Some fundamental research has been conducted to discuss the concept, the architecture, and the applications of shared manufacturing.

Firstly, the concept of shared manufacturing has been emphasized. Brandt first proposes the concept of shared manufacturing in 1990 [1]. The definition and service operations of shared manufacturing are analyzed in the sharing economy [2]. Yan et al. review supply-demand matching and scheduling in shared manufacturing [3]. Young et al. explore an extension of traditional information-sharing approaches [4]. Under the shared manufacturing mode, Jiang et al. define the concepts associated with three distinct types of shared factories, sharing production-orders, manufacturing-resources, and manufacturing-capabilities [5]. Lujak et al. propose a decentralized coordination approach for multi-robot production planning in openly shared factories [6].

Secondly, it is related to shared manufacturing architecture. He et al. build the basic organizational architecture for the sharing of manufacturing capabilities based on the sharing mode of the shared manufacturing platform [7]. Li et al. propose a brand-new Enhanced Self-organizing Agent in the context of shared manufacturing, which helps the shared manufacturing resources realize cross-sharing with self-organizing communication and negotiation mechanisms [8]. Yu et al. propose the Blockchain-based Shared manufacturing framework [9]. Rozman et al. present an extensible framework for shared manufacturing to establish trust between entities based on blockchain [10]. Zhang et al. establish a reward and punishment mechanism, a subsidy mechanism, and a cost-benefit concept that offer a new framework for improving the quality of shared manufacturing [11]. A hybrid sensing-based approach for monitoring and maintaining shared manufacturing resources is proposed [12]. Wang et al. suggest an integrated architecture to solve the problems of inefficient resource allocation in shared manufacturing as well as help suppliers’ unguaranteed credit [13].

In the third aspect, the application of shared manufacturing is a significant focus of the research. Billo et al. propose a shared manufacturing solution to assess the consolidation and reconfiguration of various industrial operations [14]. Xu et al. investigate online strategy and competitive analysis of production order scheduling problems with the rental cost of shared machines [15]. Xu et al. consider a competitive algorithm for scheduling sharing machines with a rental discount [16]. Li et al. discuss the issue of the equipment manufacturer’s optimal pricing strategy in the selling model and the servitization model [17]. Wei et al. consider two-machine hybrid flow-shop scheduling problems in shared manufacturing [18]. Ji et al. consider parallel-machine scheduling problems in shared manufacturing [19].

The manufacturing resource allocation is to allocate the manufacturing resources of the supplier properly in accordance with its own optimization goal and use the resources as efficiently as possible to accomplish the manufacturing task.

On the one hand, part of the research focuses on the construction of manufacturing resource allocation models. To realize the optimal configuration across various enterprises, Zhang et al. propose an overall architecture for the optimal allocation of manufacturing resources based on community evolution [20]. Yu et al. propose an intelligent-driven green resource allocation mechanism under 5G heterogeneous networks to ensure the high reliability of services [21]. Wu et al. establish a multi-objective integer bi-level multi-follower programming model to simultaneously maximize SoM and QoS from the perspectives of both sides [22]. Lartigau et al. propose a method based on QoS evaluation along with the geo-perspective correlation from one cloud service to another for transportation impact analysis [23]. Tong et al. establish a bi-objective model based on peer effects with an improved grey relational evaluation that aims to maximize satisfaction and minimize individual differences [24]. Aghamohammadzadeh et al. propose a novel platform entitled Blockchain-based service composition model based on Blockchain technology [25].

On the other hand, others try to design and improve the solution method of the manufacturing resource allocation model. Yang et al. present an enhanced multi-objective grey wolf optimizer for the optimal selection problem and multi-objective service composition in cloud manufacturing [26]. Zhang et al. propose an extended flower pollination algorithm to solve the manufacturing service composition problem [27]. Wang et al. develop an evolutionary game model of manufacturing service allocation framework to ensure fairness among users [28]. Que et al. construct a comprehensive mathematical evaluation model with four critical quality of service and awareness indicators, as well as propose a new information entropy immune genetic algorithm for the model’s solution [29]. Li et al. design a Gale–Shapley Algorithm-Based Approach for service composition, which can achieve better performance than the DP method when dealing with a single task or multiple tasks [30]. Gao et al. introduce an improved particle swarm optimization for dynamic service composition. As well, the local greedy algorithm and global reconfiguration method are adopted to restructure composite services dynamically [31].

