1 Introduction
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The task times may be different for each resource in the collaborative workcell;
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Each resource may not be able to execute all tasks (technological constraints);
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Precedence graph permitting, the resources can complete tasks in parallel.
2 Literature review
References | Authors | Year | Task allocation | Input data | Resolution method | Result | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Optimization of | Design | Safety and | Dynamic | Task data, | CAD | Product | Other/ | Framework | Genetic | Heuristic | ||||
productivity | workspace | ergonomics | allocation | graph, | data | characteristic | none | algorithm | ||||||
and cycle | considering | and | resources | |||||||||||
time | scheduling | flexibility | ||||||||||||
[24] | Bogner et al. | 2018 | X | X | X | Developed a mathematical model for task allocation and resolved with Heuristic | ||||||||
[23] | Chen et al. | 2013 | X | X | X | Developed a mathematical model for offline and online task scheduling with restrict resources | ||||||||
[21] | Fechter et al. | 2018 | X | X | X | X | Developed a planning system that considers layout | |||||||
[16] | Johannsmeier et al. | 2017 | X | X | X | X | Developed a planning system that results dynamic and flexible, also when unfore seen events happen | |||||||
[20] | Michalos et al. | 2018 | X | X | X | X | X | Developed a planning system that considers layout | ||||||
[25] | Nikolakis et al. | 2018 | X | X | X | Reduces time spent on a specific job | ||||||||
[26] | Pearce et al. | 2018 | X | X | X | X | X | Reduce makespan considering the physical strain | ||||||
[22] | Ranz et al. | 2017 | X | X | X | X | Developed a method for task allocation based on resources capability | |||||||
[10] | Takata et al. | 2011 | X | X | X | X | Developed a method to find the best task allocation in the manufacturing pro cess with multiple scenarios | |||||||
[17] | Tan et al. | 2010 | X | X | X | Shorter assembly time using collaboration | ||||||||
[29] | Tsarouchi et al. | 2016 | X | X | X | Developed a planning system that minimizes makespan and average resource utiliza tion; introduced body gesture to ensure human and robot interaction | ||||||||
[27] | Weckenborg et al. | 2019 | X | X | X | The results show that cycle time decrease with the utilization of cobots, and consequently, there is a productivity gain (12%) | ||||||||
[28] | Gualtieri et al. | 2019 | X | X | X | Developed a framework for assembly system con version and task alloca tion, evaluating different criteria | ||||||||
[33] | Tsarouchi et al. | 2017 | X | X | X | X | X | Developed a framework for task allocation that considers also layout | ||||||
[30] | Weckenborg et al. | 2019 | X | X | X | X | Developed a mathematical model for task balancing that aims to minimize cycle time and improve ergonomics | |||||||
[31] | Bruno et al. | 2018 | X | X | X | Task allocation exploiting different skill between robot and human, without consi dering work balancing | ||||||||
[32] | Malik et al. | 2019 | X | X | X | X | Task allocation based on task execution complexity | |||||||
[34] | Heydaryan et al | 2018 | X | X | X | X | Proves that even if pro duction time increase, col laboration improves human ergonomics and reduce risk of injury | |||||||
[35] | Antonelli et al. | 2017 | X | X | X | Task allocation method to avoid resources overload | ||||||||
[36] | Dianatfar et al. | 2019 | X | X | X | With task allocation, it is possible to reduce human fatigue and workload with out decreasing productivity | ||||||||
[37] | Yaphiar et al. | 2019 | X | X | Developed a mathematical model for task balancing in mixed-model assembly line |
3 Task allocation model for CAS
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To define a task allocation that minimizes the makespan ms, since the evaluation of the cycle time for a single station layout is meaningless;
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To identify the effects of the product and process characteristics on the task allocation in a collaborative scenario.
3.1 Nomenclature
Input variables and parameters | |
J
| Number of tasks |
i,j | Task indexes i,j = 1,...,J |
K
| Number of resources |
k
| Resource index k = 1,...,K |
P
j
| Number of immediate and transitive predecessors of task j |
p
j
| Predecessor index pj = 1,...,Pj |
S
j
| Number of immediate and transitive successors of task j; |
s
j
| Successor index sj = 1,...,Sj |
d
j
| Number of arcs connecting task j to the other tasks in the precedence graph |
t
j,k
| Task timej for resourcek (s) |
Output variables | |
Optimization variables: | |
x
j
k
t
| Assembly line balance decision variable (binary) |
y
j
i
| Decision variable representing precedence between task j and task i (binary) |
Indexes | |
Indexes adopted to evaluate the evaluate the obtained task | |
allocation: | |
p
%
| Parallelism [13] index |
t
%
| Task time index |
m
%
| Makespan index |
c
%
| Collaboration index |
Other variables used in this work | |
t
| Temporal instant (s) |
T
| Temporal horizon |
T
m
i
n
| Lower bound for the makespan (s) |
T
m
a
x
| Upper bound for the makespan (s) |
M
B
I
G
| |
U
k
| Set of the unfeasible tasks |
for resource k | |
c
| Cycle time (s) |
T
c
o
l
l
| Collaboration time (s) |
3.2 Hypotheses
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Mass production of one homogeneous product by performing J operations of a given product process (single-model line hypothesis);
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Deterministic and integral operation time;
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Each task is performed by only one resource.
