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A novel optimization method for modular facilities layout problem considering flexible processes
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52nd CIRP Conference on Manufacturing Systems 52nd CIRP Conference on Manufacturing Systems
A method for facilities layout A novel novel optimization optimization method for modular modular layout problem problem 28th CIRP Design Conference, May 2018,facilities Nantes, France considering flexible processes considering flexible processes A new methodology to analyze the functional and physical architecture of Weibo Ren, Jingqian Yu Yaoguang Hu* Ren,assembly Jingqian Wen, Wen, Yu Guan, Guan, Yaoguang Hu* identification existing productsWeibo for an oriented product family
Beijing Institute of Technology, No.5 Zhongguancun South Street, Haidian District, Beijing,100081, China Beijing Institute of Technology, No.5 Zhongguancun South Street, Haidian District, Beijing,100081, China * Corresponding author. Tel.: +86 10 68917880; E-mail address: [email protected] * Corresponding author. Tel.: +86 10 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]
With the growth of personalized customer requirements, modular manufacturing system is commonly recognized as the key to response to diverse With the growth of personalized customer requirements, modular manufacturing system is commonly recognized as the key to response to diverse production requirement in mass customization. However, there is lack of research on the optimization problem for modular facilities layout production requirement in mass customization. However, there is lack of research on the optimization problem for modular facilities layout planning. Thus, the aim of this paper is to develop a methodology for the reconfigurable modular facilities layout problem with alternative process Abstract planning. Thus, the aim of this paper is tomodel develop a methodology for theproduction reconfigurable modular problem withcosts. alternative process routings and an integrated mathematical is proposed to improve flexibility andfacilities minimizelayout material handling An improved routings and an integrated mathematical model is proposed to improve production flexibility and minimize material handling costs. An improved is developed and examples are carried out toand demonstrate the effectiveness thetomethods. Inheuristic today’salgorithm business environment, the numerical trend towards more product variety customization is unbroken.of Due this development, the need of heuristic algorithm is developed and numerical examples are carried out to demonstrate the effectiveness of the methods. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license agile and reconfigurable production systems emerged to cope with various products and 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 licensethe (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the committee 52nd CIRP Conference on Manufacturing analyze a product one product family the physical level.of Different families, however, may differ Systems. largely in terms of the number and Peer-review underorresponsibility of the on scientific committee of the 52ndproduct CIRP Conference Peer-review on Manufacturing Systems. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Keywords: modular facilities layout; modular manufacturing system; intra and inter-module layout; flexible processes system. A new methodology is proposed analyze existing products view of their functional physical architecture. The aim is to cluster Keywords: modular facilities layout; modularto manufacturing system; intra andininter-module layout; flexible and processes 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 method to describe the uncertain demand with fuzzy variables. 1. Introduction similarity between product families by providing design support to both,method production system planners and product designers. An illustrative to describe the uncertain demand with fuzzy variables. 1. Introduction Moslemipour [6] conducted a systematic review of dynamic example of a nail-clipper is used to explain the proposed methodology. AnMoslemipour industrial case study on two product families ofreview steeringofcolumns of [6] conducted a systematic dynamic and robust layout planning problems and analyzed the different Facility layout problems (FLP) isout one of the critical and evaluation thyssenkrupp Presta France is then carried to give a first industrial of the proposed approach. and robust layout planning problems and analyzed the different Facility layout problems (FLP) is one of the critical and decision approaches form three aspects: exact, heuristic and in modern manufacturing industry. In ©complex 2017 The problems Authors. Published by Elsevier B.V. decision approaches form three aspects: exact, heuristic and complex problems in modern manufacturing industry. In intelligent approaches. Lee and Kang et al. [7] focused on the general, FLP refers to determining the proper location of a Peer-review under responsibility of the scientific committee of theof28th Design Conference 2018. intelligent approaches. Lee and Kang et al. [7] focused on the general, FLP refers to determining the proper location a CIRP
facility layout problem with the method of quadratic group of machines in a specific shop floor area, which is related facility layout problem with the method of quadratic group of machines in a specific shop floor area, which is related assignment problem (QAP), and the genetic algorithm (GA) closely with the production rate and cost. In the industrial sector, assignment problem (QAP), and the genetic algorithm (GA) was applied to solve the large-scale problems. Vitayasak et al. material handling cost is responsible for 20%~50% of total was applied to solve the large-scale problems. Vitayasak et al. material handling cost is responsible for 20%~50% of total [8] considered dynamic facility problem with the change in operation cost, while reasonable layout planning can reduce it [8] considered dynamic facility problem with the change in operation cost, while reasonable layout planning can reduce it demand and Backtracking Search Algorithm (BSA) was by 10%~30% [1]. Thus, facility layout problem has become a demand and Backtracking Search Algorithm (BSA) was 10%~30% [1]. Thus, facility layout problem has become a of 1.by Introduction the product range the andbetter characteristics developed to choose solution. manufactured and/or strategic focus in industries and many methods for facility developed in to this choose the better solution. strategic focus in industries and many methods for facility assembled system. In this context, the main challenge in Besides, in recent years, with the increasingly drastic market layout have emerged over many years of research. Miguel [2] Besides,and in recent years, with the increasingly drastic market layout have emerged over many years ofinresearch. Miguel [2] Due to the fast development the domain of modelling analysis is now not only to cope with single competition, it has become the focus of many manufacturing proposed the application of mathematical optimization competition, it hasproduct become the focus of many manufacturing proposed the and application of mathematical optimization communication an ongoing trend of digitization and products, limited or existing product families, industriesa to improve the range quality of customer service and methodology in the solution of row, unequal-areas and multiindustries to able improve the quality of customer service and methodology in the solution of row, unequal-areas and multi- but digitalization, manufacturing enterprises are facing important also to be to analyze and to compare products to define maximize customer satisfaction of individual requirements. floor layout problems. Mohammad and Sadigh [3] proposed a maximize customer satisfaction of individual requirements. floor layoutinproblems. Mohammad and Sadigh [3] proposed a new challenges today’s market environments: a continuing product families. It can be observed that classical existing Manufacturing mode has come to Mass Customization (MC) novel method to solve the dynamic facility layout problems and Manufacturing mode has come Mass of Customization (MC) novel method to solve the dynamic facility layout problems and tendency towards reduction product development times and families are regrouped in to function clients or features. production because of individual customer demands and elitist non-dominated sortingofgenetic algorithm (NSGA-II) was product productionassembly becauseoriented of individual customer demands and elitist non-dominated sortingIn genetic algorithm (NSGA-II) was However, shortened product lifecycles. addition, there is an increasing product families are hardly to find. intense market competition. MC demands higher flexibilities, developed for solving the multi-objective problems. Azadeh [4] intense market competition. MCproducts demandsdiffer higher