Multi-product multi-robot local damage disassembly line balancing method under fixed work station

Abstract

The invention provides a multi-product multi-robot local damage disassembly line balancing method under a fixed workstation, and belongs to the technical field of industrial automation and robots. The method comprises the following steps: collecting basic data of a product line and a disassembly task; establishing a mixed integer linear programming model of the multi-product multi-robot local damage disassembly line balance problem with minimum beat time, total disassembly energy consumption, an energy consumption peak value and disassembly profit as optimization objectives; and solving the mixed integer linear programming model. The method aims to improve the working efficiency of the disassembly line and the overall performance of the system in the multi-product and multi-robot environment by considering the problems of assembly non-disassembly, resource limitation, robot models and the like in the actual disassembly process through reasonable task allocation and scheduling strategies. The method can be widely applied to the fields of automobile disassembly, electronic waste recovery, remanufacturing and the like.

Description

Technical Field

[0001] The present invention relates to the field of industrial automation and robotics, and in particular to a method for balancing a multi-product multi-robot local destructive disassembly line under a fixed workstation. The method is an industrial engineering method for balancing a multi-robot local destructive disassembly production line for a multi-product scenario, and is applicable to the fields of automobile disassembly, electronic waste recycling, and parts remanufacturing. The present invention aims to optimize the task allocation and scheduling of multi-robot collaborative work to improve the work efficiency, resource utilization, and system performance of the disassembly line. Background Art

[0002] With the continuous development of automation technology, robots are increasingly used in disassembly lines. Especially in the process of disassembling a variety of different products, the design and optimization of automated disassembly lines are particularly important. However, traditional disassembly line systems often have the following problems:

[0003] (1) The problem of component non-disassembly: During the disassembly process, some components cannot be disassembled due to serious failure or riveting and welding structures. However, the existing disassembly mode mainly focuses on non-destructive disassembly, which cannot effectively solve the disassembly of this type of components, resulting in disassembly failure.

[0004] (2) Energy consumption and disassembly efficiency issues: Traditional methods fail to effectively balance the energy consumption and efficiency of disassembly tasks, resulting in excessively high energy consumption peaks, which affects the economy and environmental friendliness of the system.

[0005] (3) Existing research on the balancing problem of multi-product and multi-robot disassembly lines mainly takes cycle time and energy consumption as optimization targets, ignoring the efficiency indicators that enterprises focus on. At the same time, the current disassembly mode is mainly non-destructive disassembly, and destructive disassembly has not yet been introduced into multi-product and multi-robot disassembly lines. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a new balancing method for multi-product and multi-robot local destruction disassembly lines under fixed workstations. The present invention is guided by green and high efficiency, starting from the economic benefits of the enterprise, and optimizes the overall efficiency, energy consumption and safety of the disassembly line through reasonable task allocation, scheduling strategy and local destruction strategy. It solves the problems of uneven task allocation, improper handling of component non-disassembly, high energy consumption, etc. in the prior art, and improves the work efficiency and system performance of the disassembly line in a multi-product and multi-robot environment.

[0007] The technical solution of the present invention is:

[0008] The method for balancing a multi-product multi-robot partial destruction disassembly line under a fixed workstation includes the following steps:

[0009] S1. Collect basic data on product lines and disassembly tasks, including determining candidate robot sets and collecting information on disassembly time, disassembly benefits, disassembly energy consumption, disassembly costs, etc. of different types of robots under destructive and non-destructive disassembly;

[0010] S2. Establish a mixed integer linear programming model for the multi-product multi-robot partial destruction disassembly line balancing problem with the optimization objectives of minimizing cycle time, total disassembly energy consumption, energy consumption peak and disassembly profit;

[0011] S3. Solve the mixed integer linear programming model to obtain a multi-product multi-robot local destruction and disassembly plan under a fixed workstation.

