Intelligent production scheduling method and system based on arc decomposition
Through the intelligent production scheduling method based on arc decomposition, a discrete order space-time network is established, arc space is reduced, and the production scheduling optimization model is solved, and the production scheduling solution is not costly and unfeasible in the existing technology is solved, and a fast and accurate optimal production scheduling solution is achieved, which improves production efficiency.
Patent Information
- Application Number
- CN202411725995.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-28
- Publication Date
- 2025-03-14
AI Technical Summary
When the existing production scheduling system faces multiple orders and complex constraint rules, it is difficult to quickly and accurately solve the optimal order production plan, resulting in high cost and unfeasible generation of the plan.
采用基于弧分解的智能排产方法,通过建立离散化的订单时空网络,削减弧空间,求解排产优化模型,得到智能排产计划,并向生产线发送排产指令。
It realizes the rapid and accurate solution of the optimal order production plan, reduces the cost of production schedule, improves production efficiency, and has high ductility.
Smart Images
Figure CN119624007A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of production scheduling for product manufacturing, and more specifically, to an intelligent production scheduling method based on arc decomposition. Background Art
[0002] With the continuous development of artificial intelligence technology, more and more digital factories are emerging. Digital factories have overturned the traditional production model and can realize on-demand manufacturing according to order requirements, raw material supply, production line capacity, etc., greatly improving manufacturing efficiency. However, facing the scheduling scenarios of multiple orders and complex constraint rules, manufacturing companies need to find a suitable scheduling solution to achieve the goal of reducing costs and increasing efficiency.
[0003] The production scheduling system in the prior art mainly uses heuristic methods for production scheduling, which sacrifices a certain degree of solution accuracy in order to ensure the timeliness of the algorithm. This may lead to excessively high costs for generating solutions, or even infeasible solutions. On the other hand, the main existing solution methods are to use commercial solvers directly or to use improved genetic algorithms, which have slow solution speeds and low solution accuracy. Therefore, the prior art urgently needs to design an efficient intelligent production scheduling method and system to improve the production efficiency of enterprises. Summary of the invention
[0004] In view of the shortcomings of the prior art, the purpose of the present invention is to provide an intelligent production scheduling method and system based on arc decomposition, which can quickly and accurately solve the optimal order production plan and improve production efficiency.
[0005] In order to achieve the above object, the present invention provides an intelligent production scheduling method based on arc decomposition, comprising the following steps:
[0006] Step 1: Obtain order data and production line data;
[0007] Step 2: Using the acquired order data and production line data, a discretized order space-time network is established according to a model for minimizing comprehensive production costs, wherein the order space-time network includes a plurality of arcs;
[0008] Step 3: According to the constraint information, multiple arcs in the order space-time network are reduced to obtain the reduced arc space;
[0009] Step 4: Solve the production scheduling optimization model based on the reduced arc space to obtain an intelligent production scheduling plan;
[0010] Furthermore, the method also includes step 5: sending a production scheduling instruction to the production line according to the obtained intelligent production scheduling plan.
[0011] Furthermore, the order data includes: total order set, product quantity of a single order, order product color set, single order product color, order filler type, order filler ratio value and order delivery time; the production line data includes: total production line set, production line type, base material type set, base material changeover cost, base material switching cost, color switching cost, filler switching cost and raw material arrival time.
[0012] Furthermore, the constraint information includes hard constraint information and soft constraint information; the soft constraint information includes: production line preference constraints, color preference constraints and order preference constraints; the hard constraint information includes: washing time constraints and raw material supply constraints.
[0013] Furthermore, the model for minimizing the comprehensive production cost is:
[0014]
[0015] Among them, E1 is the delay cost coefficient, E2 is the machine preference cost coefficient, and E3 is the production change cost coefficient. o is the delay cost, y mo For order o produced on production line m, Ω mo Order o prefers to be produced on machine m, The base material cost for switching from order o to o', The color cost for switching from order o to o', The filling cost for switching from order o to o', x moo' Switch to order o' on line m for order o.