flexibilities, developed for solving the multi-objective problems. Azadeh [4] demand of customization, being at the same time in a global On the product family level, mainly in two optimized cost and faster reaction time, and it presents more focused on the uncertain facility layout problem and proposed optimized cost and faster time, and it presents focused on the facility layout problem and proposed competition withuncertain competitors allanalysis over the This trend, main characteristics: (i) thereaction number of components and (ii)more the challenge to manufacturing organization forms, inevitably [9]. a novel method integrated fuzzy andworld. analytic hierarchy challenge to manufacturing organization forms, electronical). inevitably [9]. a novelismethod integrated fuzzy analysis and analytic hierarchy which inducing the development from macro to micro type of components (e.g. mechanical, electrical, However, traditional manufacturing line cannot fulfill the process (AHP). Zha and Guo et al. [5] focused on the dynamic However, traditional manufacturing line cannot fulfill the process (AHP). and Guo et al. focused on augmenting the dynamic markets, results Zha in diminished lot [5] sizes dueproposed to Classical methodologies products demand to respond quicklyconsidering to frequent mainly changessingle of task orders. facility problem with uncertain demand and a novel demand to respond to frequent task orders. facility varieties problem (high-volume with uncertaintodemand and proposed a novel product low-volume production) [1]. or solitary, alreadyquickly existing product changes families ofanalyze 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; Design method; identification closely with the production rate Family and cost. In the industrial sector,
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.2019.03.292
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Therefore, in order to implement mass customized production, researchers and manufacturing industries begin to pay more attention to the design and planning of new manufacturing paradigm. Based on our current background, modular manufacturing system is considered as the key solution for these problems [10]. The new paradigm of modular manufacturing system is first proposed by Rogers and Bottcai [11] in 1997. Modular manufacturing system, different with traditional production lines, is mainly consisted of several manufacturing modules and intelligent automated transportation system. Manufacturing modules, composed by one or several machines, can perform different assembly operations. Different manufacturing modules are connected via the intelligent automated transportation system based on different product variants, thus making it possible to produce customized products. Modular manufacturing systems become the critical factor for solving the problem in mass customization, but it also brings new great challenges to the layout and planning of manufacturing system. Though, many methods for facility layout planning have emerged over many years of research, for example, past researches have not addressed the intra and intermodules layout problem considering flexible processes in modular manufacturing system. Thus, this paper considers the flexible processes and a mixed integer mathematical model is developed to determine the layout of manufacturing modules and machines simultaneously. Improved simulated annealing (SA) is developed and numerical examples are conducted to verify the validity of the Methodology. The contributions of this research are summarized as follows. First, this paper proposed the optimization problem for modular facilities layout planning considering flexible process routings. Second, a mixed integer programming is proposed for solving the problem. Finally, SA is developed and numerical examples are conducted to certify the performance of the Methodology. As follows, Section 2 describes the modular facilities layout problem considering flexible processes and develops the mixed integer mathematical model. The detailed information about SA is shown in section 3. In section 4, numerical examples are carried out to certify the validity of proposed partition method. Conclusions and future researches are summarized in section 5. 2. Problem description and mathematical model 2.1. Problem description Compared to traditional manufacturing lines, modular manufacturing system can be made up of individual manufacturing modules, which perform specific assembly operations and are dedicated to the manufacture of part of the products. A modular manufacturing module consists of one or several functional machines which are placed in the same area. Thus, the location of the manufacturing modules and the location of the machines within the module must be determined simultaneously in this study. Besides, in modular manufacturing system, the transport of the subassemblies and components between the modules is
taken over by the intelligent automated transportation system and Automated Guided Vehicle (AGV) supply the modules just in time with the parts or sub-assemblies they need. Therefore, there exist flexible process routes in modular manufacturing system, while workers can only conduct the production in sequence in traditional manufacturing line. Just as shown in Fig. 1, the manufacturing process of a product is divided into four operations: A, B, C and D. In production line, the product has to go through four operations A, B, C and D in sequence. On the contrary, with the flexible scheduling and intelligent transportation, there exists different process routes in modular manufacturing system, for example A, B, C, D and A, C, B, D and so on, as shown in Fig. 2.
Fig. 1. Schematic diagram of production line.
Fig. 2. Schematic diagram of modular manufacturing system.
In summary, the layout problem of modular manufacturing system with flexible production processes is considered, where each class of products may contain multiple operations with different process plans. And the modular facilities layout problem assigns resource to different machines or modules, involving internal and external flows. External flows are quite costly since they are transported by AGV. It should be noted that the total material handling costs is considered in modular facilities layout problem, including internal and external flows cost. Owing to the complexity of modular manufacturing system, the following assumption is proposed in this study: 1) The requirements of the customized products are known. 2) The number and variety of modules are known and the number and variety of machines within modules are known. 3) Machines are either square or rectangular and may have unequal-areas. 4) The dimensions of machines are given, but the dimension of every module is calculated based on the machines. 5) Modules and machines within the modules may be either vertically or horizontally orientated.
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6) The parts or subassemblies are transported individually by AGV between manufacturing modules. 7) The logistics cost between machines and modules is related to the Manhattan distance between machines and modules. 8) There exist flexible process routes for customized products. 9) The distance between machines is negligible, while the distance between manufacturing modules is considered. 10) The dimensions of shop are given. 2.2. Mathematical Model Considering the alternative processes routes, this paper takes the production flexibility and logistics cost into account and a mixed integer model is established. The input sets, parameters and the decision variables are denoted as follows: (1) Sets i, j Î U m, n Î M p Î P k Î K (2) Parameters d1ij d2mn
Index of manufacturing modules. Index of machines. Index of products. Index of process routings of products.
The distance between module i and j. The distance between machines m and n within the same modules. C1 The travel cost between modules per unit. C2 The travel cost between machines within the same module per unit. Dp The demand of customized products. (xmm,ymm) Coordinate of center of machine m. (xui,yui) Coordinate of center of module i. Lm The length of machine m. Wm The width of machine m. Hm The horizontal length of machine m. Vm The vertical length of machine m. Lmax The length of floor space. Wmax The width of floor space. xuimax The upper horizontal coordinate of module i. xuimin The lower horizontal coordinate of module i. yuimax The lower vertical coordinate of module i. yuimin The upper vertical coordinate of module i. (3) Decision variables xpijk 1 if product p precedes operation on modules i and j with the kth process routing and 0 otherwise. ypmnk 1 if product p precedes operation on machine m and n within the same modules with the kth process routing and 0 otherwise. om 1 if machine m is located horizontally and 0 if machine m is located vertically. zij 1 if module i is in the right or above of the module j and 0 if module i is in the left or below of the module j.
