CN111062571B - Ingot selection and batch-to-batch integration optimization method for aluminum industry - Google Patents
Ingot selection and batch-to-batch integration optimization method for aluminum industry Download PDFInfo
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Abstract
The invention provides an ingot selection and batch-to-batch integrated optimization method for the aluminum industry, and relates to the technical field of automatic metallurgical control. Firstly, acquiring historical production contract data of an aluminum enterprise and an alternative ingot shape matched with the historical production contract data, and establishing a classifier; then obtaining product specification parameter information of the current production contract, determining an alternative ingot type matched with the product specification parameter information through a classifier, and further determining a matching relation between the current production contract and the alternative ingot type; establishing a mathematical model to quantitatively describe ingot selection and contract batch integration decision-making problems through decision variables; determining an initial ingot grouping scheme, and constructing an optimal ingot grouping scheme selection model; solving an optimal ingot group scheme selection model to obtain an optimal combination of high-quality ingot group schemes, converting the optimal combination of the high-quality ingot group schemes into a production instruction of a continuous casting process, and issuing the production instruction to a production workshop to execute production, thereby realizing the selection of ingot types of an aluminum enterprise and the integrated optimization of the same batch.
Description
Technical Field
The invention relates to the technical field of automatic metallurgical control, in particular to an ingot type selection and batch-to-batch integrated optimization method for the aluminum industry.
Background
One outstanding characteristic of the production flow in the aluminum industry is that physical and chemical reactions are continuously generated in the process of material flow, and the material flow is continuously changed in the aspects of state, property and shape. The aluminum alloy has light dead weight, excellent mechanical property and physical property, and can replace steel materials in many application scenes. The aluminum alloy product is manufactured by melting pure aluminum blocks, adding alloy components to prepare alloy liquid, casting and forming, cutting, rolling, heat treatment and finishing. Therefore, the production procedure of the aluminum industry is a typical continuous production process, and the specific production process is as follows:
(1) Injecting electrolytic aluminum liquid into a smelting furnace through a ladle, adding various chemical elements according to the requirements of customers to change the physical and chemical properties of the electrolytic aluminum liquid so as to meet the requirements of various alloy components in a contract, and for different alloy types, when the component differences are large, carrying out furnace washing operation on the smelting furnace;
(2) The aluminum alloy liquid with the proportion is then subjected to a heat preservation stage, a crystal granulating agent is added to refine crystal grains to improve the hardness and toughness of the alloy, degassing operation is carried out, and the internal structure of the aluminum alloy after casting molding is improved;
(3) Transferring molten aluminum alloy liquid from a smelting furnace to a continuous casting machine, adjusting the size of a crystallizer to change the size of a die due to the influence of the specification diversity of aluminum ingots, and then injecting the molten aluminum alloy liquid into the die for casting and forming to form the aluminum ingots;
(4) The aluminum ingot produced by the continuous casting machine has the characteristics of large-scale and batch production, and is usually cut into sub-ingots according to the same batch rule before rolling, and then the sub-ingots are rolled into aluminum plates with different sizes on a hot rolling mill.
Besides the characteristic of long production flow, the production scale of the modern aluminum industry is gradually increased, and the layout of the production line presents a parallel structure with multiple units in the same working procedure. The update of production equipment in the aluminum industry is not only the improvement of the casting capacity of a continuous casting machine, but also the rolling capacity of downstream rolling equipment, and products required by the current customer contracts tend to be characterized by multiple varieties, small batches, multiple specifications and the like. The traditional production mode is that an aluminum ingot is used for producing a product, one part of the residual materials are stored in a warehouse to be used as semi-finished products, and the other part of the residual materials are returned to the furnace for recasting. The semi-finished part of the material occupies inventory and causes inventory pressure, and retuning recast the part of the material increases production costs. Due to the contradiction between the trend of the aluminum ingot to be large-sized and the contract small lot, the total amount of the partial materials stored in the warehouse as the semi-finished products is obviously increased. In order to weaken the influence of the contradiction and respond to the change of the supply-demand relationship and improve the production efficiency of enterprises, reasonable production design is required for ingot type selection and the same batch.
In order to make an integrated decision of ingot type selection and batch combination, the aluminum industry needs to decide which ingot type in a candidate ingot type library is selected as a standard ingot type to meet the contract requirement, and meanwhile, the batch combination mode is improved as follows: a standard aluminum ingot may be batched with one or more contractual products. The batching decision for each aluminum ingot is called a batching scheme, and the collection of the batching schemes used to complete the customer contract is called a batching scheme.
Currently, to solve the problem of integrated optimization of ingot type selection and co-batch, enterprises generally adopt a manual production scheduling method which relies on subjective experience of planners: the method is to match the contract with the ingot model according to an empirical estimation method after qualitative analysis of productivity and inventory conditions of each unit by a planner. Because of the large amount of data involved in actual production, many and complex production process factors need to be considered, and the following problems exist in adopting the manual production:
(1) The planner has subjectivity in manual scheduling, and can sort all contracts according to the past experience level to prepare a feasibility scheme, so that unstable results can be caused;
(2) The manual production scheduling is a serial decision, a planner can select an ingot shape matched with a contract by utilizing a serial sequential strategy, and the serial sequential strategy has extremely short vision from the optimization perspective, and only the current optimization performance is considered when the contract is matched with the ingot shape each time, so that the utilization rate of the front material is high, the following contract is difficult to match with the ingot shape, and the utilization rate is extremely low;
(3) The large amount of production data information can not be fully considered during manual production, rough statistics is generally carried out by adopting a method of classifying according to data attributes, then partial consideration is carried out, the detail of most data information is covered by adopting a simple data classification statistical method, and the incomplete information consideration directly reduces the global optimality of ingot type selection and batch combination.