[0016] Furthermore, establishing a discretized space-time network includes discretizing time into T = (t0, t1, t2, ... tn), where each point in the space-time network represents an order o i At time t i Starting production, an arc l in the space-time network is represented by:
[0017]
[0018] Among them, i and oj represent different orders in the order library, t i Indicates order o i The time when production starts on machine m, tj represents the time when order o i After production is completed, switch to order o j The moment of production.
[0019] Furthermore, solving the production scheduling optimization model based on the reduced arc space includes calling a commercial solver to solve the production scheduling optimization model. The production scheduling optimization model is:
[0020]
[0021] Constraint (1) is
[0022]
[0023] Constraint (2) is
[0024]
[0025] The parameter w l represents the cost on arc l, including the cost from order o i Switch to order o on machine m j The switching cost and production preference cost of Indicates whether the previous order of arc l is o, if yes then it is 1, otherwise 0. l is the decision variable, indicating whether arc l is selected. If yes, it is 1, otherwise it is 0. The objective function is to minimize the cost of production scheduling. Constraint (1) indicates that each order must be assigned to a machine for production. Constraint (2) is the value range of the decision variable.
[0026] Furthermore, the delay cost is defined as:
[0027]
[0028] Among them, Delay o For delay cost, The time when production of order o is completed, The time when production starts for order o.
[0029] The present invention also discloses an order intelligent production scheduling system based on arc decomposition, which is characterized by comprising:
[0030] Data acquisition module, used to obtain order data and production line data;
[0031] A discretization module, used to establish a discretized order space-time network according to a minimized comprehensive production cost model by using the acquired order data and production line data, wherein the order space-time network includes a plurality of arcs;
[0032] The arc reduction module is used to reduce multiple arcs in the order space-time network according to the constraint information to obtain the reduced arc space;
[0033] A solution module is used to solve the production scheduling optimization model based on the reduced arc space to obtain an intelligent production scheduling plan;
[0034] And the instruction sending module: used to send production scheduling instructions to the production line according to the obtained intelligent production scheduling plan.
[0035] Furthermore, the establishment of a discretized space-time network includes discretizing time into T = (t0, t1, t2, ... tn), and each point in the space-time network represents an order o i At time t i Starting production, an arc l in the space-time network is represented by:
[0036]
[0037] Among them, i and oj represent different orders in the order library, t i Indicates order o i The time when production starts on machine m, tj represents the time when order o i After production is completed, switch to order o j The moment of production.
[0038] The beneficial effects of the present invention include at least:
[0039] (1) By minimizing the comprehensive production cost model, the cost of the production scheduling plan is greatly reduced.
[0040] (2) The arc network solution method improves the speed and quality of the solution.
[0041] (3) The special arc-based modeling method has high scalability and is convenient for subsequent development. BRIEF DESCRIPTION OF THE DRAWINGS
[0042] Figure 1 A flow chart of the intelligent production scheduling method based on arc decomposition provided by the present invention.
[0043] Figure 2 It is the arc space in the order space-time network of the present invention.
[0044] Figure 3 This is the arc space reduced by the present invention.
[0045] Figure 4 The computation time of the embodiments of the present invention at different scales is compared using a commercial solver for direct solution, an improved genetic algorithm for solution, and an arc generation distributed algorithm for solution. DETAILED DESCRIPTION
[0046] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0047] Figure 1 The steps of the intelligent production scheduling method based on arc decomposition provided by the present invention are shown, and the method specifically includes:
[0048] Step S101: Obtain order data and production line data; wherein the order data includes but is not limited to: total order set, product quantity of a single order, order product color set, single order product color, order filler type, order filler ratio value and order delivery time, etc.; production line data includes but is not limited to: total production line set, production line type, production line status, base material type set, base material changeover cost, base material switching cost, color switching cost, filler switching cost, raw material arrival time, etc.
[0049] Step S102: Establish a discretized order spatiotemporal network based on the comprehensive production cost minimization model.
[0050] (I) Establishment of a model to minimize comprehensive production costs.
