CN111062571A - Ingot type selection and combination batch integrated optimization method for aluminum industry - Google Patents
Ingot type selection and combination batch integrated optimization method for aluminum industry Download PDFInfo
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Abstract
The invention provides an ingot type selection and synthesis batch integrated optimization method for the aluminum industry, and relates to the technical field of automatic control of metallurgy. The method comprises the steps of firstly, acquiring historical production contract data of an aluminum enterprise and alternative ingot models matched with the historical production contract data, and establishing a classifier; then, acquiring 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 the ingot type selection and contract batch integration decision problems through decision variables; determining an initial ingot combination scheme, and constructing an optimal ingot combination scheme selection model; and solving the optimal ingot combination scheme selection model to obtain the optimal combination of the high-quality ingot combination schemes, converting the optimal combination of the high-quality ingot combination schemes into a production instruction of a continuous casting process, and issuing the production instruction to a production workshop to carry out production so as to realize the selection of ingot types of aluminum enterprises and the integrated optimization of the same batch.
Description
Technical Field
The invention relates to the technical field of metallurgical automatic control, in particular to an ingot type selection and combination batch integrated optimization method for the aluminum industry.
Background
An outstanding characteristic of the production flow in the aluminum industry is that the material flow continuously generates physical and chemical reactions in the process and continuously changes in state, property and shape. The aluminum alloy has light self weight and excellent mechanical property and physical property, and can replace steel materials in a plurality of application scenes. The aluminum alloy product is manufactured by melting a pure aluminum block, adding alloy components to prepare alloy liquid, casting and forming, cutting, rolling, heat treating and finish machining step by step. Therefore, the production process in the aluminum industry is a typical continuous production process, and the specific production process is as follows:
(1) the electrolytic aluminum liquid is poured into a smelting furnace through a ladle, various chemical elements are added 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 contracts, and for different alloy types, when the components of the different alloy types are greatly different, the smelting furnace needs to be washed;
(2) the aluminum alloy liquid after the proportioning is then put into a heat preservation stage, during which a crystal graining agent is added to refine grains and improve the hardness and toughness of the alloy, and degassing operation is carried out to improve the internal structure of the cast aluminum alloy;
(3) then, molten aluminum alloy liquid is transferred from a smelting furnace to a continuous casting machine, the size of a crystallizer needs to be adjusted to change the size of a mould due to the influence of the specification diversity of aluminum ingots, and then the molten aluminum alloy liquid is injected into the mould to be cast and molded to form the aluminum ingots;
(4) the aluminum ingots produced by the continuous casting machine have the characteristics of large-scale and batch production, and before rolling, the aluminum ingots are usually cut into sub-ingots according to the same batch rule, and then the sub-ingots are rolled into aluminum plates with different sizes on a hot rolling mill.
In addition to the characteristic of long production flow, the production scale of the modern aluminum industry is gradually increased, and the layout of a production line has a structure of multiple units in the same process. The updating of production equipment in the aluminum industry not only improves the casting capacity of a continuous casting machine, but also correspondingly improves the rolling capacity of downstream rolling equipment, and products required by current customer contracts tend to have the characteristics of multiple varieties, small batches, multiple specifications and the like. In the traditional production mode, one product is produced by one aluminum ingot, one part of residual materials is stored in a warehouse to be used as a semi-finished product for standby, and the other part is returned to a furnace for recasting. The material of the semi-finished product part occupies the stock, causing the stock pressure, and the re-casting in the furnace increases the production cost for the material of the part. Due to the contradiction between the large-scale trend of aluminum ingots and the small-scale contract, the total amount of partial materials stored in a warehouse as semi-finished products is increased obviously. In order to reduce the influence of the contradiction and respond to the change of supply and demand relationship and improve the production efficiency of enterprises, the ingot type selection and the contract group are required to be reasonably produced and designed.
In order to make an integrated decision of ingot type selection and contract batching, the aluminum industry needs to decide which ingot type in an alternative ingot type library is selected as a standard ingot type to meet the contract requirement, and meanwhile, the batching mode is improved as follows: a standard aluminum ingot may be batched with one or more contract products. The batching decision for each aluminum ingot is referred to as a batching scheme, and the set of batching schemes used to complete the customer contract is referred to as a batching scheme.
Currently, to solve the problem of integrated optimization of ingot type selection and batch combination, enterprises generally adopt a manual scheduling method relying on the subjective experience of planners: the method is generally characterized in that after a planner qualitatively analyzes the capacity and inventory condition of each unit, the contract is matched with the ingot model according to an empirical estimation method. Because of the large amount of data involved in the actual production, many and complicated production process factors need to be considered, and the following problems exist by adopting the manual production scheduling:
(1) the planners have subjectivity in manual production scheduling, and can sequence all contracts according to the past experience level to make a feasible scheme, so that the result is unstable;
(2) the manual scheduling is a serial decision, a planner can select an ingot type matched with a contract by using a serial sequential strategy, the serial sequential strategy has extremely short visibility from the optimization perspective, the contract and the ingot type are matched each time only by considering the current optimization performance, so that the utilization rate of the front material is high, the later contract is difficult to be matched with the ingot type, and the utilization rate is extremely low;
(3) the large amount of production data information cannot be considered completely during manual production scheduling, a method of classifying according to data attributes is generally adopted for rough statistics and then considered partially, the details of most data information are covered by a simple data classification statistical method, and the overall optimization of ingot type selection and a same batch is directly reduced due to incomplete information consideration.
