CN109934393A - An integrated optimization method for production planning and scheduling under uncertain demand - Google Patents

Abstract

The present invention relates to a kind of integrated optimization methods of the uncertain lower Production-Plan and scheduling of demand.The generation for the problems such as Production-Plan and scheduling problem solving mode is mainly traditional optimization at present, and the result of optimization is difficult to be optimal solution, and is likely to cannot achieve in technique, cannot achieve so as to cause expected productive target, and resource allocation can not be assigned.Step of the present invention is: obtaining the specific data of production plan layer and dispatch layer；The uncertain lower plan layer cost model of demand and dispatch layer cost model are established respectively according to specific data；It is optimized using improved cooperative optimization method lower planning and scheduling cost model uncertain to demand, the final production decision for obtaining least cost.The present invention be directed to some problems in Production-Plan and scheduling optimization, it is proposed a kind of optimization method with stronger global optimization ability, the optimization method have the characteristics that opening, robustness, concurrency, global convergence and to the mathematical form of problem without particular/special requirement.

Description

An integrated optimization method for production planning and scheduling under uncertain demand

technical field

The invention belongs to the technical field of information and control, relates to automation technology, and in particular relates to an integrated optimization method for production planning and scheduling under uncertain demand.

Background technique

Production planning and scheduling has always been a decision-making issue that the chemical production industry attaches great importance to. Production planning and scheduling is the use of modern advanced methods and technologies, taking into account production process requirements, production resource conditions and other production constraints, optimizing the allocation of various manufacturing resources, formulating production plans that meet the production requirements of enterprises, and strive to meet the specified time. quantity to produce the desired product. The production plan is mainly based on factors such as the demand in a certain market and the production capacity of the chemical industry itself, and makes arrangements for production, transportation, storage, etc. for a long period (usually months, quarters, years, etc.). The production scheduling is mainly aimed at the production and storage capacity of the chemical industry itself. In the case of satisfying the results of the production plan as much as possible, a short period (usually daily, weekly, etc.) production equipment and resources such as inventory are arranged.

In the production planning and scheduling problem, due to the different time scales of the two, if only one is considered to perform pure production planning optimization or pure production scheduling optimization, the optimization result is difficult to be the optimal solution, and it is very difficult to achieve the optimal solution. It may be impossible to achieve in the process, resulting in the failure of the expected production goals and the failure of resource allocation to be issued. Therefore, the integrated optimization of production planning and scheduling is of great significance to improve enterprise efficiency and reduce production costs. The production planning and scheduling problem is a typical extreme value solving problem. So far, traditional mathematical optimization methods, such as branch and bound method, gradient descent method, outer approximation algorithm, etc., are mostly used to solve production and scheduling problems. Because these methods have low solution efficiency, and lack strong adaptability and robustness. Therefore, the optimization problem with complex mathematical form is required, which is quite difficult. Based on the above problems, we only consider the production planning and production scheduling problems under the uncertainty of market demand.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the invention proposes an integrated optimization method for production planning and scheduling under uncertain demand.

The concrete steps of the present invention are:

Step 1: It is necessary to obtain the specific data of production equipment, specific production process data, management cost unit price and product type data; these data are obtained through statistics in the production process;

Step 2: Establish a production planning cost model with uncertain demand through the parameters of the management, and the component is the management cost. The production scheduling cost model is established through the production process and raw material parameters, and the components are fixed production cost and variable production cost.

① Build a system-level model, that is, build a production planning cost and production scheduling cost model

Production planning cost and production scheduling cost are the upper-level problems of the integrated model. The goal is to plan the production in the entire planning cycle according to the market demand and the constraints of its own production capacity, so as to achieve the goal of minimizing the cost in the cycle. According to the scheduling period duration T, the planning period is divided into Q scheduling periods. Production planning cost PlanningCost and production scheduling model cost SchedulingCost consists of production cost ProductionCost, inventory cost InventoryCost, transportation cost TransprotCost, shortage cost BackorderCost, fixed production cost EquipmentCost and variable production cost TaskCost.

In the formula, t represents the time period, i represents the task, I represents the task set, j represents the equipment, J represents the task set, n represents the event point, and N represents the event point set. x _i,j,n indicates whether task i is executing on device j at the beginning of event point n. B _i,j,n represents the processing amount of task i on device j at the beginning of event point n.