[0051] First, it is necessary to identify the complex constraints that need to be considered in the order production process. The constraints can be divided into hard constraints and soft constraints and processed separately. The constraints considered and accommodated by this method include but are not limited to:
[0052] i. Production line preference constraint (soft constraint): ensure large orders for large production lines and small orders for small production lines as much as possible;
[0053] ii. Color preference constraint (soft constraint): Try to ensure that some colors are only produced on some production lines and are not affected by production line preferences;
[0054] iii. Order preference constraint (soft constraint): small orders are produced on large production lines, and the immediate task before the production line must be a large order;
[0055] iv. Washing time constraint (hard constraint): Orders of different models (including color, base material and other characteristics) produced on the same production line have washing time;
[0056] v. Raw material supply constraints (hard constraints): Some orders need to be produced after the raw materials arrive.
[0057] Afterwards, an intelligent production scheduling optimization model based on complex constraints is established, and parameters and decision variables are defined and the model is constructed according to the complex constraints considered above and the comprehensive costs that may be incurred in the production process of all orders.
[0058] First, the soft constraints that need to be considered in the production scheduling problem are transformed into complex comprehensive costs that need to be considered in the model, including delay costs, machine preference costs and production change costs (base material change costs, color change costs, filler change costs) to establish the initial model OP-1 that minimizes the comprehensive production cost:
[0059]
[0060] Among them, E1 is the delay cost coefficient, E2 is the machine preference cost coefficient, and E3 is the production change cost coefficient. o is the delay cost, y mo For order o produced on production line m, Ω mo Order o prefers to be produced on machine m, The base material cost for switching from order o to o', The color cost for switching from order o to o', The filling cost for switching from order o to o', x moo′ Switch to order o' on line m for order o.
[0061] (ii) Establish a discrete order space-time network.
[0062] In the initial model OP, the decision variable is x moo′ With y mo , respectively deciding which order o' to produce next after order o is produced on machine m and on which machine m order o is produced.
[0063] After discretizing time, let the entire time axis be T = (t0, t1, t2, ... tn), and we only need to describe the above decision at each time point. Figure 2 The order space-time network diagram described in the figure is shown in the horizontal axis of the figure, and the vertical axis represents different orders. i , t i ) means an order o i In t i Start production at any time.
[0064] Therefore, an arc in the space-time network graph can be expressed as:
[0065]
[0066] This arc represents the order o i In t i Production starts on machine m at time t and is completed at time t j Switch to order at any time j Carry out production.
[0067] Step S103: reducing multiple arcs in the order space-time network.
[0068] In the order space-time network diagram, not all points are fully connected. Considering the complex production scheduling constraints, we can further reduce the number of points and arcs in the space-time network and narrow the solution space to improve the solution efficiency.
[0069] First, assuming that the machine will not have extra idle waiting time between two tasks, once the materials of the next task arrive, it will complete the production immediately. Therefore, in the arc formed by two orders, the start time of the next order is not an arbitrary value, it is equal to the completion time of the order plus the changeover time, or the arrival time of the order materials.
[0070] Second, according to complex production scheduling constraints, the solution space can also be greatly reduced. For example, two orders that do not meet the order tracking rules cannot be connected into an arc.
[0071] Step S104: Solve the production scheduling optimization model based on the reduced arc space
[0072] The complex production scheduling optimization model is rebuilt based on the order space-time network. The model is now transformed into a 0-1 integer programming model IP:
[0073]
[0074] Constraint (1) is
[0075]
[0076] Constraint (2) is
[0077]
[0078] The parameter w l represents the cost on arc l, including the cost from order o i Switch to order o on machine m j The switching cost and production preference cost of Indicates whether the previous order of arc l is o, if yes then it is 1, otherwise 0. l is the decision variable, indicating whether arc l is selected. If yes, it is 1, otherwise it is 0. The objective function is to minimize the cost of production scheduling. Constraint (1) indicates that each order must be assigned to a machine for production. Constraint (2) is the value range of the decision variable.
[0079] According to the optimization model defined above, we have designed a set of solution methods to obtain the optimal solution efficiently and accurately. The specific solution steps are as follows:
[0080] Step 1: Generate a large number of feasible arcs through parallel computing;
[0081] Step 2: The main server integrates the feasible arcs obtained by searching at each edge end to form a feasible arc set;
[0082] Step 3: Use a commercial solver to solve the simplified 0-1 integer programming model based on the feasible arc set.