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The number of resources K is equal to 2;
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The assembly line is composed by a single station consisting of one human operator and one cobot;
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Collaborative resources that share workplace and task time.
3.3 C-ALB for collaborative assembly systems
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Tasks which are not direct or transitive predecessors/successors of task j.
4 Product and process characteristics indexes
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Parallelism index p%: input parameter based on the precedence graph (product characteristic);
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Task time index t%: input parameter based on the difference of the resources task times (product and process characteristic);
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Makespan index m%: output parameter which evaluates the quality of the ms achievable with the considered task allocation (process characteristic);
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Collaboration parameter c%: output parameter that represents the shared activity between the resources [9] (process characteristic).
4.1 Parallelism index p%
4.2 Task time index t%
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If t% is very small, albeit not null, the disparity between the resources task time is high. A null value cannot be reached unless the meaningless scenario where one of the resources has null task times;
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If t% is equal to 1, the resources task times are equal on average; thus, this scenario is likely to increase the collaboration between the resources.
4.3 Makespan index m%
4.4 Collaboration parameter c%
5 Influence of the product and process characteristics on the CAS system
5.1 Influence of p% on m% and c%
J | p% [%] | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
10 | 0.08 | 0.13 | 0.2 | 0.31 | 0.4 | 0.55 | 0.6 | 0.73 | 0.82 | 0,89 |
12 | 0.06 | 0.13 | 0.22 | 0.27 | 0.42 | 0.5 | 0.6 | 0.75 | 0.82 | 0.91 |
15 | 0.04 | 0.1 | 0.19 | 0.27 | 0.42 | 0.48 | 0.6 | 0.71 | 0.76 | 0.85 |
17 | 0.07 | 0.14 | 0.25 | 0.31 | 0.41 | 0.52 | 0.59 | 0.65 | 0.71 | 0.8 |
20 | 0.05 | 0.13 | 0.19 | 0.33 | 0.39 | 0.46 | 0.6 | 0.66 | 0.7 | 0.78 |
5.2 Influence of t% on m% and c%
J | p% | ||
---|---|---|---|
10 | 0.27 | 0.488 | 0.667 |
12 | 0.27 | 0.49 | 0.67 |
15 | 0.27 | 0.48 | 0.7 |
5.3 Overall results
6 ALB problem model comparison: traditional versus C-ALB
J | p% | t% |
---|---|---|
10 | 0.27 | 0.4 |
15 | 0.67 | 0.8 |
ALB | C-ALB | Percentage | |
---|---|---|---|
Patterson-Albracht | Proposed model | difference | |
m% | 1.2 | 0.86 | − 28% |
c% | 0.1 | 0.59 | 490% |
ms (s) | 77 | 53 | − 31% |
Tcoll (s) | 5 | 31 | 520% |
Task j | Description |
---|---|
1 | Place the product base |
2 | Place the support |
3 | Place the support |
4 | Place the support |
5 | Place the support |
6 | Place the outline border |
7 | Place the outline border |
8 | Place the outline border |
9 | Place the outline border |
10 | Place the cover board |
7 Case study
Task | Operator | Robot task | Robot task |
---|---|---|---|
task times | times t% = 0.48 | times t% = 0.60 | |
1 | 1 | 3 | 3 |
2 | 3 | 6 | 5 |
3 | 3 | 6 | 5 |
4 | 3 | 6 | 5 |
5 | 3 | 6 | 5 |
6 | 7 | 14 | 10 |
7 | 7 | 14 | 10 |
8 | 7 | 14 | 10 |
9 | 7 | 14 | 10 |
10 | 10 | 22 | 20 |
8 Conclusion
-
A proper model for collaborative systems should be considered; indeed, when comparing with traditional ALB models, our C-ALB model achieves a greater throughput and collaboration.
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A difference in the task time between the resources has a minor influence on the system performance unless it is considerable (t% less than 0.4). Moreover, the number of tasks influences the performance for a lower value of p%.
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Regarding p%, precedence graphs with more parallel branches are more suitable for CAS since the proposed model shows that p% has a great influence on m%.