Flexible manufacturing resource collaborative allocation optimization method and system oriented to changeable delivery time

Abstract

The invention discloses a flexible manufacturing resource collaborative allocation optimization method and system oriented to variable delivery periods, and relates to the technical field of scheduling control, and the method comprises the steps: installing a process completion confirmation label in each work-in-process link, and directly obtaining an equipment load, a work-in-process state and the completion time; in combination with order arrival prediction and equipment health conditions, a disturbance intensity evaluation algorithm is set, the current scheduling disturbance quantity is calculated, and the disturbance intensity of each sub-problem is quantified; based on the disturbance intensity of each sub-problem and the longest response time of the system, setting an adaptive sub-problem time window algorithm, and dynamically adjusting the time window range of the to-be-rearranged task; and carrying out hierarchical division on the key tasks and the secondary tasks in the sub-problem range, carrying out parallel calculation and then carrying out merging scheduling to form an updated collaborative scheduling scheme. According to the invention, during order change, equipment failure or material shortage, the affected subset tasks can be quickly identified, the scheduling range is limited, global recalculation is avoided, and quick response is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of scheduling control, in particular to a flexible manufacturing resource collaborative scheduling optimization method and system for variable delivery time. BACKGROUND

[0002] Traditional static scheduling methods are difficult to meet the flexible production demand under variable delivery time. Enterprises need to dynamically and real-timely collaboratively schedule multi-dimensional resources such as orders, equipment, personnel and materials, so as to improve production response speed, reduce overdue risk, improve resource utilization and production efficiency, and realize the management mode from passive pursuit to active prediction.

[0003] Most traditional methods, such as batch scheduling based on heuristic rules and planning based on fixed Gantt chart, assume stable production conditions at the beginning of formulation. Once the delivery time changes or the equipment fails, manual rearrangement is required, and the response is lagging. And real-time scheduling methods usually only optimize locally for short-term or single production line, and are difficult to realize cross-resource collaboration at the whole factory or multi-workshop level, and are prone to local optimization rather than global optimization.

[0004] Therefore, the present application provides a flexible manufacturing resource collaborative scheduling optimization method and system for variable delivery time. SUMMARY

[0005] The purpose of the present application is to provide a flexible manufacturing resource collaborative scheduling optimization method and system for variable delivery time to solve the problems existing in the background art.

[0006] To achieve the above purpose, the present application provides the following technical scheme: a flexible manufacturing resource collaborative scheduling optimization method for variable delivery time, comprising the following steps: S1, uniformly deploying real-time state sensors on key equipment and stations in the production site, and installing process completion confirmation tags at each work-in-process link, directly obtaining equipment load, work-in-process state and completion time; S2, collecting order process progress, processing time and equipment availability data in real time through the PLC / SCADA system deployed on each production line; S3, using historical scheduling data and real-time collected data, combining order arrival prediction and equipment health status, calculating the current scheduling disturbance by setting a disturbance intensity evaluation algorithm, and quantifying the disturbance intensity of each sub-problem; S4, setting an adaptive sub-problem time window algorithm based on the disturbance intensity of each sub-problem and the longest response time of the system, dynamically adjusting the time window range of the tasks to be rearranged; S5, hierarchically dividing the key tasks and secondary tasks in the sub-problem range, respectively using accurate MILP solution and efficient heuristic solution, and merging the scheduling after parallel calculation to form an updated collaborative scheduling scheme.

[0007] The application further improves that the historical scheduling data is extracted from the system database to obtain the order processing time, equipment utilization, rescheduling execution time and results in a certain period in the past, including the process sequence, process processing time and switching loss of each task; through the integrated equipment health interface, the failure level and maintenance interval of each key equipment are obtained, and the failure level and maintenance interval are standardized and weighted to obtain the equipment risk impact value.

[0008] The application further improves that the disturbance intensity evaluation algorithm takes each hour as a recording period, calculates the standardized values of the total processing amount of new or changed orders, the weight of key equipment failure and the number of material gap tasks in each period; and the standardized values are weighted and synthesized to obtain the disturbance intensity ΔDis; based on the relationship between the disturbance intensity and the rescheduling response time in the same recording period, a support vector machine model is used to establish a disturbance intensity-optimal time window range relationship model, and the optimal sub-problem time window W corresponding to the current disturbance intensity is obtained through the model.

