To adjust the conservative level of the solution, the model can show different degrees of robustness, and there are

[0028] S202: Since the present invention considers only one uncertain parameter and it only appears in equation (6) of the S1 model, let Γ i ∈[0,1],Γ i It does not necessarily take an integer; the robust corresponding formula of formula (6) can be written as:

[0029]

[0030] At this point, the deterministic model that takes into account the penalty cost of delayed slab storage time is transformed into a robust model; the model is as follows:

[0031]

[0032] The robust optimization method for overhead crane scheduling of slab warehouse in steel enterprises, the robust model is solved by LINGO in step S2 as follows:

[0033] S301: Write code in LINGO software:

[0034] (1) Define the set, decision variables and constants of the established model, conduct in-depth analysis of the relevant data, classify them according to different attributes, and finally assign each type of data to the corresponding original set and derived set. As shown below:

[0035] sets:

[0036] Slab properties work / 1..n / : W, S, A, F, AJ, TC, TR, sd, ed;

[0037] Time attribute time / 1..TM / ;

[0038] Crane attribute factor / 1..c / ;

[0039] Stack location attribute location / 1..4 / :L;

[0040] Collection attribute link1(factor,time):X;

[0041] link2(work,factor):Y;

[0042] link3(work,work,factor):Z;

[0043] link4(work, time, factor):O;

[0044] link5(location,location):D;

[0045] endsets

[0046] (2) Assign values ​​to each variable based on existing data to make the written code meaningful;

[0047] (3) Write the objective function and constraints based on the robust model in S2;

[0048] S302: After the LINGO code is written, the calculation is performed and the result is obtained by multiple adjustments.

[0049] The beneficial effects of the present invention are:

[0050] 1. Through verification, it can be concluded that the present invention is correct and feasible, achieves the goal of minimizing the penalty cost of slab warehousing, improves the working efficiency of the overhead crane in the slab warehouse, and has substantial significance for the production of the enterprise.

[0051] 2. The robust optimization method of the present invention can effectively solve the optimization problem of overhead crane scheduling under the condition that the slab storage time is uncontrollable. By adjusting the robust parameters to change the conservatism of the model, it can effectively avoid external interference while maintaining positive robustness, which greatly improves the efficiency of slab storage and makes the model more realistic. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the present invention;

[0053] Figure 2 is the uncertain parameter W of the present invention, Sensitivity analysis comparison chart of Γ changes. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with specific embodiments. It is necessary to point out that the embodiments are only for illustrative purposes, and the protection scope of the present invention is not limited to the illustrative scope.

[0055] In order to establish the mathematical model of the problem under study, the symbols involved in the present invention are defined as follows:

[0056] Definition of set and subscript notation:

[0057] D represents the set of slab handling tasks;

[0058] C represents the set of overhead cranes;

[0059] H represents the set of discretized time periods, H = {1, 2, ..., Tmax};

[0060] Tmax represents the planning horizon.

[0061] Constant symbol definition:

[0062] v represents the operating speed of the overhead crane;

[0063] Δt represents the time difference between the two tasks of slab i and slab j;

[0064] δ represents the safe distance between the sky and the vehicle;

[0065] a i It indicates the estimated storage time of slab i;

[0066] The data uncertainty value (variation range) of the estimated storage time of slab i;

[0067] Γ represents the total value of the data uncertainty level of the estimated storage time of slab i;

[0068] d ij Indicates the stacking distance between slab i and slab j;

[0069] t i represents the operation process time of slab i;

[0070] l i represents the latest completion time of slab i;

[0071] B represents the penalty coefficient of unit delayed lifting time of slab i;

[0072] M represents a sufficiently large number;

[0073] Decision variable symbol definition:

[0074] X k(t) represents the position of overhead crane k at time t;

[0075] s i Indicates the actual start time of operation of slab i;

[0076] f i represents the actual completion time of the operation of slab i;

[0077] X ik ∈{0,1} means that if slab i is hoisted by overhead crane k, it is 1, otherwise it is 0;

[0078] Y ijk ∈{0,1} means that if crane k executes slab i and then slab j, it is 1, otherwise it is 0;

[0079] N itk ∈{0,1} means that if slab i is operated by an overhead crane at time t, it is 1, otherwise it is 0;

[0080] The robust optimization method for the slab warehouse crane scheduling problem of the present invention is specifically described below, including the following steps:

[0081] S1: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs. The specific implementation steps are as follows:

[0082] S101: The present invention considers the parallel scheduling of multiple slab tasks and multiple overhead cranes, while minimizing the penalty cost of slab storage delay time and meeting the time and space constraints of the overhead crane. When a slab task needs to be lifted, an overhead crane is assigned to perform the operation.