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Mathematical Model: P
U
U
P
M
M
MinC = ååå x p ijk Dp d1ij C1 + ååå y p mnk Dp d 2mn C2 (1) p =1 i =1 j =1
p =1 m =1 n =1
The objective function (1) consists of two parts, the logistics costs between manufacturing modules and the logistics costs between machines within module. Subject to: Equation (2) and (3) represent the distance between manufacturing modules and the distance between machines, respectively. (2) d 2mn = xmm - xmn + ymm - ymn (3) d1 = xu - xu + yu - yu ij
i
j
i
j
Equation (4) and (5) are applied to control the orientation of machines. Also, the both two equations compute the new length and width of machines based on the direction of machines. (4) H m = Lm (1 - om ) + Wm (5) V = W (1 - o ) + L m
m
m
m
Constraints (6)-(11) are applied to limit the location of machines. Among them, constraints (6), (7), (8) and (9) ensure that all machines are in the shop floor area. Constraints (10) and (11) guarantee that there is no overlap between any machines. (6) xmm + H m / 2 £ Lmax "m (7) xm - H / 2 ³ 0 "m m
m
ymm + Vm / 2 £ Wmax "m ymm - Vm / 2 ³ 0 "m
xmm - xmn ³ ( H m + H n ) / 2 "m ymm - ymn ³ (Vm + Vn ) / 2 "m
(8)
(9) (10) (11)
Formulas (12)-(23) are the constraints on the manufacturing models. Equation (12) and (13) are used to compute the coordinate of center of module i. Equation (14), (15), (16) and (17) are conducted to compute the lower left corner and upper right corner of module i. Constraints (18), (19), (20) and (21) ensure that all modules are in the shop floor area. Constraints (22) and (23) ensure that there is no overlap between any modules. xui = (max(( xmm + H m / 2), ( xmn + H n / 2)...) (12) + min(( xmm + H m / 2), ( xmn + H n / 2)...)) / 2
yui = (max(( ymm + Vm / 2), ( ymn + Vn / 2)...) + min(( ymm + Vm / 2), ( ymn + Vn / 2)...)) / 2
(13) xuimax = max(( xmm + H m / 2), ( xmn + H n / 2)...) $m min i max i min i max i
xu
= min(( xmm - H m / 2), ( xmn - H n / 2)...) $m
yu
= max(( ymm + Vm / 2), ( ymn + Vn / 2)...) $m
yu
= min(( ymm - Vm / 2), ( ymn - Vn / 2)...) $m
xu
£ Lmax "i
(14) (15) (16) (17) (18)
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xuimin ³ 0 "i max i min i
yu
£ Wmax "i
yu
³ 0 "i
xuimax + (1 - zi j ) xuimax + ( zi j - 1) xuimin £ xu max + ( zi j - 1) xu max + (1 - zi j ) xu min "i, j j j j
(19) (20) (21) (22)
yuimax + (1 - zi j ) yuimax + ( zi j - 1) yuimin £ yu max + ( zi j - 1) yu max + (1 - zi j ) yu min "i, j j j j
(23)
Constraints (24) and (25) imply that the product can only be handled with an optimal process route. P
å x p =1 P
p ijk
å y p =1
= 1 "p
p mnk
= 1 "p
(24) (25)
3. Simulated annealing algorithm As the extension to the classical facility layout problem, there is no doubt that the problem of modular facilities layout considering flexible processes proved to be non-deterministic polynomial (NP-hard). There exist many heuristic algorithms, such as GA (genetic algorithm), SA (Simulated annealing algorithm), PSO (Particle Swarm Optimization algorithm) and so on, are developed to handle the optimization problem with better computational performance and get a relatively accurate optimal solution in a reasonable amount of time. SA is a kind of random optimization algorithm based on the Monte-Carlo iterative solution strategy. Additionally, this method can overcome the disadvantage of local research, for which it is hard to fall into a local optimum. Thus, improved SA is carried out to solve the problem. Starting with a higher initial temperature, SA randomly searches in the solution space, using the Metropolis sampling strategy, and repeats the sampling along with temperature reduction; then, it obtains the globally optimal solution. The details of SA algorithm are shown below: 1) Set the initial parameters: initial temperature T0; cooling coefficient K in [0,1]; maximal iterations Iter; stop temperature Tmin; initial solution X0; set T= T0, E0=E(X0); 2) Set XB = X0, EB =E0; 3) Set the iterations iter=1; 4) Produce the new solution based on the current optimal solution XB and the neighborhood function. Calculate the new objective function value EN and increment ΔE=EN –EB; 5) If ΔE≤0, set XB=XN; if ΔE > 0, then P=exp(-ΔE/T(i)); 6) C=random [0,1], if P > C, set XB=XN; otherwise XB=XB; 7) If iter < Iter, set iter=iter+1, go to step 4; otherwise go to step 8; 8) If T > Tmin, set T=KT, go to step 3; otherwise report XB and EB.
3.1. Encoding scheme and fitness evaluation To determine appropriate process route, the location of manufacturing modules and the location and direction of machines within modules, this paper develops related matrix to represent the process route of products and the location and direction of machines, respectively. The location of manufacturing modules is determined by the location of machines within modules. Assuming that there are three products and five machines, if the sequence is
Product 1 chooses the second process route and products 2 and 3 choose the first process route. The next two rows present co-ordinate of center of machines and the last row shows the direction of machines. When machine is in its original orientation, the element of the corresponding position in the matrix is 1, while machine is turned 90 degrees and the element is 0. Just as shown in the sequence, the co-ordinate of center of Machine 1 is (12,3) and Machine 1 is in its original orientation. This study is concerned with the joint optimization of external flows between manufacturing modules and internal flows between machine within modules, just as shown in Equation (26). P U U P M M (26) fitness = MinC = x p D d1 C + yp D d2 C
ååå p =1 i =1 j =1
ijk
p
ij 1
ååå
mnk
p
mn
2
p =1 m =1 n =1
3.2. The generation of initial solution and neighbor solution A random feasible solution is considered as the initial solution to the problem. And a neighbor solution is generated by the replacement of an element in matrices. As for the process route of product, it can be replaced with other process route (For example, the corresponding element is changed from 1 to 2). Similarly, the orientation of machines can also be changed (For example, the corresponding element is changed from 1 to 0). Besides, the co-ordinate of center of machine can be changed by the randomly generated numbers. 3.3. Annealing function During the process of neighborhood search, all possible changes can be obtained by a large value for the initial temperature T0 and the annealing function. We set the annealing function T= KT, where K is a real number between 0 and 1. The procedure will be terminated when the current temperature is lower than the stop temperature Tmin. 4. Numerical example and discussion The major differences between this study and others are the integrated consideration of alternative process routes, the internal and external flows between manufacturing modules or machines and joint optimization of location of modules and machines within modules. In previous study [12], the assembly line is divided into 10 manufacturing modules and the detail information is shown in Fig. 3. With the constraint of assembly
Weibo Ren et al. / Procedia CIRP 81 (2019) 1201–1206 Weibo Ren et al. / Procedia CIRP 00 (2019) 000–000
line, there exists different process routes, just as shown in Fig. 3. Due to the confidentiality requirement of the company, some detail information about assembly line cannot be shown in this paper. Thus, numerical examples are solved in the next part to illustrate the application of the methodology considering these constraints with the proposed mathematical model and SA algorithm.
Fig. 3. The information with modular manufacturing system. Note: There are no sequence constraints with the module 1 and module 2, module 3, module 4. It means there exists different process route, such as: module 1- module 2module 3-module 4, or module 3-module 1 -module 2- module 4 and so on. Similarly, there are no sequence constraint with module 7, module 8, module 9.
