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Research on hybrid-load AGV dispatching problem for mixed-model automobile assembly line
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52nd CIRP Conference on Manufacturing Systems 52nd CIRP Conference on Manufacturing Systems
Research AGV dispatching problem for Research on on hybrid-load hybrid-load AGV dispatching for mixed-model mixed-model 28th CIRP Design Conference, May 2018,problem Nantes, France automobile assembly line automobile assembly line A new methodology to analyze the functional and physical architecture of Lixiang Zhang, Hu*, Yu Zhang, Yaoguang Yaoguang Hu*, Yu Guan Guanfamily identification existing products forLixiang an assembly oriented product
School of Mechanical Engineering, Beijing Institute of Technology, Beijing，China School of Mechanical Engineering, Beijing Institute of Technology, Beijing，China * Corresponding author. Tel.:+86-010-68917880. E-mail address: [email protected] * Corresponding author. Tel.:+86-010-68917880. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France
Abstract
*Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Automobile industry has marched into an age of mass customization, and begun to use mixed-model assembly lines. The demand for materials Automobile industry has marched into an age of mass customization, and begun to use mixed-model assembly lines. The demand for materials in each assembly station is constantly changing. To meet with the demand, this paper proposes a hybrid-load AGV dispatching model, which in each assembly station is constantly changing. To meet with the demand, this paper proposes a hybrid-load AGV dispatching model, which allocates different types of AGVs for different sizes of materials. With an attempt to minimize the total cost of logistics system, the genetic Abstract allocates different typestoofsolve AGVs for problem different and sizesanalyze of materials. WithThe an attempt to minimize the total costAGV of logistics system, theisgenetic algorithm is employed a real this model. results indicate that hybrid-load dispatching model better algorithm is employed to solve a real problem and analyze this model. The results indicate that hybrid-load AGV dispatching model is better than single-load or multi-load model for mixed-model automobile assembly lines. Inthan today’s business the trend towards more product variety andlines. customization is unbroken. Due to this development, the need of single-load or environment, multi-load model for mixed-model automobile assembly © 2019 Authors. Published by Elsevier This is open access article under the BY-NC-ND license agile andThe reconfigurable production systems Ltd. emerged to an cope with various products andCC product families. To design and optimize production © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2019 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/) systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to (http://creativecommons.org/licenses/by-nc-nd/3.0/) This is an open access article under the scientific CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the committee of the 52ndproduct CIRP Conference on Manufacturing Systems. analyze a product or one product family on the physical level. Different families, however, may differ largely in terms of the number and Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Keywords: AGV; dispatching; hybrid-load; genetic algorithm; automobile assembly lines system. A new methodology is proposedgenetic to analyze existing products in view of their functional and physical architecture. The aim is to cluster Keywords: AGV; dispatching; hybrid-load; algorithm; automobile assembly lines these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the To solve these problems, this paper proposes a hybrid-load 1. Introduction similarity between product families by providing design support to both, production planners and product illustrative To solvesystem these problems, this paperdesigners. proposes An a hybrid-load 1. Introduction AGV dispatching model to minimize the of total cost of logistics example of a nail-clipper is used to explain the proposed methodology. An AGV industrial case studymodel on twotoproduct families steering columns of dispatching minimize the total cost of logistics system by optimizing the allocation for different tasks. Firstly, Recently, the demand of diversification and personalization thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. system by optimizing the allocation for different tasks. Firstly, Recently, the demand of diversification and personalization according to the maximum weight that multi-load AGV can to increase, which adopt ©continues 2017 The Authors. Published by makes Elseviermore B.V. automakers according to the maximum weight that multi-load AGV can continues to increase, which makes more automakers adopt bear, all materials divided into large or small materials. mixed-model assembly lines [1] replacing mass production Peer-review underassembly responsibility the scientific of the 28th CIRP Design Conferenceare 2018. bear, all materials are divided into large or small materials. mixed-model linesof [1] replacingcommittee mass production
Then, multi-load dispatching system combines transportation assembly lines to improve the productivity and reduce Then, multi-load dispatching system combines transportation assembly lines to improve the productivity and reduce tasks of small materials. Finally, large materials are allocated product tasks of small materials. Finally, large materials are allocated manufacturing cost. In mixed-model line, different product to single-load AGVs and transportation tasks of small models are assembled on the same line [2], which needs to single-load AGVs and transportation tasks of small models are assembled on the same line [2], which needs materials are allocated to multi-load AGVs. Genetic algorithm timely and accurate material transportation. Intelligent materials are allocated to multi-load AGVs. Genetic algorithm timely and accurate material transportation. Intelligent is used to solve a real dispatching problem. Compared with logistics system (ILS) can meet with this need. ILS was is the usedproduct to solve a real dispatching problem. Compared with logistics system (ILS) can meet with this need. ILS was of 1.applied Introduction range characteristics and/or single-load model, theand total transportationmanufactured distance is reduced. to discrete manufacturing systems [3] for material single-loadinmodel, the total transportation distance is reduced. applied to discrete manufacturing systems [3] for material assembled this system. In this context, the main challenge in While AGVs used are less than multi-load model. handling in flexible assembly lines. Automatic guided vehicle While AGVs used are less than multi-load model. handling in flexible assembly lines. Automatic guided vehicle Due to the fast development in the domain of modelling and analysis is now not only to cope with single This paper is organized as follows. Section 2 provides a (AGV) is an important part of ILS to improve the flexibility. This paper is organized as follows. Section 2 provides a (AGV) is an important part of ILStrend to improve the flexibility. communication andareanmany ongoing of including digitization and products, a limited productliteratures. range or existing families, brief review of relevant Sectionproduct 3 describes the At present, there researches [4], singlebrief review of relevant literatures. Section 3 describes the At present, there are many enterprises researches [4], including single- but digitalization, manufacturing are facing important also to be able to analyze and to compare products to define problem and hybrid-load dispatching model. Section 4 uses load and multi-load AGV dispatching system. Single-load problem andfamilies. hybrid-load model. Sectionexisting 4 uses load and multi-load AGV dispatching system. challenges today’s environments: a Single-load continuing product candispatching be observed that classical genetic algorithm to Itsolve a real problem. In section 5, the means that in each vehiclemarket transports one piece of material every new genetic families algorithm to solve a in real problem. In section 5, the means that each vehicle transports onedevelopment piece of material every tendency towards reduction of product times and product are regrouped function of clients or features. hybrid-load model is compared with single-load and multitime. But multi-load vehicle can transport more than one. hybrid-load model oriented is compared with single-load andtomultitime. Butproduct multi-load vehicle can transport more than one. However, shortened lifecycles. In addition, there is an increasing assembly product families are hardly find. load dispatching model. Finally, Section 6 presents However, it is not suitable for mixed-model assembly lines. It load dispatching model. Finally, Section 6 presents However, itcustomization, is not suitablebeing for mixed-model assembly lines. It demand of at the same time in a global On the product family level, products differ mainly in two conclusions of this study and proposes plans for future is because that single-load system will waste capacity when conclusions of this(i)study and proposes plans and for (ii) future is because that single-load system willthewaste capacity when main competition with competitors all over world. This trend, characteristics: the number of components the researches. being used to load small materials and there are unnecessary researches. being used to load the smalldevelopment materials andfrom theremacro are unnecessary which is inducing to micro type of components (e.g. mechanical, electrical, electronical). works to dispatch large materials for multi-load system. works to results dispatchinlarge materialslotforsizes multi-load markets, diminished due tosystem. augmenting Classical methodologies considering mainly single products product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which 2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license an efficient definition and identify possible optimization potentials in the existing causes difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems. production system, it is important to have a precise knowledge comparison of different product families. Addressing this Keywords: Assembly; DesignInmethod; Family identification manufacturing cost. mixed-model line, different
Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems.