[0083] A matrix is ​​established for each slab that needs to be lifted. Specifically, let i be the slab task and k be the overhead crane.

[0084] S102: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs:

[0085]

[0086] Formula (1) is the objective function that takes into account the penalty cost of slab storage delay into account. Formula (2) and Formula (3) indicate that each slab storage task can only be performed by one overhead crane, and the slab storage task can only be performed once. Formula (4) indicates that the operating speed of the overhead crane when performing the slab storage task is subject to realistic constraints. Formula (5) indicates that the two overhead cranes must maintain a safe distance when performing the slab storage task. Formula (6) indicates that the actual start time of slab i is not earlier than the expected storage time. Formulas (7) and (8) indicate that the time window of each task is constrained. Formula (9) indicates that slab i is lifted before slab j is lifted. Formula (10) indicates that the sum of the number of working overhead cranes must not exceed the sum of the available overhead cranes in the slab warehouse. Formulas (11), (12) and (13) define the value range of the variables.

[0087] S2: Generate a robust model

[0088] According to the characteristics of the robust model, the robust optimization method of Bertsimas is used to take into account the uncertainty of the slab storage operation time and perform robust optimization on the S1 mathematical model. The specific method is as follows:

[0089] S201: To achieve robustness, first assume that the storage time is is the interval variation, and a new parameter Γ is introduced to obtain the optimal value of the objective function when Γ data change.

[0090] If Γ = 0, it means that the impact of the storage time deviation is completely ignored; as the value of Γ increases, the cost of robustness increases.

[0091] Finally, add the parameter Γ i To adjust the conservative level of the solution, the model can show different degrees of robustness, and there are

[0092] S202: Since the present invention considers only one uncertain parameter and it only appears in equation (6) of the S1 model, let Γ i ∈[0,1],Γ i It does not necessarily take an integer. The robust corresponding formula of formula (6) can be written as:

[0093]

[0094] At this point, the deterministic model that takes into account the penalty cost of delayed slab storage time is transformed into a robust model. The model is as follows:

[0095]

[0096] S3: LINGO solves the robust model

[0097] Write the code in LINGO software, perform calculations after writing, and adjust the results multiple times, including the following steps:

[0098] S301: Define the set, decision variables and constants of the established model, conduct in-depth analysis of the relevant data, classify them according to different attributes, and finally assign each type of data to the corresponding original set and derived set. As shown below:

[0099] sets:

[0100] Slab properties work / 1..n / : W, S, A, F, AJ, TC, TR, sd, ed;

[0101] Time attribute time / 1..TM / ;

[0102] Crane attribute factor / 1..c / ;

[0103] Stack location attribute location / 1..4 / :L;

[0104] Collection attribute link1(factor,time):X;

[0105] link2(work,factor):Y;

[0106] link3(work,work,factor):Z;

[0107] link4(work, time, factor):O;

[0108] link5(location,location):D;

[0109] endsets

[0110] S302: assigning values ​​to each variable according to the existing data, so that the written code has substantive meaning;

[0111] S303: Write the objective function and constraints according to the robust model in S2.

[0112] S4: Sensitivity analysis of uncertain parameters

[0113] A sensitivity analysis of the robust optimization results was carried out based on the three uncertain influencing factors: changes in the number of slab tasks, changes in storage time, and changes in adjustment parameters.

[0114] S5: Data Analysis

[0115] The influence of different uncertain parameters on the S2 robust model is compared through line graphs, and the risk resistance of the S2 robust model in the face of different interferences is tested.

[0116] A real case is: This paper takes the continuous casting-hot rolling process slab library of a domestic steel group as an example, inputs actual values, and uses LINGO to solve and verify the correctness and robustness of the model.

[0117] The present invention is demonstrated by taking a domestic steel group as an example, and setting the delay penalty cost coefficient, the overhead crane operation speed, the safety distance to be maintained between overhead crane operations, the overhead crane operation time, the number of stacks, the stack positions, etc. are all determined parameters.