Restrictions:

production balance

demand balance

production capacity constraints

In each production scheduling cycle, the expected output of the production plan cannot exceed the maximum production capacity

Pro, Inv, Tra, Bac represent production, inventory, transportation and shortage respectively;

4. Supplementary constraints

In the process of collaborative iterative solution, each scheduling period is regarded as a sub-discipline, and the minimum inconsistency between sub-disciplines is regarded as the constraint of the system-level planning period. τ is used to represent the difference between the planned expected output and the scheduled solution output. Pro _s,t represents the production plan solution output, Pro _s,t ′ represents the production scheduling solution output. μ is the relaxation factor in the complementary constraints.

②Build a subject-level model, that is, build a production planning and production scheduling model

Production planning and production scheduling are the lower-level problems of the integrated model. The goal is to arrange production resources and equipment in time sequence according to the optimization results of production planning and in combination with the constraints of resources and equipment in their own scheduling cycle. The results are close. The model of each production scheduling cycle is established using a state task network. Considering the demand uncertainty of the product, the uncertain decision variables are expressed based on the scenario method, and the occurrence probability corresponding to each demand uncertainty scenario k is Pk. Using the two-stage stochastic programming method, the production quantity PRO is the decision variable of the first stage, and the inventory quantity INV, the transportation quantity TRA, and the shortage quantity BAC are the decision variables of the second stage. The total cost of the production scheduling model consists of two parts, the fixed start-up cost of the equipment, EquipmentCost, and the material handling cost, TaskCost.

Production planning objective function:

k is the uncertain demand scenario, K is the set of uncertain demand scenarios, λ is the penalty function factor, and its value affects the degree of influence of the system-level optimization results on the subject-level optimization; s represents the material state, S _p represents the material set, and α , β, γ, and δ represent the unit price of production costs, the unit price of inventory costs, the unit price of transportation costs and the unit price of shortage costs;

Restrictions:

1. Production balance

2. Demand balance

3. Production capacity constraints

In each production scheduling cycle, the expected output of the production plan cannot exceed the maximum production capacity

4. Supplementary constraints

In the process of collaborative iterative solution, each scheduling period is regarded as a sub-discipline, and the minimum inconsistency among sub-disciplines is regarded as the constraint of the system-level planning period. τ is used to represent the difference between the planned expected output and the scheduled solution output. Pro _s,t represents the production plan solution output, Pro _s,t ′ represents the production scheduling solution output. μ is the relaxation factor in the complementary constraints.

Production scheduling objective function:

In the formula, τ _s is the deviation value between the value obtained from the discipline-level optimization and the value transmitted at the system level, and λ is the system-level deviation weight factor. Depending on the value, it can affect the production plan optimization result and the magnitude of the production scheduling optimization. The larger the effect, the stronger the impact, that is, the closer the point of production scheduling self-optimization is to the result delivered by the production plan.

Restrictions:

Inequality constraints

allocation constraints

Processing Capability Constraints

Reserve constraints

sequence constraints

δij is the time required for device i to process task _j

2. Equality constraints

2.1 Material balance constraints

ST _s,n represents the inventory of material state s at event point n; D _s,n represents the delivery volume of material state s at event point n; Represents the generation distribution coefficient of the material state s when the task i operation is performed, Then it represents the consumption distribution coefficient of the material state s when the task i operation is performed. Ij represents the set of tasks that device j can perform, and Ji represents the set of devices that perform task i.

Step 3 uses the improved collaborative optimization algorithm to solve the production planning and scheduling problem under uncertain demand. Specific steps are as follows:

① First, solve the system-level problem according to the uncertain market demand, and solve to obtain the output of the production plan and the corresponding output Pro _s,t of each production scheduling period of each product, and pass these values as the target point to Q subject-level questions;

②The production scheduling solves the optimal production cost according to the target point transmitted by the production planning model and combines its own constraints, and obtains the specific output Pro _s,t ′ of each product in each production scheduling cycle, and the total cost is recorded as TotalCost, which means SchedulingCost _t and Overall Scheduling Fee Sum. like The algorithm stops and outputs the current optimal solution; otherwise, go to step 3, and the total cost is recorded as

ε represents the threshold;

③ The system level obtains the difference and The obtained difference sum is used as a supplementary constraint for the next round of solution optimization. And pass the new optimized result yield to each production scheduling cycle. Record the cost PlanningCost' of the new production plan;

④The production scheduling is optimized according to the newly delivered target point, the return value is delivered to the system level, and the cost of each scheduling cycle is recorded as SchedulingCost _t ′ and the overall scheduling cost And note the new overall cost as:

⑤Compare the overall cost of the two times,

θ represents the iterative convergence threshold.