2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an©open article Published under theby CC BY-NC-ND 2212-8271 2017access The Authors. Elsevier B.V. license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of scientific the scientific committee theCIRP 52ndDesign CIRPConference Conference2018. on Manufacturing Systems. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2019.03.251
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2. Literature review 2.1. Automobile assembly lines and logistics systems Previously, single-model assembly lines were widely used in various industries to increase production efficiency, and a large number of forklifts were used for material handling because the types of materials were fixed. Nowadays, our life has been greatly improved, and higher requirements have been placed on product personalization and diversification. Automobile production have been shifting to mass customization mode, and mixed-model assembly lines are used [1]. There are more than one models assembled on the same automobile assembly line. Set Parts Supply (SPS) [2] is used to transport all parts of one car from supermarket area to each station. In this way, all parts are transported as a unit load, so the flexibility of SPS are not enough. Plenty of studies have been conducted on various types of logistics systems that use AGVs to transport parts, which can improve the flexibility. And there are some characteristics about AGV used in logistics systems: • • • •
Autonomous path planning, high level of flexibility The system operates steadily and safely High degree of intelligence and fewer staff members Battery driven, green and environmentally friendly
single-load system, which proves the superiority of multi-load system. Adaptive genetic algorithm [9] is used to solve scheduling problems, where machines and AGVs are operating simultaneously. The dispatching problem of AGV in the automated warehouse system [10] is solved by using genetic algorithm. In flexible manufacturing systems, adaptive genetic algorithm is used to dispatch parts and AGVs together [11] to minimize the idle time of machining center, which solves a large variety problem. 3. Model construction 3.1. Problem description Now, more and more automakers begin to use mixed-model automobile assembly lines. In this situation, a lot of different cars are assembled on the same assembly line, so the materials required for each station are constantly changing. If singleload AGVs are used, when most materials are small, the carrying capacity of AGVs will be wasted. When the material demand in the logistics system is dominated by large materials, the use of multi-load AGV system will increase unnecessary dispatching, because most AGVs can only carry one piece of material. Thus, this paper proposes a hybrid-load AGV dispatching model to avoid these problems to reduce the cost of material transportation.
According to the number of the material of every AGV loading, it can be divided into single-load [5] and multi-load dispatching system [6]. Each single-load AGV transports one piece of material every time, and each multi-load AGV can transport more than one. The characteristics of single-load and multi-load AGV dispatching models from previous literatures are summarized as follows in Table 1. Table 1. Characteristics of single-load and multi-load dispatching models. single-load model
multi-load model
dispatching difficulty
easier
more difficulty
work efficiency
lower
higher
number of AGV
more
less
AGV capability requirements
lower
higher
system adaptability
higher
lower
2.2. Genetic algorithm In multi-load AGV dispatching systems, allocating tasks to AGVs is a combinatorial optimization problem. This kind of problem is NP-hard [7]. When the problem scale is large, using traditional method is difficult to obtain a satisfactory solution in a limited time. Heuristic algorithms have brought us a new solution for this type of problems. Genetic algorithm is a global and parallel heuristic algorithm with high efficiency and high quality of solution, which is usually used to solve dispatching problems. To minimize the total operational cost and AGV empty-loading ratio, hybrid multi-objective genetic algorithm [8] is used to optimize multi-load AGV dispatching and routing in flexible manufacturing systems, and the result is compared with
Fig. 1. Schematic diagram of one assembly line and material transportation process (S represents a single-load AGV, and M represents a multi-load AGV).
