Integrated Optimization Method for Production Planning and Scheduling Oriented to Market Demand Uncertainty

Abstract

The present invention discloses an integrated optimization method for production planning and scheduling facing market demand uncertainty, including: S1: initializing the parameters and population of the algorithm; S2: passing each particle into the production planning layer to calculate the optimal cost and production indicators; S3: passing the production indicators of each particle into the production scheduling layer to calculate the sum of costs for all scheduling periods; S4: calculating the objective function of each particle and evaluating it; S5: updating the positions of all particles; S6: executing steps S2 - S4; S7: determining whether the convergence condition is met. If it is met, the optimal production plan and scheduling results are output; if not, return to S5. The present invention effectively solves the problem that the optimal solution effect of production planning and scheduling is not ideal or even infeasible due to market demand uncertainty through a three-layer structural model of a market demand uncertainty layer, a production planning layer, and a production scheduling layer.

Description

Technical Field

[0001] The present invention relates to the technical field of algorithm optimization applications, and particularly to an integrated optimization method for production planning and scheduling facing market demand uncertainty. Background Art

[0002] Production planning and scheduling is a crucial link in the daily operation of process enterprises and an important basis for production decision-making in process enterprises. Production planning and scheduling directly determine the economic benefits and decision-making level of process enterprises and play a positive role in the market competitiveness of enterprises. The specific objects and time spans targeted by production planning and production scheduling are different, which leads to contradictions and conflicts between production planning and production scheduling, and infeasible solutions will occur when each is optimized. Therefore, integrating production planning and scheduling for comprehensive optimization plays a crucial role in solving the problem of mutual conflict between production planning and scheduling. However, in the actual production process, it is usually affected by uncertain factors, such as uncertain market demand, which leads to an unsatisfactory optimal solution effect of production planning and scheduling, or even infeasibility. Therefore, the integrated optimization research on uncertain production planning and scheduling has research value.

[0003] Currently, the existing technologies generally conduct research and improvement on production uncertainty in the production environment. For example, a "method for setting critical chain buffers based on production uncertainty" disclosed in a Chinese patent document, with the publication number CN107944695B. This invention first obtains the priority coefficients of customers and orders, then uses a heuristic algorithm to generate a scheduling plan based on priority rules, and then performs left and right shift operations on the obtained scheduling plan to obtain two new scheduling plans, and compares the start times of each process to obtain the free float of each process. The process with zero free float is the critical chain process, thereby obtaining the critical chain, and then setting the buffer sizes of input, project, and resource buffers based on the free float and the improved root mean square method. This invention improves the root mean square method by combining resource utilization and variability measurement. For the problem of the influence of a large number of uncertain factors on buffer calculation in a complex production environment, it corrects the calculation result of the root mean square method by accurately measuring the variability of process processing time. Although it effectively improves the accuracy of buffer calculation, it does not solve the problem that the optimal solution effect of production planning and scheduling is unsatisfactory or even infeasible due to market demand uncertainty. Summary of the Invention

[0004] The present invention aims to overcome the problem that the optimal solution effect of production planning and scheduling is unsatisfactory due to market demand uncertainty in the prior art, and provides an integrated optimization method for production planning and scheduling facing market demand uncertainty.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] An integrated optimization method for production planning and scheduling facing market demand uncertainty, comprising the following steps: S1: Initialize the parameters and population of the algorithm; S2: Pass each particle into the production planning layer, and calculate the optimal cost and production indicators through a mathematical model; S3: Pass the production indicators of each particle into the production scheduling layer, and calculate the sum of costs for all scheduling periods through a mathematical model and rolling iterative optimization; S4: Calculate the objective function of each particle and evaluate it to obtain the individual optimal point, average individual optimal point, and global optimal point of each particle; S5: Update the positions of all particles through a position update formula;

[0007] S6: Execute steps S2 - S4; S7: Determine whether the convergence condition is met. If it is met, output the optimal production plan and scheduling results; if not, return to S5. The present invention provides an integrated optimization method for production planning and scheduling with market demand uncertainty of a three - layer structure. Through the objective function, that is, the structural model of the three layers of the market demand uncertainty layer, production planning layer, and production scheduling layer, it effectively solves the problem that the optimal solution effect of production planning and scheduling is not ideal or even infeasible due to market demand uncertainty.