[0009] The application further improves that the adaptive sub-problem time window algorithm is constructed based on the cooperation of the particle swarm algorithm and the annealing algorithm, and the specific steps include: S41, determining the decision variable as the scheduling parameter, including the start time, processing sequence and switching sequence of each order on each equipment; S42, initializing the particle swarm, and randomly generating an initial scheduling parameter set for each particle; S43, setting the fitness function Fd; S44, setting the fitness threshold, generating a new position for the particle with a fitness greater than the set fitness threshold by local disturbance; for the particle with a fitness less than or equal to the set fitness threshold, feeding back the corresponding task to the disturbance intensity evaluation algorithm to recalculate the sub-problem time window and update the set of tasks to be scheduled, and re-entering step S43; S45, calculating the absolute value of the fitness difference value of the new and old particle positions to obtain the fitness difference value; S46, setting the maximum difference threshold Δmax, when the fitness difference value is less than or equal to Δmax, updating the annealing update probability according to the particle swarm algorithm for re-updating; otherwise, directly replacing the old position with the new position; S47, after each iteration, calculating the difference between the actual processing load and the average load of each equipment, if the difference is greater than the set threshold, returning to step S44, otherwise terminating the iteration and outputting the current scheduling parameter.

[0010] A further improvement of this invention is that the fitness function Fd calculates the scheduling accuracy fitness and the load balancing fitness respectively by using a differential algorithm, combining the disturbance intensity ΔDis output by the disturbance intensity evaluation algorithm and the sub-problem time window W, and then weighted summing the two to obtain the total fitness.

[0011] A further improvement of this invention is that the scheduling accuracy fitness is obtained by calculating the average percentage of the absolute values ​​of the deviations between the predicted and actual completion times of each critical task, and subtracting this average value from the baseline value 1; the load balancing fitness is obtained by calculating the absolute value of the difference between the standard deviation of the actual load of each device and the standard deviation of the predicted load of the current sub-problem at the same time node in all historical recording periods, reflecting the degree of load balancing.

[0012] A further improvement of this invention is that the annealing update probability is obtained by calculating an exponential function of the fitness difference value with the natural constant e as the base and the ratio of k×Td, where k is the Boltzmann constant and Td is a temperature parameter that gradually decreases with the number of iterations.

[0013] A further improvement of this invention is that the real-time status sensor collects equipment load rate and operating status at fixed time intervals, and the process completion tag is automatically written into the MES system at the end of each process. The collected data is transmitted to the central dispatch and control system through industrial Ethernet or wireless network, and the system will dynamically update steps S3–S5 according to the received real-time data.

[0014] A further improvement of this invention is that the critical equipment fault weight includes counting the number of faults of the current equipment within the period. Average downtime per failure The original fault impact value was obtained. To each device Normalization is mapped to the range [0,1] to obtain the fault weights of critical equipment.

[0015] On the other hand, the present invention provides a flexible manufacturing resource collaborative allocation and optimization system for variable delivery times, comprising: The data acquisition module is used to uniformly deploy real-time status sensors on key equipment and workstations in the production site, and install process completion confirmation tags on each work-in-process stage to directly acquire equipment load, work-in-process status and completion time; through the PLC / SCADA system deployed on each production line, it collects process progress, processing time and equipment availability data of each order in real time; The disturbance intensity assessment algorithm construction module is used to calculate the current scheduling disturbance amount by using historical scheduling data and real-time collected data, combined with order arrival prediction and equipment health status, and quantifying the disturbance intensity of each sub-problem by setting the disturbance intensity assessment algorithm; The task reordering module is used to set an adaptive sub-problem time window algorithm based on the perturbation intensity of each sub-problem and the longest system response time, and dynamically adjust the time window range of the tasks to be reordered. The scheduling solution module is used to divide the critical and secondary tasks within the scope of the sub-problem into layers, and then use precise MILP solution and efficient heuristic solution respectively. After parallel computation, the schedules are merged to form an updated collaborative scheduling scheme.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention first constructs a sub-problem partitioning strategy based on local perturbation awareness to achieve rapid identification and scheduling region limitation of affected subset tasks, thereby improving response speed and avoiding global recalculation; 2. A dynamic granular scheduling mechanism is introduced to adaptively adjust the solution range based on the urgency of the task and the degree of resource conflict, taking into account both rapid local optimization and the quality of the overall solution. 3. Construct a resource coordination graph model based on the weighting of key resource bottlenecks to realize the modeling and synchronous allocation of the coupling relationship of resources such as equipment, manpower, and materials. Attached Figure Description

[0017] Figure 1 This is a flowchart of the flexible manufacturing resource collaborative allocation optimization method for multiple delivery periods according to the present invention; Figure 2 This is a schematic diagram of the flexible manufacturing resource collaborative allocation and optimization system for variable delivery times according to the present invention. Detailed Implementation

[0018] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0019] The term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three cases: A exists alone, A and B exist simultaneously, and B exists alone.