[0118] Table 1 Deterministic parameter settings

[0119]

[0120] Firstly, the feasibility of the robust model is verified by performing three scales of operations according to the changes in the number of slab tasks.

[0121] Based on basic numerical values, the present invention analyzes and studies the optimal solutions of the objective functions of three different scale slab tasks when the number of overhead cranes is fixed to 2. LINGO solves and obtains three minimum operation times of 12, 36 and 144 respectively.

[0122] Table 2 Results of solving the basic numerical model using LINGO 11 software

[0123]

[0124] Taking into account the actual production situation in the continuous casting-hot rolling process, the penalty cost coefficient B of the delayed slab storage time is added to the objective function to enhance the anti-interference ability of the model. The present invention takes the penalty cost coefficient of the delayed slab storage time as 2 as an example for calculation, and LINGO solves the minimum penalty costs as 13, 39, and 156 respectively. The results are compared and analyzed, and the minimum slab storage time is greater than the basic value when the delayed penalty cost is considered.

[0125] Table 3 Results of penalty cost model solved by LINGO 11 software

[0126]

[0127] In addition, there are some uncertain influencing factors in the slab warehouse crane scheduling problem, such as: the data uncertainty value (variation range) of the number of slabs in operation and the actual slab storage time, and the total value and partial value of the robust adjustment parameter. The total value of the robust adjustment parameter is obtained by summing up the respective adjustment parameters of all slab tasks.

[0128] In order to enhance the immunity of the objective function under the condition of delay penalty cost, the corresponding robust model is established. Its conservatism is changed by adjusting the robust parameters, so that it can maintain positive robustness while effectively avoiding external interference and improve the efficiency of slab storage.

[0129] The uncertainty parameter settings are shown in Table 4.

[0130] Table 4 Uncertainty parameter settings

[0131]

[0132] In order to verify the anti-risk ability of the robust model and study the impact of different variables on the objective function, the present invention conducts experimental discussion on uncertain factors through sensitivity analysis. In small-scale data, the number of slab tasks, the change of storage time, and the impact of the change of robust parameter Γ on the results are respectively used as experimental objects, and sensitivity analysis is performed. The robust optimization results are shown in Table 5. Among them, the analysis of the impact of slab task W is through examples 1, 2, 5, and 6; the analysis of the change interval of slab storage The influence of is analyzed through examples 1, 3, 5, and 7; the influence of the robust parameter Γ is analyzed through examples 1, 5, 4, and 8.

[0133] Table 5 Comparison of robust optimization results

[0134]

[0135] From Table 5, we can conclude that:

[0136] Uncertain factors have different influences on the scheduling of overhead cranes in slab warehouses: when the number of slab tasks W is at a smaller task scale, the objective function value increases with the increase of the number of tasks W, while in larger-scale examples, the objective function value shows a strong fluctuation growth trend; the range of slab storage time changes The wider the interval, the smaller the fluctuation of the optimal solution of the objective function, which means that the interval of variation of the slab storage time is The impact on the objective function is positively correlated and fluctuates smoothly; the larger the value of the robust parameter Γ, the greater the robustness, the more conservative the objective function, and the higher the value of the optimal solution.

[0137] In general, the robust parameter Γ has a strong influence on the minimum slab storage time model considering the delay penalty cost. When the deviation between the actual slab storage time and the expected storage time is small, the optimal solution can be obtained; when the deviation between the actual slab storage time and the expected storage time is large, a conservative solution that meets all constraints can still be obtained, which reflects the optimization significance of establishing a robust model. In an ideal environment, the overhead crane can lift the slab according to the original production operation plan; when uncontrollable factors have an impact, the robust optimization model can also give a conservative result to reasonably schedule the slab warehouse overhead crane operation, so that the operation plan for the slab warehouse is still feasible, and the overall operation of the continuous casting process is in a stable state.

[0138] It can be understood that the above specific description of the present invention is only used to illustrate the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that the present invention can still be modified or replaced by equivalents to achieve the same technical effects; as long as the use requirements are met, they are within the protection scope of the present invention.