[0008] As a preferred solution of the present invention, the uncertainty mathematical model of the production planning layer in S2 is as follows:

[0009]

[0010] 0 ≤ Pro s，t ≤ MaxPro s

[0011] 0 ≤ Inv s，t ≤ MaxInv s

[0012] 0 ≤ Tra s，t ≤ MaxTra s

[0013] 0 ≤ Bac s，t ≤ MaxBac s

[0014] Among them, ProductionCost t represents the production cost, TransportCost t represents the transportation cost, BackorderCost t represents the shortage cost, InventoryCost t represents the storage cost, T represents an overall planning period, s represents a certain type of product, Sp Represents the set of product categories, α s Represents the production cost of product s, β s Represents the storage cost of product s, γ s Represents the transportation cost of product s, δ s Represents the shortage cost of product s, Pro s，t Represents the production quantity of product s in the t - time period, Inv s，t Represents the storage quantity of product s in the t - time period, Tra s，t Represents the transportation quantity of product s in the t - time period, Bac s，t Represents the shortage quantity of product s in the t - time period, Is the top - level market demand uncertainty model, that is, the optimal market demand passed from the objective function to the planning layer.

[0015] As a preferred embodiment of the present invention, the uncertainty mathematical model of the production scheduling layer in S3 is as follows:

[0016]

[0017] εMax s ≥Pro s -Schedling s

[0018] εMax s ≥Schedling s -Pro s

[0019] Pro s -Schedling s +(1 - u)M≥εMax s

[0020] Schedling s -Pro s +uM≥sMax s

[0021] u∈{0, 1}

[0022] M = +∞

[0023]

[0024] Among them, EquipmentCost represents the fixed startup cost of the equipment, TaskCost represents the variable cost of the equipment that changes with the increase in the quantity of products produced and the production time, i represents the production task, j represents the production equipment, n represents the event point, I represents the set of all production tasks, J represents the set of all production equipment, N represents the set of all event points, Wi，j，n Indicates whether task i is running on device j at event point n, W i，j，n = 1 indicates that task i is running on device j at event point n, EquipmenCost i Indicates the fixed startup cost of the device when running production task i, TaskCost i Indicates the variable cost of the device when running production task i, B i，j，n Indicates the length of time for running task i on device j at event point n, and M is a very large positive number.

[0025] As a preferred embodiment of the present invention, the objective function in S4 is as follows:

[0026]

[0027] Among them, BacCost is the additional cost for shortages.

[0028] As a preferred embodiment of the present invention, the position update formula in S5 is as follows:

[0029] X i，j (n + 1) = p i，j (n) + α|C j (n) - X i，j (n)|ln(1 / u i，j )u i，j ∈[0, 1]

[0030]

[0031] Among them, X i，j is the position of the particle, C j represents the average optimal position of the particles, P i，j represents the individual optimal point of the particle, G j represents the global optimal point of the particle, and M and D respectively represent the number of particles and the dimension of the particles.

[0032] As a preferred embodiment of the present invention, the convergence condition in S7 is specifically: the result does not change within the specified number of iterations.

[0033] Therefore, the present invention has the following beneficial effects: The present invention provides an integrated optimization method for production planning and scheduling under market demand uncertainty with a three-layer structure. Through the objective function, that is, the structural model of the three layers of the market demand uncertainty layer, the production planning layer, and the production scheduling layer, it effectively solves the problem that the optimal solution effect of production planning and scheduling is not ideal or even infeasible due to market demand uncertainty. Brief Description of the Drawings

[0034] Figure 1It is the flowchart of the method of the present invention.

[0035] Figure 2 It is the schematic diagram of the three - layer model structure of the present invention.