As shown in Fig. 1, there are ten assembly stations selected from a company's P platform gearbox assembly line. Different sizes of materials need to be transported from warehouse to the assembly station by single-load or multi-load AGV. There are three different models (C1/C2/C3) assembled on the same
Lixiang Zhang et al. / Procedia CIRP 81 (2019) 1059–1064 Lixiang Zhang et al. / Procedia CIRP 00 (2019) 000–000
automobile assembly line from station P02 to station P11. Materials that need to be transported by single-load AGVs, will be picked from warehouse and stored in BUF 1 temporarily, while materials that need to be transported by multi-load AGVs, will be stored in BUF2. The single-load AGV moves to BUF 1 from the waiting area, transports one piece of material to P04, and then returns to the waiting area. The multi-load AGV needs to transport two pieces of materials from BUF 2 to two different assembly stations (P08 & P02) and then returns to the waiting area. Above all, we make some reasonable assumptions about the logistics system in order to describe the problem clearly. l l l
The weight of every material is no more than the weight that single-load can bear All tasks are from warehouse to assembly stations Multi-load AGV can bear any two pieces of materials when the total weight is no more than AGV can bear
3.2. Mathematical model In view of the fact that the existing AGV dispatching system is difficult to adapt to mass customization production of automobiles, this paper proposes a hybrid-load AGV dispatching model. Before dispatching, all materials are classified according to its weight. Large materials enter into the single-load dispatching system, while small materials enter into multi-load dispatching system. After multi-load dispatching system optimizes the combination of transportation tasks of small materials, multi-load AGVs are arranged to complete combined transportation tasks, and single-load AGVs are arranged to complete material transportation tasks that cannot be combined. The variables used in this paper are defined as follows:
n The number of tasks ns The number of single-load AGV used nm The number of multi-load AGV used ps The unit cost of single-load AGV pm The unit cost of multi-load AGV pus The cost of unit transportation distance for single-load AGV pum The cost of unit transportation distance for multi-load AGV Lis The number of material of the i-th single-load AGV loading Lim The number of material of the i-th multi-load AGV loading Liw The i-th AGV carrying weight Lw max The maximum weight of AGV can bear, single-load AGV is 7 and multi-load AGV is 5 Dsi Transportation distance of the i-th single-load AGV Dmi Transportation distance of the i-th multi-load AGV ì1 ; Task i is completed by a single-load AGV Tis = í î0 ; Otherwise ì1 ; Task i is completed by a multi-load AGV Tim = í î0 ; Otherwise
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To minimize the total cost of material transportation, the object function is constructed as shown in Eq. (1). First part represents the transportation cost of single-load AGVs, second part represents the transportation cost of multi-load AGVs, third part represents the purchase cost of single-load AGVs, and forth part represents the purchase cost of multi-load AGVs. æ min ç pus è
ns
å D i =1
si
+ pum
nm
å D i =1
mi
(1)
ö + ns ps + nm pm ÷ ø
(2) (3)
Liw £ Lw max
(4) Eq. (2) means that a single-load AGV carries one piece of material and a multi-load AGV carries one piece or two pieces of materials at one time. Eq. (3) indicates that the weight of each AGV carrying materials cannot be greater than the weight that the AGV can bear. Eq. (4) indicates that each task can only be performed once. 4. Computational experiments This paper does not consider the path planning of transportation tasks, so it only needs to solve material transportation combinatorial problem in multi-load AGV dispatching system. The solution process includes three steps: l l l
Classifying material transportation tasks Optimizing the combination of small materials Allocating AGVs for all tasks
We selected 20 material transportation tasks on the gearbox assembly line of a company’s P platform, as shown in Table 2. Table 2. Transportation tasks. Order
1
2
3
4
5
6
7
destination
P09
P02
P07
P07
P04
P04
P11
weight
4
3
1
2
1
7
6
Order
8
9
10
11
12
13
14
destination
P08
P03
P06
P03
P08
P11
P02 3
weight
4
1
3
2
4
4
Order
15
16
17
18
19
20
destination
P10
P02
P04
P04
P04
P10
weight
6
6
3
1
2
5
4.1. Classification All transportation tasks are classified according to the maximum load weight that multi-load AGV can bear. As shown in Fig. 2, when the weight of the task is greater than or equal to multi-load AGV can bear, the task is assigned to single-load tasks. Otherwise, the task is assigned to multi-load tasks.
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The transportation tasks of small materials that need to be combined by multi-load AGV dispatching system are obtained by classification as shown in Table 3. Table 3. Small material transportation tasks. Order
1
2
3
4
5
8
9
10
destination
P09
P02
P07
P07
P04
P08
P03
P06 3
weight
4
3
1
2
1
4
1
Order
11
12
13
14
17
18
19
destination
P03
P08
P11
P02
P04
P04
P04
weight
2
4
4
3
3
1
2
Fig. 3. Pseudocode for genetic algorithm.
4.2. Optimization of small material transportation tasks This paper uses genetic algorithm to solve the problem of combination of transportation tasks of small materials in multi-load AGV dispatching system as shown in Fig. 3. The symmetric distance matrix is shown in Table 4. Table 4. Symmetric distance matrix (A represents warehouse). A
1
2
3
4
5
6
7
A
0
1
635
0
2
275
402
0
3
620
152
387
0
4
134
543
183
528
0
5
456
411
327
301
365
0
6
447
230
214
215
356
309
0
7
200
477
117
462
108
314
290
0
8
130
546
187
531
46
367
359
111
8
9
10
0
9
209
467
150
452
187
288
280
137
185
0
10
369
308
136
293
277
344
120
211
281
201
0
Using real coding is more efficient than using binary coding, and it has higher computational accuracy [12]. In this paper, the task sequence number is selected as gene to code, which can efficiently avoid generating illegal solutions. It’s well known that the quality of initial population affects the convergence speed of heuristic algorithm. This article uses the method as shown in Fig. 4 to generate initial population. All tasks are arranged according to the weight of the material from small to large. Then selecting the current transportation task that the material is the smallest combines with the task that the material is largest (e.g. 1 and 19), and removing those two transportation tasks from all tasks, until all tasks are combined. The above steps are cycled for certain times to produce the required number of initial individuals. There are single-point crossing, multi-point crossing, and partial matching crossing. This paper is similar to TSP problem, in which each task is executed only once. It is more appropriate to use partial matching cross as shown in Fig. 5, which is not easy to destroy good individuals and generate illegal solutions. Generating two points as crossover points (P1, P2), chromosome segments ((8, 18, 1) and (11, 19, 2)) from two individuals are exchanged. Then, according to the mapping matrix, the repetitive genes of each individual are replaced to produce a legal individual. Variation is an important step to jump out of the local optimal solution. In this paper, single-point variation is used as shown in Fig. 6. Generating mutation point (P) and variant gene (5), the gene of the mutation point is exchanged into variant gene (11à5), and replacing the repeated gene (5à11, this 5 is the gene of individual before mutation).
Fig. 2. Pseudocode for task classification.