Therefore, by analyzing the production process of the aluminum enterprise, on the premise of ensuring the production quality and process constraint of the customer contract, the ingot shape selection and the same batch in the aluminum industry are integrated and optimized, and the method has very important significance in optimizing the production process and the product quality design level in the aluminum industry, improving the production efficiency of the enterprise and reducing the production cost.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an ingot type selection and batch-to-batch integration optimization method for the aluminum industry, which realizes the integration decision of ingot type selection and batch-to-batch integration, thereby improving the material utilization rate of an aluminum enterprise, reducing the stock pressure, improving the production efficiency and reducing the production cost.
In order to solve the technical problems, the invention adopts the following technical scheme: an ingot selection and batch-to-batch integrated optimization method for aluminum industry comprises the following steps:
step 1: product specification parameter information in an aluminum enterprise historical production contract and specification parameter information of an alternative ingot matched with the historical production contract are obtained, and clustering treatment is carried out on the information to obtain a classifier, wherein the specific method comprises the following steps:
step 1-1: acquiring product specification parameter information in a historical production contract;
the product specification parameters in the historical production contract include a contract preferred alloy series, an alternative alloy series, a contract delivery period, a contract delivery type, a contract status, a number of aluminum plate orders, an aluminum plate under-gauge number, an aluminum plate order thickness, an aluminum plate order maximum width, an aluminum plate order minimum width, an aluminum plate order maximum length, an aluminum plate order minimum length, an aluminum plate order maximum weight, and an aluminum plate order minimum weight;
step 1-2: acquiring a set of alternative ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of alternative ingot types, and each alternative ingot type specification parameter information comprises an alloy type, thickness, width and weight;
step 1-3: clustering the acquired product specification parameter information in the historical production contract and specification parameter information of an alternative ingot matched with the historical production contract, and clustering contracts with the same alloy type, the same delivery period and the same thickness to obtain a classifier;
the classifier has the functions of: when the product specification parameter of a certain production contract is input, determining an alternative ingot type set matched with the production contract by the classifier;
step 2: obtaining product specification parameter information of a current production contract of an aluminum enterprise, inputting the product specification parameter information into the classifier obtained in the step 1, and determining an alternative ingot shape matched with the current production contract, wherein the specific method comprises the following steps of:
step 2-1: acquiring product specification parameter information of a current production contract;
step 2-2: inputting product specification parameter information of the current production contract into the classifier obtained in the step 1, and determining a specification parameter information set of an alternative ingot type matched with the current production contract;
step 3: according to the specification parameters of the alternative ingot type and the specification parameters of the current production contract and the smelting and continuous casting production process rules determined in the step 2, the matching relationship between the current production contract and the alternative ingot type is determined, specifically:
relationship one: the first-selected alloy series of the production contract i is the same as the alloy series of the ingot type k or one of the alternative alloy series of the production contract i is the same as the alloy series of the ingot type k, and the production contract i is matched with the ingot type k;
relationship II: the weight of the aluminum plate of the production contract i is smaller than that of the ingot type k, and the production contract i is matched with the ingot type k;
relationship III: the width of the aluminum plate of the production contract i is smaller than the width of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship four: the thickness of the aluminum plate of the production contract i is smaller than that of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship five: the difference value of the width of the aluminum plate of the production contract i and the width of the ingot type k is within the range of a maximum width difference threshold epsilon allowed by the process, and epsilon is more than 0, and the production contract i is matched with the ingot type k;
relationship six: the difference value between the thickness of the aluminum plate in the production contract i and the thickness of the ingot type k is within the range of a maximum thickness difference threshold value delta allowed by the process, and delta is more than 0, and the production contract i is matched with the ingot type k;
step 4: according to the product specification parameter information of the current production contract and the specification parameter information of the alternative ingot type matched with the production contract in phase, on the premise of meeting the batch process constraint, establishing a mathematical model to quantitatively describe the ingot type selection and contract batch integrated decision problem, wherein the method comprises the following steps:
step 4-1: for any alternative ingot type K, K epsilon K, K is a set of alternative ingot types, and all production contract sets N matched with the alternative ingot types are obtained according to the matching relation between the production contracts determined in the step 3 and the alternative ingot types k ＝{i∈N|m ik =1 }, where N represents the set of all production contracts, m ik Is a binary parameter, when m ik When=1, it means that the production contract i matches the ingot k, when m ik When=0, it means that the production contract i does not match the ingot k;
step 4-2: for any alternative ingot shape k, the set of production contracts N matching the ingot shape determined according to step 4-1 k Determining a feasible production and same ingot combination scheme set P of ingot k k The method comprises the steps of carrying out a first treatment on the surface of the The feasible contract ingot combination scheme set P of the ingot k k Any feasible contract ingot grouping scheme P epsilon P k From n-dimensional vector a 1kp ，a 2kp ，...，a nkp Description in which arbitrary component a ikp The feasible contract ingot grouping scheme p representing the ingot k is the number of aluminum plates produced by the contract i, i epsilon N k The following process constraints need to be satisfied, as shown in equation (1), equation (2) and equation (3):