[0020] Example 1 Figure 1 The flowchart of the flexible manufacturing resource collaborative allocation optimization method for variable delivery times disclosed in this embodiment is shown, and the steps are as follows: S1. Distribute real-time status sensors evenly on key equipment and workstations in the production site, and install process completion confirmation tags at each work-in-process stage to directly obtain equipment load, work-in-process status and completion time. S2. Through the PLC / SCADA system deployed on each production line, real-time data on the process progress, processing time and equipment availability of each order are collected. S3. Utilizing historical scheduling data and real-time collected data, combined with order arrival predictions and equipment health status, calculate the current scheduling disturbance amount by setting a disturbance intensity assessment algorithm, and quantify the disturbance intensity of each sub-problem; The historical scheduling data is extracted from the system database, including order processing time, equipment utilization, rescheduling execution time, and results over a certain period. This data encompasses the process sequence, processing time, and changeover losses for each task. Through an integrated equipment health interface, the fault levels and maintenance intervals of key equipment are obtained. These fault levels and maintenance intervals are standardized and then weighted and summed to obtain the equipment risk impact value. Introducing historical scheduling and equipment health data makes disturbance assessment more comprehensive, considering both fault risk and maintenance needs. It also improves the predictive ability for system anomalies (such as equipment failure and material shortages) and enhances the robustness of rescheduling decisions.

[0021] The disturbance intensity assessment algorithm uses an hourly recording period to calculate the standardized values ​​of the total processing volume of newly added or changed orders, the fault weight of critical equipment, and the number of material shortage tasks within each period. These standardized values ​​are then weighted to synthesize the disturbance intensity ΔDis. Based on the relationship between disturbance intensity and rescheduling response time within the same historical recording period, a support vector machine model is used to establish a disturbance intensity-optimal time window range relationship model. This model yields the optimal sub-problem time window W corresponding to the current disturbance intensity. It can dynamically adjust the sub-problem range, enabling both rapid response and guaranteed scheduling quality under different disturbance scenarios. The fault weight of critical equipment includes the number of faults of the current equipment within the period. This reflects the degree of "instability" of the equipment, specifically the average downtime per failure. The original fault impact value was obtained. To each device Normalization is mapped to the range [0,1] to obtain the fault weights of critical equipment.

[0022] S4. Based on the perturbation intensity of each sub-problem and the longest response time of the system, set an adaptive sub-problem time window algorithm to dynamically adjust the time window range of the tasks to be rearranged. The adaptive subproblem time window algorithm is constructed based on the combined use of particle swarm optimization and annealing algorithms. The specific steps include: S41. Determine the decision variables as scheduling parameters, including the start time, processing sequence, and switching sequence of each order on each device; S42. Initialize the particle swarm and randomly generate an initial set of scheduling parameters for each particle. S43. Set the fitness function Fd; The fitness function Fd calculates the scheduling accuracy fitness and the load balancing fitness respectively by using a differential algorithm, combined with the disturbance intensity ΔDis output by the disturbance intensity evaluation algorithm and the sub-problem time window W, and then weights and sums the two to obtain the total fitness. The scheduling accuracy fitness is obtained by calculating the average percentage of the absolute values ​​of the deviations between the predicted and actual completion times of each critical task, and subtracting this average value from the baseline value of 1. The load balancing fitness is calculated by calculating the absolute value of the difference between the standard deviation of the actual load of each device and the standard deviation of the predicted load of the current subproblem at the same time point in all historical recording periods, reflecting the degree of load balancing. A composite fitness function that integrates disturbance intensity and time window parameters is defined to balance scheduling accuracy and resource load balancing. A clear multi-objective evaluation index is provided for the particle swarm / annealing algorithm to improve the direction of optimization.

[0023] By calculating the scheduling accuracy fitness and load balancing fitness separately, the impact of scheduling schemes on delinquency rates and equipment utilization can be evaluated in a fine-grained manner; by comparing historical standard deviations with current forecasts, the load distribution can be made more balanced, reducing equipment bottlenecks and idle waste.