Therefore, by analyzing the production process of the aluminum enterprise, the ingot type selection and the contract batch in the aluminum industry are integrated and optimized on the premise of ensuring the contract production quality and the process constraint of a client, and the method has very important significance for optimizing the production process and the product quality design level of the aluminum industry, improving the production efficiency of the enterprise and reducing the production cost.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art, and provides an ingot type selection and contract batch integration optimization method for the aluminum industry, so that the ingot type selection and contract batch integration decision is realized, the material utilization rate of an aluminum enterprise is improved, the inventory pressure is reduced, the production efficiency is improved, and the production cost is reduced.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an ingot type selection and contract batch integrated optimization method for the aluminum industry comprises the following steps:
step 1: the method comprises the following steps of obtaining product specification parameter information in historical production contracts of aluminum enterprises and specification parameter information of alternative ingot types matched with the historical production contracts, and clustering 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 comprise a preferred alloy series of the contract, a candidate alloy series, a contract delivery date, a contract delivery type, a contract state, an aluminum plate ordering block number, an aluminum plate shortage block number, an aluminum plate ordering thickness, an aluminum plate ordering maximum width, an aluminum plate ordering minimum width, an aluminum plate ordering maximum length, an aluminum plate ordering minimum length, an aluminum plate ordering maximum weight and an aluminum plate ordering minimum weight;
step 1-2: acquiring a set of candidate ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of candidate ingot types, and each candidate ingot type specification parameter information comprises an alloy type, a thickness, a width and a weight;
step 1-3: clustering the obtained product specification parameter information in the historical production contract and the specification parameter information of the alternative ingot type matched with the historical production contract, and clustering the contracts with the same shape and alloy type, the same delivery date and the same thickness to obtain a classifier;
the classifier has the following functions: when the product specification parameters of a certain production contract are input, determining an alternative ingot type set matched with the production contract by the classifier;
step 2: acquiring 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 type matched with the current production contract, wherein the specific method comprises the following steps:
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 the specification parameter information set of the alternative ingot type matched with the current production contract;
and step 3: according to the specification parameters of the alternative ingot mold and the specification parameters of the current production contract determined in the step 2 and the smelting and continuous casting production process rules, determining the matching relationship between the current production contract and the alternative ingot mold, which specifically comprises the following steps:
relationship one: the first 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 called to be matched with the ingot type k;
the second relation: if the weight of the aluminum plate in the production contract i is less than that of the ingot type k, the production contract i is called to be matched with the ingot type k;
relationship three: the width of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is four: the thickness of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is five: the width difference value of the aluminum plate of the production contract i and the width difference value of the ingot type k is within the range of the maximum width difference threshold epsilon allowed by the process, and if epsilon is more than 0, the production contract i is called to be matched with the ingot type k;
the relationship six: the thickness difference value of the aluminum plate of the production contract i and the thickness difference value of the ingot type k is within the maximum thickness difference threshold value delta range allowed by the process, and if delta is greater than 0, the production contract i is called to be matched with the ingot type k;
and 4, step 4: according to the product specification parameter information of the current production contract and the specification parameter information of the alternative ingot mold matched with the production contract, on the premise of meeting the batching process constraint, a mathematical model is established to quantitatively describe the ingot mold selection and contract batching integrated decision problem, and the specific method is as follows:
step 4-1: for any alternative ingot type K, K belongs to K, K is the set of alternative ingot types, and all production contract sets N matched with the ingot types are obtained according to the matching relation between the production contract determined in the step 3 and the alternative ingot typesk＝{i∈N|mik1, where N represents the set of all production contracts, mikIs a binary parameter when mikWhen 1, the production contract i is matched with the ingot type k, and when m isikWhen the value is 0, the production contract i is not matched with the ingot type k;
step 4-2: for any alternative ingot type k, according to the production contract set N matched with the ingot type determined in the step 4-1kDetermining feasible production of ingot type k and ingot scheme set Pk(ii) a The feasible combined ingot scheme set P of the ingot type kkAny feasible combined ingot combination scheme P belongs to PkFrom n-dimensional vector a1kp，a2kp，...，ankpDescription of any component a thereinikpThe number of aluminum plates produced by contract i according to the feasible contract ingot combination scheme p of the ingot type k is shown, i belongs to NkThe following process constraints need to be satisfied, as shown in equations (1), (2) and (3):
wherein q isiWeight of a single aluminum plate representing production contract i, diNumber of aluminum plates, Q, required for production contract ikRepresents the weight of the alternative ingot type k;
step 4-3, determining a feasible combined ingot scheme set P of all ingot types according to the step 4-2, wherein the set P is ∪k∈KPkAnd mapping the ingot type selection and the feasible combined ingot scheme selection as a mathematical model decision variable, wherein the decision variable comprises:
1) setting a decision variable z of 0-1kWhen ingot type k is selected for production, zkValue is 1, otherwise zkThe value is 0;
2) setting an integer variable xkpAnd representing that the feasible ingot combination scheme P is belonged to PkThe number of uses of (2);