wherein q i Represents the weight of the single aluminum plate producing contract i, d i Represents the number of aluminum plates required by production contract i, Q k Representing the weight of the candidate ingot form k;
step 4-3: all possible contract ingot combination scheme sets P= U-shaped gate according to all the ingot type possible contract ingot combination schemes determined in the step 4-2 k∈K P k Ingot is madeThe selection and the selection of the feasible contract ingot group scheme are mapped into mathematical model decision variables, wherein the decision variables comprise:
1) Setting a decision variable z of 0-1 k When selecting ingot type k for production, z k Take a value of 1, otherwise z k The value is 0;
2) Setting an integer variable x kp Representing a viable contract ingot grouping scheme P epsilon P k The number of uses of (2);
step 4-4: according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot grouping scheme set determined in the step 4-2, a production contract product specification parameter constraint is established, and the method specifically comprises the following steps:
step 4-4-1: establishing a production contract that the total quantity of each contract product produced by an aluminum enterprise meets the customer contract or generates the surplus material product, namely that the total quantity of each contract product produced by the aluminum enterprise meets at least the demand quantity of the customer contract product, wherein the part exceeding the demand quantity of the order is temporarily stored in a warehouse area as the surplus material and is sold to future customers, wherein the production contract is specifically shown as a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used in the production contract and the selected alternative ingot types, namely allowing the ingot type ingot grouping scheme to be used only when a certain ingot type is selected, wherein the ingot type ingot grouping scheme is specifically shown as a formula (5):
wherein, for any alternative ingot k, M k Is constant, the size is the predicted value of the number of aluminum ingots used by the alternative ingot k, and the value of z is ensured k 0, arbitrary x kp Is 0, when z k Is 1, there is x kp Greater than 0, as specifically shown in equation (6):
step 4-4-3: the number constraint of the alternative ingot types selected by the aluminum enterprise to complete the production contract is established, and the number constraint is specifically shown as a formula (7):
wherein l is a constant, the value of which is the number of candidate ingot types selected from a library of candidate ingot types for producing the contract product;
step 4-5: according to a viable contract ingot grouping scheme, multiplying cost coefficients by two cost losses of material cutting loss and residual material inventory respectively, and establishing an objective function F of ingot selection and integration decision problem of the same batch 0 Specifically, as shown in formula (8):
wherein c kp Is the material cutting loss when the ingot k uses the ingot combination scheme p, alpha is the material cutting loss cost coefficient, O i The number of plate briquettes exceeding the requirement of the production contract i is the number of the surplus materials with the same alloy and the same specification as the production contract i, and beta is the inventory cost coefficient caused by the production of the surplus materials with unit weight;
material cutting loss c when the ingot k uses the ingot grouping scheme p kp The calculation method of (2) is shown as follows:
the production of the quantity O of the surplus materials with the same alloy and the same specification as the contract i i The calculation method of (2) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F 0 The following formula is shown:
step 5: determining an initial ingot setting scheme, inputting the initial ingot setting scheme into formulas (4) - (8), and relaxing a decision variable z k And x kp Constructing an optimal ingot group scheme selection model;
the specific method for determining the initial ingot grouping scheme comprises the following steps:
step 5-1: starting an aluminum ingot for any alternative ingot shape k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sequencing the production contracts with the matching relation with the alternative ingot shape k according to the descending order of the weight of the aluminum plates, and sorting the production contracts belonging to the production contract set N k Sequentially executing the steps 5-3 to 5-6 for each contract, and assembling ingots for all aluminum plates in each contract;
step 5-3: sequencing the started aluminum ingots according to the descending order of the weight of the assembled ingots;
step 5-4: searching the started aluminum ingots according to the sequence, if the residual weight of a certain aluminum ingot is larger than the weight of the aluminum plate in the current production contract i, executing the step 5-5, otherwise, starting a new aluminum ingot, and executing the step 5-3 again;
step 5-5: judging whether the current number of aluminum plates which are not batched in the production contract i is 0, if the current number of aluminum plates which are not batched in the production contract i is not 0, turning to the step 5-6, otherwise, finishing the ingot grouping in the production contract i, and executing the step 5-7;
step 5-6: assembling aluminum plates of the production contract i onto the searched activated aluminum ingots, subtracting 1 from the number of ungrouped aluminum plates of the production contract i, and re-executing the step 5-4;
step 5-7: recording ingot shapes of all enabled aluminum ingots, production contracts of group ingots on the aluminum ingots and the corresponding aluminum plate numbers; each enabled aluminum ingot is a feasible ingot grouping scheme, and repeated ingot grouping schemes are deleted to obtain an initial ingot grouping scheme;
step 6: solving an optimal ingot group scheme selection model; for each alternative ingot type, obtaining a shadow price of a corresponding constraint, taking the shadow price as input, constructing a new ingot grouping scheme generation model and solving, adding the new ingot grouping scheme meeting a high-quality ingot grouping scheme test criterion into an optimal ingot grouping scheme selection model, determining whether an ungenerated high-quality ingot grouping scheme exists based on the high-quality ingot grouping scheme test criterion, turning to the step 7 if the ungenerated high-quality ingot grouping scheme does not exist for any alternative ingot type k, otherwise, generating a new high-quality ingot grouping scheme according to the high-quality ingot grouping scheme generation model, adding the optimal ingot grouping scheme selection model, and repeatedly executing the step 6;