[0036] Figure 3 It is the flowchart of the method of the embodiment of the present invention.

[0037] Figure 4 It is the schematic diagram of the rolling iterative optimization of the embodiment of the present invention. Detailed implementation manners

[0038] The present invention will be further described below in conjunction with the accompanying drawings and detailed implementation manners.

[0039] As Figure 1 shown, the integrated optimization method for production planning and scheduling facing market demand uncertainty includes the following steps: S1: Initialize the parameters and population of the algorithm; S2: Pass each particle into the production planning layer, and calculate the optimal cost and production indicators through a mathematical model; S3: Pass the production indicators of each particle into the production scheduling layer, and calculate the sum of costs of all scheduling periods through a mathematical model and rolling iterative optimization; S4: Calculate the objective function of each particle and evaluate it to obtain the individual optimal point, average individual optimal point and global optimal point of each particle; S5: Update the positions of all particles through the position update formula; S6: Execute steps S2 - S4; S7: Determine whether the convergence condition is met. If it is met, output the optimal production plan and scheduling result; if not, return to S5.

[0040] In one embodiment, as Figure 3 shown, the integrated optimization method for production planning and scheduling facing market demand uncertainty specifically includes: Step 1: Initialize the parameters and population of the improved quantum - behavior particle swarm algorithm.

[0041] Step 2: Pass each particle into the production planning layer to calculate the optimal cost and production indicators.

[0042] The uncertainty mathematical model of the production planning layer is:

[0043]

[0044] 0≤Pro s，t ≤MaxPro s

[0045] 0≤Inv s，t ≤MaxInv s

[0046] 0≤Tra s，t ≤MaxTra s

[0047] 0 ≤ Bac s，t ≤ MaxBac s

[0048] Where PlaningCost represents the total planned cost, ProductionCost t represents the production cost, TransportCost t represents the transportation cost, BackorderCost t represents the shortage cost, InventoryCost t represents the storage cost. T represents an overall planning period, s represents a certain type of product, S p represents the set of product types, α s represents the production cost of product s, β s represents the storage cost of product s, γ s represents the transportation cost of product s, δ s represents the shortage cost of product s, Pro s，t represents the production quantity of product s in the t time period, Inv s，t represents the storage quantity of product s in the t time period, Tra s，t represents the transportation quantity of product s in the t time period, Bac s，t represents the shortage quantity of product s in the t time period, MaxPro s represents the maximum production quantity, MaxInv s represents the maximum storage quantity, MaxTra s represents the maximum storage capacity, MaxBac s represents the maximum shortage quantity. Where is the optimal market demand passed from the top-level market demand uncertainty model to the planning layer.

[0049] Step 3: The production indicators of each particle are passed to the production scheduling layer, and the sum of the costs for all scheduling periods is calculated through rolling iterative optimization as shown Figure 4 below.

[0050] The uncertainty mathematical model of the production scheduling layer is:

[0051]

[0052] εMax s ≥ Pro s - Schedling s

[0053] εMax s ≥ Schedling s - Pro s

[0054] Pro s -Schedling s +(1 - u)M ≥ εMax s

[0055] Schedling s -Pro s +uM ≥ εMax s

[0056] u ∈ {0, 1}

[0057] M = +∞

[0058]

[0059] Among them, SchedulingCost represents the total cost of production scheduling, and ω are coefficients set artificially, Pro s and Schedling s represent the production volume given by the production plan and the actual production volume of production scheduling, εMax s represents the consistency coefficient between the production plan and production scheduling, EquipmentCost represents the fixed startup cost of the equipment, and TaskCost represents the variable cost of the equipment that changes with the increase in the number of products produced and production time. i represents the production task, j represents the production equipment, and n represents the event point. I represents the set of all production tasks, J represents the set of all production equipment, and N represents the set of all event points. The 0 - 1 state variable W i，j，n represents whether task i is running on equipment j at event point n. If W i，j，n = 1, it means that task i is running on equipment j at event point n. EquipmenCost i represents the fixed startup cost of the equipment when running production task i. TaskCost i represents the variable cost of the equipment when running production task i. B i，j，n represents the length of time that task i is running on equipment j at event point n. M is a very large positive number.

