Manufacturing resources coordination organisation and tasks allocation approach inspired by the endocrine regulation principle

: To solve the manufacturing resources coordination and tasks allocation problem in dynamic manufacturing environments, a mathematical model, aiming to minimise tardiness penalties and reduce manufacturing cost, is established. Considering the influences of the emergency in the manufacturing system, a novel task allocation approach, based on the hormone regulation principle, is proposed. This proposed approach is characterised by high efficiency, low communication, and fine robustness. The experimental results verify that this coordination approach not only can reduce processing costs effectively in a static environment but also has a good control performance against disturbances in a dynamic environment.


Introduction
With the development of market globalisation, manufacturing companies are facing more and more complex and significant trends of cultural diversification, lifestyle individuality, global activity, and environmental consideration [1]. To deal with these challenges, the scale of modern manufacturing system becomes increasingly larger and the control structure becomes more complicated. Under this condition, a reasonable and rapid manufacturing coordination mechanism is a crucial way to reduce emergency impacts on production system [2]. However, it is a challenge to get a reasonable balance between production tasks and manufacturing resources. In a complex system, a change cannot occur alone due to the complex relationship, and it may trigger chain changes to the other systems, which is named change propagation [3]. If the change propagation is handled improperly, it will ruin the normal production process, and have a negative effect on the manufacturing system stability. Therefore, the manufacturing control system should possess the ability to handle and incorporate these changes [4]. Thus, an efficient coordination approach for manufacturing system is necessary to be studied to guarantee the production optimisation.
Recently, lots of approaches have been studied in the literature to solve the coordination optimisation problems between manufacturing system tasks and manufacturing resources using mathematical modelling, constraint satisfaction, heuristics, and meta-heuristics-based computation methods. Some valuable research studies are described as below. Barenji et al. [5] proposed a multi-agent-based dynamic scheduling system for manufacturing flow lines using the Prometheus methodology considering the dynamic customer demands and internal disturbances. Gong and Tang [6] analysed the coordinated dispatching problems in the productive process of manufacturing system parallel machine and proposed two heuristic algorithms. However, these two algorithms were difficult to implement in practice, due to its large value. Wang and Tang [7] proposed the mixed algorithm of Lagrangian relaxation (LR) and column generation, and solved real-time scheduling problems of the parallel machine, thus achieving a better convergence performance than the traditional LR algorithm. Han et al. [8] proposed a utilisation-based scheduling selection strategy to strike a balance between data freshness and system schedulability, including search-based switch, adjustment-based switch, and instant switch (IS). Komenda et al. [9] modelled the coordinated control machine of a distributed discrete system based on the Petri net approach, and the control performance of the model was compared and analysed. Zhang and Cao [10] presented a novel coordination algorithm based on contract net protocol (CNP) to improve the efficiency and performance of the control system to some degree. Tillenius et al. [11] proposed a novel resource-aware scheduling approach that can detect resource sensitivity and predict the performance improvements. The coordination mechanism based on CNP has features of simple strategy and easy application, but actually, it is a kind of explicit coordination mechanism [12][13][14][15][16][17][18].
Most of the literature mentioned above is implemented in the multi-agent manufacturing system, and utilised direct negotiation mechanisms between the participants in the system. That means, when some tasks need coordination between the participants, they must know who should be asked first and how to link up with the others. These coordination algorithms have the flaw of overcommunication. When the manufacturing environment becomes complicated and the processing tasks become numerous, the multiagent system based on the direct negotiation mechanism usually has the phenomenon of too much information interaction, which leads to the problem of response delay and low decision-making efficiency [19][20][21][22][23].
Recently, as the artificial intelligence research continues, the intelligent model of the human body information processing mechanism is becoming a new research hotspot. The system structure and function, such as the diversity, complexity, reliability, adaptability, and high efficiency of its regulating mechanism, are worthy to be referred to in the research of the manufacturing system [24][25][26][27]. The endocrine system is the core of the human body information processing system, in which complex and unique information processing mechanisms could provide researchers with more guidance. The coordinated method based on endocrine system regulating mechanism is a kind of implicit dynamic coordination method, which could direct and deploy various independent individuals to the total required tasks of the present system immediately [28]. The process of coordination and cooperation between internal manufacturing resources is similar to regulating the effects of hormone concentration changes in body fluids [29].