Fig. 4. The process of generating initial individual.
Lixiang Zhang et al. / Procedia CIRP 81 (2019) 1059–1064 Lixiang Zhang et al. / Procedia CIRP 00 (2019) 000–000
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4.3. AGV allocation According to above genetic algorithm, the best AGV allocation plans are as shown in Table 6 and Table 7. From Table 2, we can find the destination and weight of task 8 and task 12 are equal, so two plans are equal. Table 6. AGV allocation plan 1 task
6
7
15
16
17
20
AGV
S1
S2
S3
S4
S4
S6
task
3
13
4
10
5
AGV
Fig. 5. The process of crossover.
M3
M4
8
1
18
2
M1 9
M5
19 M2
12
11
M6
14 M7
Table 7. AGV allocation plan 2. task
6
7
15
16
17
20
AGV
S1
S2
S3
S4
S4
S6
task
3
13
4
10
5
AGV
This article uses roulette method [13] to select the best individual from all individuals. Every individual is selected according to the selection probability, which is computed as shown in Eq. (5) (6). The individual's selection probability is equal to the proportion of the individual's fitness value and the sum of fitness values. The parameters of genetic algorithm used in this paper are shown in Table 5.
pi =
fi
å f
Where: C is a constant
a single-load AGV penalty weight b multi-load AGV capacity waste penalty weight ei i-th multi-load AGV wasted capacity fi the fitness of i-th individual pi the probability of i-th individual selected
M4
12 M5
18
8
value
population size
20
maximum genetic generation
200
crossover probability
0.8
variation probability
0.1
α
200
β
19 M2
9 M6
11
14 M7
(5) (6)
5.1. Comparison with single-load AGV dispatching model Compared with single-load AGV dispatching model, the main advantages of the proposed model are that the total transportation distance and the number of AGVs used are reduced, so material transportation cost is reduced. Taking this solution problem as an example, as shown in Fig. 7, the transportation distance is reduced by 21.4%, and the number of AGV used decreased by 35%. 5.2. Comparison with multi-load AGV dispatching model Compared with multi-load AGV dispatching model, the main advantage of the model is that the complexity of the solution is greatly reduced. Taking this solution problem as an example, there are 20 tasks. When using multi-load AGV dispatching model, the complexity is 20!. In contrast, hybridload AGV dispatching model processes large materials separately and then processes small material transportation tasks. So the solution complexity is only 15! +5!. When dealing with large-scale complex problems, the model proposed in this paper has obvious advantages.
Table 5. The parameters of genetic algorithm. parameter
2
M1
5. Discussion
Fig. 6. The process of variation.
f = C - å Dsi - å Dmi - a ns - b å ei
M3
1
100 Fig. 7. (a) Distance; (b) The number of AGVs used.
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6. Conclusion In this paper, by analyzing the advantages and disadvantages of single-load and multi-load AGV dispatching model, a hybrid-load AGV dispatching model is proposed. The transportation tasks of large materials are removed from all tasks. The transportation tasks of small materials are dispatched by multi-load AGV dispatching system, and finally AGVs are uniformly allocated to complete all transportation tasks. The results of genetic algorithm indicate that hybridload AGV dispatching model greatly improves the efficiency of material transportation and reduces the cost of material transportation and the complexity of problem solving, which is more suitable for mixed-model automobile assembly lines in mass customization condition. For future research, AGV path planning under hybrid-load AGV dispatching model and material transportation problem with time window will be considered, which makes hybridload AGV dispatching model closer for real problems. Acknowledgement The authors would like to thank the National Key R&D Program of China (Project No. 2016YFD0701105) and the National Natural Science Foundation of China (Project No. 51675051). We express our sincere thanks to Lovol Heavy Industry Co., Ltd. for the case verification. References [1] Bukchin J, Dar-El E M, Rubinovitz J. Mixed model assembly line design in a make-to-order environment. Computers & Industrial Engineering, 2002; 41(4):405-421.
[2] Jainury S M, Ramli R, Ab Rahman M N, et al. Integrated Set Parts Supply system in a mixed-model assembly line. Computers & Industrial Engineering, 2014; 75:266-273. [3] Qi B Y, Yang Q L, Zhou Y Y. Application of AGV in intelligent logistics system. Asia International Symposium on Mechatronics. IET; 2016. [4] B.A.Peters, J.S.Smith, and S.Venkatesh. A control classification of automated guided vehicles. International Journal of Industrial Engineering, 1996. [5] ShabnamRezapour, RezaZanjirani-Farahani, ElnazMiandoabchi. A machine-to-loop assignment and layout design methodology for tandem AGV systems with single-load vehicles. International Journal of Production Research, 2011; 49(12):29. [6] Ümit Bilge, Tanchoco J M A. AGV systems with multi-load carriers: Basic issues and potential benefits. Journal of Manufacturing Systems, 1997; 16(3):159-174. [7] Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. [8] Umar U A, Ariffin M K A, Ismail N, etal. Hybrid multiobjective genetic algorithms for integrated dynamic scheduling and routing of jobs and automated-guided vehicle (AGV) in flexible manufacturing systems (FMS) environment. The International Journal of Advanced Manufacturing Technology, 2015; 81(9-12):2123-2141. [9] Sanches D S , Rocha J D S , Castoldi M F , et al. An Adaptive Genetic Algorithm for Production Scheduling on Manufacturing Systems with Simultaneous Use of Machines and AGVs. Journal of Control, Automation and Electrical Systems, 2015; 26(3):225-234. [10] Sainan L. Optimization problem for AGV in automated warehouse system. IEEE International Conference on Service Operations & Logistics. IEEE, 2008. [11] Simultaneous scheduling of parts and automated guided vehicles in an FMS environment using adaptive genetic algorithm. The International Journal of Advanced Manufacturing Technology, 2006; 29(5-6):584589. [12] by Z Michalewic. Genetic Algorithms + Data Structures = Evolution Programs. Springer Berlin Heidelberg, 1996. [13] Thierens D, Goldberg D E. Convergence Models of Genetic Algorithm Selection Schemes. Parallel Problem Solving from Nature - PPSN III, International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature, Jerusalem, Israel, October 9-14, 1994; Proceedings. DBLP, 1994;119-129.