As a dynamic process, shared manufacturing resource allocation is full of changes in the whole process of task execution. The service party offers the use of manufacturing resources and has the right to enter or exit the shared manufacturing process as it sees fit. The demanders provide tasks to be performed and modify or cancel the tasks given out according to their interests. This paper studies how manufacturing resource variation in task execution alters resource allocation. Before beginning a sub-task, the platform provides the optimal configuration of the entire task according to the change in resources. If the manufacturing resources for the candidate remain the same, follow the initial configuration strategy. However, if there is a change in the candidate’s manufacturing resources, they will need to be reconfigured according to the new situation. Therefore, the most significant difference between the manufacturing resource allocation in shared manufacturing and static resource allocation is that the shared manufacturing resource allocation is carried out along with the advancement of sub-tasks, real-time monitoring, and real-time configuration. The primary notations are shown in Table 1.

There are the following provisions:(1)

One resource can only complete one sub-task.

Requirements take the form of a set of tasks and can be denoted as SMTSET={SMTi|i=1, 2, …, n} , where SMTi refers to the ith sub-task. Resources take the form of a set of the candidate’s manufacturing resources. They are marked as SMRSET={SMRij|i=1, 2, …, n; j=1, 2, …, mi} , where the number of the candidate’s manufacturing resources for SMTi is mi , and SMRij represents the jth candidate’s manufacturing resource that can complete the sub-task SMTi .

As an example, consider the case of four sub-tasks. The result of the configuration is 2−1−1−3 before SMT1 starts. SMT1 is performed by SMR12 , SMT2 is performed by SMR21 , SMT3 is performed by SMR31 , and SMT4 is performed by SMR43 . Before the start of SMT2 , the manufacturing resource allocation is 2−2−1 . SMT2 is performed by SMR22 , and the subsequent arrangements are SMR32 for SMT3 and SMR41 for SMT4 . Before SMT3 starts, continue with the current manufacturing resource allocation of 1−2 . SMT3 is performed by SMR31 , and SMT4 is performed by SMR42 . Before SMT4 starts, the configuration result for SMT4 , based on the current candidate’s manufacturing resources, is 1 , and SMT4 is performed by SMR41 , as shown in Fig. 2.

In the whole manufacturing resource allocation, the demanders of manufacturing services, acting as the task’s initiators, give careful consideration to the manufacturing task’s overall quality. The suppliers of manufacturing resources complete the task according to the customized requirements of the demand for manufacturing services. Thus, the demander’s satisfaction directly affects the supplier’s evaluation. Therefore, the service quality indicators become the optimization target of the dynamic allocation model.

The processing cost C is the total of all costs incurred during the production process, from task preparation to completion. The processing cost C is mainly composed of the actual processing cost C1 , the personnel technical cost C2 , and the logistics cost C3 .

Actual processing cost C1 : it is the cost associated with the actual workpieces that were processed using available equipment. The actual processing cost is judged by providers based on historical processing costs and experience, and the specific actual processing cost value is given.

Personnel technical cost C2 : it is the cost of paying related personnel, that is, the cost of human resources for direct or indirect guidance, design, and processing by technicians or experts. The personnel technical cost is evaluated by providers based on the historical processing cost and experience, and a specific personnel technical cost value is provided.

Logistics cost C3 : it is the related cost of the workpieces or materials due to the logistics process. The logistics cost is determined by providers based on the particular geographic location of the workpieces or materials and the historical transportation experience. The specific logistics cost is then given.

Eq. (1) is employed to calculate the processing cost C.(1) C=∑i=1n[∑j=1miuij(C1(ij)+C2(ij))]+∑i=1n−1[∑j=1mi∑k=1mi+1uiju(i+1)kC3(ij, (i+1)k)]

The processing time T is the total amount of time required for manufacturing tasks, from preparation to completion. Processing time T mainly consists of the actual processing time T1 , the adjustment time T2 , the standby time T3 , and the logistics time T4 .

Actual processing time T1 : it is the amount of time it takes for manufacturing resources to complete actually processing the workpieces. The actual processing time is estimated by providers based on historical processing time and experience.

Adjustment time T2 : it is the time for the unified deployment and debugging of soft resources such as software and human resources for the execution of tasks. The adjustment time is given by providers based on the time of the historic resources call.

Standby time T3 : it refers to the time due to system and path delays when soft resources such as software and labor perform tasks. The standby time is determined by providers based on the completion time of the historical tasks.

Logistics time T4 : it is the logistics time of the actual workpieces or materials. The logistics time is given by providers based on the geographic location and historical experience of the specific sources of the workpieces and materials.