step 4-4: establishing the constraint of the production contract product specification parameters according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot combination scheme set determined in the step 4-2, which is specifically as follows:
step 4-4-1: establishing a production contract in which the total amount of each contract product produced by the aluminum enterprise is required to meet the customer contract or produce the extra product, namely, the total amount of each contract product produced by the aluminum enterprise at least meets the product demand of the customer contract, and the part exceeding the demand of the order is temporarily stored in a storage area as the extra material and sold to a future customer, as shown in a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used by the production contract and the selected alternative ingot type, namely, only when a certain ingot type is selected, the ingot grouping scheme of the ingot type is allowed to be used, as shown in formula (5):
wherein, for any alternative ingot type k, MkIs a constant, is an estimated value of the number of aluminum ingots used in the alternative ingot type k, and is guaranteed when z iskIs 0, arbitrary xkpIs 0 when z iskIs 1, there is xkpGreater than 0, as shown in equation (6):
step 4-4-3: establishing the quantity constraint of alternative ingot types selected by the aluminum enterprise to complete the production contract, which is specifically shown as a formula (7):
wherein, l is a constant, and the value of l is the number of the alternative ingot models which are selected from the alternative ingot model library and used for producing contract products;
and 4-5: according to the feasible ingot combination scheme, the cost losses of the material cutting loss and the residual material inventory are respectively multiplied by a cost coefficient, and an objective function F of an integrated decision problem of ingot type selection and combination batch is established0Specifically, as shown in formula (8):
wherein, ckpIs the amount of material loss when ingot type k uses the ingot-grouping scheme p, α is the material loss cost coefficient, OiThe number of the plate blank blocks exceeding the requirement of the production contract i, namely the number of the produced surplus materials with the same alloy and the same specification as those of the production contract i, and β is a stock cost coefficient brought by the surplus materials with the unit weight;
the ingot type k uses ingot forming methodCutting loss of material c in case of pattern pkpThe calculation method of (a) is shown as follows:
producing the residual material quantity O with the same alloy and the same specification as the contract iiThe calculation method of (a) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F0As shown in the following equation:
and 5: determining an initial ingot combination scheme, inputting the initial ingot combination scheme into formulas (4) - (8), and relaxing a decision variable zkAnd xkpConstructing an optimal ingot-combination scheme selection model according to the integer requirement;
the specific method for determining the initial ingot forming scheme comprises the following steps:
step 5-1: starting an aluminum ingot for any alternative ingot type k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sorting the production contracts which can be matched with the alternative ingot types k according to the descending order of the weight of the aluminum plate, and collecting N which belongs to the production contract setkStep 5-3 to step 5-6 are sequentially executed for each contract, and ingot assembly is carried out on all aluminum plates in each contract;
step 5-3: sorting the started aluminum ingots according to the descending order of the weights of the grouped ingots;
step 5-4: searching the started aluminum ingots in sequence, if the residual weight of a certain aluminum ingot is greater 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 number of the aluminum plates which are not batched currently in the production contract i is 0, if the remaining number is not 0, turning to the step 5-6, otherwise, finishing ingot grouping in the production contract i when the aluminum plates in the production contract i are already grouped, and executing the step 5-7;
and 5-6: c, putting the aluminum plate ingots of the production contract i on the searched started aluminum ingots, reducing the number of the aluminum plates which are not batched of the production contract i by 1, and re-executing the step 5-4;
and 5-7: recording ingot types of all started aluminum ingots, production contracts of ingot groups on the aluminum ingots and the number of corresponding aluminum plates; each started aluminum ingot is a feasible ingot combination scheme, and a repeated ingot combination scheme is deleted to obtain an initial ingot combination scheme;
step 6: solving an optimal ingot combination scheme selection model; for each alternative ingot type, obtaining a shadow price corresponding to constraint of each alternative ingot type, taking the shadow price as input, constructing a new ingot combination scheme generation model and solving the shadow price, then adding a new ingot combination scheme meeting the high-quality ingot combination scheme test criterion into an optimal ingot combination scheme selection model, determining whether an unformed high-quality ingot combination scheme exists or not based on the high-quality ingot combination scheme test criterion, if any alternative ingot type k does not have the unformed high-quality ingot combination scheme, turning to the step 7, otherwise, generating a new high-quality ingot combination scheme according to the high-quality ingot combination scheme generation model and adding the optimal ingot combination scheme selection model, and repeatedly executing the step 6;
for any alternative ingot type k, the objective function of the new ingot combination scheme generation model is as follows:
wherein, piiShadow price, θ, for the corresponding constraint of equation (4)kThe price is the shadow price of the corresponding constraint of the formula (5), and the sigma is the shadow price of the corresponding constraint of the formula (7);
meanwhile, the new ingot scheme generation model meets the production process constraint formula (1) and the production process constraint formula (2);
the solving method of the new ingot scheme generation model comprises the following steps:
step 6-1: in preparation forIngot selection type k and production contract subset NkFor input, set NkAll contracts in pii/qiSorting the values in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched from 1 st to i th contract onto ingot type k; defining a decision variable xiRepresenting the number of aluminum plates of the ith batch on the ingot type k; the state transition formula is:
wherein the content of the first and second substances,
represents the total weight of aluminum sheets that have been batched to ingot type k from contract 1 to contract i-1; the decision set defining the number of aluminum slabs allowed to be batched to ingot type k under contract i at state v is:
step 6-3: defining an optimal function f [ i ]][v]Represents the optimal value of the corresponding objective function (12) when the total weight of the aluminum plates from the 1 st to the ith contract batch to the ingot type k does not exceed v, and the sum of the values of the objective function and the corresponding objective function is 1kQ, the total weight v of the aluminum plates batched onto the ingot k is 1kCalculating the corresponding optimal function f [ i ] according to equation (15)][v]；
Step 6-4: f [ | N calculated according to the formula (15)k|][Qk]Is the optimal value of the objective function (12); if f [ | Nk|][Qk]If the number is more than or equal to 0, indicating that a high-quality ingot forming scheme cannot be generated; otherwise, for any i ═ 1., | Nk|，v＝1，...，QkIf f [ i ]][v]If < 0, the corresponding (x) is deduced reversely according to the formula (15)i，xi-1，x1) Value ofLet a1kp＝x1，...，ai-1，kp＝xi-1，aikp＝xi，
Obtaining a corresponding high-quality ingot forming scheme;
and 7: all the initial ingot combination schemes and the high-quality ingot combination schemes generated in the steps 5 and 6 are substituted into production contract product specification parameter constraint formulas (4) - (8), and meanwhile, a decision variable z is ensuredkAnd xkpSolving the equations (4) - (8) to obtain the optimal combination of the high-quality ingot combining schemes, converting the optimal combination of the high-quality ingot combining schemes into a production instruction of a continuous casting process, and sending the production instruction to a production workshop to execute production.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the ingot type selection and contract batch integration optimization method for the aluminum industry, provided by the invention, can assist production managers to master batch of customer contracts from a common view point of process quality design and production organization arrangement, and perform ingot type selection according to batch results; but also can straighten the matching relation between the customer contract and the ingot model, and provides effective support for the selection of the ingot model and the integrated optimization of the contract batch. The ingot type selection and integrated batch optimization method for the aluminum industry can balance the capacity allocation between the smelting unit and the continuous casting unit, complete all orders by using the predetermined alternative ingot types, and greatly reduce the resetting times of the crystallizer parameters, thereby reducing the production time, improving the utilization rate of equipment and reducing the production cost.
Drawings
Fig. 1 is a flowchart of an ingot type selection and contract lot integrated optimization method for the aluminum industry according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a production decision process for ingot type selection and integrated optimization of a contract lot in the aluminum industry according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, an integrated optimization method for ingot type selection and contract batch oriented to the aluminum industry, as shown in fig. 1, includes the following steps:
step 1: the method comprises the following steps of obtaining product specification parameter information in historical production contracts of aluminum enterprises and specification parameter information of alternative ingot types matched with the historical production contracts, and clustering 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 comprise a preferred alloy series of the contract, a candidate alloy series, a contract delivery date, a contract delivery type, a contract state, an aluminum plate ordering block number, an aluminum plate shortage block number, an aluminum plate ordering thickness, an aluminum plate ordering maximum width, an aluminum plate ordering minimum width, an aluminum plate ordering maximum length, an aluminum plate ordering minimum length, an aluminum plate ordering maximum weight and an aluminum plate ordering minimum weight;
step 1-2: acquiring a set of candidate ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of candidate ingot types, and each candidate ingot type specification parameter information comprises an alloy type, a thickness, a width and a weight;
step 1-3: clustering the obtained product specification parameter information in the historical production contract and the specification parameter information of the alternative ingot type matched with the historical production contract, and clustering the contracts with the same shape and alloy type, the same delivery date and the same thickness to obtain a classifier;
the classifier has the following functions: when the product specification parameters of a certain production contract are input, determining an alternative ingot type information set matched with the production contract by the classifier;
step 2: acquiring 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 type matched with the current production contract, wherein the specific method comprises the following steps:
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 the specification parameter information set of the alternative ingot type matched with the current production contract;
and step 3: according to the specification parameters of the alternative ingot mold and the specification parameters of the current production contract determined in the step 2 and the smelting and continuous casting production process rules, determining the matching relationship between the current production contract and the alternative ingot mold, which specifically comprises the following steps:
relationship one: the first 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 called to be matched with the ingot type k;
the second relation: if the weight of the aluminum plate in the production contract i is less than that of the ingot type k, the production contract i is called to be matched with the ingot type k;
relationship three: the width of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is four: the thickness of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is five: the width difference value of the aluminum plate of the production contract i and the width difference value of the ingot type k is within the range of the maximum width difference threshold epsilon allowed by the process, and if epsilon is more than 0, the production contract i is called to be matched with the ingot type k;
the relationship six: the thickness difference value of the aluminum plate of the production contract i and the thickness difference value of the ingot type k is within the maximum thickness difference threshold value delta range allowed by the process, and if delta is greater than 0, the production contract i is called to be matched with the ingot type k;
and 4, step 4: according to the product specification parameter information of the current production contract and the specification parameter information of the alternative ingot mold matched with the production contract, on the premise of meeting the batching process constraint, a mathematical model is established to quantitatively describe the ingot mold selection and contract batching integrated decision problem, and the specific method is as follows:
step 4-1: determining any alternative ingot type K, K belongs to K, K is the set of alternative ingot types according to the step 3The matching relation between the determined production contract and the alternative ingot type obtains all the production contract sets N matched with the ingot typek＝{i∈N|mik1, where N represents the set of all production contracts, mikIs a binary parameter when mikWhen 1, the production contract i is matched with the ingot type k, and when m isikWhen the value is 0, the production contract i is not matched with the ingot type k;
step 4-2: for any alternative ingot type k, according to the production contract set N matched with the ingot type determined in the step 4-1kDetermining feasible production of ingot type k and ingot scheme set Pk(ii) a The feasible combined ingot scheme set P of the ingot type kkAny feasible combined ingot combination scheme P belongs to PkFrom n-dimensional vector a1kp，a2kp，...，ankpDescription of any component a thereinikpThe number of aluminum plates produced by contract i according to the feasible contract ingot combination scheme p of the ingot type k is shown, i belongs to NkThe following process constraints need to be satisfied, as shown in equations (1), (2) and (3):
wherein q isiWeight of a single aluminum plate representing production contract i, diNumber of aluminum plates, Q, required for production contract ikRepresents the weight of the alternative ingot type k;
step 4-3, determining a feasible combined ingot scheme set P of all ingot types according to the step 4-2, wherein the set P is ∪k∈KPkAnd mapping the ingot type selection and the feasible combined ingot scheme selection as a mathematical model decision variable, wherein the decision variable comprises:
1) setting a decision variable z of 0-1kWhen the ingot type k is selected for production,zkvalue is 1, otherwise zkThe value is 0;
2) setting an integer variable xkpAnd representing that the feasible ingot combination scheme P is belonged to PkThe number of uses of (2);
step 4-4: establishing the constraint of the production contract product specification parameters according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot combination scheme set determined in the step 4-2, which is specifically as follows:
step 4-4-1: establishing the total amount of each contract product produced by the aluminum enterprise to meet the process constraint of a customer contract or generating a residual material product, namely, the total amount of each contract product produced by the aluminum enterprise at least meets the product demand of the customer contract, and the part exceeding the demand of an order is temporarily stored in a library area as the residual material and sold to a future customer contract, as shown in a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used by the production contract and the selected alternative ingot type, namely, only when a certain ingot type is selected, the ingot grouping scheme of the ingot type is allowed to be used, as shown in formula (5):
wherein, for any alternative ingot type k, MkIs a constant, is an estimated value of the number of aluminum ingots used in the alternative ingot type k, and is guaranteed when z iskIs 0, arbitrary xkpIs 0 when z iskIs 1, there is xkpGreater than 0, as shown in equation (6):
step 4-4-3: establishing the quantity constraint of alternative ingot types selected by the aluminum enterprise to complete the production contract, which is specifically shown as a formula (7):
wherein, l is a constant, and the value of l is the number of the alternative ingot models which are selected from the alternative ingot model library and used for producing contract products;
and 4-5: according to the feasible ingot combination scheme, the two cost losses of material cutting loss and residual material inventory are respectively multiplied by penalty coefficients, and an objective function F of an integrated decision problem of ingot type selection and combination batch is established0Specifically, as shown in formula (8):
wherein, ckpIs the amount of material loss when ingot type k uses the ingot-grouping scheme p, α is the material loss cost coefficient, OiIs the number of slab pieces exceeding the requirement of the production contract i, i.e., the number of remainders produced with the same alloy and the same specification as those of the contract i, and β is the inventory cost coefficient due to the unit weight of the remainders produced.
Material loss c when ingot type k uses ingot combination scheme pkpThe calculation method of (a) is shown as follows:
producing the residual material quantity O with the same alloy and the same specification as the contract iiThe calculation method of (a) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F0As shown in the following equation:
and 5: determining an initial ingot-forming scheme, and forming the initial ingot-forming schemeInputting equations (4) - (8), relaxation decision variable zkAnd xkpConstructing an optimal ingot-combination scheme selection model according to the integer requirement;
the specific method for determining the initial ingot forming scheme comprises the following steps:
step 5-1: starting an aluminum ingot for any alternative ingot type k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sorting the production contracts which can be matched with the alternative ingot types k according to the descending order of the weight of the aluminum plate, and collecting N which belongs to the production contract setkStep 5-3 to step 5-6 are sequentially executed for each contract, and ingot assembly is carried out on all aluminum plates in each contract;
step 5-3: sorting the started aluminum ingots according to the descending order of the weights of the grouped ingots;
step 5-4: searching the started aluminum ingots in sequence, if the residual weight of a certain aluminum ingot is greater 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 number of the aluminum plates which are not batched currently in the production contract i is 0, if the remaining number is not 0, turning to the step 5-6, otherwise, finishing ingot grouping in the production contract i when the aluminum plates in the production contract i are already grouped, and executing the step 5-7;
and 5-6: c, putting the aluminum plate ingots of the production contract i on the searched started aluminum ingots, reducing the number of the aluminum plates which are not batched of the production contract i by 1, and re-executing the step 5-4;
and 5-7: recording ingot types of all started aluminum ingots, production contracts of ingot groups on the aluminum ingots and the number of corresponding aluminum plates; each started aluminum ingot is a feasible ingot combination scheme, and a repeated ingot combination scheme is deleted to obtain an initial ingot combination scheme;