for any alternative ingot type k, the objective function of constructing the new ingot set scheme generation model is as follows:
wherein pi i Shadow price for constraint corresponding to equation (4), θ k The shadow price of the constraint corresponding to the formula (5) is calculated, and sigma is the shadow price of the constraint corresponding to the formula (7);
meanwhile, the new ingot composition scheme generation model meets the production process constraint formula (1) and formula (2);
the solving method of the new ingot group scheme generation model comprises the following steps:
step 6-1: with alternative ingot k and production contract subset N k For input, pair set N k According to pi i /q i The values are arranged in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-th contracts; definition of decision variable x i Representing the number of aluminum plates batched onto the ingot k in the same batch; the state transition formula is:
wherein,,
representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-1 st contract; the decision set defining the number of aluminium slabs that contract i allows to batch onto ingot shape k at state v is:
step 6-3: defining an optimal function f [ i ]][v]Representing the optimal value of the corresponding objective function (12) when the total weight of aluminium sheets batched onto ingot form k from the 1 st to the i-th contract does not exceed v, for any contract i=1 k Total weight v=1, the term, Q of aluminum plates batched onto ingot type k k Calculating the corresponding optimal function f [ i ] according to the formula (15)][v]；
Step 6-4: f|N calculated according to formula (15) k |][Q k ]I.e. the optimal value of the objective function (12); if f [ |N k |][Q k ]Not less than 0, indicating that a high-quality ingot group scheme cannot be generated; otherwise, for any i=1,., |n k |，v＝1，...，Q k If f [ i ]][v]< 0, then the corresponding (x) is back-deduced according to equation (15) i ，x i-1 ，x 1 ) Take the value of a, let a 1kp ＝x 1 ，...，a i-1，kp ＝x i-1 ，a ikp ＝x i ，
The corresponding high-quality ingot assembly scheme can be obtained;
step 7: substituting all the initial ingot assembling schemes and the high-quality ingot assembling schemes generated in the step 5 and the step 6 into a constraint formula (4) of the specification parameters of the production contract products- (8) while ensuring the decision variable z k And x kp Solving the formulas (4) - (8) to obtain the optimal combination of the high-quality ingot group schemes, converting the optimal combination of the high-quality ingot group schemes into a production instruction of the continuous casting process, and issuing the production instruction to a production workshop to execute production.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: the ingot type selection and batch integration optimization method for the aluminum industry provided by the invention not only can assist production managers to grasp the batch of customer contracts from the common view of process quality design and production organization arrangement, but also can select the ingot type according to the batch result; and the matching relation between the customer contract and the ingot model can be straightened, and effective support is provided for the ingot model selection and the integration optimization of the same batch. The ingot type selection and batch integration optimization method for the aluminum industry can balance the capacity distribution between smelting and continuous casting units, and can finish all orders by using the predetermined alternative ingot types, so that the resetting times of crystallizer parameters can be greatly reduced, the production time is shortened, the utilization rate of equipment is improved, and the production cost is reduced.
Drawings
FIG. 1 is a flow chart of an integrated optimization method for ingot type selection and co-batch for the aluminum industry provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a production decision process for ingot type selection and integrated optimization of the same batch in the aluminum industry according to an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
In this embodiment, an ingot type selection and batch-to-batch integrated optimization method for aluminum industry, as shown in fig. 1, includes the following steps:
step 1: product specification parameter information in an aluminum enterprise historical production contract and specification parameter information of an alternative ingot matched with the historical production contract are obtained, and clustering treatment is carried out on the information to obtain a classifier, wherein the specific method comprises the following steps:
step 1-1: acquiring product specification parameter information in a historical production contract;
the product specification parameters in the historical production contract include a contract preferred alloy series, an alternative alloy series, a contract delivery period, a contract delivery type, a contract status, a number of aluminum plate orders, an aluminum plate under-gauge number, an aluminum plate order thickness, an aluminum plate order maximum width, an aluminum plate order minimum width, an aluminum plate order maximum length, an aluminum plate order minimum length, an aluminum plate order maximum weight, and an aluminum plate order minimum weight;
step 1-2: acquiring a set of alternative ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of alternative ingot types, and each alternative ingot type specification parameter information comprises an alloy type, thickness, width and weight;
step 1-3: clustering the acquired product specification parameter information in the historical production contract and specification parameter information of an alternative ingot matched with the historical production contract, and clustering contracts with the same alloy type, the same delivery period and the same thickness to obtain a classifier;
the classifier has the functions of: when the product specification parameter of a certain production contract is input, determining an alternative ingot type information set matched with the production contract by the classifier;
step 2: obtaining product specification parameter information of a current production contract of an aluminum enterprise, inputting the product specification parameter information into the classifier obtained in the step 1, and determining an alternative ingot shape matched with the current production contract, wherein the specific method comprises the following steps of:
step 2-1: acquiring product specification parameter information of a current production contract;
step 2-2: inputting product specification parameter information of the current production contract into the classifier obtained in the step 1, and determining a specification parameter information set of an alternative ingot type matched with the current production contract;