4.1. Numerical example To illustrate the application of proposed model and algorithm, numerical examples are presented and conducted to provide reasonable solution for designers. There are four customized products (P1-P4) and twelve machines (M1-M12) within seven manufacturing modules (Module 1-Module 7). The dimension of machines and the composition of manufacturing modules is shown in Table 1 and the length and width of machines are randomly generated. The alternative process routes of customized products are shown in Table2. As shown in Table 1, M1 and M2 belong to Module 1 and the dimension of M1 and M2 is (4,2) and (3,3). The same is true in other machines and modules. Besides, for convenient calculation, the internal flows between machines is set to 2 and the external flows between manufacturing modules is set to 4, the demand of four personalized products is set to 1:2:1:1.5. The length and width of floor space is set 100 and the distance between manufacturing modules is set 0.5.
1205 5
M3-M4-M8-M5-M9-M10 M3-M4-M6-M7-M9-M10-M11-M12
P4
M6-M7-M3-M4-M9-M10-M11-M12
The improved SA is conducted to solve the problem. After the preliminary experiment, the initial temperature of SA is set to 1,000; the Monte-Carlo iterative number is set to 50; the coefficient of the annealing function is set to 0.99, and the stop temperature is set to 1. The search time of SA is 52.34s and the iterative process of SA is shown in Figure 4. The result of the SA is shown in Table 3 and based on the location of machines, the situation of manufacturing modules can be calculated shown in Table 4. The location of manufacturing modules and the location and orientation of machines is shown in Figure 5. The selected process of products is 1, 2, 1 and 2. As seen in Table 3, the elements in second and third rows shows the coordinate of centre of machine and the elements in fourth row present the direction of machine. As shown in Figure 4, Table 3 and Table 4, the location of machines and manufacturing modules is determined and there is no overlap between machines and manufacturing modules and the total cost is 652, which verify the validity of proposed Methodology. Table 3. The information of result. M
1
2
3
4
Xm
4
Ym
2
D
0
5
6
7
1.5
8
1.5
6.5
1
1
8
9
10
11
4
8
1.5
7
2.5
6
0
1
0
1.5
14
14
14
18.5
19
9.5
2.5
11
7
3
8.5
1
1
1
1
0
0
Table 1. The information of machines and modules. Modules
1
Machines Lm Wm
1 4 2
2 2 3 3
3 6 3
3 4 4 2
5 6 5
4 6 4 3
5 7 3 3
8 5 5
Table 2. The flexible process of products. Products P1 P2 P3
Flexible process M1-M2-M5-M8-M11-M12 M1-M2-M8-M5-M11-M12 M1-M2-M6-M7-M8-M9-M10 M6-M7-M1-M2-M8-M9-M10 M3-M4-M5-M8-M9-M10
6 9 6 4
Fig 4. The iterative process of SA.
7 10 5 4
11 6 3
12 5 4
12
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5. Conclusion Considering the flexible process routes, a mixed integer model was developed to determine the location of manufacturing modules and machines and reduce the total logistics cost between modules and machines. Then, a SAbased approach was applied to solve the problem. To illustrate the application of methodology, serval numerical examples were carried out. The computational results demonstrated that the efficiency and feasibility in design of modular manufacturing system. Obviously, there exist some limitations in this study. First, uncertain demand of customized products should be considered in future work. Besides, make algorithm improvement. Though, SA algorithm can obtain optimal or approximate optimal results, there also exist some problems.
Fig 5. The result of modular layout problem. Table 4. The location of manufacturing module. Module
1
2
3
4
5
6
7
Xm
2.5
7
8
1.5
14
14
19
Ym
2
7
2.5
7.5
2.5
9
5.5
4.2. Discussion Based on the reference, there are many Based on the reference, there are many heuristic algorithms are carried out to solve the problem. Thus, it is necessary to verify the efficiency of proposed method. GA is applied to solve the experiment in section 4.1, and the encoding scheme, fitness evaluation and mutation operation of GA is similar with the method in SA. The tournament method is applied to select individuals during the selection operation. During the crossover operation, two individuals are randomly selected and the position of individuals is randomly chosen for the crossover operation. is used. The developed GA is used. The maximum evolution algebra is set to 800, and set the initial group to 40, the probability of the crossover and mutation operations is 0.9 and 0.1, respectively. The optimization result obtained by GA is 683, higher than the result by SA and the search time (72.43s) is longer than SA (52.34s), which verify the efficiency of the improved SA. In order to testify the performance of mathematical model and SA algorithm, serval numerical examples with randomly generated data is presented and carried out. The information and results of numerical examples are shown in Table 5. As shown in Table 5, proposed methodology can be applied not only in small cases, but also in large-scale cases, which verify the practicality of method in reality. Table 5. The information and results of numerical. No
Machines
Modules
Products
time/s (SA)
time/s (GA)
1
6
3
2
14.99
19.35
2
10
6
3
30.02
49.36
3
12
7
4
52.34
72.43
4
16
10
5
88.52
111.34
5
20
12
5
130.17
176.11
6
25
16
6
202.46
281.46
7
30
18
7
293.21
353.32
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] Tompkins J A, White J A, Bozer Y A, et al. Facilities Planning. New work: John Wiley & Sons, Inc,2003. [2] Anjos, M. F., & Vieira, M. V. C. 2017. Mathematical optimization approaches for facility layout problems: the state-of-the-art and future research directions. European Journal of Operational Research, 261(1), 116. [3] Pourhassan, M. R., & Raissi, S. 2017. An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem. Journal of Industrial Information Integration, 8. [4] Azadeh, A., Moghaddam, M., Nazari, T., & Sheikhalishahi, M. 2016. Optimization of facility layout design with ambiguity by an efficient fuzzy multivariate approach. The International Journal of Advanced Manufacturing Technology, 84(1-4), 565-579. [5] Zha, S., Guo, Y., Huang, S., Wang, F., & Huang, X.. 2017. Robust facility layout design under uncertain product demands . Procedia Cirp, 63, 354359. [6] Moslemipour, G. , Lee, T. S. , & Rilling, D. . 2012. A review of intelligent approaches for designing dynamic and robust layouts in flexible manufacturing systems. International Journal of Advanced Manufacturing Technology, 60(1-4), 11-27. [7] Lee H Y , Kang S , Chae J . 2015. Mutation effects in a genetic algorithm for a facility layout problem in QAP form. International Journal of Advanced Logistics, 4(3):170-179. [8] Vitayasak, S. , Pongcharoen, P. , & Hicks, C. . (2016). A tool for solving stochastic dynamic facility layout problems with stochastic demand using either a genetic algorithm or modified backtracking search algorithm. International Journal of Production Economics, 190: 146-157. [9] Wang, Z., Zhang, M., Sun, H., & Zhu, G. 2016. Effects of standardization and innovation on mass customization: an empirical investigation. Technovation, 48-49, 79-86. [10] Shaik, A. M., Rao, V. V. S. K., & Rao, C. S. 2015. Development of modular manufacturing systems—a review. International Journal of Advanced Manufacturing Technology, 76(5-8), 789-802. [11] Rogers, G. G., & Bottaci, L. 1997. Modular production systems: a new manufacturing paradigm. Journal of Intelligent Manufacturing, 8(2), 147156. [12] Ren W, Wen J, Guan Y, Hu Y. 2018. Research on assembly module partition for flexible production in mass customization. Procedia CIRP, v 72, p 744-749.