Therefore, based on these similarities between the manufacturing system and the biological organisms, many researchers have started to concentrate on some bionic intelligent manufacturing control approaches [30,31]. In these studies about bionic manufacturing system, there are two typical research directions that one is mimicking the biological evolution method (just like gene) and the other is utilising the biology swarm intelligence to set up intelligent manufacturing control architecture [32][33][34]. Undoubtedly there are some valuable research results, but few related research studies have been done on manufacturing coordination mechanism between resources and tasks based on the endocrine-inspired idea. Therefore, there is an important problem left whether we can utilise the rapid coordination mechanism, inspired by the regulatory mechanism of the endocrine system, in the intelligent manufacturing control system. Thus, in this study, we proposed an implicit coordination approach, inspired by the endocrine regulating principle, to improve the manufacturing performance.
The remainder of the paper is organised as follows: in Section 2, the mathematical model is presented. In Section 3, the task allocation algorithm inspired by the endocrine regulating mechanism is proposed. Then, Section 4 simulation describes the experiment results and comparisons. Finally, we end the paper with some conclusions and future research in Section 5.

Problem modelling
Under the production mode of distributed manufacturing system, multiple optional process routes are generally used for the productive tasks in manufacturing enterprises. Each work piece in the production task should choose one processing route from multiple available manufacturing resources. The final targets are to minimise tardiness penalties and reduce manufacturing cost. There are some conflicts among these targets, and therefore the process may do well on one side, but performs badly on another side. Owing to this conflict, the manufacturing task allocation approach must seek a balance between these targets.
In this section, a mathematical model for manufacturing resource coordination is described firstly. The notations of the model are i: machine index (i = 1, 2, …, m), p j : jth kind of work piece, P: task including many kinds of work pieces p j (j = 1, 2, …, n), N j : quantity of work pieces p j , r: processing route index, t jri : processing time of every work piece p j on machine i in the processing route r, c jri : processing cost per time unit for every work piece p j on machine i in the processing route r, M jr : quantity of machines needed for every work piece p j in process route r, N jr : quantity of work pieces p j in process route r, TC jr : transportation cost of every work piece p j in process route r, R j : quantity of available process routes for work pieces p j , MCT: the maximum completion time of all work pieces, D P : delivery date of the task P, C p (P): total processing cost of the task P, C T (P): total transportation cost of the task P, C total (P): total cost of the task P.
The mathematical model for the cost of a task can be described as Objective function: where Equation (1) denotes the objective of this model, minimising the total product cost, which consists of the processing cost C p (P) (as shown in (2)) and the transportation cost C T (P) (as shown in (3)). Constraints are as follows: The constraints of the coordinative optimisation problem of manufacturing tasks and resources are to ensure all process tasks to match corresponding resources and be finished in a specific time. Therefore, (4) presents that the quantity of one kind of work pieces should be equal to the sum of work pieces in different processing routes, and (5) ensures the production task P should be finished before the delivery date. Some required assumptions for the model are as follows: (i) All the work pieces are independent and are available at time zero.
(ii) There are no precedence relationships between the operations of different work pieces, but there are precedence relationships between different operations of the same work piece.
(iii) All the machine tools are available at time zero.
(iv) Each machine only can process one operation at a time.
(v) Pre-emptive operation is not allowed.

Task allocation algorithm inspired by the endocrine regulating mechanism
In the biology area, the endocrine system is the collection of glands of an organism that secrete hormones directly into the circulatory system to sustain the adaptive reactions to the different stimulates. Also, it is an information signal system in biology system, such as the nervous system. They all utilise some efficient regular mechanism to regulate the dynamic balance in the biological body, which is mostly similar to the solving process of the 'taskresource' matching problem. It also means that the manufacturing system keeps normal working state without disturbance, i.e. hormone concentration (productive state of manufacturing resource) in body fluid is stable, and its responses to stimulation (emergency) when external stimulation (emergency) occurs. With mutual effect among hormones, the working state of each organ is regulated by a new process of dynamic balanced state. The principle of hormone regulation mechanism in the endocrine system is as follows. Farhy defined the basic law for modelling as the secretion of hormones by endocrine glands. In this model, the hormone regulation complies with Hill function, which is composed of the rising function F up (C) and decreasing function F down (C), shown in (6) where C is the variable of hormone concentration, T is a threshold of hormone concentration, and T > 0, n is the Hill coefficient and n > 1.