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52nd CIRP Conference on Manufacturing Systems 52nd CIRP Conference on Manufacturing Systems
Research AGV dispatching problem for Research on on hybrid-load hybrid-load AGV dispatching for mixed-model mixed-model 28th CIRP Design Conference, May 2018,problem Nantes, France automobile assembly line automobile assembly line A new methodology to analyze the functional and physical architecture of Lixiang Zhang, Hu*, Yu Zhang, Yaoguang Yaoguang Hu*, Yu Guan Guanfamily identification existing products forLixiang an assembly oriented product
School of Mechanical Engineering, Beijing Institute of Technology, Beijing，China School of Mechanical Engineering, Beijing Institute of Technology, Beijing，China * Corresponding author. Tel.:+86-010-68917880. E-mail address: [email protected] * Corresponding author. Tel.:+86-010-68917880. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France
Abstract
*Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Automobile industry has marched into an age of mass customization, and begun to use mixed-model assembly lines. The demand for materials Automobile industry has marched into an age of mass customization, and begun to use mixed-model assembly lines. The demand for materials in each assembly station is constantly changing. To meet with the demand, this paper proposes a hybrid-load AGV dispatching model, which in each assembly station is constantly changing. To meet with the demand, this paper proposes a hybrid-load AGV dispatching model, which allocates different types of AGVs for different sizes of materials. With an attempt to minimize the total cost of logistics system, the genetic Abstract allocates different typestoofsolve AGVs for problem different and sizesanalyze of materials. WithThe an attempt to minimize the total costAGV of logistics system, theisgenetic algorithm is employed a real this model. results indicate that hybrid-load dispatching model better algorithm is employed to solve a real problem and analyze this model. The results indicate that hybrid-load AGV dispatching model is better than single-load or multi-load model for mixed-model automobile assembly lines. Inthan today’s business the trend towards more product variety andlines. customization is unbroken. Due to this development, the need of single-load or environment, multi-load model for mixed-model automobile assembly © 2019 Authors. Published by Elsevier This is open access article under the BY-NC-ND license agile andThe reconfigurable production systems Ltd. emerged to an cope with various products andCC product families. To design and optimize production © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2019 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/) systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to (http://creativecommons.org/licenses/by-nc-nd/3.0/) This is an open access article under the scientific CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the committee of the 52ndproduct CIRP Conference on Manufacturing Systems. analyze a product or one product family on the physical level. Different families, however, may differ largely in terms of the number and Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Keywords: AGV; dispatching; hybrid-load; genetic algorithm; automobile assembly lines system. A new methodology is proposedgenetic to analyze existing products in view of their functional and physical architecture. The aim is to cluster Keywords: AGV; dispatching; hybrid-load; algorithm; automobile assembly lines these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the To solve these problems, this paper proposes a hybrid-load 1. Introduction similarity between product families by providing design support to both, production planners and product illustrative To solvesystem these problems, this paperdesigners. proposes An a hybrid-load 1. Introduction AGV dispatching model to minimize the of total cost of logistics example of a nail-clipper is used to explain the proposed methodology. An AGV industrial case studymodel on twotoproduct families steering columns of dispatching minimize the total cost of logistics system by optimizing the allocation for different tasks. Firstly, Recently, the demand of diversification and personalization thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. system by optimizing the allocation for different tasks. Firstly, Recently, the demand of diversification and personalization according to the maximum weight that multi-load AGV can to increase, which adopt ©continues 2017 The Authors. Published by makes Elseviermore B.V. automakers according to the maximum weight that multi-load AGV can continues to increase, which makes more automakers adopt bear, all materials divided into large or small materials. mixed-model assembly lines [1] replacing mass production Peer-review underassembly responsibility the scientific of the 28th CIRP Design Conferenceare 2018. bear, all materials are divided into large or small materials. mixed-model linesof [1] replacingcommittee mass production
Then, multi-load dispatching system combines transportation assembly lines to improve the productivity and reduce Then, multi-load dispatching system combines transportation assembly lines to improve the productivity and reduce tasks of small materials. Finally, large materials are allocated product tasks of small materials. Finally, large materials are allocated manufacturing cost. In mixed-model line, different product to single-load AGVs and transportation tasks of small models are assembled on the same line [2], which needs to single-load AGVs and transportation tasks of small models are assembled on the same line [2], which needs materials are allocated to multi-load AGVs. Genetic algorithm timely and accurate material transportation. Intelligent materials are allocated to multi-load AGVs. Genetic algorithm timely and accurate material transportation. Intelligent is used to solve a real dispatching problem. Compared with logistics system (ILS) can meet with this need. ILS was is the usedproduct to solve a real dispatching problem. Compared with logistics system (ILS) can meet with this need. ILS was of 1.applied Introduction range characteristics and/or single-load model, theand total transportationmanufactured distance is reduced. to discrete manufacturing systems [3] for material single-loadinmodel, the total transportation distance is reduced. applied to discrete manufacturing systems [3] for material assembled this system. In this context, the main challenge in While AGVs used are less than multi-load model. handling in flexible assembly lines. Automatic guided vehicle While AGVs used are less than multi-load model. handling in flexible assembly lines. Automatic guided vehicle Due to the fast development in the domain of modelling and analysis is now not only to cope with single This paper is organized as follows. Section 2 provides a (AGV) is an important part of ILS to improve the flexibility. This paper is organized as follows. Section 2 provides a (AGV) is an important part of ILStrend to improve the flexibility. communication andareanmany ongoing of including digitization and products, a limited productliteratures. range or existing families, brief review of relevant Sectionproduct 3 describes the At present, there researches [4], singlebrief review of relevant literatures. Section 3 describes the At present, there are many enterprises researches [4], including single- but