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52nd CIRP Conference on Manufacturing Systems 52nd CIRP Conference on Manufacturing Systems
A method for facilities layout A novel novel optimization optimization method for modular modular layout problem problem 28th CIRP Design Conference, May 2018,facilities Nantes, France considering flexible processes considering flexible processes A new methodology to analyze the functional and physical architecture of Weibo Ren, Jingqian Yu Yaoguang Hu* Ren,assembly Jingqian Wen, Wen, Yu Guan, Guan, Yaoguang Hu* identification existing productsWeibo for an oriented product family
Beijing Institute of Technology, No.5 Zhongguancun South Street, Haidian District, Beijing,100081, China Beijing Institute of Technology, No.5 Zhongguancun South Street, Haidian District, Beijing,100081, China * Corresponding author. Tel.: +86 10 68917880; E-mail address: [email protected] * Corresponding author. Tel.: +86 10 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]
With the growth of personalized customer requirements, modular manufacturing system is commonly recognized as the key to response to diverse With the growth of personalized customer requirements, modular manufacturing system is commonly recognized as the key to response to diverse production requirement in mass customization. However, there is lack of research on the optimization problem for modular facilities layout production requirement in mass customization. However, there is lack of research on the optimization problem for modular facilities layout planning. Thus, the aim of this paper is to develop a methodology for the reconfigurable modular facilities layout problem with alternative process Abstract planning. Thus, the aim of this paper is tomodel develop a methodology for theproduction reconfigurable modular problem withcosts. alternative process routings and an integrated mathematical is proposed to improve flexibility andfacilities minimizelayout material handling An improved routings and an integrated mathematical model is proposed to improve production flexibility and minimize material handling costs. An improved is developed and examples are carried out toand demonstrate the effectiveness thetomethods. Inheuristic today’salgorithm business environment, the numerical trend towards more product variety customization is unbroken.of Due this development, the need of heuristic algorithm is developed and numerical examples are carried out to demonstrate the effectiveness of the methods. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license agile and reconfigurable production systems emerged to cope with various products and 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 licensethe (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the committee 52nd CIRP Conference on Manufacturing analyze a product one product family the physical level.of Different families, however, may differ Systems. largely in terms of the number and Peer-review underorresponsibility of the on scientific committee of the 52ndproduct CIRP Conference Peer-review on Manufacturing Systems. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Keywords: modular facilities layout; modular manufacturing system; intra and inter-module layout; flexible processes system. A new methodology is proposed analyze existing products view of their functional physical architecture. The aim is to cluster Keywords: modular facilities layout; modularto manufacturing system; intra andininter-module layout; flexible and processes 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 method to describe the uncertain demand with fuzzy variables. 1. Introduction similarity between product families by providing design support to both,method production system planners and product designers. An illustrative to describe the uncertain demand with fuzzy variables. 1. Introduction Moslemipour [6] conducted a systematic review of dynamic example of a nail-clipper is used to explain the proposed methodology. AnMoslemipour industrial case study on two product families ofreview steeringofcolumns of [6] conducted a systematic dynamic and robust layout planning problems and analyzed the different Facility layout problems (FLP) isout one of the critical and evaluation thyssenkrupp Presta France is then carried to give a first industrial of the proposed approach. and robust layout planning problems and analyzed the different Facility layout problems (FLP) is one of the critical and decision approaches form three aspects: exact, heuristic and in modern manufacturing industry. In ©complex 2017 The problems Authors. Published by Elsevier B.V. decision approaches form three aspects: exact, heuristic and complex problems in modern manufacturing industry. In intelligent approaches. Lee and Kang et al. [7] focused on the general, FLP refers to determining the proper location of a Peer-review under responsibility of the scientific committee of theof28th Design Conference 2018. intelligent approaches. Lee and Kang et al. [7] focused on the general, FLP refers to determining the proper location a CIRP
facility layout problem with the method of quadratic group of machines in a specific shop floor area, which is related facility layout problem with the method of quadratic group of machines in a specific shop floor area, which is related assignment problem (QAP), and the genetic algorithm (GA) closely with the production rate and cost. In the industrial sector, assignment problem (QAP), and the genetic algorithm (GA) was applied to solve the large-scale problems. Vitayasak et al. material handling cost is responsible for 20%~50% of total was applied to solve the large-scale problems. Vitayasak et al. material handling cost is responsible for 20%~50% of total [8] considered dynamic facility problem with the change in operation cost, while reasonable layout planning can reduce it [8] considered dynamic facility problem with the change in operation cost, while reasonable layout planning can reduce it demand and Backtracking Search Algorithm (BSA) was by 10%~30% [1]. Thus, facility layout problem has become a demand and Backtracking Search Algorithm (BSA) was 10%~30% [1]. Thus, facility layout problem has become a of 1.by Introduction the product range the andbetter characteristics developed to choose solution. manufactured and/or strategic focus in industries and many methods for facility developed in to this choose the better solution. strategic focus in industries and many methods for facility assembled system. In this context, the main challenge in Besides, in recent years, with the increasingly drastic market layout have emerged over many years of research. Miguel [2] Besides,and in recent years, with the increasingly drastic market layout have emerged over many years ofinresearch. Miguel [2] Due to the fast development the domain of modelling analysis is now not only to cope with single competition, it has become the focus of many manufacturing proposed the application of mathematical optimization competition, it hasproduct become the focus of many manufacturing proposed the and application of mathematical optimization communication an ongoing trend of digitization and products, limited or existing product families, industriesa to improve the range quality of customer service and methodology in the solution of row, unequal-areas and multiindustries to able improve the quality of customer service and methodology in the solution of row, unequal-areas and multi- but digitalization, manufacturing enterprises are facing important also to be to analyze and to compare products to define maximize customer satisfaction of individual requirements. floor layout problems. Mohammad and Sadigh [3] proposed a maximize customer satisfaction of individual requirements. floor layoutinproblems. Mohammad and Sadigh [3] proposed a new challenges today’s market environments: a continuing product families. It can be observed that classical existing Manufacturing mode has come to Mass Customization (MC) novel method to solve the dynamic facility layout problems and Manufacturing mode has come Mass of Customization (MC) novel method to solve the dynamic facility layout problems and tendency towards reduction product development times and families are regrouped in to function clients or features. production because of individual customer demands and elitist non-dominated sortingofgenetic algorithm (NSGA-II) was product productionassembly becauseoriented of individual customer demands and elitist non-dominated sortingIn genetic algorithm (NSGA-II) was However, shortened product lifecycles. addition, there is an increasing product families are hardly to find. intense market competition. MC demands higher flexibilities, developed for solving the multi-objective problems. Azadeh [4] intense market competition. MCproducts demandsdiffer higher flexibilities, developed for solving the multi-objective problems. Azadeh [4] demand of customization, being