CN118114808A - An integrated optimization method for process planning and resource scheduling of batch tasks - Google Patents

Abstract

The invention belongs to the technical field of resource allocation, and particularly relates to a process planning and resource scheduling integrated optimization method for batch tasks, which comprises the following steps: step one: the description of the process flow, alternative operations, and operation times is as follows: the resource distribution system, such as the manufacturing module and the logistics module, can simultaneously execute multiple types of tasks J= { J ₁,J₂,...,J_q }, and a resource set R= { R ₁,R₂,…,R_k }, wherein each task J _i can be divided into different stepsCan be expressed as follows: specifically, each step S _i,j may consist of a different process route, noted as: That is, step S _i,j has a u _i,j procedure route (u _i,j＝|S_i,j |), and procedure route L _i,j,u can be represented as a different sequence of operations. The invention utilizes transition time delay S ³ PR to carry out modeling analysis on the resource distribution system, aims at minimizing task completion time, and plans a process and a resource scheduling scheme.

Description

An integrated optimization method for process planning and resource scheduling of batch tasks

Technical Field

The present invention belongs to the technical field of resource configuration, and in particular relates to a process planning and resource scheduling integrated optimization method for batch tasks.

Background Art

Systems involving hardware or software resources (e.g., robots, machines, computing resources, etc.) such as manufacturing modules, logistics and transportation systems, and multi-threaded software systems can all be abstracted as resource allocation systems. In the research related to resource allocation systems, process planning and resource scheduling are core technologies that aim to achieve higher system throughput by optimizing parameters such as the number of resources and the order of processes.

Process planning focuses on selecting and sequencing production operations without considering the quantity or status of resources, while resource scheduling problems require allocating resources to selected operations. The integrated optimization problem of process planning and scheduling, called Integrated Process Planning and Scheduling, IPPS, has better system performance than individual optimization and has been widely studied in recent years.

IPPS solution methods can be divided into two types: exact methods and inexact methods, as follows:

For the former, branch-constrained methods, branch-and-cut procedures, and mixed-integer linear programming problems (MILPPs) are common techniques, among which MILPPs is the most widely used. However, these exact methods can only handle single-batch tasks, and it becomes complicated when considering batch tasks;

Therefore, imprecise algorithms such as heuristic algorithms and intelligent algorithms are gradually applied. In essence, heuristic algorithms are optimized based on the search direction guided by rules summarized from actual process planning and scheduling. The efficiency and diversity of intelligent optimization algorithms in global optimization make them more popular than heuristic techniques. Some new methods (such as machine learning, deep learning, and reinforcement learning) are also being tried. These algorithms can provide approximations in a very short time, and the results are very dependent on the encoding, decoding, and operations used.

Existing research focuses more on new approximate solution algorithms without the need to establish mathematical models, such as the Redis method proposed from the data cache level, which divides different job channels to allocate resources. However, the resource coupling relationship between batch tasks is more complex and the processing time is longer, which will be a great challenge. How to model and analyze the resource allocation system and realize the integrated optimal planning of process planning and resource scheduling of batch tasks has become an urgent problem to be solved. To this end, we propose a method to model and analyze the resource allocation system using the transition delay S ³ PR, with the goal of minimizing the task completion time, and an integrated optimization method for process planning and resource scheduling of batch tasks.

Summary of the invention

The purpose of the present invention is to provide a process planning and resource scheduling integrated optimization method for batch tasks, which can use the transition delay S ³ PR to model and analyze the resource allocation system, and plan the process and resource scheduling scheme with the goal of minimizing the task completion time.

The technical solution adopted by the present invention is as follows:

A method for integrated optimization of process planning and resource scheduling of batch tasks, comprising the following steps:

Step 1: Describe the process flow, available operations, and operation time as follows:

Resource allocation systems, such as manufacturing modules and logistics modules, can simultaneously execute multiple types of tasks J = {J ₁ ,J ₂ ,...,J _q }, resource sets R = {R ₁ ,R ₂ ,…,R _k }, where each task _Ji can be divided into different steps It can be expressed as follows:

Specifically, each step Si _,j can be composed of different process routes, recorded as:

That is, step S _i,j has process routing u _i,j (u _i,j = |S _i,j |), and the process routing L _i,j,u can be expressed as different operation sequences, denoted as:

Each operation requires the specification of a resource in Represents a mapping from operations O to resources R; operations that require the same resources compete for resources, such as machine tools, automated guided vehicles, robots, etc.