step 6: solving an optimal ingot combination scheme selection model; for each alternative ingot type, obtaining a shadow price corresponding to constraint of each alternative ingot type, taking the shadow price as input, constructing a new ingot combination scheme generation model and solving the shadow price, then adding a new ingot combination scheme meeting the high-quality ingot combination scheme test criterion into an optimal ingot combination scheme selection model, determining whether an unformed high-quality ingot combination scheme exists or not based on the high-quality ingot combination scheme test criterion, if any alternative ingot type k does not have the unformed high-quality ingot combination scheme, turning to the step 7, otherwise, generating a new high-quality ingot combination scheme according to the high-quality ingot combination scheme generation model and adding the optimal ingot combination scheme selection model, and repeatedly executing the step 6;
for any alternative ingot type k, the objective function of the new ingot combination scheme generation model is as follows:
wherein, piiShadow price, θ, for the corresponding constraint of equation (4)kThe price is the shadow price of the corresponding constraint of the formula (5), and the sigma is the shadow price of the corresponding constraint of the formula (7);
meanwhile, the new ingot scheme generation model meets the production process constraint formula (1) and the production process constraint formula (2);
the solving method of the new ingot scheme generation model comprises the following steps:
step 6-1: with alternative ingot type k and production contract subset NkFor input, set NkAll contracts in pii/qiArranging the values in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched from 1 st to i th contract onto ingot type k; defining a decision variable xiRepresenting the number of aluminum plates of the ith batch on the ingot type k; the state transition formula is:
wherein the content of the first and second substances,
represents the total weight of aluminum sheets that have been batched to ingot type k from contract 1 to contract i-1; the decision set defining the number of aluminum slabs allowed to be batched to ingot type k under contract i at state v is:
step 6-3: defining an optimal function f [ i ]][v]Represents the optimal value of the corresponding objective function (12) when the total weight of the aluminum plates from the 1 st to the ith contract batch to the ingot type k does not exceed v, and the sum of the values of the objective function and the corresponding objective function is 1kQ, the total weight v of the aluminum plates batched onto the ingot k is 1kCalculating the corresponding optimal function f [ i ] according to equation (15)][v]；
Step 6-4: f [ | N calculated according to the formula (15)k|][Qk]Is the optimal value of the objective function (12); if f [ | Nk|][Qk]If the number is more than or equal to 0, indicating that a high-quality ingot forming scheme cannot be generated; otherwise, for any i ═ 1., | Nk|，v＝1，...，QkIf f [ i ]][v]If < 0, the corresponding (x) is deduced reversely according to the formula (15)i，xi-1，x1) Is taken as value of a1kp＝x1，...，ai-1，kp＝xi-1，aikp＝xi，
Thus obtaining the corresponding high-quality ingot-forming scheme.
And 7: all the initial ingot combination schemes and the high-quality ingot combination schemes generated in the steps 5 and 6 are substituted into production contract product specification parameter constraint formulas (4) - (8), and meanwhile, a decision variable z is ensuredkAnd xkpSolving equations (4) - (8) to obtain the optimal combination of the high-quality ingot combining schemes, as shown in fig. 2, converting the optimal combination of the high-quality ingot combining schemes into a production instruction of a continuous casting process, and sending the production instruction to a production workshop to execute production.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present 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 solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (7)
1. An ingot type selection and combination batch integrated optimization method for the aluminum industry is characterized in that: the method comprises the following steps:
step 1: acquiring product specification parameter information in a historical production contract of an aluminum enterprise and specification parameter information of alternative ingot types matched with the historical production contract, and clustering the information to obtain a classifier;
the classifier has the following functions: when the product specification parameters of a certain production contract are input, determining an alternative ingot type set matched with the production contract by the classifier;
step 2: acquiring 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 type matched with the current production contract;
and step 3: determining the matching relation between the current production contract and the alternative ingot mold according to the specification parameters of the alternative ingot mold determined in the step 2, the specification parameters of the current production contract and the smelting and continuous casting production process rules;
and 4, 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, on the premise of meeting the batching process constraint, establishing a mathematical model comprising decision variables and the production contract product specification parameter constraint, and carrying out quantitative description on the ingot type selection and contract batching integrated decision problem;
and 5: determining an initial ingot combination scheme, inputting the initial ingot combination scheme into the mathematical model established in the step 4, relaxing the integer requirement of the decision variables, and constructing an optimal ingot combination scheme selection model;
step 6: solving an optimal ingot combination scheme selection model; for each alternative ingot type, obtaining a shadow price corresponding to constraint of each alternative ingot type, taking the shadow price as input, constructing a new ingot combination scheme generation model and solving the shadow price, then adding a new ingot combination scheme meeting the high-quality ingot combination scheme test criterion into an optimal ingot combination scheme selection model, determining whether an unformed high-quality ingot combination scheme exists or not based on the high-quality ingot combination scheme test criterion, if any alternative ingot type k does not have the unformed high-quality ingot combination scheme, turning to the step 7, otherwise, generating a new high-quality ingot combination scheme according to the high-quality ingot combination scheme generation model and adding the optimal ingot combination scheme selection model, and repeatedly executing the step 6;
and 7: and (4) substituting all the initial ingot forming schemes and the high-quality ingot forming schemes generated in the steps (5) and (6) into the mathematical model established in the step (4), simultaneously ensuring the integer requirement of a decision variable, 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 sending the production instruction to a production workshop for production.