If a hormone x is controlled by a set of hormones I = {1, 2,…, i} simultaneously, the secretion speed of hormone x is determined by the concentration of these hormones, which is shown in (7) where S x0 represents the initial secretion speed of hormone x, C i is the concentration of hormone i, and coefficient a i is a positive constant associated with hormone i. For example, the glucagon secreted by pancreatic islet α-cells has the function of raising blood sugar concentration, on the contrary, the insulin secreted by pancreatic islet β-cells has the function of reducing blood sugar concentration. When the blood sugar concentration is low, islet α-cells promote the glucagon secretion, and hormone regulation complies with up-Hill function for rapidly improving the blood sugar concentration, on the contrary, when the blood sugar concentration is high, islet β-cells promote the insulin secretion, and hormone regulation complies with down-Hill function for agilely reducing the blood-sugar concentration. Since hormone regulation has the characteristics of monotonicity and non-negativity, the affection of one hormone to another hormone can only be the stimulation or inhabitation. In biology, insulin and glucagon exist at the same time, and have the function of mutual antagonism to regulate blood sugar concentration.
Therefore, in view of optimising allocation problem between manufacturing resources and tasks, it can provide an effective solution to simulate the dynamic coordination algorithm of endocrine system hormone regulating principle in 'neuro and body fluid' regulating network. Thus, inspired by such effective biological mechanism, a novel task allocation algorithm is proposed and illustrated in the following contents.
This allocation algorithm is based on the endocrine regulation principle to improve the control performance in the shop floor level. Hormones are utilised as communication mediators. Since the endocrine regulation is a type of indirect coordination method between participants which could lead to rapid coordination among all system resources, the participants need to secret hormones in the environment to effect the other participants' decision-making. To mimic the endocrine regulation mechanism, special hormone agents are created among those different agents (order agents, route agents, and resource agents) as shown in Fig. 1. These hormone agents travel across the workshop topology virtually to perceive information and send messages similar to the hormone regulation mechanism in the endocrine system.
In this task allocation process, hormone agents have a designated spread direction. They can move from the order agents carrying the task information to the other agents, and they also can move from the resource agents carrying the machine information to the other agents. Hormone agents from the route agents move to the upper controller, and the others from the order agents move to the lower controller. The hormone information will be updated and stored in a specified area to be used by other agents.
To simulate the regulation process of the endocrine system to solve the coordinative optimisation problem between production tasks and resources in the manufacturing system, the concept of hormone should be defined.
After receiving the process tasks, stimulus information is delivered from the order agents to the resource agents, the hormone information h x can be expressed as a triple h x (Job_id, Num, Info), where, (i) Job_id represents the number of process tasks. (ii) Num represents the amount of parts in this process task. (iii) Info represents the other processing information about this process task, such as technological process, processing method, processing charges etc.
The hormone information h y , which is provided feedback from the route agents, can be expressed as a tetrad h y (Route_id, c, t, ρ), where (i) Route_id represents the number of the multi-process routes.
(ii) c represents the total cost of the selected process route. (iii) t represents the total processing time of the selected process route. (iv) ρ represents the value of the hormone secretion.
As soon as the tasks come from the order agents, the Shop Floor Environment Manager will take the following steps to find an efficiency processing route to finish the tasks.
Step 1: Firstly, Job_P will be decomposed when the task arrives at the shop floor. The Shop Floor Environment Manager will generate R P process routes with the consideration of the manufacturing resource information. With the restraining conditions, the parts quantity Num x in each process route will be generated randomly, just as follows. At the same time, the sum of all variables of rand corresponding to each processing route for the jth kind of work pieces need to be equal to 1. Step 2: According to the initial task allocation, the order agents will generate hormone agents, which will take the hormone information h x (Job_id, Num, Info) move to the lower controller.

If (N P ×min (T rp ) > D P ), then
Step 3: The resource agents perceive the hormone information h x from the upstream, and then calculate the objective values according to the proposed model. When the objective value in each process route is evaluated, the route agents will secrete the hormone information h y (Route_id, c, t, ρ). Also, at the same time, the hormone value ρ will be calculated as follows:  where Δρ = Q Num jr × C jr (9) In (8), ρ jr represents the amount of hormone secretion in route r for the jth kind of work pieces, and α represents hormone's retention rate. In addition, t represents the number of times. For example, if t represents the second execution of step 3, t + 1 represents the third execution of step 3. In (9), Q is a known fixed constant, and Num jr is the product number in process route r for the jth kind of work pieces.
Step 4: The hormone agents will move to the upper controller with the hormone h y (Route_id, c, t, ρ).
Step 5: With the Shop Floor Environment Manager sensing feedback hormone h y (Route_id, c, t, ρ), the Shop Floor Environment Manager will reallocate the part quantities in every process route based on the hormone value ρ, where the allocation based on the hormone value represents that the proposed method allocates based on the ratio of the hormone value and performs rounding. Then the hormone information h x (Job_id, Num, Info) is updated. When the order agent acquires a scheme, it checks whether the scheme satisfies the constraint conditions, and sends the scheme to the route agents that have the ability to complete it.