at the same time in a global On the product family level, mainly in two optimized cost and faster reaction time, and it presents more focused on the uncertain facility layout problem and proposed optimized cost and faster time, and it presents focused on the facility layout problem and proposed competition withuncertain competitors allanalysis over the This trend, main characteristics: (i) thereaction number of components and (ii)more the challenge to manufacturing organization forms, inevitably [9]. a novel method integrated fuzzy andworld. analytic hierarchy challenge to manufacturing organization forms, electronical). inevitably [9]. a novelismethod integrated fuzzy analysis and analytic hierarchy which inducing the development from macro to micro type of components (e.g. mechanical, electrical, However, traditional manufacturing line cannot fulfill the process (AHP). Zha and Guo et al. [5] focused on the dynamic However, traditional manufacturing line cannot fulfill the process (AHP). and Guo et al. focused on augmenting the dynamic markets, results Zha in diminished lot [5] sizes dueproposed to Classical methodologies products demand to respond quicklyconsidering to frequent mainly changessingle of task orders. facility problem with uncertain demand and a novel demand to respond to frequent task orders. facility varieties problem (high-volume with uncertaintodemand and proposed a novel product low-volume production) [1]. or solitary, alreadyquickly existing product changes families ofanalyze 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; Design method; identification closely with the production rate Family and cost. In the industrial sector,
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.2019.03.292
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Therefore, in order to implement mass customized production, researchers and manufacturing industries begin to pay more attention to the design and planning of new manufacturing paradigm. Based on our current background, modular manufacturing system is considered as the key solution for these problems [10]. The new paradigm of modular manufacturing system is first proposed by Rogers and Bottcai [11] in 1997. Modular manufacturing system, different with traditional production lines, is mainly consisted of several manufacturing modules and intelligent automated transportation system. Manufacturing modules, composed by one or several machines, can perform different assembly operations. Different manufacturing modules are connected via the intelligent automated transportation system based on different product variants, thus making it possible to produce customized products. Modular manufacturing systems become the critical factor for solving the problem in mass customization, but it also brings new great challenges to the layout and planning of manufacturing system. Though, many methods for facility layout planning have emerged over many years of research, for example, past researches have not addressed the intra and intermodules layout problem considering flexible processes in modular manufacturing system. Thus, this paper considers the flexible processes and a mixed integer mathematical model is developed to determine the layout of manufacturing modules and machines simultaneously. Improved simulated annealing (SA) is developed and numerical examples are conducted to verify the validity of the Methodology. The contributions of this research are summarized as follows. First, this paper proposed the optimization problem for modular facilities layout planning considering flexible process routings. Second, a mixed integer programming is proposed for solving the problem. Finally, SA is developed and numerical examples are conducted to certify the performance of the Methodology. As follows, Section 2 describes the modular facilities layout problem considering flexible processes and develops the mixed integer mathematical model. The detailed information about SA is shown in section 3. In section 4, numerical examples are carried out to certify the validity of proposed partition method. Conclusions and future researches are summarized in section 5. 2. Problem description and mathematical model 2.1. Problem description Compared to traditional manufacturing lines, modular manufacturing system can be made up of individual manufacturing modules, which perform specific assembly operations and are dedicated to the manufacture of part of the products. A modular manufacturing module consists of one or several functional machines which are placed in the same area. Thus, the location of the manufacturing modules and the location of the machines within the module must be determined simultaneously in this study. Besides, in modular manufacturing system, the transport of the subassemblies and components between the modules is
taken over by the intelligent automated transportation system and Automated Guided Vehicle (AGV) supply the modules just in time with the parts or sub-assemblies they need. Therefore, there exist flexible process routes in modular manufacturing system, while workers can only conduct the production in sequence in traditional manufacturing line. Just as shown in Fig. 1, the manufacturing process of a product is divided into four operations: A, B, C and D. In production line, the product has to go through four operations A, B, C and D in sequence. On the contrary, with the flexible scheduling and intelligent transportation, there exists different process routes in modular manufacturing system, for example A, B, C, D and A, C, B, D and so on, as shown in Fig. 2.
Fig. 1. Schematic diagram of production line.
Fig. 2. Schematic diagram of modular manufacturing system.
In summary, the layout problem of modular manufacturing system with flexible production processes is considered, where each class of products may contain multiple operations with different process plans. And the modular facilities layout problem assigns resource to different machines or modules, involving internal and external flows. External flows are quite costly since they are transported by AGV. It should be noted that the total material handling costs is considered in modular facilities layout problem, including internal and external flows cost. Owing to the complexity of modular manufacturing system, the following assumption is proposed in this study: 1) The requirements of the customized products are known. 2) The number and variety of modules are known and the number and variety of machines within modules are known. 3) Machines are either square or rectangular and may have unequal-areas. 4) The dimensions of machines are given, but the dimension of every module is calculated based on the machines. 5) Modules and machines within the modules may be either vertically or horizontally orientated.
Weibo Ren et al. / Procedia CIRP 81 (2019) 1201–1206 Weibo Ren et al. / Procedia CIRP 00 (2019) 000–000
6) The parts or subassemblies are transported individually by AGV between manufacturing modules. 7) The logistics cost between machines and modules is related to the Manhattan distance between machines and modules. 8) There exist flexible process routes for customized products. 9) The distance between machines is negligible, while the distance between manufacturing modules is considered. 10) The dimensions of shop are given. 2.2. Mathematical Model Considering the alternative processes routes, this paper takes the production flexibility and logistics cost into account and a mixed integer model is established. The input sets, parameters and the decision variables are denoted as follows: (1) Sets i, j Î U m, n Î M p Î P k Î K (2) Parameters d1ij d2mn
Index of manufacturing modules. Index of machines. Index of products. Index of process routings of products.
The distance between module i and j. The distance between machines m and n within the same modules. C1 The travel cost between modules per unit. C2 The travel cost between machines within the same module per unit. Dp The demand of customized products. (xmm,ymm) Coordinate of center of machine m. (xui,yui) Coordinate of center of module i. Lm The length of machine m. Wm The width of machine m. Hm The horizontal length of machine m. Vm The vertical length of machine m. Lmax The length of floor space. Wmax The width of floor space. xuimax The upper horizontal coordinate of module i. xuimin The lower horizontal coordinate of module i. yuimax The lower vertical coordinate of module i. yuimin The upper vertical coordinate of module i. (3) Decision variables xpijk 1 if product p precedes operation on modules i and j with the kth process routing and 0 otherwise. ypmnk 1 if product p precedes operation on machine m and n within the same modules with the kth process routing and 0 otherwise. om 1 if machine m is located horizontally and 0 if machine m is located vertically. zij 1 if module i is in the right or above of the module j and 0 if module i is in the left or below of the module j.