2. The integrated optimization method for ingot type selection and contract group batch facing aluminum industry as claimed in claim 1, wherein: the specific method of the step 1 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 comprise a preferred alloy series of the contract, a candidate alloy series, a contract delivery date, a contract delivery type, a contract state, an aluminum plate ordering block number, an aluminum plate shortage block number, an aluminum plate ordering thickness, an aluminum plate ordering maximum width, an aluminum plate ordering minimum width, an aluminum plate ordering maximum length, an aluminum plate ordering minimum length, an aluminum plate ordering maximum weight and an aluminum plate ordering minimum weight;
step 1-2: acquiring a set of candidate ingot type specification parameter information matched with historical production contracts, wherein each historical production contract is matched with a plurality of candidate ingot types, and each candidate ingot type specification parameter information comprises an alloy type, a thickness, a width and a weight;
step 1-3: and clustering the obtained product specification parameter information in the historical production contract and the specification parameter information of the alternative ingot type matched with the historical production contract, and clustering the contracts with the same shape and alloy type, the same delivery date and the same thickness to obtain the classifier.
3. The integrated optimization method for ingot type selection and contract group batch facing aluminum industry as claimed in claim 1, wherein: the specific method of the step 2 comprises the following steps:
step 2-1: acquiring product specification parameter information of a current production contract;
step 2-2: and (3) inputting the product specification parameter information of the current production contract into the classifier obtained in the step (1), and determining the 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 contract group batch facing aluminum industry as claimed in claim 1, wherein: the matching relationship between the current production contract and the alternative ingot type determined in the step 3 is specifically as follows:
relationship one: the first 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 called to be matched with the ingot type k;
the second relation: if the weight of the aluminum plate in the production contract i is less than that of the ingot type k, the production contract i is called to be matched with the ingot type k;
relationship three: the width of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is four: the thickness of the aluminum plate in the production contract i is smaller than that of the ingot type k, and the production contract i is called to be matched with the ingot type k;
the relationship is five: the width difference value of the aluminum plate of the production contract i and the width difference value of the ingot type k is within the range of the maximum width difference threshold epsilon allowed by the process, and if epsilon is more than 0, the production contract i is called to be matched with the ingot type k;
the relationship six: and (3) the difference value between the thickness of the aluminum plate of the production contract i and the thickness of the ingot type k is within the maximum thickness difference threshold value delta range allowed by the process, and j is greater than 0, so that the production contract i is called to be matched with the ingot type k.
5. The method of claim 4, wherein the method comprises the following steps: the specific method of the step 4 comprises the following steps:
step 4-1: for any alternative ingot type K, K belongs to K, K is the set of alternative ingot types, and all production contract sets N matched with the ingot types are obtained according to the matching relation between the production contract determined in the step 3 and the alternative ingot typesk＝{i∈N|mik1, where N represents the set of all production contracts, mikIs a binary parameter when mikWhen 1, the production contract i is matched with the ingot type k, and when m isikWhen the value is 0, the production contract i is not matched with the ingot type k;
step 4-2: for any alternative ingot type k, according to the production contract set N matched with the ingot type determined in the step 4-1kDetermining feasible production of ingot type k and ingot scheme set Pk(ii) a The feasible combined ingot scheme set P of the ingot type kkAny feasible combined ingot combination scheme P belongs to PkFrom n-dimensional vector a1kp，a2kp，...，ankpDescription of any component a thereinikpThe number of aluminum plates produced by contract i according to the feasible contract ingot combination scheme p of the ingot type k is shown, i belongs to NkThe following process constraints need to be satisfied, as shown in equations (1), (2) and (3):
wherein q isiWeight of a single aluminum plate representing production contract i, diNumber of aluminum plates, Q, required for production contract ikRepresents the weight of the alternative ingot type k;
step 4-3, determining a feasible combined ingot scheme set P of all ingot types according to the step 4-2, wherein the set P is ∪k∈KPkAnd mapping the ingot type selection and the feasible combined ingot scheme selection as a mathematical model decision variable, wherein the decision variable comprises:
1) setting a decision variable z of 0-1kWhen ingot type k is selected for production, zkValue is 1, otherwise zkThe value is 0;
2) setting an integer variable xkpAnd representing that the feasible ingot combination scheme P is belonged to PkThe number of uses of (2);
step 4-4: establishing the constraint of the production contract product specification parameters according to the production contract product specification parameters obtained in the step 2 and the feasible contract ingot combination scheme set determined in the step 4-2, which is specifically as follows:
step 4-4-1: establishing the total amount of each contract product produced by the aluminum enterprise to meet the process constraint of a customer contract or generating a residual material product, namely, the total amount of each contract product produced by the aluminum enterprise at least meets the product demand of the customer contract, and the part exceeding the demand of an order is temporarily stored in a library area as the residual material and sold to a future customer contract, as shown in a formula (4):
step 4-4-2: establishing a logical relationship between the ingot grouping scheme used by the production contract and the selected alternative ingot type, namely, only when a certain ingot type is selected, the ingot grouping scheme of the ingot type is allowed to be used, as shown in formula (5):