[0083] The final result is an intelligent production schedule, including the production machine corresponding to the order, the production start time, the end time, and the production change sequence between different orders. Order delays, machine preferences, and the comprehensive cost of production change will also be accurately calculated.
[0084] Step 105: Send a production scheduling instruction to the production line according to the obtained intelligent production scheduling plan.
[0085] Example: Production scheduling for an engineering plastics manufacturer
[0086] Take the example of a plastic factory that receives a large number of different types of engineering plastic production orders every day: there are a total of 7 production lines (machines) in the factory to produce products, including 4 large production lines with high capacity and 3 small production lines with low capacity. Each production line can be used to produce different types of products, and different types of products have different colors, base materials, fillers, filler ratios and other properties.
[0087] First, we obtained the order and production line data: read the total order set, the number of products in a single order, the order product color set, the single order product color, the order filler type, the order filler ratio value, and the delivery time from the order pool; read the total production line set, production line type, base material type set, base material changeover cost, base material switching cost, color switching cost, filler switching cost, and raw material arrival time from the storage;
[0088] First, it is necessary to identify the complex constraints that need to be considered in the order production process. The constraints can be divided into hard constraints and soft constraints and handled separately.
[0089] After that, an intelligent production scheduling optimization model based on complex constraints is established, and parameters, decision variables are defined and the model is constructed according to the complex constraints considered above and the comprehensive costs that may be generated in the production process of all orders. The relevant parameters and decision variable definitions used in the model are shown in Table 1:
[0090] Table 1. Parameter description
[0091]
[0092]
[0093] We first perform preprocessing and transform the soft constraints that need to be considered in the production scheduling problem into complex comprehensive costs that need to be considered in the model, including delay costs, machine preference costs and production change costs (base material change costs, color change costs, filler change costs).
[0094] Specifically:
[0095] a. Delay costs:
[0096]
[0097] In order to facilitate the subsequent model solution, it can be linearized as:
[0098]
[0099] Delay o ≥0
[0100]
[0101] Delay o ≤M(1-μ o2
[0102] μ o1 +μ o2 ≥1
[0103] b. Machine preference cost: Machine preference coefficient Ω for all orders mo Corresponding.
[0104] c.Production changeover cost: includes base material production changeover cost, color production changeover cost, and filler production changeover cost.
[0105] Among them, the base material production change cost directly corresponds to the production change matrix:
[0106] The color changeover cost is defined by color depth:
[0107]
[0108] The cost of packing replacement is penalized in the following order: packing type → packing presence → packing ratio:
[0109] Finally, we set the penalty coefficients for delay cost, machine preference cost, and production change cost as follows:
[0110] E1=7200000, E2=12000, E3=600
[0111] Based on the above definition, the complex production scheduling optimization initial model (mixed integer programming model) OMIP can be written:
[0112] Objective function: Minimize comprehensive production cost
[0113]
[0114] Constraints:
[0115] a. Only one production line can be selected for one order
[0116]
[0117] b. Each production line can only receive one order after its virtual starting point, that is, each production line starts with one order
[0118]
[0119] c. Each production line can only receive one order before its virtual end point, that is, each production line ends with one order.
[0120]
[0121] d. For any preceding order of any production line, there is one or no subsequent order.
[0122]
[0123] e. For any subsequent order of any production line, there is one or no preceding order.
[0124]
[0125] f. The raw materials of the order arrive before the start of production
[0126]
[0127] g. The start time of the order must be greater than the end time of the previous order. If the two product types are different, two hours (2*60 minutes) of washing time must be added.
[0128]
[0129] h. For idle machines, the order start time is 0. For non-idle machines, the order start time is less than the large number M.