[0012] As a specific implementation of the present invention, the objective function of the mixed integer linear programming model includes:

[0013] Minimize the cycle time: minf 1 =CT

[0014] Minimize total energy consumption:

[0015] Workstation energy consumption peak indicator, used to balance the load of each workstation:

[0016] minf 3 =maxSE k

[0017] Disassembly profit indicator:

[0018]

[0019] Where CT is the workstation cycle time; S is the number of fixed workstations; SE k is the total energy consumption of the robots assigned to workstation k; W k Indicates the workstation startup variable. If workstation k is in the startup state, then W k =1, otherwise W k =0; where SE k represents the energy consumption of workstation k, which consists of two parts: the energy consumption when the robot performs the disassembly task and the standby energy consumption. When the workstation is not in use, the energy consumption of the robot in the workstation is zero; R is the total number of robots; N is the total number of disassembly tasks; x ikr Assign variables to tasks. If robot r in station k disassembles task i, then x ikr =1, otherwise x ikr =0; T ir It indicates the actual disassembly time of robot r to perform task i. Its value is related to the robot model and disassembly mode. r Indicates the energy consumption per unit operation time of the robot; SEr represents the standby energy consumption of robot r per unit time; y kr Assign variables to robots. If robot r is assigned to station k, then y kr =1, otherwise y kr =0;L ir represents the actual disassembly benefit of robot r performing task i; c ir represents the actual disassembly cost of robot r performing task i. The above disassembly benefits and disassembly costs are related to the robot model and disassembly mode. s represents the unit time cost of opening a workstation; h i represents the hazard attribute variable. When task i is in danger, h i =1, otherwise h i =0;ch i Additional dismantling costs to handle hazardous tasks i;

[0020] As a specific implementation of the present invention, the mixed integer linear programming model also includes the following constraints:

[0021]

[0022]

[0023] In the formula, e iRepresents the destructive disassembly feasibility value of each task i. It indicates the feasibility of task i when it is disassembled in destructive disassembly mode. Usually, we use multi-granularity indicators and expert scoring method to determine it. For details, please refer to L.Guo, X.Zhang, Multi-granularity feasibility evaluation method of the partialdestructive disassembly for an end-of-life product, (nd). https: / / doi.org / 10.1007 / s00170-021-07673-4 / Published.; L.Guo, Z.Zhang, T.Wu, Y.Zeng, Y.Zhang, X.Xie, A grey wolf optimization algorithm for solving partial destructivedisassembly line balancing problem consider feasibility evaluation and noisepollution, Advanced Engineering Informatics 60(2024).https: / / doi.org / 10.1016 / j.aei.2024.102418; K. Wang, J. Guo, B. Du, Y. Li, H. Tang, X. Li, L. Gao, A novel MILP model and an improved genetic algorithm for disassembly line balancing and sequence planning with partial destructive mode, Comput Ind Eng 186(2023).https: / / doi.org / 10.1016 / j.cie.2023.109704;e max is the threshold value of the feasibility of destruction and disassembly; represents the disassembly mode. There are two main disassembly modes: destructive disassembly and non-destructive disassembly. If task i in robot r is in destructive disassembly mode, then otherwise d i represents the demand attribute variable. When task i has a recycling demand value, d i =1, otherwise d i =0; Rt irRtd represents the time it takes robot r to disassemble task i using a non-destructive disassembly method; ir represents the time it takes robot r to disassemble task i using the destructive disassembly method; CN ir is the disassembly cost of the i-th task when robot r performs non-destructive disassembly; CD ir is the disassembly cost of the i-th task when performing destructive disassembly under robot r; BN ir is the benefit of task i when using non-destructive disassembly under robot r; BD ir is the benefit of task i when destructive disassembly is used under robot r; L ir represents the actual disassembly benefit of robot r performing task i, which takes into account the different disassembly modes of the task; N is the set of disassembly task numbers; R is the set of robot numbers;

[0024] As a specific implementation of the present invention, the mixed integer linear programming model also includes the following constraints:

[0025]

[0026] This constraint indicates that the tasks need to satisfy the task priority relationship, where IP p (j) is the set of immediate predecessor tasks of task i in product p; P is a set of multiple products;

[0027]

[0028] This constraint indicates that the start time of the task that follows it must be after the end time of its predecessor task; j represents the start time of task j; Ts i represents the start time of task i;

[0029]

[0030] This constraint indicates that the task assigned later in the same robot must wait for the disassembly of all the tasks assigned earlier in the same robot to be completed before it can be disassembled; where z ijkr is a priority variable. If tasks i and j are both assigned to robot r in station k, and task i is executed before task j, then z ijkr =1, otherwise z ijkr =0.