Step 2: Establish the transition delay S ³ PR model based on the description of tasks, steps, routes, operations, and resources;

Among them, the transition delay S ³ PR model Defined as a set of subnets A combination of and They are the starting place, the ending place, the activity place and the resource place respectively; the description of tasks, steps, routes, operations and resources, and the transition delay S ³ PR model is established according to Algorithm 1 in Table A below;

Table A Algorithm 1

Step 3: Establish a mixed integer linear programming model that integrates process planning and resource scheduling, as follows:

3.1) Objective function:

This study aims to reasonably determine the process path and manage resources to minimize the task completion time. The optimization objectives are as follows:

min z (1)

3.2) State transition constraints:

The state of the resource allocation system can be represented by a finite tag sequence M ₀ , M ₁ ,…, M _h of the transition delay S ³ PR model:

Formula (2) ensures the correctness of the state transition, where σ _i =[σ _i (t ₁ ),...,σ _i (t _m )] ^T is the emission count vector of the i-th stage; in other words, σ _i (t) ≥ 1 means that the operation corresponding to transition t is executed and the corresponding resources are occupied;

3.3) Task completion time constraints:

Let the emission completion vector τ _i =[τ _i (t ₁ ),τ _i (t ₂ ),…,τ _i (t _m )] ^T represent the emission completion time of the transition in the i-th stage, where τ _i (t) = 0 means that transition t is not enabled in this stage and the global clock starts from 0; the maximum completion time is defined as the maximum completion time of all tasks, that is, the maximum value of the maximum emission completion time of all transitions, which can be expressed as:

Considering the objective function (2), the above nonlinear constraints can be transformed into:

3.4) Transition emission completion time constraint:

Given a transition delay S ³ PR model N = <P, T, F, δ>, it can be divided into a process subnet N ^o = <P _O , T, F _O , δ> and a resource subnet N ^r = <P _R , T, F _R , δ>, where P _O = P _B ∪P _E ∪P _A , P _R = P _R ;

Given a transition delay S ³ PR model N = <P, T, F, δ>, a transition t is enabled in the transition delay S ³ PR if and only if the transition t is enabled in both subnets N ^o and N ^r ; in other words, the transition sets for the two subnets are the same, and the enabling of the transitions is subject to the common constraints of the two subnets; then the transition constraints in the process subnet N ^o and the resource subnet N ^r are defined as process constraints and resource constraints, respectively;

Since no resources have been used before phase 1, the first emission completion vector τ ₁ is expressed as:

τ ₁ ＝σ ₁ ⊙δ (4)

Among them, ⊙ represents the Hadamard product, that is,

Starting from phase 2, the emission completion time of transitions will be subject to two constraints, as follows:

First, consider the process constraints:

Defined as the set of initial transitions, the enabling of transitions _t∈TB is limited only by resource constraints; the transfer between processes is defined by the matrix In other words, if the transition t _j in stage i is the transition in stage i′ After execution,

Therefore, the following constraints need to be satisfied:

The above formula can be expressed as:

Where D(x) is defined as the sum of a matrix x or a vector x;

In order to satisfy the process constraints, transition tj _′ needs to satisfy Right now,

Among them, G _o ∈ {0,1} ^m×m is defined as the transition-predecessor-transition matrix, where:

In addition, the following constraints need to be met:

Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^No can be expressed as:

Furthermore, the above constraints can be transformed into the following linear constraints:

in, τ＝[τ ₁ ,τ ₂ ,…,τ _h ], H is a very large number;

Second, consider resource constraints:

Since the number of resources may be greater than 1, transition _tj only needs to use the resources released from transition _tj′ when every resource is used. The relationship between transition _tj in stage i and other transitions _tk is represented by yi _,j∈ {0,1} ^m×1 . If transition _tk is emitted in stage i and the emission time is no later than _tj , then yi _,j (k)＝1, otherwise yi _,j (k)＝0, that is,

The above formula can be further transformed into the following linear constraint:

Among them, ε is a very small number, and H is a very large number;

Therefore, when transition _tj starts firing, all the triggered transitions are represented as The corresponding resources used The cumulative number is described as follows:

Furthermore, the above constraints can be transformed into the following linear constraints:

Among them, _Gr∈ {0,1} ^k×m represents the transition-resource relationship matrix between resources and transitions:

Assume that the transition _tj in stage i uses the resources released by the transition _tj′ in stage i′, using the matrix Indicates that if all resources are triggered when transition t _j is used, a transition t _j′ must be selected, namely:

in, For the quantity of each resource, it can be expressed as:

Furthermore, the above constraints can be transformed into the following linear constraints:

Among them, ε is a very small number, and H is a very large number;

In addition, the following constraints need to be met:

in, is a row vector with all elements equal to 1;

Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^Nr can be expressed as:

The above formula can be further transformed into the following linear constraint:

3.5) Integrate the mixed integer linear programming model:

Through equations (1)-(13), the mixed integer linear programming model can be described as follows:

Step 4: Use the Gurobi optimization toolbox in MATLAB to solve the optimal solution of the linear model and conduct experimental analysis.

The technical effects achieved by the present invention are:

The present invention provides an integrated optimization method for process planning and resource scheduling of batch tasks, which can select process operations and reasonably schedule resources for different batch tasks according to the workflow to minimize the task completion time, making up for the defects of existing precise mathematical models and providing theoretical support for non-precise algorithms, planning processes and resource scheduling solutions.

The present invention provides an integrated optimization method for process planning and resource scheduling of batch tasks, which realizes a resource allocation system such as a manufacturing module and a logistics module through the Internet of Things technology. It can simultaneously execute multiple types of tasks and complete resource collection. It is suitable for process planning and resource scheduling of batch tasks to cope with the challenges brought about by more complex resource coupling relationships between batch tasks.

The present invention provides a batch task process planning and resource scheduling integrated optimization method. Given the description of tasks, steps, routes, operations, and resources, a transition delay S ³ PR model is established according to Algorithm 1. These factors are considered to meet the needs of processing various sudden problems on the batch task site, effectively reduce concurrency, and extend the working time of the method.

The process planning and resource scheduling integrated optimization method for batch tasks of the present invention takes process constraints and resource constraints into consideration, and can refine the precise mathematical model to make the planning of process and resource scheduling schemes more accurate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for integrated optimization of process planning and resource scheduling for batch tasks of the present invention;

FIG2 is a flow chart of two tasks of an embodiment of the present invention;

FIG3 is a schematic diagram of a transition delay S ³ PR model of the present invention;

FIG. 4 is a statistical diagram of the process planning and resource scheduling results of the present invention.

DETAILED DESCRIPTION

In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

As shown in Figure 1-4, a method for integrated optimization of process planning and resource scheduling for batch tasks includes the following steps:

Step 1: Describe the process flow, available operations, and operation time as follows:

Resource allocation systems, such as manufacturing modules and logistics modules, can simultaneously execute multiple types of tasks J = {J ₁ ,J ₂ ,…,J _q }, resource set R = {R ₁ ,R ₂ ,…,R _k }, implemented through the Internet of Things technology, suitable for process planning and resource scheduling of batch tasks, where each task _Ji can be divided into different steps It can be expressed as follows:

Specifically, each step Si _,j can be composed of different process routes, recorded as:

That is, step S _i,j has process routing u _i,j (u _i,j = |S _i,j |), and the process routing L _i,j,u can be expressed as different operation sequences, denoted as:

Each operation requires the specification of a resource in Represents a mapping from operations O to resources R; operations that require the same resources compete for resources, such as machine tools, automated guided vehicles, robots, etc.

In this embodiment, the system is composed of two tasks J = {J ₁ , J ₂ } and six resources R = {R ₁ , R ₂ , C ₁ ..., C ₄ }. The details of the process are as follows:

Step 2: Establish the transition delay S ³ PR model based on the description of tasks, steps, routes, operations, and resources;

Among them, the transition delay S ³ PR model Defined as a set of subnets A combination of and They are the starting place, the ending place, the activity place and the resource place; the description of tasks, steps, routes, operations and resources. According to the algorithm 1 in Table A below, the transition delay S ³ PR model is established, which takes into account various factors to meet the processing of various emergencies on the batch task site, effectively reduce concurrency and extend the working time of this method;