Claims

1. A robust optimization method for overhead crane scheduling in a slab warehouse of a steel enterprise, characterized in that: The method is a robust optimization method for the slab warehouse crane scheduling problem considering penalty costs, and comprises the following steps: S1: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs; S2: Model robustness Taking the uncertainty of slab storage operation time into consideration, the S1 mathematical model is robustly optimized to transform the slab storage deterministic model into a robust model with uncertainty. S3: LINGO solves the robust model Define the set, decision variables and constants of the model established by S2, assign various types of data to the corresponding original set and derived set, and write the objective function and constraints according to the robust model in S2; perform calculations after the LINGO code is written, and adjust the results multiple times; S4: Sensitivity analysis of uncertain parameters Sensitivity analysis of robust optimization results is conducted for three uncertain factors: changes in slab task quantity, changes in storage time, and changes in adjustment parameters. S5: Data Analysis The influence of different uncertain parameters on the S2 robust model is compared through line graphs, and the risk resistance of the S2 robust model in the face of different interferences is tested.

2. The robust optimization method for overhead crane scheduling in a slab warehouse of a steel enterprise according to claim 1 is characterized in that: The specific implementation steps of step S1 are as follows: S101: Establish a matrix for each variable that needs to be considered. Specifically, let i be the slab task, B be the penalty coefficient of the unit delayed lifting time of slab i, s i is the actual start time of slab i, a i is the expected storage time of slab i, f i is the actual completion time of slab i; S102: Establish a mathematical model for overhead crane scheduling with the goal of minimizing delay penalty costs: X k(t) -v·Δt≤X k(t+Δt) ≤X k(t) +v·Δt,k∈C,t=1,2,...,Tmax (3-4) X k(t) ≤X k+1(t) -δ,k∈C,t=1,2,...,Tmax (3-5) Formula (1) is the objective function that takes into account the penalty cost of slab storage delay into account. Formula (2) and Formula (3) indicate that each slab storage task can only be performed by one overhead crane, and the slab storage task can only be performed once. Formula (4) indicates that the operating speed of the overhead crane when performing the slab storage task is subject to realistic constraints. Formula (5) indicates that the two overhead cranes must maintain a safe distance when performing the slab storage task. Formula (6) indicates that the actual start time of slab i is not earlier than the expected storage time. Formulas (7) and (8) indicate that the time window of each task is constrained. Formula (9) indicates that slab i is lifted before slab j is lifted. Formula (10) indicates that the sum of the number of working overhead cranes must not exceed the sum of the available overhead cranes in the slab warehouse. Formulas (11), (12) and (13) define the value range of the variables.

3. The robust optimization method for overhead crane scheduling in a slab warehouse of a steel enterprise according to claim 1 is characterized in that: The method for generating a robust model in step S2 is: S201: taking into account the uncertainty of the slab storage operation time, the S1 mathematical model is robustly optimized; According to the characteristics of the robust model, Bertsimas' robust optimization method is used; To achieve robustness, we first assume that the storage time is is the interval variation, and then a new parameter Γ is introduced to find the optimal value of the objective function when Γ data changes; If Γ = 0, it means that the impact of the storage time deviation is completely ignored; as the value of Γ increases, the cost of robustness increases; Finally, add the parameter Γ i To adjust the conservative level of the solution, the model can show different degrees of robustness, and there are S202: Since the present invention considers only one uncertain parameter and it only appears in equation (6) of the S1 model, let Γ i ∈[0,1],Γ i It does not necessarily take an integer; the robust corresponding formula of formula (6) can be written as: At this point, the deterministic model that takes into account the penalty cost of delayed slab storage time is transformed into a robust model; the model is as follows: St(3-2)—(3-5),(3-7)—(3-15).

4. The method for robust optimization of overhead crane scheduling for slab warehouse of steel enterprises according to claim 1 is characterized in that: The step S2 performs LINGO solution on the robust model as follows: S301: Write code in LINGO software: (1) Define the set, decision variables and constants of the established model, conduct in-depth analysis of the relevant data, classify them according to different attributes, and finally assign each type of data to the corresponding original set and derived set; as shown below: sets: Slab properties work / 1..n / : W, S, A, F, AJ, TC, TR, sd, ed; Time attribute time / 1..TM / ; Crane attribute factor / 1..c / ; Stack location attribute location / 1..4 / :L; Collection attribute link1(factor,time):X; link2(work,factor):Y; link3(work,work,factor):Z; link4(work, time, factor):O; link5(location,location):D; endsets (2) Assign values ​​to each variable based on existing data to make the written code meaningful; (3) Write the objective function and constraints based on the robust model in S2; S302: After the LINGO code is written, the calculation is performed and the result is obtained by multiple adjustments.

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