step 3: according to the specification parameters of the alternative ingot type and the specification parameters of the current production contract and the smelting and continuous casting production process rules determined in the step 2, the matching relationship between the current production contract and the alternative ingot type is determined, specifically:
relationship one: the first-selected alloy series of the production contract i is the same as the alloy series of the ingot type k or one of the alternative alloy series of the production contract i is the same as the alloy series of the ingot type k, and the production contract i is matched with the ingot type k;
relationship II: the weight of the aluminum plate of the production contract i is smaller than that of the ingot type k, and the production contract i is matched with the ingot type k;
relationship III: the width of the aluminum plate of the production contract i is smaller than the width of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship four: the thickness of the aluminum plate of the production contract i is smaller than that of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship five: the difference value of the width of the aluminum plate of the production contract i and the width of the ingot type k is within the range of a maximum width difference threshold epsilon allowed by the process, and epsilon is more than 0, and the production contract i is matched with the ingot type k;
relationship six: the difference value between the thickness of the aluminum plate in the production contract i and the thickness of the ingot type k is within the range of a maximum thickness difference threshold value delta allowed by the process, and delta is more than 0, and the production contract i is matched with the ingot type k;
step 4: according to the product specification parameter information of the current production contract and the specification parameter information of the alternative ingot type matched with the production contract in phase, on the premise of meeting the batch process constraint, establishing a mathematical model to quantitatively describe the ingot type selection and contract batch integrated decision problem, wherein the method comprises the following steps:
step 4-1: for any alternative ingot type K, K epsilon K, K is a set of alternative ingot types, and all production contract sets N matched with the alternative ingot types are obtained according to the matching relation between the production contracts determined in the step 3 and the alternative ingot types k ＝{i∈N|m ik =1 }, where N represents the set of all production contracts, m ik Is a binary parameter, when m ik When=1, it means that the production contract i matches the ingot k, when m ik When=0, it means that the production contract i does not match the ingot k;
step 4-2: for any alternative ingot shape k, matching the ingot shape determined according to step 4-1Production contract set N k Determining a feasible production and same ingot combination scheme set P of ingot k k The method comprises the steps of carrying out a first treatment on the surface of the The feasible contract ingot combination scheme set P of the ingot k k Any feasible contract ingot grouping scheme P epsilon P k From n-dimensional vector a 1kp ，a 2kp ，...，a nkp Description in which arbitrary component a ikp The feasible contract ingot grouping scheme p representing the ingot k is the number of aluminum plates produced by the contract i, i epsilon N k The following process constraints need to be satisfied, as shown in equation (1), equation (2) and equation (3):
wherein q i Represents the weight of the single aluminum plate producing contract i, d i Represents the number of aluminum plates required by production contract i, Q k Representing the weight of the candidate ingot form k;
step 4-3: all possible contract ingot combination scheme sets P= U-shaped gate according to all the ingot type possible contract ingot combination schemes determined in the step 4-2 k∈K P k Mapping ingot type selection and feasible contract ingot group scheme selection into mathematical model decision variables, wherein the decision variables comprise:
1) Setting a decision variable z of 0-1 k When selecting ingot type k for production, z k Take a value of 1, otherwise z k The value is 0;
2) Setting an integer variable x kp Representing a viable contract ingot grouping scheme P epsilon P k The number of uses of (2);
step 4-4: according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot grouping scheme set determined in the step 4-2, a production contract product specification parameter constraint is established, and the method specifically comprises the following steps:
step 4-4-1: establishing a process constraint that the total quantity of each contract product produced by an aluminum enterprise meets the customer contract or generates the surplus product, namely that the total quantity of each contract product produced by the aluminum enterprise meets at least the demand of the customer contract product, wherein the part exceeding the demand of the order is temporarily stored in a warehouse area as the surplus product and sold to future customer contracts, and the method is specifically shown as a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used in the production contract and the selected alternative ingot types, namely allowing the ingot type ingot grouping scheme to be used only when a certain ingot type is selected, wherein the ingot type ingot grouping scheme is specifically shown as a formula (5):
wherein, for any alternative ingot k, M k Is constant, the size is the predicted value of the number of aluminum ingots used by the alternative ingot k, and the value of z is ensured k 0, arbitrary x kp Is 0, when z k Is 1, there is x kp Greater than 0, as specifically shown in equation (6):
step 4-4-3: the number constraint of the alternative ingot types selected by the aluminum enterprise to complete the production contract is established, and the number constraint is specifically shown as a formula (7):
wherein l is a constant, the value of which is the number of candidate ingot types selected from a library of candidate ingot types for producing the contract product;
step 4-5: according to the feasibilityThe method comprises the steps of combining ingot solutions, multiplying two cost losses of material cutting loss and residual material stock by penalty coefficients respectively, and establishing an objective function F of an ingot selection and combined batch integration decision problem 0 Specifically, as shown in formula (8):
wherein c kp Is the material cutting loss when the ingot k uses the ingot combination scheme p, alpha is the material cutting loss cost coefficient, O i The number of plate billets exceeding the demand of the production contract i, namely the number of residual materials with the same alloy and the same specification as the production contract i, and beta is the inventory cost coefficient caused by the production of residual materials with unit weight.