[0060] Step 4: Calculate the objective function of each particle.

[0061] The mathematical model of market demand uncertainty at the top layer, which is the objective function of the particle, is as follows:

[0062]

[0063] Among them, BacCost is the additional cost of shortage, k represents different demand scenarios, and P(k) represents the probability under demand scenario k.

[0064] Step 5: By evaluating the objective function of each particle, that is, the quality of the objective function of each particle, find the individual optimal point, average individual optimal point, and global optimal point of each particle.

[0065] Step 6: Update the positions of all particles through the position update formula of the improved quantum-behaved particle swarm optimization algorithm based on Levy flight.

[0066] The position update formula of the improved quantum-behaved particle swarm optimization algorithm is as follows:

[0067] X i，j (n + 1) = p i，j (n) ± α|C j (n) - X i，j (n)|ln(1 / u i，j )u i，j ∈[0, 1]

[0068]

[0069] Where n represents the current iteration number, α represents a manually set parameter, between 0.25 and 0.5, u i，j and represents a random number from 0 to 1, X i，j is the position of the particle, C j represents the average particle optimal position, P i，j represents the individual optimal point of the particle, G j represents the global optimal point of the particle, M and D respectively represent the number of particles and the dimension of the particles.

[0070] Step 7: Pass each particle into the production planning layer to calculate the optimal cost and production indicators.

[0071] Step 8: Pass the production indicators of each particle into the production scheduling layer, and calculate the sum of costs for all scheduling periods through rolling iterative optimization.

[0072] Step 9: Calculate the objective function of each particle.

[0073] Step 10: Update the individual optimal point, average individual optimal point, and global optimal point of each particle by evaluating the objective function of each particle.

[0074] Step 11: Judge whether the convergence condition is satisfied, that is, if the result does not change in the specified number of iterations, it can be considered convergent. If so, output the optimal production plan and scheduling results. If not, jump to Step 6 to continue the optimization.

[0075] The present invention integrates and optimizes the production plan and scheduling under market demand uncertainty by means of an improved quantum-behaved particle swarm algorithm, and proposes an integrated optimization method for the production plan and scheduling under market demand uncertainty with a three-layer structure. This integrated model and its improved optimization method have better solving capabilities, providing some theoretical guiding significance for solving the problem of production plan and scheduling under uncertainty.

[0076] The present invention provides an integrated optimization method for the production plan and scheduling under market demand uncertainty with a three-layer structure. By Figure 2 means of the objective function shown as the structural model of three layers, namely the market demand uncertainty layer, the production plan layer and the production scheduling layer, it effectively solves the problem that the optimal solution effect of the production plan and scheduling is not ideal or even infeasible due to the market demand uncertainty.

[0077] As mentioned above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be thought of without creative efforts shall be covered within the protection scope of the present invention.

Claims

1. An integrated optimization method for production planning and scheduling facing market demand uncertainty, characterized in that It includes the following steps: S1: Construct a three-layer structure model composed of a market demand uncertainty layer, a production planning layer, and a production scheduling layer, and initialize the parameters and population of the improved quantum-behaved particle swarm optimization algorithm; S2: Input the market demand represented by each particle into the production planning layer, and calculate the optimal cost and production indicators through a mathematical model; S3: Input the production indicators of each particle obtained from the solution of the planning layer model into the production scheduling layer, and calculate the sum of costs for all scheduling periods through a mathematical model and rolling iterative optimization; S4: Calculate the objective function of each particle and evaluate it to obtain the individual optimal point, average individual optimal point, and global optimal point of each particle; S5: Update the positions of all particles through the position update formula of the improved quantum-behaved particle swarm optimization algorithm; S6: Execute steps S2 - S4; S7: Determine whether the convergence condition is met. If it is met, output the optimal production plan and scheduling results; if not, return to S5.