wherein, for any alternative ingot type k, MkIs a constant, is an estimated value of the number of aluminum ingots used in the alternative ingot type k, and is guaranteed when z iskIs 0, arbitrary xkpIs 0 when z iskIs 1, there is xkpGreater than 0, as shown in equation (6):
step 4-4-3: establishing the quantity constraint of alternative ingot types selected by the aluminum enterprise to complete the production contract, which is specifically shown as a formula (7):
wherein, l is a constant, and the value of l is the number of the alternative ingot models which are selected from the alternative ingot model library and used for producing contract products;
and 4-5: according to the feasible ingot combination scheme, the cost losses of the material cutting loss and the residual material inventory are respectively multiplied by a cost coefficient, and an objective function F of an integrated decision problem of ingot type selection and combination batch is established0Specifically, as shown in formula (8):
wherein, ckpIs the amount of material loss when ingot type k uses the ingot-grouping scheme p, α is the material loss cost coefficient, OiThe number of the plate blank blocks exceeding the requirement of the production contract i, namely the number of the produced surplus materials with the same alloy and the same specification as those of the production contract i, and β is a stock cost coefficient brought by the surplus materials with the unit weight;
material loss c when ingot type k uses ingot combination scheme pkpThe calculation method of (a) is shown as follows:
producing the residual material quantity O with the same alloy and the same specification as the contract iiThe calculation method of (a) is shown as follows:
substituting the formula (9) and the formula (10) into the objective function (8), and merging to obtain the objective function F0As shown in the following equation:
6. the method of claim 5, wherein the method comprises the following steps: the specific method for determining the initial ingot forming scheme in the step 5 comprises the following steps:
step 5-1: starting an aluminum ingot for any alternative ingot type k, and sequentially executing the steps 5-2 to 5-6;
step 5-2: sorting the production contracts which can be matched with the alternative ingot types k according to the descending order of the weight of the aluminum plate, and collecting N which belongs to the production contract setkStep 5-3 to step 5-6 are sequentially executed for each contract, and ingot assembly is carried out on all aluminum plates in each contract;
step 5-3: sorting the started aluminum ingots according to the descending order of the weights of the grouped ingots;
step 5-4: searching the started aluminum ingots in sequence, if the residual weight of a certain aluminum ingot is greater 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 number of the aluminum plates which are not batched currently in the production contract i is 0, if the remaining number is not 0, turning to the step 5-6, otherwise, finishing ingot grouping in the production contract i when the aluminum plates in the production contract i are already grouped, and executing the step 5-7;
and 5-6: c, putting the aluminum plate ingots of the production contract i on the searched started aluminum ingots, reducing the number of the aluminum plates which are not batched of the production contract i by 1, and re-executing the step 5-4;
and 5-7: recording ingot types of all started aluminum ingots, production contracts of ingot groups on the aluminum ingots and the number of corresponding aluminum plates; each enabled aluminum ingot is a feasible ingot grouping scheme, and the repeated ingot grouping scheme is deleted to obtain an initial ingot grouping scheme.
7. The method of claim 6, wherein the method comprises the following steps: the objective function of the new ingot composition scheme generation model constructed in the step 6 is as follows:
wherein, piiShadow price, θ, for the corresponding constraint of equation (4)kThe price is the shadow price of the corresponding constraint of the formula (5), and the sigma is the shadow price of the corresponding constraint of the formula (7);
meanwhile, the new ingot scheme generation model meets the production process constraint formula (1) and the production process constraint formula (2);
the solving method of the new ingot scheme generation model comprises the following steps:
step 6-1: with alternative ingot type k and production contract subset NkFor input, set NkAll contracts in pii/qiArranging the values in ascending order;
step 6-2: defining a state variable v representing the total weight of aluminum sheets that have been batched from 1 st to i th contract onto ingot type k; defining a decision variable xiRepresenting the number of aluminum plates of the ith batch on the ingot type k; the state transition formula is:
wherein the content of the first and second substances,
represents the total weight of aluminum sheets that have been batched to ingot type k from contract 1 to contract i-1; the decision set defining the number of aluminum slabs allowed to be batched to ingot type k under contract i at state v is:
step 6-3: defining an optimal function f [ i ]][v]Represents the optimal value of the corresponding objective function (12) when the total weight of the aluminum plates from the 1 st to the ith contract batch to the ingot type k does not exceed v, and the sum of the values of the objective function and the corresponding objective function is 1kQ, the total weight v of the aluminum plates batched onto the ingot k is 1kCalculating the corresponding optimal function f [ i ] according to equation (15)][v]；
Step 6-4: f [ | N calculated according to the formula (15)k|][Qk]Is the optimal value of the objective function (12); if f [ | Nk|][Qk]If the number is more than or equal to 0, indicating that a high-quality ingot forming scheme cannot be generated; otherwise, for any i ═ 1., | Nk|，v＝1，...，QkIf f [ i ]][v]If < 0, the corresponding (x) is deduced reversely according to the formula (15)i，xi-1，x1) Is taken as value of a1kp＝x1，...，ai，j，kp＝xi-1，
Thus obtaining the corresponding high-quality ingot-forming scheme.
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| 张浩 等: "考虑订单组批特性的特种铝锭组炉优化", 《控制理论与应用》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112348240A (en) * | 2020-10-28 | 2021-02-09 | 中冶南方工程技术有限公司 | Two-stage batching method and system for automatic sampling of bulk raw fuel |
| CN112348240B (en) * | 2020-10-28 | 2022-08-05 | 中冶南方工程技术有限公司 | Two-stage batching method and system for automatic sampling of bulk raw fuel |
| CN112801562A (en) * | 2021-04-14 | 2021-05-14 | 江苏金恒信息科技股份有限公司 | Batching system and method based on steel product inspection stage |
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| CN111062571B (en) | 2023-06-30 |
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