Material cutting loss c when the ingot k uses the ingot grouping scheme p kp The calculation method of (2) is shown as follows:
the production of the quantity O of the surplus materials with the same alloy and the same specification as the contract i i The calculation method of (2) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F 0 The following formula is shown:
step 5: determining an initial ingot setting scheme, inputting the initial ingot setting scheme into formulas (4) - (8), and relaxing a decision variable z k And x kp Constructing an optimal ingot group scheme selection model;
the specific method for determining the initial ingot grouping scheme comprises the following steps:
step 5-1: starting an aluminum ingot for any alternative ingot shape k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sequencing the production contracts with the matching relation with the alternative ingot shape k according to the descending order of the weight of the aluminum plates, and sorting the production contracts belonging to the production contract set N k Sequentially executing the steps 5-3 to 5-6 for each contract, and assembling ingots for all aluminum plates in each contract;
step 5-3: sequencing the started aluminum ingots according to the descending order of the weight of the assembled ingots;
step 5-4: searching the started aluminum ingots according to the sequence, if the residual weight of a certain aluminum ingot is larger than the weight of the aluminum plate in the current production contract i, executing the step 5-5, otherwise, starting a new aluminum ingot, and executing the step 5-3 again;
step 5-5: judging whether the current number of aluminum plates which are not batched in the production contract i is 0, if the current number of aluminum plates which are not batched in the production contract i is not 0, turning to the step 5-6, otherwise, finishing the ingot grouping in the production contract i, and executing the step 5-7;
step 5-6: assembling aluminum plates of the production contract i onto the searched activated aluminum ingots, subtracting 1 from the number of ungrouped aluminum plates of the production contract i, and re-executing the step 5-4;
step 5-7: recording ingot shapes of all enabled aluminum ingots, production contracts of group ingots on the aluminum ingots and the corresponding aluminum plate numbers; each enabled aluminum ingot is a feasible ingot grouping scheme, and repeated ingot grouping schemes are deleted to obtain an initial ingot grouping scheme;
step 6: solving an optimal ingot group scheme selection model; for each alternative ingot type, obtaining a shadow price of a corresponding constraint, taking the shadow price as input, constructing a new ingot grouping scheme generation model and solving, adding the new ingot grouping scheme meeting a high-quality ingot grouping scheme test criterion into an optimal ingot grouping scheme selection model, determining whether an ungenerated high-quality ingot grouping scheme exists based on the high-quality ingot grouping scheme test criterion, turning to the step 7 if the ungenerated high-quality ingot grouping scheme does not exist for any alternative ingot type k, otherwise, generating a new high-quality ingot grouping scheme according to the high-quality ingot grouping scheme generation model, adding the optimal ingot grouping scheme selection model, and repeatedly executing the step 6;
for any alternative ingot type k, the objective function of constructing the new ingot set scheme generation model is as follows:
wherein pi i Shadow price for constraint corresponding to equation (4), θ k The shadow price of the constraint corresponding to the formula (5) is calculated, and sigma is the shadow price of the constraint corresponding to the formula (7);
meanwhile, the new ingot composition scheme generation model meets the production process constraint formula (1) and formula (2);
the solving method of the new ingot group scheme generation model comprises the following steps:
step 6-1: with alternative ingot k and production contract subset N k For input, pair set N k According to pi i /q i The values are arranged in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-th contracts; definition of decision variable x i Representing the number of aluminum plates batched onto the ingot k in the same batch; the state transition formula is:
wherein,,
representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-1 st contract; the decision set defining the number of aluminium slabs that contract i allows to batch onto ingot shape k at state v is:
step 6-3: defining an optimal function f [ i ]][v]Representing the optimal value of the corresponding objective function (12) when the total weight of aluminium sheets batched onto ingot form k from the 1 st to the i-th contract does not exceed v, for any contract i=1 k Total weight v=1, the term, Q of aluminum plates batched onto ingot type k k Calculating the corresponding optimal function f [ i ] according to the formula (15)][v]；
Step 6-4: f|N calculated according to formula (15) k |][Q k ]I.e. the optimal value of the objective function (12); if f [ |N k |][Q k ]Not less than 0, indicating that a high-quality ingot group scheme cannot be generated; otherwise, for any i=1,., |n k |，v＝1，...，Q k If f [ i ]][v]< 0, then the corresponding (x) is back-deduced according to equation (15) i ，x i-1 ，x 1 ) Take the value of a, let a 1kp ＝x 1 ，...，a i-1，kp ＝x i-1 ，a ikp ＝x i ，
The corresponding high-quality ingot assembly scheme can be obtained.
Step 7: substituting all the initial ingot-forming schemes and the high-quality ingot-forming schemes generated in the steps 5 and 6 into the production contract product specification parameter constraint formulas (4) - (8) while ensuring the decision variable z k And x kp Solving the formulas (4) - (8) to obtain the optimal combination of the high-quality ingot assembly schemes, converting the optimal combination of the high-quality ingot assembly schemes into a production instruction of a continuous casting process, and issuing the production instruction to a production workshop to execute production as shown in fig. 2.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (6)
1. An ingot selection and batch-to-batch integrated optimization method for the aluminum industry is characterized in that: the method comprises the following steps:
step 1: obtaining product specification parameter information in an aluminum enterprise historical production contract and specification parameter information of an alternative ingot type matched with the historical production contract, and clustering the information to obtain a classifier;
the classifier has the functions of: when the product specification parameter of a certain production contract is input, determining an alternative ingot type set matched with the production contract by the classifier;
step 2: obtaining product specification parameter information of a current production contract of an aluminum enterprise, inputting the product specification parameter information into the classifier obtained in the step 1, and determining an alternative ingot shape matched with the current production contract;
step 3: determining a matching relation between the current production contract and the alternative ingot type according to the specification parameters of the alternative ingot type and the specification parameters of the current production contract and the smelting and continuous casting production technological rules determined in the step (2);
relationship one: the first-selected alloy series of the production contract i is the same as the alloy series of the ingot type k or one of the alternative alloy series of the production contract i is the same as the alloy series of the ingot type k, and the production contract i is matched with the ingot type k;
relationship II: the weight of the aluminum plate of the production contract i is smaller than that of the ingot type k, and the production contract i is matched with the ingot type k;
relationship III: the width of the aluminum plate of the production contract i is smaller than the width of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship four: the thickness of the aluminum plate of the production contract i is smaller than that of the ingot shape k, and the production contract i is matched with the ingot shape k;
relationship five: the difference value of the width of the aluminum plate of the production contract i and the width of the ingot type k is within the range of a maximum width difference threshold epsilon allowed by the process, and epsilon is more than 0, and the production contract i is matched with the ingot type k;
relationship six: the difference value between the thickness of the aluminum plate in the production contract i and the thickness of the ingot type k is within the range of a maximum thickness difference threshold delta allowed by the process, and delta is more than 0, and the production contract i is matched with the ingot type k;
step 4: according to the product specification parameter information of the current production contract and the specification parameter information of the alternative ingot type matched with the production contract in phase, establishing a mathematical model comprising decision variables and the specification parameter constraint of the production contract product on the premise of meeting the batch process constraint, and quantitatively describing the ingot type selection and the batch integration decision problem of the contract;
step 5: determining an initial ingot grouping scheme, inputting the initial ingot grouping scheme into the mathematical model established in the step 4, relaxing the integer requirement of the decision variable, and constructing an optimal ingot grouping scheme selection model;
step 6: solving an optimal ingot group scheme selection model; for each alternative ingot type, obtaining a shadow price of a corresponding constraint, taking the shadow price as input, constructing a new ingot grouping scheme generation model and solving, adding the new ingot grouping scheme meeting a high-quality ingot grouping scheme test criterion into an optimal ingot grouping scheme selection model, determining whether an ungenerated high-quality ingot grouping scheme exists based on the high-quality ingot grouping scheme test criterion, turning to the step 7 if the ungenerated high-quality ingot grouping scheme does not exist for any alternative ingot type k, otherwise, generating a new high-quality ingot grouping scheme according to the high-quality ingot grouping scheme generation model, adding the optimal ingot grouping scheme selection model, and repeatedly executing the step 6;
step 7: substituting all the initial ingot-forming schemes and the high-quality ingot-forming schemes generated in the step 5 and the step 6 into the mathematical model established in the step 4, simultaneously ensuring the integer requirement of decision variables, solving the mathematical model to obtain the optimal combination of the high-quality ingot-forming schemes, converting the optimal combination of the high-quality ingot-forming schemes into a production instruction of a continuous casting process, and transmitting the production instruction to a production workshop to perform production.