2. The integrated optimization method for production planning and scheduling facing market demand uncertainty according to claim 1, characterized in that The uncertainty mathematical model of the production planning layer in S2 is as follows: 0 ≤ Pro s，t ≤ MaxPro s 0 ≤ Inv s，t ≤ MaxInv s 0 ≤ Tra s，t ≤ MaxTra s 0 ≤ Bac s，t ≤ MaxBac s Among them, PlaningCost represents the total planned cost, ProductionCost t represents the production cost, TransportCost t represents the transportation cost, BackorderCost t represents the shortage cost, InventoryCost t represents the storage cost, T represents an overall planning period, s represents a certain type of product, S p represents the set of product types, α s represents the production cost of product s, β s represents the storage cost of product s, γ s represents the transportation cost of product s, δ s represents the shortage cost of product s, Pro s,t represents the production quantity of product s in the t - time period, Inv s,t represents the storage quantity of product s in the t - time period, Tra s,t represents the transportation quantity of product s in the t - time period, Bac s，t represents the shortage quantity of product s in the t - time period, MaxPro s represents the maximum production quantity, MaxInv s represents the maximum storage quantity, MaxTra s represents the maximum storage capacity, MaxBac s represents the maximum shortage quantity, is the optimal market demand passed from the top - level market demand uncertainty model to the planning layer.

3. The integrated optimization method for production planning and scheduling facing market demand uncertainty according to claim 1, characterized in that, The uncertainty mathematical model of the production scheduling layer in S3 is as follows: εMax s ≥Pro s -Schedling s εMax s ≥ Scheduling s -Pro s Pro s - Schedling s +(1 - u)M ≥ εMax s Schedling s -Pro s +uM≥εMax s u∈{0，1} M＝+∞ Among them, SchedulingCost represents the total cost of production scheduling, and ω are coefficients set by humans, Pro s and Schedling s represent the production volume given by the production plan and the actual production volume of the production scheduling, εMax s represents the consistency coefficient between the production plan and the production scheduling, EquipmentCost represents the fixed startup cost of the equipment, TaskCost represents the variable cost of the equipment that changes with the increase in the number of products produced and the production time, i represents the production task, j represents the production equipment, n represents the event point, I represents the set of all production tasks, J represents the set of all production equipment, N represents the set of all event points, W i，j，n represents whether task i is running on equipment j at event point n, EquipmenCost i represents the fixed startup cost of the equipment when running production task i, TaskCost i represents the variable cost of the equipment when running production task i, B i，j，n represents the length of time for running task i on equipment j at event point n, s represents a certain type of product, S p represents the set of product types.

4. The integrated optimization method for production planning and scheduling facing market demand uncertainty according to claim 1, characterized in that The objective function in S4 is as follows: Among them, PlaningCost represents the total planned cost, and SchedulingCost represents the total cost of production scheduling. and ω are coefficients set by humans, εMax s represents the consistency coefficient between the production plan and the production scheduling. s represents a certain type of product, and S p represents the set of product types. T represents an overall planning period, t represents a certain time period, BacCost is the additional cost of shortage, k represents different demand scenarios, and P(k) represents the probability under demand scenario k.

5. The integrated optimization method for production planning and scheduling oriented to market demand uncertainty according to claim 1, characterized in that The position update formula in S5 is as follows: X i，j (n + 1) = p i，j (n) ± α|C j (n) - X i，j (n)|ln(1 / u i，j )u i，j ∈[0, 1] where n represents the current iteration number, α represents a parameter set by a person, which is between 0.25 and 0.5, u i，j and represents a random number between 0 and 1, X i，j is the position of the particle, C j represents the average optimal position of the particles, P i，j represents the individual optimal point of the particle, G j represents the global optimal point of the particle, and M and D represent the number of particles and the dimension of the particles respectively.

6. The integrated optimization method for production planning and scheduling facing market demand uncertainty according to any one of claims 1-5, characterized in that The specific convergence condition in S7 is that the result does not change within the specified number of iterations.

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