Step 6: To get optimal results, the heritable matrix X m , describing m kinds of possible allocation solutions, is used as a solution space for crossover and mutation operation, just as follows: In expression X m (shown in (10)), each line x i represents a feasible allocation scheme i, and each array element x ij represents the parts quantity of the process route j in allocation scheme i. Based on the objective function, each candidate allocation scheme is calculated, and variable h ri is obtained from (11), which is used to find and reserve the optimal result in matrix X m It should be pointed out that after crossover and mutation, each scheme still needs to meet constraint (4). From (11), we can find that the feasible solution has a smaller probability of being selected for crossover and mutation operation when the total cost is lower. This approach will reserve a better feasible solution, and lead the feasible solution to the optimal one.
Step 7: Set N as cycle-index of this algorithm. Step 8: Detect dynamic event. If the manufacturing system detects an emergency event, the controller will detect the event type first, and then update the related hormone variables. When the controller has updated the hormone information, the algorithm will go back to Step 3.
Step 9: The end.
The proposed approach is mainly inspired by the hormone regulation mechanism of the endocrine system. Two mutual effecting hormone variables are set up to mimic the hormone regulation mechanism, and it matches the tasks with the processing routes easily. The main operation process of the above approach is shown in Fig. 2.

Coordination optimisation between manufacturing task and resource
To illustrate the effectiveness and performance of the proposed approach, an example for controlling the manufacturing resource coordination and task allocation is given and tested. There are a set P = {P1, P2, P3, P4} of tasks with different processing cost and a set M = (m 1 , m 2 , m 3 ,…, m 9 ) of machines with several types of processing routes. The C++ programme of the proposed algorithm was run to simulate the example with a 3.20 GHz Intel Pentium (R) PC. The production information of manufacturing tasks is shown in Table 1. By adopting the proposed task allocation approach based on an endocrine regulating mechanism to coordinate the manufacturing tasks and resources, the job shop agent receives the tasks when the tasks transport to the job shop, and then the order agents perform process decomposition, with results shown in Table 1. According to the proposed task allocation approach, hormone h x (Job_id, Num, Info) can be constructed, in which Num = [Num 1 , Num 2 , Num 3 , Num 4 , Num 5 , Num 6 , Num 7 , Num 8 , Num 9 , Num 10 , Num 11 , Num 12 ] T represents the allotted number of processing tasks in each process route. There are three process routes for each task form (see Table 1 (1), the objective function could be expressed as min C total (P) = C RP × Num + C TRP × Num where C RP = [32,24,37,37,50,67,29,24,32,12,28,22] and C TRP = In the process of calculation, set maximum iteration as N = 30, feasible solution space as m = 5, hormone retention rate of hormone secretion in this algorithm as α = 0.9, and then the result is obtained by following the concrete coordination and task allocation steps mentioned above, which is shown in Table 2. As shown in Table 2, it can be seen that the proposed approach can achieve the optimal or near-optimal solutions and reduce the total production cost through multiple mutual coordination of two hormones. To prove the superiority of the performance of the proposed algorithm, we compare it with the other two algorithms, particle swarm optimisation algorithm combines with simulated annealing algorithm (PSO-SA) and branch and bound algorithm (B&B) in linear interactive and general optimizer (LINGO), through experiments (as shown in Table 3). It is found that although PSO-SA and B&B could solve the problem and achieve  the optimal or near-optimal solutions. However, there still exist some disadvantages, such as complicated encoding sequences design, verbose computing process, and slow convergence speed. Also, the calculation and runtime will increase greatly when variables in solving processes are too many and the scale of the problem is too large. Especially for B&B in LINGO, it critically affects the computational efficiency of model. Comparatively speaking, the proposed task allocation algorithm, based on the endocrine regulation mechanism, characterises itself by simple structure, fast convergence speed, more accurate optimal solutions etc.

Dynamic coordination of emergency
There are many types of uncertain events that have occurred in a practical manufacturing system, which always influences the running productive tasks. Generally speaking, two kinds of these uncertain disturbances are typical, which are resource-related disturbances (coming from the manufacturing resources, such as machine malfunction, machine recovery etc.) and source-related disturbances (caused by the changes in processing tasks, such as urgent tasks, existing task cancellation etc.). To verify the agility and adaptability in terms of dealing with a dynamic emergency, the machine malfunction is considered in this section.