digitalization, manufacturing are facing important also to be able to analyze and to compare products to define problem and hybrid-load dispatching model. Section 4 uses load and multi-load AGV dispatching system. Single-load problem andfamilies. hybrid-load model. Sectionexisting 4 uses load and multi-load AGV dispatching system. challenges today’s environments: a Single-load continuing product candispatching be observed that classical genetic algorithm to Itsolve a real problem. In section 5, the means that in each vehiclemarket transports one piece of material every new genetic families algorithm to solve a in real problem. In section 5, the means that each vehicle transports onedevelopment piece of material every tendency towards reduction of product times and product are regrouped function of clients or features. hybrid-load model is compared with single-load and multitime. But multi-load vehicle can transport more than one. hybrid-load model oriented is compared with single-load andtomultitime. Butproduct multi-load vehicle can transport more than one. However, shortened lifecycles. In addition, there is an increasing assembly product families are hardly find. load dispatching model. Finally, Section 6 presents However, it is not suitable for mixed-model assembly lines. It load dispatching model. Finally, Section 6 presents However, itcustomization, is not suitablebeing for mixed-model assembly lines. It demand of at the same time in a global On the product family level, products differ mainly in two conclusions of this study and proposes plans for future is because that single-load system will waste capacity when conclusions of this(i)study and proposes plans and for (ii) future is because that single-load system willthewaste capacity when main competition with competitors all over world. This trend, characteristics: the number of components the researches. being used to load small materials and there are unnecessary researches. being used to load the smalldevelopment materials andfrom theremacro are unnecessary which is inducing to micro type of components (e.g. mechanical, electrical, electronical). works to dispatch large materials for multi-load system. works to results dispatchinlarge materialslotforsizes multi-load markets, diminished due tosystem. augmenting Classical methodologies considering mainly single products product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which 2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license an efficient definition and identify possible optimization potentials in the existing causes difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems. production system, it is important to have a precise knowledge comparison of different product families. Addressing this Keywords: Assembly; DesignInmethod; Family identification manufacturing cost. mixed-model line, different
Peer-review under responsibility of the scientific committee of the 52nd CIRP Conference on Manufacturing Systems.
2212-8271 © 2019 The Authors. Published by Elsevier Ltd. This is an©open article Published under theby CC BY-NC-ND 2212-8271 2017access The Authors. Elsevier B.V. license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of scientific the scientific committee theCIRP 52ndDesign CIRPConference Conference2018. on Manufacturing Systems. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2019.03.251
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2. Literature review 2.1. Automobile assembly lines and logistics systems Previously, single-model assembly lines were widely used in various industries to increase production efficiency, and a large number of forklifts were used for material handling because the types of materials were fixed. Nowadays, our life has been greatly improved, and higher requirements have been placed on product personalization and diversification. Automobile production have been shifting to mass customization mode, and mixed-model assembly lines are used [1]. There are more than one models assembled on the same automobile assembly line. Set Parts Supply (SPS) [2] is used to transport all parts of one car from supermarket area to each station. In this way, all parts are transported as a unit load, so the flexibility of SPS are not enough. Plenty of studies have been conducted on various types of logistics systems that use AGVs to transport parts, which can improve the flexibility. And there are some characteristics about AGV used in logistics systems: • • • •
Autonomous path planning, high level of flexibility The system operates steadily and safely High degree of intelligence and fewer staff members Battery driven, green and environmentally friendly
single-load system, which proves the superiority of multi-load system. Adaptive genetic algorithm [9] is used to solve scheduling problems, where machines and AGVs are operating simultaneously. The dispatching problem of AGV in the automated warehouse system [10] is solved by using genetic algorithm. In flexible manufacturing systems, adaptive genetic algorithm is used to dispatch parts and AGVs together [11] to minimize the idle time of machining center, which solves a large variety problem. 3. Model construction 3.1. Problem description Now, more and more automakers begin to use mixed-model automobile assembly lines. In this situation, a lot of different cars are assembled on the same assembly line, so the materials required for each station are constantly changing. If singleload AGVs are used, when most materials are small, the carrying capacity of AGVs will be wasted. When the material demand in the logistics system is dominated by large materials, the use of multi-load AGV system will increase unnecessary dispatching, because most AGVs can only carry one piece of material. Thus, this paper proposes a hybrid-load AGV dispatching model to avoid these problems to reduce the cost of material transportation.
According to the number of the material of every AGV loading, it can be divided into single-load [5] and multi-load dispatching system [6]. Each single-load AGV transports one piece of material every time, and each multi-load AGV can transport more than one. The characteristics of single-load and multi-load AGV dispatching models from previous literatures are summarized as follows in Table 1. Table 1. Characteristics of single-load and multi-load dispatching models. single-load model
multi-load model
dispatching difficulty
easier
more difficulty
work efficiency
lower
higher
number of AGV
more
less
AGV capability requirements
lower
higher
system adaptability
higher
lower
2.2. Genetic algorithm In multi-load AGV dispatching systems, allocating tasks to AGVs is a combinatorial optimization problem. This kind of problem is NP-hard [7]. When the problem scale is large, using traditional method is difficult to obtain a satisfactory solution in a limited time. Heuristic algorithms have brought us a new solution for this type of problems. Genetic algorithm is a global and parallel heuristic algorithm with high efficiency and high quality of solution, which is usually used to solve dispatching problems. To minimize the total operational cost and AGV empty-loading ratio, hybrid multi-objective genetic algorithm [8] is used to optimize multi-load AGV dispatching and routing in flexible manufacturing systems, and the result is compared with
Fig. 1. Schematic diagram of one assembly line and material transportation process (S represents a single-load AGV, and M represents a multi-load AGV).