[0130]
[0131] i. The start time of the order is greater than or equal to 0
[0132]
[0133] j. The start time of the virtual last order is equal to the end time
[0134]
[0135] k. The end time of an order is equal to the start time of the order plus the production time of the order quantity, where Pmo is the time required to produce a unit of product for order o on production line m, and is the number of products required for order o
[0136]
[0137] 1. Production line switching feasibility constraints
[0138]
[0139] m. Production line order preference: large orders, large production lines
[0140] n o ≥5000,o∈O (1) ,Ω mo =1(o∈O (1) ,m∈M (1) )
[0141] n. Production line order preference: small order, small production line
[0142]
[0143] o.Production line order preference: Light color order auxiliary line production
[0144]
[0145] p. Range of decision variables
[0146]
[0147] (ii) Establish a discrete order space-time network.
[0148] In OMIP, the decision variable is x moo' With y mo , respectively deciding which order o' to produce next after order o is produced on machine m and on which machine m order o is produced.
[0149] After discretizing time, let the entire time axis be T = (t0, t1, t2, ... tn), and we only need to describe the above decision at each time point. Figure 2 The order space-time network diagram described in the figure is shown in the horizontal axis of the figure, and the vertical axis represents different orders. i , t i ) means an order o i In t iStart production at any time.
[0150] Therefore, an arc in the space-time network graph can be expressed as:
[0151]
[0152] This arc represents the order o i In t i Production starts on machine m at time t and is completed at time t j Switch to order at any time j Carry out production.
[0153] Afterwards, the method described above is used to reduce multiple arcs in the order space-time network. The reduced arc space is as follows: Figure 3 shown.
[0154] Based on the order spatiotemporal network, a complex production scheduling optimization model is reconstructed. According to the optimization model defined above, we specifically designed a set of solution methods to obtain the optimal solution efficiently and accurately. The specific solution steps are as follows:
[0155] Step 1: Generate a large number of feasible arcs through parallel computing;
[0156] Referring to the process of OP to IP, if we want to construct an IP that meets the actual production needs based on OMIP, we need to obtain all feasible arc combinations L. This step completes the arc set for reduction processing. Specifically, we first describe the production line by state: for each production line, there is an initial order and then arranges to decide whether the next order can be produced, and gives the cost of production change, which can be expressed as the deterministic matrix C moo′ and D moo′ Only arcs that satisfy the constraints (f)-(p) in the original problem model are feasible arcs and the corresponding costs of the arcs can be calculated through the above production change cost matrix and the constraint (m) production preference. Then we generate a set of arcs specific to each type of production line based on the material arrival time of each order and the production time on a specific machine.
[0157] The generation of feasible arcs can be pre-computed in a distributed manner on a large server (or multiple small servers) through parallel computing methods. Since feasible arcs contain a large number of hard constraints, a large amount of search space will be cut during the distributed search for feasible arcs, and because of the discretization of time and the limited number of orders, the number of feasible arcs must be limited. The converted arc model is an integer programming model that is relatively easy to solve, so this method is suitable for solving large-scale production scheduling problems with real-time response.
[0158] Step 2: The main server integrates the feasible arcs obtained by searching at each edge end to form a feasible arc set;
[0159] Step 3: Use a commercial solver to solve the simplified 0-1 integer programming model based on the feasible arc set.
[0160] Finally, the generated scheduling and production plan report is obtained.
[0161] Figure 4 The difference in operation time of using commercial solvers directly to solve, improved genetic algorithms to solve, and arc generation distributed algorithms to solve at different scales is shown. It can be seen that both the solution time and the solution quality are far better than using commercial solvers directly to solve, or using improved genetic algorithms to solve. The solution time of the method proposed in the present invention does not increase exponentially with the solution scale, but basically tends to be stable, and can maintain a very stable solution performance to meet the needs of real-world scenarios.
[0162] Although the content of the present invention has been described in detail through the above preferred embodiments, it should be appreciated that the above description should not be considered as a limitation of the present invention. After reading the above content, it will be apparent to those skilled in the art that various modifications and substitutions of the present invention will occur. Therefore, the protection scope of the present invention should be limited by the appended claims.
Claims
1. An order intelligent scheduling method based on arc decomposition, characterized in that: The following steps are involved: Step 1: Obtain order data and production line data; Step 2: Using the acquired order data and production line data, a discretized order space-time network is established according to a model for minimizing comprehensive production costs, wherein the order space-time network includes a plurality of arcs; Step 3: According to the constraint information, multiple arcs in the order space-time network are reduced to obtain the reduced arc space; Step 4: Solve the production scheduling optimization model based on the reduced arc space to obtain an intelligent production scheduling plan.