Assuming that when the 20th piece in task P4 starts to be produced in the test above, the manufacturing equipment m 2 malfunctions suddenly. Then, after maintenance, when the 40th piece begins to be produced, manufacturing equipment m 2 is repaired and the production will resume.
In this experiment, when the 20th piece in task P4 begins to be produced, the manufacturing equipment m 2 malfunctions suddenly. Then the m 2 resource agent sends a request to its route agent. The attribute of the affecting process route 4-1 will be changed, and due to no processing ability in this process route, the route agent set the hormone secretion ρ of process route 4-1 to 0. The work pieces allocated in this route should be reallocated to the other two routes, therefore, the shop agent perceives the request, and update the hormone h x in the public environment, in which the total number of task P4 in hormone h x , Num, will update to 30. After a second rapid coordinative optimisation to the remaining P4 task in process routes 4-2 and 4-3, the hormone quantum of routes 4-2 and 4-3 increase remarkably, and finally the route agent send the new hormone h y back to the public environment. When task P4 comes to the 40th, manufacturing equipment is put on production after a repair, and process route 4-1 put back on production, and hormone secretion ρ in hormone h y resumes, hormone h x will change once again, thus making the remaining tasks optimised again without disturbing normal production. The whole coordination process is shown in Table 4 and Fig. 3.
As shown in Table 4, when a malfunction occurs, the machining state of manufacturing (the value of ρ) will change. It will lead to the change of Num in hormone h x , and the change of machining state will lead to changes of different process route hormone secretion ρ in h y . Moreover, it will influence the allocation Num rp of different process routes, and finally, the production system reaches a new dynamic balance through the steps in this algorithm. Fig. 3 shows the curve of each process hormone secretion ρ in the treating process of an emergency. It can be found from Fig. 3 that the proposed approach could reflect matching degree between task and resource well through reasonable formula designing of hormone secretion ρ. In addition, when an emergency occurs, the manufacturing control system can realise the present production state according to residual information of each process route, and then it makes actions correspondingly and rapidly by utilising the proposed approach.
Meanwhile, compared with traditional coordination mechanisms, e.g. CNP, this algorithm has less traffic volume and avoids deadlock in the dynamic coordination process. In the above   Num represents actual pieces to be processed in task P4, n′ represents processed pieces, Num rp represents the pieces to be processed after each process route is allocated, ρ represents corresponding hormone secretion in hormone h y .
case, four tasks need to be processed and could be completed with three manufacturing resources in the system. If a traditional CNP coordination mechanism is used, each task should go through four stages of bidding document information release, bidding, bidwinning notice and signing. It needs 8 (2 × 3 + 2) times communications and the total communication times is 32 (2 × 3 × 4 + 2 × 4). However, if this implicit coordination method based on the endocrine regulating mechanism is adopted, the total communication times for completing all the tasks allocation and process is 20 (4 × 3 + 4 × 2). Furthermore, with a more complicated manufacturing control system, the advantages of this implicit coordination method on communication are increasingly significant. Therefore, it shows from the above experiment that the proposed coordination and allocation approach is simple, stable, and reliable, and it has good optimising ability in static task allocation and high adaptability in dealing with dynamic disturbance. Additionally, in the process of communication coordination, it could effectively reduce the communication of control system, decrease the complexity of the manufacturing system, and avoid deadlock. Hence, it can contribute to a further improvement of the robustness, agility, and adaptability of manufacturing system control.

Conclusions
To decrease the production cost of the manufacturing process, a mathematical model is set up for the coordination problem between the multiple process routes existing in productive tasks and the productive resources existing in product processing. Considering the defects of the traditional coordination mechanism in the manufacturing control system and the condition of satisfying the restraint of resource processing ability and productive task delivery date, a task allocation algorithm based on the endocrine regulating principle is proposed. Using a simple coordinating control strategy, the complexity of the problem of manufacturing system resource and task optimal configuration is reduced, information communication in system coordination control is decreased, and deadlock is avoided. Therefore, the response ability of the control system to the emergency is improved, the adaptability of the manufacturing system is enhanced, and finally, it provides an effective technical solution for the problem of processing task and manufacturing resource allocation and coordination.
However, the task allocation and resource coordination problem is an intricate optimisation problem. The research is inspired by the hormone regular mechanism which lacks effective mathematic proof of reasonable analysis on this mechanism, and the experiments of the proposed approach are only simulated in the laboratory. Thus, the research in the future will focus on the following issues: (i) a reasonable mathematical model for manufacturing emergency, (ii) improving the proposed approach for dynamic job shop control system efficiently.