2. The method for optimizing the selection and the integration of the same batch of ingot shapes for the aluminum industry according to claim 1, which is characterized in that: the specific method of the step 1 is as follows:
step 1-1: acquiring product specification parameter information in a historical production contract;
the product specification parameters in the historical production contract include a contract preferred alloy series, an alternative alloy series, a contract delivery period, a contract delivery type, a contract status, a number of aluminum plate orders, an aluminum plate under-gauge number, an aluminum plate order thickness, an aluminum plate order maximum width, an aluminum plate order minimum width, an aluminum plate order maximum length, an aluminum plate order minimum length, an aluminum plate order maximum weight, and an aluminum plate order minimum weight;
step 1-2: acquiring a set of alternative ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of alternative ingot types, and each alternative ingot type specification parameter information comprises an alloy type, thickness, width and weight;
step 1-3: and clustering the acquired product specification parameter information in the historical production contract and specification parameter information of the alternative ingot matched with the historical production contract, and clustering the contracts with the same alloy type, the same delivery period and the same thickness to obtain the classifier.
3. The method for optimizing the selection and the integration of the same batch of ingot shapes for the aluminum industry according to claim 1, which is characterized in that: the specific method of the step 2 is as follows:
step 2-1: acquiring product specification parameter information of a current production contract;
step 2-2: inputting the product specification parameter information of the current production contract into the classifier obtained in the step 1, and determining a specification parameter information set of the alternative ingot type matched with the current production contract.
4. The integrated optimization method for ingot type selection and batch-to-batch for aluminum industry according to claim 3, wherein the method comprises the following steps: the specific method of the step 4 is as follows:
step 4-1: for any alternative ingot shape K, K epsilon K, K is the set of alternative ingot shapes, all the ingot shapes are obtained according to the matching relation between the production contract and the alternative ingot shape determined in the step 3Matched production contract set N k ＝{i∈N|m ik =1 }, where N represents the set of all production contracts, m ik Is a binary parameter, when m ik When=1, it means that the production contract i matches the ingot k, when m ik When=0, it means that the production contract i does not match the ingot k;
step 4-2: for any alternative ingot shape k, the set of production contracts N matching the ingot shape determined according to step 4-1 k Determining a feasible production and same ingot combination scheme set P of ingot k k The method comprises the steps of carrying out a first treatment on the surface of the The feasible contract ingot combination scheme set P of the ingot k k Any feasible contract ingot grouping scheme P epsilon P k From n-dimensional vector a 1kp ,a 2kp ,…,a nkp Description in which arbitrary component a ikp The feasible contract ingot grouping scheme p representing the ingot k is the number of aluminum plates produced by the contract i, i epsilon N k The following process constraints need to be satisfied, as shown in equation (1), equation (2) and equation (3):
wherein q i Represents the weight of the single aluminum plate producing contract i, d i Represents the number of aluminum plates required by production contract i, Q k Representing the weight of the candidate ingot form k;
step 4-3: all possible contract ingot combination scheme sets P= U-shaped gate according to all the ingot type possible contract ingot combination schemes determined in the step 4-2 k∈K P k Mapping ingot type selection and feasible contract ingot group scheme selection into mathematical model decision variables, wherein the decision variables comprise:
1) Setting a decision variable z of 0-1 k When selecting ingot type k for production, z k Take a value of 1, otherwise z k The value is 0;
2) Setting an integer variable x kp Representing a viable contract ingot grouping scheme P epsilon P k The number of uses of (2);
step 4-4: according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot grouping scheme set determined in the step 4-2, a production contract product specification parameter constraint is established, and the method specifically comprises the following steps:
step 4-4-1: establishing a process constraint that the total quantity of each contract product produced by an aluminum enterprise meets the customer contract or generates the surplus product, namely that the total quantity of each contract product produced by the aluminum enterprise meets at least the demand of the customer contract product, wherein the part exceeding the demand of the order is temporarily stored in a warehouse area as the surplus product and sold to future customer contracts, and the method is specifically shown as a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used in the production contract and the selected alternative ingot types, namely allowing the ingot type ingot grouping scheme to be used only when a certain ingot type is selected, wherein the ingot type ingot grouping scheme is specifically shown as a formula (5):
wherein, for any alternative ingot k, M k Is constant, the size is the predicted value of the number of aluminum ingots used by the alternative ingot k, and the value of z is ensured k 0, arbitrary x kp Is 0, when z k Is 1, there is x kp Greater than 0, as specifically shown in equation (6):