As shown in Fig. 1, there are ten assembly stations selected from a company's P platform gearbox assembly line. Different sizes of materials need to be transported from warehouse to the assembly station by single-load or multi-load AGV. There are three different models (C1/C2/C3) assembled on the same
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automobile assembly line from station P02 to station P11. Materials that need to be transported by single-load AGVs, will be picked from warehouse and stored in BUF 1 temporarily, while materials that need to be transported by multi-load AGVs, will be stored in BUF2. The single-load AGV moves to BUF 1 from the waiting area, transports one piece of material to P04, and then returns to the waiting area. The multi-load AGV needs to transport two pieces of materials from BUF 2 to two different assembly stations (P08 & P02) and then returns to the waiting area. Above all, we make some reasonable assumptions about the logistics system in order to describe the problem clearly. l l l
The weight of every material is no more than the weight that single-load can bear All tasks are from warehouse to assembly stations Multi-load AGV can bear any two pieces of materials when the total weight is no more than AGV can bear
3.2. Mathematical model In view of the fact that the existing AGV dispatching system is difficult to adapt to mass customization production of automobiles, this paper proposes a hybrid-load AGV dispatching model. Before dispatching, all materials are classified according to its weight. Large materials enter into the single-load dispatching system, while small materials enter into multi-load dispatching system. After multi-load dispatching system optimizes the combination of transportation tasks of small materials, multi-load AGVs are arranged to complete combined transportation tasks, and single-load AGVs are arranged to complete material transportation tasks that cannot be combined. The variables used in this paper are defined as follows:
n The number of tasks ns The number of single-load AGV used nm The number of multi-load AGV used ps The unit cost of single-load AGV pm The unit cost of multi-load AGV pus The cost of unit transportation distance for single-load AGV pum The cost of unit transportation distance for multi-load AGV Lis The number of material of the i-th single-load AGV loading Lim The number of material of the i-th multi-load AGV loading Liw The i-th AGV carrying weight Lw max The maximum weight of AGV can bear, single-load AGV is 7 and multi-load AGV is 5 Dsi Transportation distance of the i-th single-load AGV Dmi Transportation distance of the i-th multi-load AGV ì1 ; Task i is completed by a single-load AGV Tis = í î0 ; Otherwise ì1 ; Task i is completed by a multi-load AGV Tim = í î0 ; Otherwise
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To minimize the total cost of material transportation, the object function is constructed as shown in Eq. (1). First part represents the transportation cost of single-load AGVs, second part represents the transportation cost of multi-load AGVs, third part represents the purchase cost of single-load AGVs, and forth part represents the purchase cost of multi-load AGVs. æ min ç pus è
ns
å D i =1
si
+ pum
nm
å D i =1
mi
(1)
ö + ns ps + nm pm ÷ ø
(2) (3)
Liw £ Lw max
(4) Eq. (2) means that a single-load AGV carries one piece of material and a multi-load AGV carries one piece or two pieces of materials at one time. Eq. (3) indicates that the weight of each AGV carrying materials cannot be greater than the weight that the AGV can bear. Eq. (4) indicates that each task can only be performed once. 4. Computational experiments This paper does not consider the path planning of transportation tasks, so it only needs to solve material transportation combinatorial problem in multi-load AGV dispatching system. The solution process includes three steps: l l l
Classifying material transportation tasks Optimizing the combination of small materials Allocating AGVs for all tasks
We selected 20 material transportation tasks on the gearbox assembly line of a company’s P platform, as shown in Table 2. Table 2. Transportation tasks. Order
1
2
3
4
5
6
7
destination
P09
P02
P07
P07
P04
P04
P11
weight
4
3
1
2
1
7
6
Order
8
9
10
11
12
13
14
destination
P08
P03
P06
P03
P08
P11
P02 3
weight
4
1
3
2
4
4
Order
15
16
17
18
19
20
destination
P10
P02
P04
P04
P04
P10
weight
6
6
3
1
2
5
4.1. Classification All transportation tasks are classified according to the maximum load weight that multi-load AGV can bear. As shown in Fig. 2, when the weight of the task is greater than or equal to multi-load AGV can bear, the task is assigned to single-load tasks. Otherwise, the task is assigned to multi-load tasks.
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The transportation tasks of small materials that need to be combined by multi-load AGV dispatching system are obtained by classification as shown in Table 3. Table 3. Small material transportation tasks. Order
1
2
3
4
5
8
9
10
destination
P09
P02
P07
P07
P04
P08
P03
P06 3
weight
4
3
1
2
1
4
1
Order
11
12
13
14
17
18
19
destination
P03
P08
P11
P02
P04
P04
P04
weight
2
4
4
3
3
1
2
Fig. 3. Pseudocode for genetic algorithm.
4.2. Optimization of small material transportation tasks This paper uses genetic algorithm to solve the problem of combination of transportation tasks of small materials in multi-load AGV dispatching system as shown in Fig. 3. The symmetric distance matrix is shown in Table 4. Table 4. Symmetric distance matrix (A represents warehouse). A
1
2
3
4
5
6
7
A
0
1
635
0
2
275
402
0
3
620
152
387
0
4
134
543
183
528
0
5
456
411
327
301
365
0
6
447
230
214
215
356
309
0
7
200
477
117
462
108
314
290
0
8
130
546
187
531
46
367
359
111
8
9
10
0
9
209
467
150
452
187
288
280
137
185
0
10
369
308
136
293
277
344
120
211
281
201
0
Using real coding is more efficient than using binary coding, and it has higher computational accuracy [12]. In this paper, the task sequence number is selected as gene to code, which can efficiently avoid generating illegal solutions. It’s well known that the quality of initial population affects the convergence speed of heuristic algorithm. This article uses the method as shown in Fig. 4 to generate initial population. All tasks are arranged according to the weight of the material from small to large. Then selecting the current transportation task that the material is the smallest combines with the task that the material is largest (e.g. 1 and 19), and removing those two transportation tasks from all tasks, until all tasks are combined. The above steps are cycled for certain times to produce the required number of initial individuals. There are single-point crossing, multi-point crossing, and partial matching crossing. This paper is similar to TSP problem, in which each task is executed only once. It is more appropriate to use partial matching cross as shown in Fig. 5, which is not easy to destroy good individuals and generate illegal solutions. Generating two points as crossover points (P1, P2), chromosome segments ((8, 18, 1) and (11, 19, 2)) from two individuals are exchanged. Then, according to the mapping matrix, the repetitive genes of each individual are replaced to produce a legal individual. Variation is an important step to jump out of the local optimal solution. In this paper, single-point variation is used as shown in Fig. 6. Generating mutation point (P) and variant gene (5), the gene of the mutation point is exchanged into variant gene (11à5), and replacing the repeated gene (5à11, this 5 is the gene of individual before mutation).