[0031]

[0032] This constraint means that when two tasks are assigned to the same robot at the same workstation, the later assigned task must wait for the earlier assigned task to be completed before it can start disassembly; where Ψ is a maximum value; K represents the set of multi-robot site numbers, and R represents the set of robot numbers, that is, the set of candidate robots. Different robot models result in different disassembly times.

[0033]

[0034] This constraint indicates that the end time of the task cannot exceed the takt time of the current workstation; where Ts i represents the start time of task i; T ir It represents the actual disassembly time of robot r to perform task i. Its value is related to the robot model and disassembly mode.

[0035]

[0036] This constraint states that the start time of each task is non-negative.

[0037] As a specific implementation of the present invention, the mixed integer linear programming model also includes the following constraints:

[0038]

[0039] The above two constraints limit the priorities that tasks under different assigned work conditions need to meet.

[0040]

[0041] This constraint limits the total energy consumption of all robots in each workstation to not exceed the highest peak energy consumption, where OE r is the energy consumption per unit time of robot r; SE r is the standby energy consumption per unit time of robot r; SE k is the total energy consumption of the robots assigned to workstation k.

[0042]

[0043] The above constraints respectively limit the number of workstations that can be opened, the order in which workstations are opened, the number of robots in each workstation, and allow some robots in the candidate robot set not to participate in the disassembly. max Indicates the maximum number of robots that can be accommodated at each workstation.

[0044] Beneficial effects:

[0045] The present invention designs a method for balancing a multi-product multi-robot local destructive disassembly line under a fixed workstation. The method is an industrial engineering method for balancing a multi-robot local destructive disassembly production line for a multi-product scenario, and is applicable to the fields of automobile disassembly, electronic waste recycling, and parts remanufacturing. Considering that the current research on multi-robot disassembly mainly focuses on non-destructive disassembly, ignoring the situation where the task cannot be disassembled due to the uncertainty of the quality of retired products, destructive disassembly is introduced to solve this problem. In addition, there is no accurate model for the existing model of the balancing problem of multi-product multi-robot local destructive disassembly line under a fixed workstation, which is mainly a conceptual model, resulting in the inability to verify the correctness of the proposed model. In order to solve the above problems, this study takes cycle time, total energy consumption, energy consumption peak and disassembly profit as optimization objectives, constructs a mixed integer linear programming model for the balancing problem of multi-product multi-robot local destructive disassembly line under a fixed workstation, and verifies the correctness of the model through two retired products.

[0046] The present invention solves the problems of resource waste, high energy consumption, and low disassembly efficiency in multi-robot disassembly lines through reasonable task allocation, local destruction strategy, and non-disassembly processing. Through multi-objective optimization, it is possible to balance cycle time, energy consumption, and disassembly profit, and significantly improve the overall efficiency of the disassembly line. This method is not only suitable for automobile disassembly, but can also be widely used in multiple fields such as electronic waste recycling and parts remanufacturing, and has high practical value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below.

[0048] Figure 1 It is a schematic diagram of a multi-product multi-robot partial destruction and disassembly line under a fixed workstation;

[0049] Figure 2 It is a task priority relationship and task attribute information diagram of two retired products in Example 1;

[0050] Figure 3 This is a schematic diagram of the single-objective optimal solution obtained by GUROBI in a multi-product and multi-robot test case. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below in conjunction with the embodiments and drawings.

[0052] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Description of symbols and decision variables:

[0054] Table 1 Symbols and decision variables description

[0055]

[0056]

[0057] In order to facilitate understanding of the meaning of the embodiments and other formulas in the subsequent parts of the application documents, a table of symbols and decision variables in Table 1 is provided hereby. Unless otherwise specified, the meanings of the symbols and decision variables described below that are the same as those in Table 1 are the same as those explained in Table 1.

[0058] The present invention will be further described below in conjunction with embodiments:

[0059] In the following embodiments, unless otherwise specified, the operations described are routine operations in the art.