Beneficial effects: The objective of the present invention is to propose an integrated optimization method with strong global optimization ability, which has openness, Robustness, parallelism, global convergence, and no special requirements for the mathematical form of the problem. The technical scheme of the present invention is to decompose the production planning and scheduling problem under uncertain demand into a system-level and a plurality of subject-level problems, and then adopt the branch and bound method, and the method of penalty function and relaxation factor to make the system The interaction between the level and the discipline level, speeding up the solution speed, and finally obtaining an integrated optimization method with the lowest production cost.

Description of drawings

Figure 1 is the state task network diagram of the example;

FIG. 2 is a comparison of the cost of the algorithm of the present invention and the plan part of the simple scheduling optimization result.

Detailed ways:

A multi-product batch chemical production plant can produce two products (P ₁ , P ₂ ) from three raw materials (A, B, C) through heating, chemical reaction, separation and other processes. The state task network diagram of its technological process is shown in Figure 1. The reaction processes of Reaction 1, Reaction 2 and Reaction 3 can all be carried out in Reactor 1 and Reactor 2. The production planning period considered in the calculation example is 40 hours, and the production planning period is divided into 5 production scheduling periods.

The data of the production scheduling process is shown in Table 1 and 2, the data of the cost part is shown in Table 3, and the data of the cost part of the production plan is shown in Table 4.

Table 1 Production equipment process data

Table 2 Material status data (--- means unlimited)

Table 3 Production scheduling cost data

Table 4 Production planning cost data

The uncertain market demand is shown in Table 5.

Table 5 Market demand in different dispatch periods

When the market demand of the product is uncertain, it is assumed that the probability of occurrence of each discrete scenario is equal, and the decision maker is risk-neutral, that is, the probability of the three demand scenarios is 1/3, and the optimal relaxation factor is 11. The improved collaborative optimization model and collaborative optimization algorithm solution strategy, the obtained planning and scheduling results under demand uncertainty are shown in Table 6.

Table 6 adopts the optimization result of the algorithm of the present invention

For the convenience of comparison, we use the traditional simple production scheduling optimization method to solve the problem of this group of scenarios, and the optimized cost result is $17049.88. The specific data and cost data of each scheduling period are shown in Table 7.

Table 7 Optimization results using pure scheduling

As shown in Figure 2, according to the comparison between the results of pure scheduling optimization and the algorithm proposed by the present invention, we can find that the overall cost of the algorithm of the present invention is reduced by 34.53%. In the cost of simple scheduling optimization, the cost of production scheduling is low, but the shortage cost is high, mainly because the simple scheduling optimization only considers the market demand of the current scheduling cycle, and does not coordinate the entire production planning cycle and the cost of each production scheduling cycle. market demand. In the optimization solution according to the algorithm proposed in the present invention, the market demand of each production scheduling period is considered as a whole, and the cost of production planning and the cost of production scheduling are also comprehensively considered, so as to achieve the result of optimal overall cost.

Claims (1)