2. The method for intelligent order scheduling based on arc decomposition according to claim 1, characterized in that: The method also includes step 5: sending a production scheduling instruction to the production line according to the obtained intelligent production scheduling plan.
3. The method for intelligent order scheduling based on arc decomposition according to claim 1, characterized in that: The order data includes: total order set, product quantity of a single order, order product color set, single order product color, order filler type, order filler ratio value and order delivery time; the production line data includes: total production line set, production line type, base material type set, base material changeover cost, base material switching cost, color switching cost, filler switching cost and raw material arrival time.
4. The method for intelligent order scheduling based on arc decomposition according to claim 1, characterized in that: The constraint information includes hard constraint information and soft constraint information; The soft constraint information includes: production line preference constraints, color preference constraints and order preference constraints; the hard constraint information includes: washing time constraints and raw material supply constraints.
5. The method for intelligent order scheduling based on arc decomposition according to any one of claims 1 to 4, characterized in that: The model for minimizing the comprehensive production cost is: Among them, E1 is the delay cost coefficient, E2 is the machine preference cost coefficient, and E3 is the production change cost coefficient. o is the delay cost, y mo For order o produced on production line m, Ω mo Order o prefers to be produced on machine m, The base material cost for switching from order o to o', The color cost for switching from order o to o', The filling cost for switching from order o to o', x moo 'Switch to order o on line m for order o'.
6. The method for intelligent order scheduling based on arc decomposition according to claim 5, characterized in that: Establishing a discretized space-time network includes discretizing time into T = (t0, t1, t2, ... t n ), each point in the spatiotemporal network represents an order o i At time t i Starting production, an arc l in the space-time network is represented by: Among them, i and j Represents different orders in the order library, t i Indicates order o i The time when production starts on machine m, t j Indicates order o i After production is completed, switch to order o j The moment of production.
7. The method for intelligent order scheduling based on arc decomposition according to claim 6, characterized in that: Solving the production scheduling optimization model based on the reduced arc space includes calling a commercial solver to solve the production scheduling optimization model. The production scheduling optimization model is: Constraint (1) is Constraint (2) is The parameter w l represents the cost on arc l, including the cost from order o i Switch to order o on machine m j The switching cost and production preference cost of Indicates whether the previous order of arc l is o, if yes then it is 1, otherwise 0. l is the decision variable, indicating whether arc l is selected. If yes, it is 1, otherwise it is 0. The objective function is to minimize the cost of production scheduling. Constraint (1) indicates that each order must be assigned to a machine for production. Constraint (2) is the value range of the decision variable.
8. The method for intelligent order scheduling based on arc decomposition according to claim 5, characterized in that: The delay cost is defined as: Among them, Delay o For delay cost, The time when production of order o is completed, The time when production starts for order o.
9. An order intelligent scheduling system based on arc decomposition, characterized in that: include: Data acquisition module, used to obtain order data and production line data; A discretization module, used to establish a discretized order space-time network according to a minimized comprehensive production cost model by using the acquired order data and production line data, wherein the order space-time network includes a plurality of arcs; The arc reduction module is used to reduce multiple arcs in the order space-time network according to the constraint information to obtain the reduced arc space; A solution module is used to solve the production scheduling optimization model based on the reduced arc space to obtain an intelligent production scheduling plan; And the instruction sending module: used to send production scheduling instructions to the production line according to the obtained intelligent production scheduling plan.
10. The order intelligent production scheduling system based on arc decomposition according to claim 9, characterized in that: The establishment of a discretized space-time network includes discretizing time into T = (t0, t1, t2, ... t n ), each point in the spatiotemporal network represents an order o i At time t i Starting production, an arc l in the space-time network is represented by: Among them, i and j Represents different orders in the order library, t i Indicates order o i The time when production starts on machine m, t j Indicates order o i After production is completed, switch to order o j The moment of production.