Table A Algorithm 1

In this embodiment, as shown in FIG3 , a transition delay S ³ PR model is established according to Algorithm 1, wherein _PB = {p ₁ , p ₇ }, _PE = {p ₆ , p ₁₂ }, _PA = {p ₂ , p ₃ , p ₄ , p ₅ , p ₈ , p ₉ , p ₁₀ , p ₁₁ }, _PR = {p ₁₃ , p ₁₄ }, T = {t ₁ , t ₂ , ..., t ₁₁ }, and the relationship between operation, transition and delay time is shown in Table B below:

Table B Relationship between operation, transition and delay time

Step 3: Establish a mixed integer linear programming model that integrates process planning and resource scheduling, as follows:

3.1) Objective function:

This study aims to reasonably determine the process path and manage resources to minimize the task completion time. The optimization objectives are as follows:

min z (1)

3.2) State transition constraints:

The state of the resource allocation system can be represented by a finite tag sequence M ₀ , M ₁ ,…, M _h of the transition delay S ³ PR model:

Formula (2) ensures the correctness of the state transition, where σ _i =[σ _i (t ₁ ),...,σ _i (t _m )] ^T is the emission count vector of the i-th stage; in other words, σ _i (t) ≥ 1 means that the operation corresponding to transition t is executed and the corresponding resources are occupied;

3.3) Task completion time constraints:

Let the emission completion vector τ _i =[τ _i (t ₁ ),τ _i (t ₂ ),…,τ _i (t _m )] ^T represent the emission completion time of the transition in the i-th stage, where τ _i (t) = 0 means that transition t is not enabled in this stage and the global clock starts from 0; the maximum completion time is defined as the maximum completion time of all tasks, that is, the maximum value of the maximum emission completion time of all transitions, which can be expressed as:

Considering the objective function (2), the above nonlinear constraints can be transformed into:

3.4) Transition emission completion time constraint:

Given a transition delay S ³ PR model N = <P, T, F, δ>, it can be divided into a process subnet N ^o = <P _O , T, F _O , δ> and a resource subnet N ^r = <P _R , T, F _R , δ>, where P _O = P _B ∪P _E ∪P _A , P _R = P _R ;

Given a transition delay S ³ PR model N = <P, T, F, δ>, a transition t is enabled in the transition delay S ³ PR if and only if the transition t is enabled in both subnets N ^o and N ^r ; in other words, the transition sets for the two subnets are the same, and the enabling of the transitions is subject to the common constraints of the two subnets; then the transition constraints in the process subnet N ^o and the resource subnet N ^r are defined as process constraints and resource constraints, respectively;

Since no resources have been used before phase 1, the first emission completion vector τ ₁ is expressed as:

τ ₁ ＝σ ₁ ⊙δ (4)

Among them, ⊙ represents the Hadamard product, that is,

Starting from phase 2, the emission completion time of transitions will be subject to two constraints, as follows:

First, consider the process constraints:

Defined as the set of initial transitions, the enabling of transitions _t∈TB is limited only by resource constraints; the transfer between processes is defined by the matrix In other words, if the transition _tj in stage i is the transition in stage i′ After execution,

Therefore, the following constraints need to be satisfied:

The above formula can be expressed as:

Where D(x) is defined as the sum of a matrix x or a vector x;

In order to satisfy the process constraints, transition tj _′ needs to satisfy Right now,

Among them, G _o ∈ {0,1} ^m×m is defined as the transition-predecessor-transition matrix, where:

In addition, the following constraints need to be met:

Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^No can be expressed as:

Furthermore, the above constraints can be transformed into the following linear constraints:

in, τ＝[τ ₁ ,τ ₂ ,...,τ _h ], H is a very large number;

Second, consider resource constraints:

Since the number of resources may be greater than 1, transition _tj only needs to use the resources released from transition _tj′ when every resource is used. The relationship between transition _tj in stage i and other transitions _tk is represented by yi _,j∈ {0,1} ^m×1 . If transition _tk is emitted in stage i and the emission time is no later than _tj , then yi _,j (k)＝1, otherwise yi _,j (k)＝0, that is,

The above formula can be further transformed into the following linear constraint:

Among them, ε is a very small number, and H is a very large number;

Therefore, when transition _tj starts firing, all the triggered transitions are represented as The corresponding resources used The cumulative number is described as follows:

Furthermore, the above constraints can be transformed into the following linear constraints:

Among them, _Gr∈ {0,1} ^k×m represents the transition-resource relationship matrix between resources and transitions:

Assume that the transition _tj in stage i uses the resources released by the transition _tj′ in stage i′, using the matrix Indicates that if all resources are triggered when transition t _j is used, a transition t _j′ must be selected, namely:

in, For the quantity of each resource, it can be expressed as:

Furthermore, the above constraints can be transformed into the following linear constraints:

Among them, ε is a very small number, and H is a very large number;

In addition, the following constraints need to be met:

in, is a row vector with all elements equal to 1;

Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^Nr can be expressed as:

The above formula can be further transformed into the following linear constraint:

3.5) Integrate the mixed integer linear programming model:

Through equations (1)-(13), the mixed integer linear programming model can be described as follows:

Step 4: Use the Gurobi optimization toolbox in MATLAB to solve the optimal solution of the linear model and conduct experimental analysis.

In this embodiment, consider that the batch size of both tasks is 3, that is, both Job ₁ and Job ₂ need to be completed three times, and the process planning and resource scheduling results are shown in Figure 4. The results show that the first and third work of Job ₁ is completed by resource C ₁ , while the second work is completed by resource C _2. The time occupied by each resource by the operation is shown in Figure 4.

In summary, the present invention can select process operations for different batch tasks according to the workflow and reasonably schedule resources to minimize the task completion time, which makes up for the defects of the existing precise mathematical model and provides theoretical support for the imprecise algorithm.

The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims (10)