The calculation formula is as Eq. (2).(2) T=∑i=1n[∑j=1miuij(T1(ij)+T2(ij)+T3(ij))]+∑i=1n−1[∑j=1mi∑k=1mi+1uiju(i+1)kT4(ij, (i+1)k)]

The processing quality Q is the task’s value of processing quality. According to the capability and level of complexity of the workpieces, the quality value of the equipment is given by providers. The calculation formula is Eq. (3).(3) Q=∑i=1n∑j=1miuijq(ij)n

An optimal allocation model considering shared manufacturing resources is established, taking the lowest processing cost, the shortest processing time, and the most considerable processing quality as the optimization objectives. At the same time, the model must also conform to the constraints of maximum cost, maximum time, and minimum quality, as well as the constraint that only one candidate’s manufacturing resource completes each task, as Eq. (4) shows.

(4) maxF=(CmaxC, TmaxT, QQmin)Ts.t.{C≤CmaxT≤TmaxQ≥Qmin∑j=1miuij=1uij={1, if SMRij is selected0, otherwiseu(i+1)k={1, if SMR(i+1)k is selected0, otherwisei=1, 2, …, n

The optimal allocation of shared manufacturing resources considering the entries and exits of manufacturing resources is a typical NP-hard problem, so intelligent algorithms are used to solve it. This study will design an NSGA-II and a MOPSO algorithm for the model.

Based on the resource allocation performed before the start of SMT1 , the operating results of the NSGA-II and MOPSO algorithms are analyzed.

In NSGA-II, when the iteration number is 110, the average values of resource allocation of SMT1 with different population sizes are calculated, and the evolutions are shown in Fig. 6. Obviously, the average values of fitness remain stable after the population size reaches 120. Similarly, when the population size is 120, the average values of fitness of SMT1 running 10 times under different iterations are calculated, and the evolutions are shown in Fig. 7. Obviously, the average values of fitness remain stable after the iteration number reaches 110.

In MOPSO algorithm, when the iteration number is 30, the average values of resource allocation of SMT1 with different population sizes are calculated, and the evolutions are shown in Fig. 8. Obviously, the average values of fitness remain stable after the population size reaches 70. Similarly, when the population size is 70, the average values of fitness of SMT1 running 10 times under different iterations are calculated, and the evolutions are shown in Fig. 9. Obviously, the average values of fitness remain stable after the iteration number reaches 30.

According to the above experiments, the optimal settings of parameters for operation in the NSGA-II and MOPSO algorithms have been obtained. Therefore, the population size in the NSGA-II is set to 120, and the population size in the MOPSO algorithm is set to 70. The parameters in the NSGA-II and MOPSO algorithms are listed in Table 12.

The model’s resource allocation for each sub-tasks is obtained, as shown in Table 13.

Before SMT1 starts, shared manufacturing resource allocation is that sub-task SMT1 is performed by resource SMR11 , SMT2 is performed by SMR22 , SMT3 is performed by SMR31 , and SMT4 is performed by SMR43 . During SMT1 processing, the configured resources SMR11 , SMR22 , SMR31 , and SMR43 will be locked. After SMT1 is completed, SMR22 , SMR31 , and SMR43 are unlocked and free.

Before SMT2 starts, new resources are found to enter based on the monitoring of the candidate’s manufacturing resources, so shared manufacturing resources need to be reconfigured. At this point, SMT2 is performed by SMR25 , SMT3 is performed by SMR34 , and SMT4 is performed by SMR45 . During SMT2 processing, configured resources SMR25 , SMR34 , and SMR45 will be locked. After SMT2 is completed, SMR34 and SMR45 are unlocked and free.

Before SMT3 starts, no change in the candidate’s manufacturing resources is detected, so the allocation is maintained. That is, SMT3 is performed by SMR34 , and SMT4 is performed by SMR45 . The configured resources SMR34 and SMR45 will be locked during SMT3 processing. After SMT3 is completed, SMR45 is unlocked and free.

Before SMT4 starts, some of the candidate’s manufacturing resources are detected to exit, so the resources are reconfigured, and SMT4 is performed by SMR44 .

Finally, with the progress of the sub-tasks, the dynamic manufacturing resource allocation is completed.

The optimal resource allocation obtained by running two algorithms overlaps, as shown in Table 14, proves the effectiveness of the model.

Through repeated experiments, it is found that the NSGA-II can generate more stable populations than the MOPSO algorithm. Figs. 10 and 11 are three-dimensional graphs of the results of multiple runs under the NSGA-II and MOPSO algorithms. On the other hand, the evolution of the running time in two algorithms with different iteration numbers is shown in Fig. 12. When the iteration count of the two algorithms is less than 20, there is not much of a difference in the running times—both take about 5 s. However, with an increase in iteration numbers, the MOPSO algorithm operates much more rapidly than the NSGA-II.