[0060] A method for balancing a multi-product multi-robot partial destruction disassembly line under a fixed workstation, the method comprising the following steps:

[0061] S1. Determine the candidate robot set and collect information such as disassembly time, disassembly income, disassembly energy consumption, and disassembly cost of different models of robots in different disassembly modes;

[0062] S2. Establish a mixed integer linear programming model for the balance problem of multi-product multi-robot partial destruction disassembly line with the optimization objectives of minimizing cycle time, total disassembly energy consumption, energy consumption peak and disassembly profit.

[0063] In addition, the present invention proposes a new multi-objective function of a multi-product multi-robot local destruction disassembly line and constructs its mixed integer programming model. In order to improve the solution efficiency, the model is linearized, including the following steps:

[0064] S21. Considering the cycle time, energy consumption, resource constraints and disassembly profit, the following objective function is constructed:

[0065] Minimize the cycle time: minf 1 =CT

[0066] Minimize total energy consumption:

[0067] Workstation energy consumption peak indicators:

[0068] minf 3 =maxSE k

[0069] Disassembly profit indicator:

[0070]

[0071] Where, CT is the workstation cycle time; SE k is the total energy consumption of the robots assigned to workstation k; W k Indicates the workstation startup variable. If workstation k is in the startup state, then W k =1, otherwise W k =0; where SE k It consists of two parts: the energy consumption when the robot performs the disassembly task and the standby energy consumption. ikr Assign variables to tasks. If robot r in station k disassembles task i, then x ikr =1, otherwise x ikr =0; T ir It indicates the actual disassembly time of robot r to perform task i. Its value is related to the robot model and disassembly mode. r represents the standby energy consumption of robot r per unit time; y kr Assign variables to robots. If robot r is assigned to station k, then y kr =1, otherwise y kr =0;L ir represents the actual disassembly benefit of robot r performing task i; c ir represents the actual disassembly cost of robot r performing task i. The above disassembly benefit and disassembly cost are related to the robot model and disassembly mode. s represents the unit time cost of opening a workstation; h i represents the hazard attribute variable. When task i is in danger, h i =1, otherwise h i =0;ch i Additional disassembly costs to handle hazardous tasks

[0072] S22. The local destruction strategy is adjusted based on the priority of the disassembly task, the robot task disassembly time, the disassembly benefit, the disassembly cost and the non-disassembly of the component:

[0073]

[0074] Where e irepresents the feasibility value of destructive disassembly, which is determined by multi-granularity indicators and expert scoring method; e max is the threshold value of the feasibility of destruction and disassembly; represents the disassembly mode. If task i in robot r is in destructive disassembly mode, then otherwise d i represents the demand attribute variable. When task i has a recycling demand value, d i =1, otherwise d i =0; Rt ir Rtd represents the time it takes robot r to disassemble task i using a non-destructive disassembly method; ir represents the time it takes robot r to disassemble task i using the destructive disassembly method; CN ir is the disassembly cost of the i-th task when robot r performs non-destructive disassembly; CD ir is the disassembly cost of the i-th task when performing destructive disassembly under robot r; BN ir is the benefit of task i when using non-destructive disassembly under robot r; BD ir is the benefit of task i when destructive disassembly is used under robot r; L ir represents the actual disassembly benefit of robot r performing task i, which takes into account the different disassembly modes of the task;

[0075] S23, dynamically adjusting the task priority relationship based on the current load of each robot, the task sequence and the workstation cycle time, the energy consumption peak, the number of workstations and the number of robots:

[0076]

[0077] This constraint indicates that the tasks need to satisfy the task priority relationship, where IP p (j) is the set of immediate predecessor tasks of task i; P is a set of multiple products;

[0078]

[0079] This constraint indicates that the start time of the task that follows it must be after the end time of its predecessor task; j represents the start time of task j;

[0080]

[0081] This constraint indicates that the task assigned later in the same robot must wait for the disassembly of all the tasks assigned earlier in the same robot to be completed before it can be disassembled. ijkr is a priority variable. If tasks i and j are both assigned to robot r in station k, and task i is executed before task j, then zijkr =1, otherwise z ijkr =0.