Fig. 2. Pseudocode for task classification.
Fig. 4. The process of generating initial individual.
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4.3. AGV allocation According to above genetic algorithm, the best AGV allocation plans are as shown in Table 6 and Table 7. From Table 2, we can find the destination and weight of task 8 and task 12 are equal, so two plans are equal. Table 6. AGV allocation plan 1 task
6
7
15
16
17
20
AGV
S1
S2
S3
S4
S4
S6
task
3
13
4
10
5
AGV
Fig. 5. The process of crossover.
M3
M4
8
1
18
2
M1 9
M5
19 M2
12
11
M6
14 M7
Table 7. AGV allocation plan 2. task
6
7
15
16
17
20
AGV
S1
S2
S3
S4
S4
S6
task
3
13
4
10
5
AGV
This article uses roulette method [13] to select the best individual from all individuals. Every individual is selected according to the selection probability, which is computed as shown in Eq. (5) (6). The individual's selection probability is equal to the proportion of the individual's fitness value and the sum of fitness values. The parameters of genetic algorithm used in this paper are shown in Table 5.
pi =
fi
å f
Where: C is a constant
a single-load AGV penalty weight b multi-load AGV capacity waste penalty weight ei i-th multi-load AGV wasted capacity fi the fitness of i-th individual pi the probability of i-th individual selected
M4
12 M5
18
8
value
population size
20
maximum genetic generation
200
crossover probability
0.8
variation probability
0.1
α
200
β
19 M2
9 M6
11
14 M7
(5) (6)
5.1. Comparison with single-load AGV dispatching model Compared with single-load AGV dispatching model, the main advantages of the proposed model are that the total transportation distance and the number of AGVs used are reduced, so material transportation cost is reduced. Taking this solution problem as an example, as shown in Fig. 7, the transportation distance is reduced by 21.4%, and the number of AGV used decreased by 35%. 5.2. Comparison with multi-load AGV dispatching model Compared with multi-load AGV dispatching model, the main advantage of the model is that the complexity of the solution is greatly reduced. Taking this solution problem as an example, there are 20 tasks. When using multi-load AGV dispatching model, the complexity is 20!. In contrast, hybridload AGV dispatching model processes large materials separately and then processes small material transportation tasks. So the solution complexity is only 15! +5!. When dealing with large-scale complex problems, the model proposed in this paper has obvious advantages.
Table 5. The parameters of genetic algorithm. parameter
2
M1
5. Discussion
Fig. 6. The process of variation.
f = C - å Dsi - å Dmi - a ns - b å ei
M3
1
100 Fig. 7. (a) Distance; (b) The number of AGVs used.
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6. Conclusion In this paper, by analyzing the advantages and disadvantages of single-load and multi-load AGV dispatching model, a hybrid-load AGV dispatching model is proposed. The transportation tasks of large materials are removed from all tasks. The transportation tasks of small materials are dispatched by multi-load AGV dispatching system, and finally AGVs are uniformly allocated to complete all transportation tasks. The results of genetic algorithm indicate that hybridload AGV dispatching model greatly improves the efficiency of material transportation and reduces the cost of material transportation and the complexity of problem solving, which is more suitable for mixed-model automobile assembly lines in mass customization condition. For future research, AGV path planning under hybrid-load AGV dispatching model and material transportation problem with time window will be considered, which makes hybridload AGV dispatching model closer for real problems. Acknowledgement The authors would like to thank the National Key R&D Program of China (Project No. 2016YFD0701105) and the National Natural Science Foundation of China (Project No. 51675051). We express our sincere thanks to Lovol Heavy Industry Co., Ltd. for the case verification. References [1] Bukchin J, Dar-El E M, Rubinovitz J. Mixed model assembly line design in a make-to-order environment. Computers & Industrial Engineering, 2002; 41(4):405-421.
[2] Jainury S M, Ramli R, Ab Rahman M N, et al. Integrated Set Parts Supply system in a mixed-model assembly line. Computers & Industrial Engineering, 2014; 75:266-273. [3] Qi B Y, Yang Q L, Zhou Y Y. Application of AGV in intelligent logistics system. Asia International Symposium on Mechatronics. IET; 2016. [4] B.A.Peters, J.S.Smith, and S.Venkatesh. A control classification of automated guided vehicles. International Journal of Industrial Engineering, 1996. [5] ShabnamRezapour, RezaZanjirani-Farahani, ElnazMiandoabchi. A machine-to-loop assignment and layout design methodology for tandem AGV systems with single-load vehicles. International Journal of Production Research, 2011; 49(12):29. [6] Ümit Bilge, Tanchoco J M A. AGV systems with multi-load carriers: Basic issues and potential benefits. Journal of Manufacturing Systems, 1997; 16(3):159-174. [7] Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. [8] Umar U A, Ariffin M K A, Ismail N, etal. Hybrid multiobjective genetic algorithms for integrated dynamic scheduling and routing of jobs and automated-guided vehicle (AGV) in flexible manufacturing systems (FMS) environment. The International Journal of Advanced Manufacturing Technology, 2015; 81(9-12):2123-2141. [9] Sanches D S , Rocha J D S , Castoldi M F , et al. An Adaptive Genetic Algorithm for Production Scheduling on Manufacturing Systems with Simultaneous Use of Machines and AGVs. Journal of Control, Automation and Electrical Systems, 2015; 26(3):225-234. [10] Sainan L. Optimization problem for AGV in automated warehouse system. IEEE International Conference on Service Operations & Logistics. IEEE, 2008. [11] Simultaneous scheduling of parts and automated guided vehicles in an FMS environment using adaptive genetic algorithm. The International Journal of Advanced Manufacturing Technology, 2006; 29(5-6):584589. [12] by Z Michalewic. Genetic Algorithms + Data Structures = Evolution Programs. Springer Berlin Heidelberg, 1996. [13] Thierens D, Goldberg D E. Convergence Models of Genetic Algorithm Selection Schemes. Parallel Problem Solving from Nature - PPSN III, International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature, Jerusalem, Israel, October 9-14, 1994; Proceedings. DBLP, 1994;119-129.