1. the integrated optimization method of production planning and scheduling under a demand uncertainty, is characterized in that, the step of this method comprises: Step 1: It is necessary to obtain the specific data of production equipment, specific production process data, management cost unit price and product type data; these data are obtained through statistics in the production process; Step 2: Establish a production planning cost model with uncertain demand through management parameters, and the components are management costs; establish a production scheduling cost model through production process and raw material parameters, and the components are fixed production costs and variable production costs; ① Build a system-level model, that is, build a production planning cost and production scheduling cost model Production planning cost and production scheduling cost are the upper-level problems of the integrated model. The goal is to plan the production in the entire planning cycle according to the market demand and the constraints of its own production capacity, so as to achieve the purpose of minimizing the cost in the cycle; according to the scheduling The cycle duration is T, and the planning cycle is divided into Q scheduling cycles. The production planning cost PlanningCost and the production scheduling model cost SchedulingCost are composed of the production cost ProductionCost, inventory cost InventoryCost, transportation cost TransprotCost, shortage cost BackorderCost, fixed production cost EquipmentCost and variable production cost TaskCost composition; In the formula, t represents the time period, i represents the task, I represents the task set, j represents the equipment, J represents the task set, n represents the event point, N represents the event point set; x _{i, j, n} represents the start of the event point n. Whether task i is executed on device j; B _i,j,n represents the processing amount of task i on device j at the beginning of event point n; Restrictions: production balance demand balance production capacity constraints In each production scheduling cycle, the expected output of the production plan cannot exceed the maximum production capacity Pro, Inv, Tra, Bac represent production, inventory, transportation and shortage respectively; 4. Supplementary constraints In the process of collaborative iterative solution, each scheduling cycle is used as a sub-discipline, and the inconsistency between sub-disciplines is minimized as a constraint of the system-level planning cycle; τ is used to represent the difference between the planned expected output and the scheduled solution output; Pro _s,t represents the production plan solution output, Pro _s,t ′ represents the production scheduling solution output; μ is the relaxation factor in the supplementary constraints; ②Build a subject-level model, that is, build a production planning and production scheduling model Production planning and production scheduling are the lower-level problems of the integrated model. The goal is to arrange production resources and equipment in time sequence according to the optimization results of production planning and in combination with the constraints of resources and equipment in their own scheduling cycle. The model of each production scheduling cycle is established by the state task network; considering the demand uncertainty of the product, the uncertain decision variables are expressed based on the scenario method, and the occurrence probability corresponding to each demand uncertainty scenario k is Pk; The two-stage stochastic programming method is applied. The production volume PRO is the first-stage decision variable, and the inventory volume INV, transportation volume TRA, and shortage BAC are the second-stage decision variables; TaskCost consists of two parts; Production planning objective function: k is the uncertain demand scenario, K is the set of uncertain demand scenarios, λ is the penalty function factor, and its value affects the degree of influence of the system-level optimization results on the subject-level optimization; s represents the material state, S _p represents the material set, and α , β, γ, and δ represent the unit price of production costs, the unit price of inventory costs, the unit price of transportation costs and the unit price of shortage costs; Restrictions: 1. Production balance 2. Demand balance 3. Production capacity constraints In each production scheduling cycle, the expected output of the production plan cannot exceed the maximum production capacity 4. Supplementary constraints In the process of collaborative iterative solution, each scheduling cycle is used as a sub-discipline, and the inconsistency between sub-disciplines is minimized as a constraint of the system-level planning cycle; τ is used to represent the difference between the planned expected output and the scheduled solution output; Pro _s,t represents the production plan solution output, Pro _s,t ′ represents the production scheduling solution output; μ is the relaxation factor in the supplementary constraints; Production scheduling objective function: In the formula, τ _s is the deviation value between the value obtained from the discipline-level optimization and the value transmitted at the system level, and λ is the system-level deviation weight factor. Depending on the value, it can affect the production plan optimization result and the magnitude of the production scheduling optimization. The greater the impact, the stronger the impact, that is, the closer the point of production scheduling self-optimization is to the result delivered by the production plan; Restrictions: Inequality constraints allocation constraints Processing Capability Constraints Reserve constraints sequence constraints δij is the time required for device i to process task _j 2. Equality constraints 2.1 Material balance constraints ST _s,n represents the inventory of material state s at event point n; D _s,n represents the delivery volume of material state s at event point n; Represents the generation distribution coefficient of the material state s when the task i operation is performed, Then it represents the consumption distribution coefficient of material state s when performing task i operation; I _j represents the task set that equipment j can perform, and J _i represents the equipment set that performs task i; Step 3 uses an improved collaborative optimization algorithm to solve the production planning and scheduling problem under uncertain demand. The specific steps are as follows: ① First, solve the system-level problem according to the uncertain market demand, and solve to obtain the output of the production plan and the corresponding output Pro _s,t of each production scheduling period of each product, and pass these values as the target point to Q subject-level questions; ②The production scheduling solves the optimal production cost according to the target point transmitted by the production planning model and combines its own constraints, and obtains the specific output Pro _s,t ′ of each product in each production scheduling cycle, and the total cost is recorded as TotalCost, which means SchedulingCost _t and Overall Scheduling Fee sum; if The algorithm stops and outputs the current optimal solution; otherwise, go to step 3, and the total cost is recorded as ε represents the threshold; ③ The system level obtains the difference and Use the obtained difference sum as a supplementary constraint to carry out the next round of solution optimization; pass the new optimization result output to each production scheduling cycle; record the cost of the new production plan PlanningCost'; ④The production scheduling is optimized according to the newly delivered target point, the return value is delivered to the system level, and the cost of each scheduling cycle is recorded as SchedulingCost _t ′ and the overall scheduling cost And note the new overall cost as: ⑤Compare the overall cost of the two times, θ represents the iterative convergence threshold.