[0024] S44. Set a fitness threshold. Perform local perturbation to generate new positions for particles with fitness greater than the set fitness threshold. For particles with fitness less than or equal to the set fitness threshold, feed back their corresponding tasks to the perturbation intensity evaluation algorithm to recalculate the sub-problem time window and update the set of tasks to be scheduled, and then send them back to step S43. S45. Calculate the absolute value of the fitness difference between the old and new particle positions to obtain the fitness difference value; S46. Set the maximum difference threshold Δmax. When the fitness difference value is less than or equal to Δmax, update the annealing update probability according to the particle swarm algorithm; otherwise, directly replace the old position with the new position. The annealing update probability is obtained by calculating the exponential function of the fitness difference value with the natural constant e as the base and the ratio of k×Td, where k is the Boltzmann constant and Td is the temperature parameter that gradually decreases with the number of iterations.

[0025] S47. After each iteration, calculate the difference between the actual processing load and the average load of each device. If the difference is greater than the set threshold, return to step S44; otherwise, terminate the iteration and output the current scheduling parameters.

[0026] S5. Divide the key tasks and secondary tasks within the scope of the sub-problem into layers, and use exact MILP and efficient heuristic solutions respectively. After parallel computation, merge the schedules to form an updated collaborative scheduling scheme.

[0027] The real-time status sensor collects equipment load rate and operating status at fixed time intervals. The process completion tag is automatically written into the MES system at the end of each process. The collected data is transmitted to the central dispatch and control system through industrial Ethernet or wireless network. The system will dynamically update steps S3-S5 based on the received real-time data.

[0028] The threshold and weight settings can be set by default according to the present invention, or they can be set by the operator.

[0029] Example 2 Figure 2 This invention presents a framework diagram of a flexible manufacturing resource collaborative allocation and optimization system for variable delivery times. Based on the same inventive concept as Embodiment 1, this invention provides a flexible manufacturing resource collaborative allocation and optimization system for variable delivery times, comprising: The data acquisition module is used to uniformly deploy real-time status sensors on key equipment and workstations in the production site, and install process completion confirmation tags on each work-in-process stage to directly acquire equipment load, work-in-process status and completion time; through the PLC / SCADA system deployed on each production line, it collects process progress, processing time and equipment availability data of each order in real time; The disturbance intensity assessment algorithm construction module is used to calculate the current scheduling disturbance amount by using historical scheduling data and real-time collected data, combined with order arrival prediction and equipment health status, and quantifying the disturbance intensity of each sub-problem by setting the disturbance intensity assessment algorithm; The task reordering module is used to set an adaptive sub-problem time window algorithm based on the perturbation intensity of each sub-problem and the longest system response time, and dynamically adjust the time window range of the tasks to be reordered. The scheduling solution module is used to divide the critical and secondary tasks within the scope of the sub-problem into layers, and then use precise MILP solution and efficient heuristic solution respectively. After parallel computation, the schedules are merged to form an updated collaborative scheduling scheme.

[0030] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0031] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0032] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0033] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0034] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for collaborative allocation and optimization of flexible manufacturing resources for flexible manufacturing with varying delivery times, characterized by: Includes the following steps: S1. Distribute real-time status sensors evenly on key equipment and workstations in the production site, and install process completion confirmation tags at each work-in-process stage to directly obtain equipment load, work-in-process status and completion time. S2. Through the PLC / SCADA system deployed on each production line, real-time data on the process progress, processing time and equipment availability of each order are collected. S3. Utilizing historical scheduling data and real-time collected data, combined with order arrival predictions and equipment health status, calculate the current scheduling disturbance amount by setting a disturbance intensity assessment algorithm, and quantify the disturbance intensity of each sub-problem; S4. Based on the perturbation intensity of each sub-problem and the longest response time of the system, set an adaptive sub-problem time window algorithm to dynamically adjust the time window range of the tasks to be rearranged. S5. Divide the key tasks and secondary tasks within the scope of the sub-problem into layers, and use exact MILP and efficient heuristic solutions respectively. After parallel computation, merge the schedules to form an updated collaborative scheduling scheme.

2. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 1, characterized in that: The historical scheduling data is obtained by extracting order processing time, equipment utilization, rescheduling execution time and results from the system database within a certain period of the past. It includes the process sequence, process processing time and switching loss of each task. Through the integrated equipment health interface, the fault level and maintenance interval of each key equipment are obtained. The fault level and maintenance interval are standardized and then weighted and summed to obtain the equipment risk impact value.

3. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 2, characterized in that: The disturbance intensity assessment algorithm uses one hour as a recording period, calculates the standardized values ​​of the total processing volume of newly added or changed orders, the fault weight of key equipment, and the number of material shortage tasks in each period; and weights and synthesizes the disturbance intensity ΔDis by weighting each standardized value; based on the relationship between disturbance intensity and rescheduling response time in the same historical recording period, a support vector machine model is used to establish a disturbance intensity-optimal time window range relationship model, and the optimal sub-problem time window W corresponding to the current disturbance intensity is obtained through this model.

4. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 3 is characterized in that: The adaptive subproblem time window algorithm is constructed based on the combined use of particle swarm optimization and annealing algorithms. The specific steps include: S41. Determine the decision variables as scheduling parameters, including the start time, processing sequence, and switching sequence of each order on each device; S42. Initialize the particle swarm and randomly generate an initial set of scheduling parameters for each particle. S43. Set the fitness function Fd; S44. Set a fitness threshold. Perform local perturbation to generate new positions for particles with fitness greater than the set fitness threshold. For particles with fitness less than or equal to the set fitness threshold, feed back their corresponding tasks to the perturbation intensity evaluation algorithm to recalculate the sub-problem time window and update the set of tasks to be scheduled, and then send them back to step S43. S45. Calculate the absolute value of the fitness difference between the old and new particle positions to obtain the fitness difference value; S46. Set the maximum difference threshold Δmax. When the fitness difference is less than or equal to Δmax, update the annealing update probability according to the particle swarm algorithm; otherwise, directly replace the old position with the new position. S47. After each iteration, calculate the difference between the actual processing load and the average load of each device. If the difference is greater than the set threshold, return to step S44; otherwise, terminate the iteration and output the current scheduling parameters.

5. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 4, characterized in that: The fitness function Fd calculates the scheduling accuracy fitness and load balancing fitness respectively by using a differential algorithm, combined with the disturbance intensity ΔDis output by the disturbance intensity evaluation algorithm and the sub-problem time window W, and then weights and sums the two to obtain the total fitness.

6. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 5, characterized in that: The scheduling accuracy fitness is obtained by calculating the average percentage of the absolute values ​​of the deviations between the predicted and actual completion times of each critical task, and subtracting this average value from the baseline value of 1. The load balancing fitness is obtained by calculating the absolute value of the difference between the standard deviation of the actual load of each device and the standard deviation of the predicted load of the current sub-problem at the same time point in all historical recording periods, reflecting the degree of load balancing.

7. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 6, characterized in that: The annealing update probability is obtained by calculating an exponential function of the fitness difference value with the natural constant e as the base and the ratio of k×Td, where k is the Boltzmann constant and Td is a temperature parameter that gradually decreases with the number of iterations.

8. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 7, characterized in that: The real-time status sensor collects equipment load rate and operating status at fixed time intervals. The process completion tag is automatically written into the MES system at the end of each process. The collected data is transmitted to the central dispatch and control system through industrial Ethernet or wireless network. The system will dynamically update steps S3-S5 based on the received real-time data.

9. The method for collaborative allocation and optimization of flexible manufacturing resources for variable delivery times as described in claim 3, characterized in that: The critical equipment failure weight includes counting the number of failures of the current equipment within the period. Average downtime per failure The original fault impact value was obtained. To each device Normalization is mapped to the range [0,1] to obtain the fault weights of critical equipment.

10. A flexible manufacturing resource collaborative allocation and optimization system for variable delivery times, used to execute the flexible manufacturing resource collaborative allocation and optimization system for variable delivery times as described in any one of claims 1-9, characterized in that: include: The data acquisition module is used to uniformly deploy real-time status sensors on key equipment and workstations in the production site, and install process completion confirmation tags at each work-in-process stage to directly acquire equipment load, work-in-process status and completion time. By deploying PLC / SCADA systems on each production line, real-time data on process progress, processing time, and equipment availability for each order are collected. The disturbance intensity assessment algorithm construction module is used to calculate the current scheduling disturbance amount by using historical scheduling data and real-time collected data, combined with order arrival prediction and equipment health status, and quantifying the disturbance intensity of each sub-problem by setting the disturbance intensity assessment algorithm; The task reordering module is used to set an adaptive sub-problem time window algorithm based on the perturbation intensity of each sub-problem and the longest system response time, and dynamically adjust the time window range of the tasks to be reordered. The scheduling solution module is used to divide the critical and secondary tasks within the scope of the sub-problem into layers, and then use precise MILP solution and efficient heuristic solution respectively. After parallel computation, the schedules are merged to form an updated collaborative scheduling scheme.

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