[0082]

[0083] This constraint means that when two tasks are assigned to the same robot at the same workstation, the later assigned task must wait until the earlier assigned task is completed before it can start disassembly; where Ψ is a maximum value.

[0084]

[0085] This constraint indicates that the end time of the task cannot exceed the takt time of the current workstation; where Ts i represents the start time of task i; T ir It represents the actual disassembly time of robot r to perform task i. Its value is related to the robot model and disassembly mode.

[0086]

[0087] This constraint states that the start time of each task is non-negative.

[0088] S24. Workstation allocation needs to meet the task disassembly priority relationship, energy consumption constraints, and workstation quantity constraints:

[0089]

[0090]

[0091] The above two constraints limit the priorities that tasks under different assigned work conditions need to meet.

[0092]

[0093] This constraint limits the total energy consumption of all robots in each workstation to not exceed the highest peak energy consumption, where OE r is the energy consumption per unit time of robot r; SE r is the standby energy consumption per unit time of robot r; SE k is the total energy consumption of the robots assigned to workstation k.

[0094]

[0095] The above constraints respectively limit the number of workstations that can be opened, the order in which workstations are opened, the number of robots in each workstation, and allow some robots in the candidate robot set to not participate in the disassembly.

[0096] S3. In order to improve the solving efficiency, the above model is linearized, and a solver is used to solve the above mixed integer linear programming model;

[0097] There are nonlinear variables in the above model, but most mathematical solvers cannot handle nonlinear MIP models, and solving nonlinear MIP models will increase the solution time. Therefore, it is necessary to linearize the model to verify the correctness of the model and promote the optimization of the model.

[0098] There is x in objective 2 and constraint ikr ,T ir For the product of integer variables and continuous variables, this embodiment uses the Big-M rule for linearization. Introducing auxiliary variables u ikr Represents x ikr With T ir The product of and introduces the following linear constraints:

[0099]

[0100] In addition, standby energy consumption also involves nonlinear products. We once again introduce an auxiliary variable v kr to denote the product of these two variables. The linearization constraints we add are as follows.

[0101]

[0102] The linearized equation for objective 2 is as follows

[0103]

[0104] In target 4, there exists x ikr , L ir -C ir and kr , W k , where y kr , W k Used v kr Therefore, we also need to introduce a variable w ikr To represent x ikr ×(L ir -C ir ) and add the following constraints:

[0105]

[0106] The linearized equation for objective 4 is as follows

[0107]

[0108] In order to further illustrate the effects of the present invention, specific examples are used to illustrate the present invention.

[0109] Since the proposed problem of balancing a multi-product multi-robot partial destruction disassembly line under fixed workstations is a new problem, there is no available test case. Therefore, the present invention modifies an existing multi-product multi-robot test case. The priority relationship and task attributes of the two products in the specific case are as follows: Figure 2 As shown in , other auxiliary parameters are U = 2, R = 2, and the non-destructive and destructive disassembly times of the 9 candidate robots for different disassembly tasks. This example uses GUROBI10.0.1, running on the 12th generation Intel(R) Core(TM) i5-12400, with a main frequency of 2.50GHz. Each of the four objectives is used as an optimization target, and the results are shown in Table 2. The results give the Gantt charts of the four solutions, as shown in Figure 3 shown.

[0110] Combination Figure 3 The disassembly scheme of the multi-product multi-robot partial destruction disassembly line balance problem under fixed workstations can be described as follows:

[0111] (1) Each workstation has at most two robots performing disassembly simultaneously. For example, in Scheme CD, each workstation has two robots of different models, while in Scheme B, the second workstation has only one robot.

[0112] (2) All tasks conform to the priority relationship, for example, task 3 is disassembled before task 5;

[0113] (3) All dangerous tasks and demand tasks can only use non-destructive disassembly, such as dangerous task 2 and demand task 3;

[0114] (4) Tasks whose destructive disassembly feasibility value is greater than the specified threshold can only choose the destructive disassembly mode, such as Task 8.

[0115] Table 2 Optimization results of test cases

[0116]

[0117] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the embodiments of the present invention should be covered within the protection scope of the present invention.