step 4-4-3: the number constraint of the alternative ingot types selected by the aluminum enterprise to complete the production contract is established, and the number constraint is specifically shown as a formula (7):
wherein l is a constant, the value of which is the number of candidate ingot types selected from a library of candidate ingot types for producing the contract product;
step 4-5: according to a viable contract ingot grouping scheme, multiplying cost coefficients by two cost losses of material cutting loss and residual material inventory respectively, and establishing an objective function F of ingot selection and integration decision problem of the same batch 0 Specifically, as shown in formula (8):
wherein c kp Is the material cutting loss when the ingot k uses the ingot combination scheme p, alpha is the material cutting loss cost coefficient, O i The number of plate briquettes exceeding the requirement of the production contract i is the number of the surplus materials with the same alloy and the same specification as the production contract i, and beta is the inventory cost coefficient caused by the production of the surplus materials with unit weight;
material cutting loss c when the ingot k uses the ingot grouping scheme p kp The calculation method of (2) is shown as follows:
the production of the quantity O of the surplus materials with the same alloy and the same specification as the contract i i The calculation method of (2) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F 0 The following formula is shown:
5. the method for optimizing the selection and the integration of the same batch of ingot shapes for the aluminum industry according to claim 4, which is characterized in that: the specific method for determining the initial ingot grouping scheme in the step 5 is as follows:
step 5-1: starting an aluminum ingot for any alternative ingot shape k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sequencing the production contracts with the matching relation with the alternative ingot shape k according to the descending order of the weight of the aluminum plates, and sorting the production contracts belonging to the production contract set N k Sequentially executing the steps 5-3 to 5-6 for each contract, and assembling ingots for all aluminum plates in each contract;
step 5-3: sequencing the started aluminum ingots according to the descending order of the weight of the assembled ingots;
step 5-4: searching the started aluminum ingots according to the sequence, if the residual weight of a certain aluminum ingot is larger than the weight of the aluminum plate in the current production contract i, executing the step 5-5, otherwise, starting a new aluminum ingot, and executing the step 5-3 again;
step 5-5: judging whether the current number of aluminum plates which are not batched in the production contract i is 0, if the current number of aluminum plates which are not batched in the production contract i is not 0, turning to the step 5-6, otherwise, finishing the ingot grouping in the production contract i, and executing the step 5-7;
step 5-6: assembling aluminum plates of the production contract i onto the searched activated aluminum ingots, subtracting 1 from the number of ungrouped aluminum plates of the production contract i, and re-executing the step 5-4;
step 5-7: recording ingot shapes of all enabled aluminum ingots, production contracts of group ingots on the aluminum ingots and the corresponding aluminum plate numbers; each enabled aluminum ingot is a viable ingot grouping scheme, and duplicate ingot grouping schemes are deleted to obtain an initial ingot grouping scheme.
6. The integrated optimization method for ingot type selection and batch-to-batch for aluminum industry according to claim 5, which is characterized in that: the objective function of the model for constructing the new ingot set scheme generation in the step 6 is as follows:
wherein pi i Shadow price for constraint corresponding to equation (4), θ k The shadow price of the constraint corresponding to the formula (5) is calculated, and sigma is the shadow price of the constraint corresponding to the formula (7);
meanwhile, the new ingot composition scheme generation model meets the production process constraint formula (1) and formula (2);
the solving method of the new ingot group scheme generation model comprises the following steps:
step 6-1: with alternative ingot k and production contract subset N k For input, pair set N k According to pi i /q i The values are arranged in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-th contracts; definition of decision variable x i Representing the number of aluminum plates batched onto the ingot k in the same batch; the state transition formula is:
wherein,,
representing the total weight of aluminum sheets that have been batched onto ingot type k from the 1 st to the i-1 st contract; the decision set defining the number of aluminium slabs that contract i allows to batch onto ingot shape k at state v is:
step 6-3: defining an optimal function f [ i ]][v]Represents the optimum value of the corresponding objective function (12) for the total weight of aluminium sheets batched onto ingot form k from 1 st to i th to not exceed v, for any contract i=1, …, |n k Total weight v=1, …, Q of aluminum plates batched onto ingot k k Calculating the corresponding optimal function f [ i ] according to the formula (15)][v]；
Step 6-4: f|N calculated according to formula (15) k |][Q k ]I.e. the optimal value of the objective function (12); if f [ |N k |][Q k ]Not less than 0, indicating that a high-quality ingot group scheme cannot be generated; otherwise, for any i=1, …, |n k |，v＝1,…,Q k If f [ i ]][v]<0, then the corresponding (x) is back-deduced according to equation (15) i ,x i-1 ,x 1 ) Take the value of a, let a 1kp ＝x 1 ,…,a i-1,kp ＝x i-1 ,a ikp ＝x i ,a i+1,kp ＝0,…,
The corresponding high-quality ingot assembly scheme can be obtained.
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| 考虑订单组批特性的特种铝锭组炉优化;张浩 等;《控制理论与应用》;第36卷(第10期);第1-8页 * |
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