1. A method for integrated optimization of process planning and resource scheduling of batch tasks, characterized in that it comprises the following steps: Step 1: Describe the process flow, available operations, and operation time; Step 2: Establish the transition delay S ³ PR model based on the description of tasks, steps, routes, operations, and resources; Step 3: Establish a mixed integer linear programming model integrating process planning and resource scheduling; Step 4: Use the Gurobi optimization toolbox in MATLAB to solve the optimal solution of the linear model and conduct experimental analysis. 2. According to claim 1, a method for integrated optimization of process planning and resource scheduling of batch tasks, characterized in that: step 1 comprises: A resource allocation system, wherein the resource allocation system can simultaneously execute several types of tasks J = {J ₁ , J ₂ , ..., J _q }, a resource set R = {R ₁ , R ₂ , ..., R _k }, wherein each task _Ji can be divided into different steps It can be expressed as follows: Specifically, each step Si _,j can be composed of different process routes, recorded as: That is, step S _i,j has a process route u _i,j (u _i,j = |S _i,j |), and the process route L _i,j,u can be expressed as several operation sequences, denoted as: Furthermore, each operation specifies a resource in Represents a mapping from operations O to resources R. 3. According to claim 2, a method for integrated optimization of process planning and resource scheduling for batch tasks is characterized in that: the resource allocation system includes a manufacturing module for executing several types of tasks and a logistics module for resource aggregation. 4. The process planning and resource scheduling integrated optimization method for batch tasks according to claim 1, characterized in that: the transition delay S ³ PR model is: and is defined as a set of subnets A combination of and They are starting place, ending place, activity place and resource place; Among them, set P _B = {p ₁ , p ₇ }, P _E = {p ₆ , p ₁₂ }, P _A = {p ₂ , p ₃ , p ₄ , p ₅ , p ₈ , p ₉ , p ₁₀ , p ₁₁ }, P _R = {p ₁₃ , p ₁₄ }, T = {t ₁ , t ₂ ,..., t ₁₁ }. 5. The process planning and resource scheduling integrated optimization method for batch tasks according to claim 1 is characterized in that: the step three comprises the following steps: M1: Establish the objective function; M2: state transition constraint; M3: Task completion time constraint; M4: Transition launch completion time constraint; M5: Integrating mixed-integer linear programming models. 6. The process planning and resource scheduling integrated optimization method for batch tasks according to claim 1 is characterized in that: the objective function is: min z (1) It is used as the optimization target. 7. A method for integrated optimization of process planning and resource scheduling of batch tasks according to claim 1, characterized in that: the state of the resource allocation system in step M2 is represented by a finite tag sequence M ₀ , M ₁ , ..., M _h of a transition delay S ³ PR model, as follows: Formula (2) ensures the correctness of the state transition, where σ _i =[σ _i (t ₁ ),...,σ _i (t _m )] ^T is the emission count vector of the i-th stage; and σ _i (t)≥1 means that the operation corresponding to transition t is executed and the corresponding resources are occupied. 8. A method for integrated optimization of process planning and resource scheduling of batch tasks according to claim 1, characterized in that: in step M3, let the emission completion vector τ _i =[τ _i (t ₁ ),τ _i (t ₂ ),...,τ _i (t _m )] ^T represent the emission completion time of the i-th stage transition; Where τ _i (t) = 0 means that transition t is not enabled in this phase, and the global clock starts from 0; the maximum completion time is defined as the maximum completion time of all tasks, or the maximum value of the maximum emission completion time of all transitions, as follows: Considering the objective function (2), the above nonlinear constraints can be transformed into: 9. A method for integrated optimization of process planning and resource scheduling of batch tasks according to claim 1, characterized in that: in said step M4, a transition delay S ³ PR model N = <P, T, F, δ> is set, which is divided into a process subnet N ^o = <P _O , T, F _O , δ> and a resource subnet N ^r = <P _R , T, F _R , δ>, wherein P _O = P _B ∪P _E ∪P _A , P _R = P _R ; Assume a transition delay S ³ PR model N = <P, T, F, δ>, and only when transition t is enabled in both subnets N ^o and N ^r , the transition t is enabled in the transition delay S ³ PR, so that the transition sets for the two subnets are the same, and the enabling of transitions is subject to the common constraints of the two subnets; then define the transition constraints in the process subnet N ^o and the resource subnet N ^r as process constraints and resource constraints respectively; Since no resources have been used before phase 1, the first emission completion vector τ ₁ is expressed as: τ ₁ ＝σ ₁ ⊙δ (4) Among them, ⊙ represents the Hadamard product, that is, Starting from phase 2, the emission completion time of the transition will be subject to two constraints, as follows: First, consider the process constraints: Defined as the set of initial transitions, the enabling of transitions _t∈TB is limited only by resource constraints; the transfer between processes is defined by the matrix Represents that if the transition t _j of the i-th stage is executed after the transition t _j′ ∈ ^·· t _j of the i′th stage, then Therefore, the following constraints need to be met: The above formula can be expressed as: Where D(x) is defined as the sum of a matrix x or a vector x; In order to satisfy the process constraints, the transition t _j′ must satisfy t _j′ ∈ ^·· t _j , that is: Among them, G _o ∈ {0,1} ^m×m is defined as the transition-predecessor-transition matrix, where: In addition, the following constraints must be met: Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^No is expressed as: The above constraints are transformed into the following linear constraints: in, τ＝[τ ₁ ,τ ₂ ,...,τ _h ], H is a very large number; Second, consider resource constraints: When every resource is utilized, transition _tj needs to use the resources released from transition _tj′ ; the relationship between transition _tj in stage i and other transitions _tk is represented by y _i,j ∈{0,1} ^m×1 ; If transition t _k is emitted in stage i and the emission time is no later than t _j , then yi _,j (k) = 1, otherwise _yi,j (k) = 0, that is, The above formula is transformed into the following linear constraint: Among them, ε is a very small number, and H is a very large number; Therefore, when transition _tj starts firing, all the triggered transitions are represented as The corresponding resources used The cumulative number is described as follows: The above constraints are transformed into the following linear constraints: Among them, _Gr∈ {0,1} ^k×m represents the transition-resource relationship matrix between resources and transitions: Assume that the transition _tj in stage i uses the resources released by the transition _tj′ in stage i′, using the matrix Indicates that if all resources are triggered when transition t _j is used, a transition t _j′ must be selected, namely: in, For the quantity of each resource, it can be expressed as: The above constraints are transformed into the following linear constraints: Among them, ε is a very small number, and H is a very large number; In addition, the following constraints are met: in, is a row vector with all elements equal to 1; Based on the above constraints, the completion time constraint of transition _tj in subnetwork ^Nr is expressed as: The above formula is transformed into the following linear constraint: 10. The process planning and resource scheduling integrated optimization method for batch tasks according to claim 1, characterized in that: in step M5, the mixed integer linear programming model is described as follows through equations (1)-(13):