Claims

1. A balancing method for a multi-product multi-robot partial destruction disassembly line under a fixed workstation, characterized in that: The following steps are involved: S1. Collect basic data on product lines and disassembly tasks, including disassembly time, disassembly revenue, disassembly energy consumption, and disassembly cost data of different robot models in different disassembly modes; S2. Establish a mixed integer linear programming model for the multi-product multi-robot partial destruction disassembly line balancing problem with the optimization objectives of minimizing cycle time, total disassembly energy consumption, energy consumption peak and disassembly profit; S3. Solve the mixed integer linear programming model to obtain a multi-product multi-robot local destruction and disassembly solution under a fixed workstation.

2. According to the method for balancing a multi-product multi-robot local destruction disassembly line under a fixed workstation as described in claim 1, it is characterized in that: The objective function of the mixed integer linear programming model in step S2 is as follows: Minimize the takt time: minf1=CT Minimize total energy consumption: Workstation energy consumption peak indicators: minf3=maxSE k Disassembly profit indicator: Where CT is the workstation cycle time; S is the number of fixed workstations; SE k is the total energy consumption of the robots assigned to workstation k; W k Indicates the workstation startup variable. If workstation k is in the startup state, then W k =1, otherwise W k =0; R is the total number of robots; N is the total number of disassembly tasks; x ikr Assign variables to tasks. If robot r in station k disassembles task i, then x ikr =1, otherwise x ikr =0; T ir represents the actual disassembly time of robot r performing task i; OE r Indicates the energy consumption per unit operation time of the robot; SE r represents the standby energy consumption of robot r per unit time; y kr Assign variables to robots. If robot r is assigned to station k, then y kr =1, otherwise y kr =0;L ir represents the actual disassembly benefit of robot r performing task i; c ir represents the actual disassembly cost of robot r performing task i; c s represents the unit time cost of opening a workstation; h i represents the hazard attribute variable. When task i is in danger, h i =1, otherwise h i =0;ch i Additional disassembly costs to handle hazardous tasks i.

3. The balancing method for a multi-product multi-robot local destruction disassembly line under a fixed workstation according to claim 2, characterized in that: The mixed integer linear programming model in step S2 also includes the following constraints: In the formula, e i represents the feasibility value of destruction and disassembly of each task i; e max is the threshold value of the feasibility of destruction and disassembly; represents the disassembly mode. If task i in robot r is in destructive disassembly mode, then otherwise d i represents the demand attribute variable. When task i has a recycling demand value, d i =1, otherwise d i =0; Rt ir represents the time it takes for robot r to disassemble task i using the non-destructive disassembly method; Rtd ir represents the time it takes robot r to disassemble task i using the destructive disassembly method; CN ir is the disassembly cost of the i-th task when robot r performs non-destructive disassembly; CD ir is the disassembly cost of the i-th task when performing destructive disassembly under robot r; BN ir is the benefit of task i when using non-destructive disassembly under robot r; BD ir is the benefit of task i when destructive disassembly is used under robot r; N is the set of disassembly task numbers; R is the set of robot numbers.

4. The balancing method for a multi-product multi-robot local destruction disassembly line under a fixed workstation according to claim 3, characterized in that: The mixed integer linear programming model in step S2 also includes the following constraints: In the formula, x jkr Assign variables to tasks. If robot r in station k disassembles task j, then x jkr =1, otherwise x jkr =0;IP p (j) is the set of immediate predecessor tasks of task i in product p; P is the product set; Ts i , Ts j Respectively represent the start time of tasks i and j; Ψ is a maximum value; z ijkr is a priority variable. If tasks i and j are both assigned to robot r in station k, and task i is executed before task j, then z ijkr =1, otherwise z ijkr =0.

5. The balancing method for a multi-product multi-robot local destruction disassembly line under a fixed workstation according to claim 4, characterized in that: The mixed integer linear programming model in step S2 also includes the following constraints: In the formula, z jikr is a priority variable. If tasks i and j are both assigned to robot r in station k, and task j is executed before task i, then z jikr =1, otherwise z jikr = 0; K is the set of multi-robot site numbers; S is the number of workstations; NR max Maximum number of robots per station.

Images