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Mathematical Model: P
U
U
P
M
M
MinC = ååå x p ijk Dp d1ij C1 + ååå y p mnk Dp d 2mn C2 (1) p =1 i =1 j =1
p =1 m =1 n =1
The objective function (1) consists of two parts, the logistics costs between manufacturing modules and the logistics costs between machines within module. Subject to: Equation (2) and (3) represent the distance between manufacturing modules and the distance between machines, respectively. (2) d 2mn = xmm - xmn + ymm - ymn (3) d1 = xu - xu + yu - yu ij
i
j
i
j
Equation (4) and (5) are applied to control the orientation of machines. Also, the both two equations compute the new length and width of machines based on the direction of machines. (4) H m = Lm (1 - om ) + Wm (5) V = W (1 - o ) + L m
m
m
m
Constraints (6)-(11) are applied to limit the location of machines. Among them, constraints (6), (7), (8) and (9) ensure that all machines are in the shop floor area. Constraints (10) and (11) guarantee that there is no overlap between any machines. (6) xmm + H m / 2 £ Lmax "m (7) xm - H / 2 ³ 0 "m m
m
ymm + Vm / 2 £ Wmax "m ymm - Vm / 2 ³ 0 "m
xmm - xmn ³ ( H m + H n ) / 2 "m ymm - ymn ³ (Vm + Vn ) / 2 "m
(8)
(9) (10) (11)
Formulas (12)-(23) are the constraints on the manufacturing models. Equation (12) and (13) are used to compute the coordinate of center of module i. Equation (14), (15), (16) and (17) are conducted to compute the lower left corner and upper right corner of module i. Constraints (18), (19), (20) and (21) ensure that all modules are in the shop floor area. Constraints (22) and (23) ensure that there is no overlap between any modules. xui = (max(( xmm + H m / 2), ( xmn + H n / 2)...) (12) + min(( xmm + H m / 2), ( xmn + H n / 2)...)) / 2
yui = (max(( ymm + Vm / 2), ( ymn + Vn / 2)...) + min(( ymm + Vm / 2), ( ymn + Vn / 2)...)) / 2
(13) xuimax = max(( xmm + H m / 2), ( xmn + H n / 2)...) $m min i max i min i max i
xu
= min(( xmm - H m / 2), ( xmn - H n / 2)...) $m
yu
= max(( ymm + Vm / 2), ( ymn + Vn / 2)...) $m
yu
= min(( ymm - Vm / 2), ( ymn - Vn / 2)...) $m
xu
£ Lmax "i
(14) (15) (16) (17) (18)
Weibo Ren et al. / Procedia CIRP 81 (2019) 1201–1206 Weibo Ren et al. / Procedia CIRP 00 (2019) 000–000
1204 4
xuimin ³ 0 "i max i min i
yu
£ Wmax "i
yu
³ 0 "i
xuimax + (1 - zi j ) xuimax + ( zi j - 1) xuimin £ xu max + ( zi j - 1) xu max + (1 - zi j ) xu min "i, j j j j
(19) (20) (21) (22)
yuimax + (1 - zi j ) yuimax + ( zi j - 1) yuimin £ yu max + ( zi j - 1) yu max + (1 - zi j ) yu min "i, j j j j
(23)
Constraints (24) and (25) imply that the product can only be handled with an optimal process route. P
å x p =1 P
p ijk
å y p =1
= 1 "p
p mnk
= 1 "p
(24) (25)
3. Simulated annealing algorithm As the extension to the classical facility layout problem, there is no doubt that the problem of modular facilities layout considering flexible processes proved to be non-deterministic polynomial (NP-hard). There exist many heuristic algorithms, such as GA (genetic algorithm), SA (Simulated annealing algorithm), PSO (Particle Swarm Optimization algorithm) and so on, are developed to handle the optimization problem with better computational performance and get a relatively accurate optimal solution in a reasonable amount of time. SA is a kind of random optimization algorithm based on the Monte-Carlo iterative solution strategy. Additionally, this method can overcome the disadvantage of local research, for which it is hard to fall into a local optimum. Thus, improved SA is carried out to solve the problem. Starting with a higher initial temperature, SA randomly searches in the solution space, using the Metropolis sampling strategy, and repeats the sampling along with temperature reduction; then, it obtains the globally optimal solution. The details of SA algorithm are shown below: 1) Set the initial parameters: initial temperature T0; cooling coefficient K in [0,1]; maximal iterations Iter; stop temperature Tmin; initial solution X0; set T= T0, E0=E(X0); 2) Set XB = X0, EB =E0; 3) Set the iterations iter=1; 4) Produce the new solution based on the current optimal solution XB and the neighborhood function. Calculate the new objective function value EN and increment ΔE=EN –EB; 5) If ΔE≤0, set XB=XN; if ΔE > 0, then P=exp(-ΔE/T(i)); 6) C=random [0,1], if P > C, set XB=XN; otherwise XB=XB; 7) If iter < Iter, set iter=iter+1, go to step 4; otherwise go to step 8; 8) If T > Tmin, set T=KT, go to step 3; otherwise report XB and EB.
3.1. Encoding scheme and fitness evaluation To determine appropriate process route, the location of manufacturing modules and the location and direction of machines within modules, this paper develops related matrix to represent the process route of products and the location and direction of machines, respectively. The location of manufacturing modules is determined by the location of machines within modules. Assuming that there are three products and five machines, if the sequence is
Product 1 chooses the second process route and products 2 and 3 choose the first process route. The next two rows present co-ordinate of center of machines and the last row shows the direction of machines. When machine is in its original orientation, the element of the corresponding position in the matrix is 1, while machine is turned 90 degrees and the element is 0. Just as shown in the sequence, the co-ordinate of center of Machine 1 is (12,3) and Machine 1 is in its original orientation. This study is concerned with the joint optimization of external flows between manufacturing modules and internal flows between machine within modules, just as shown in Equation (26). P U U P M M (26) fitness = MinC = x p D d1 C + yp D d2 C
ååå p =1 i =1 j =1
ijk
p
ij 1
ååå
mnk
p
mn
2
p =1 m =1 n =1
3.2. The generation of initial solution and neighbor solution A random feasible solution is considered as the initial solution to the problem. And a neighbor solution is generated by the replacement of an element in matrices. As for the process route of product, it can be replaced with other process route (For example, the corresponding element is changed from 1 to 2). Similarly, the orientation of machines can also be changed (For example, the corresponding element is changed from 1 to 0). Besides, the co-ordinate of center of machine can be changed by the randomly generated numbers. 3.3. Annealing function During the process of neighborhood search, all possible changes can be obtained by a large value for the initial temperature T0 and the annealing function. We set the annealing function T= KT, where K is a real number between 0 and 1. The procedure will be terminated when the current temperature is lower than the stop temperature Tmin. 4. Numerical example and discussion The major differences between this study and others are the integrated consideration of alternative process routes, the internal and external flows between manufacturing modules or machines and joint optimization of location of modules and machines within modules. In previous study [12], the assembly line is divided into 10 manufacturing modules and the detail information is shown in Fig. 3. With the constraint of assembly
Weibo Ren et al. / Procedia CIRP 81 (2019) 1201–1206 Weibo Ren et al. / Procedia CIRP 00 (2019) 000–000
line, there exists different process routes, just as shown in Fig. 3. Due to the confidentiality requirement of the company, some detail information about assembly line cannot be shown in this paper. Thus, numerical examples are solved in the next part to illustrate the application of the methodology considering these constraints with the proposed mathematical model and SA algorithm.
Fig. 3. The information with modular manufacturing system. Note: There are no sequence constraints with the module 1 and module 2, module 3, module 4. It means there exists different process route, such as: module 1- module 2module 3-module 4, or module 3-module 1 -module 2- module 4 and so on. Similarly, there are no sequence constraint with module 7, module 8, module 9.
4.1. Numerical example To illustrate the application of proposed model and algorithm, numerical examples are presented and conducted to provide reasonable solution for designers. There are four customized products (P1-P4) and twelve machines (M1-M12) within seven manufacturing modules (Module 1-Module 7). The dimension of machines and the composition of manufacturing modules is shown in Table 1 and the length and width of machines are randomly generated. The alternative process routes of customized products are shown in Table2. As shown in Table 1, M1 and M2 belong to Module 1 and the dimension of M1 and M2 is (4,2) and (3,3). The same is true in other machines and modules. Besides, for convenient calculation, the internal flows between machines is set to 2 and the external flows between manufacturing modules is set to 4, the demand of four personalized products is set to 1:2:1:1.5. The length and width of floor space is set 100 and the distance between manufacturing modules is set 0.5.
1205 5
M3-M4-M8-M5-M9-M10 M3-M4-M6-M7-M9-M10-M11-M12
P4
M6-M7-M3-M4-M9-M10-M11-M12
The improved SA is conducted to solve the problem. After the preliminary experiment, the initial temperature of SA is set to 1,000; the Monte-Carlo iterative number is set to 50; the coefficient of the annealing function is set to 0.99, and the stop temperature is set to 1. The search time of SA is 52.34s and the iterative process of SA is shown in Figure 4. The result of the SA is shown in Table 3 and based on the location of machines, the situation of manufacturing modules can be calculated shown in Table 4. The location of manufacturing modules and the location and orientation of machines is shown in Figure 5. The selected process of products is 1, 2, 1 and 2. As seen in Table 3, the elements in second and third rows shows the coordinate of centre of machine and the elements in fourth row present the direction of machine. As shown in Figure 4, Table 3 and Table 4, the location of machines and manufacturing modules is determined and there is no overlap between machines and manufacturing modules and the total cost is 652, which verify the validity of proposed Methodology. Table 3. The information of result. M
1
2
3
4
Xm
4
Ym
2
D
0
5
6
7
1.5
8
1.5
6.5
1
1
8
9
10
11
4
8
1.5
7
2.5
6
0
1
0
1.5
14
14
14
18.5
19
9.5
2.5
11
7
3
8.5
1
1
1
1
0
0
Table 1. The information of machines and modules. Modules
1
Machines Lm Wm
1 4 2
2 2 3 3
3 6 3
3 4 4 2
5 6 5
4 6 4 3
5 7 3 3
8 5 5
Table 2. The flexible process of products. Products P1 P2 P3
Flexible process M1-M2-M5-M8-M11-M12 M1-M2-M8-M5-M11-M12 M1-M2-M6-M7-M8-M9-M10 M6-M7-M1-M2-M8-M9-M10 M3-M4-M5-M8-M9-M10
6 9 6 4
Fig 4. The iterative process of SA.
7 10 5 4
11 6 3
12 5 4
12
Weibo Ren et al. / Procedia CIRP 81 (2019) 1201–1206 Weibo Ren et al. / Procedia CIRP 00 (2019) 000–000
1206 6
5. Conclusion Considering the flexible process routes, a mixed integer model was developed to determine the location of manufacturing modules and machines and reduce the total logistics cost between modules and machines. Then, a SAbased approach was applied to solve the problem. To illustrate the application of methodology, serval numerical examples were carried out. The computational results demonstrated that the efficiency and feasibility in design of modular manufacturing system. Obviously, there exist some limitations in this study. First, uncertain demand of customized products should be considered in future work. Besides, make algorithm improvement. Though, SA algorithm can obtain optimal or approximate optimal results, there also exist some problems.
Fig 5. The result of modular layout problem. Table 4. The location of manufacturing module. Module
1
2
3
4
5
6
7
Xm
2.5
7
8
1.5
14
14
19
Ym
2
7
2.5
7.5
2.5
9
5.5
4.2. Discussion Based on the reference, there are many Based on the reference, there are many heuristic algorithms are carried out to solve the problem. Thus, it is necessary to verify the efficiency of proposed method. GA is applied to solve the experiment in section 4.1, and the encoding scheme, fitness evaluation and mutation operation of GA is similar with the method in SA. The tournament method is applied to select individuals during the selection operation. During the crossover operation, two individuals are randomly selected and the position of individuals is randomly chosen for the crossover operation. is used. The developed GA is used. The maximum evolution algebra is set to 800, and set the initial group to 40, the probability of the crossover and mutation operations is 0.9 and 0.1, respectively. The optimization result obtained by GA is 683, higher than the result by SA and the search time (72.43s) is longer than SA (52.34s), which verify the efficiency of the improved SA. In order to testify the performance of mathematical model and SA algorithm, serval numerical examples with randomly generated data is presented and carried out. The information and results of numerical examples are shown in Table 5. As shown in Table 5, proposed methodology can be applied not only in small cases, but also in large-scale cases, which verify the practicality of method in reality. Table 5. The information and results of numerical. No
Machines
Modules
Products
time/s (SA)
time/s (GA)
1
6
3
2
14.99
19.35
2
10
6
3
30.02
49.36
3
12
7
4
52.34
72.43
4
16
10
5
88.52
111.34
5
20
12
5
130.17
176.11
6
25
16
6
202.46
281.46
7
30
18
7
293.21
353.32
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] Tompkins J A, White J A, Bozer Y A, et al. Facilities Planning. New work: John Wiley & Sons, Inc,2003. [2] Anjos, M. F., & Vieira, M. V. C. 2017. Mathematical optimization approaches for facility layout problems: the state-of-the-art and future research directions. European Journal of Operational Research, 261(1), 116. [3] Pourhassan, M. R., & Raissi, S. 2017. An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem. Journal of Industrial Information Integration, 8. [4] Azadeh, A., Moghaddam, M., Nazari, T., & Sheikhalishahi, M. 2016. Optimization of facility layout design with ambiguity by an efficient fuzzy multivariate approach. The International Journal of Advanced Manufacturing Technology, 84(1-4), 565-579. [5] Zha, S., Guo, Y., Huang, S., Wang, F., & Huang, X.. 2017. Robust facility layout design under uncertain product demands . Procedia Cirp, 63, 354359. [6] Moslemipour, G. , Lee, T. S. , & Rilling, D. . 2012. A review of intelligent approaches for designing dynamic and robust layouts in flexible manufacturing systems. International Journal of Advanced Manufacturing Technology, 60(1-4), 11-27. [7] Lee H Y , Kang S , Chae J . 2015. Mutation effects in a genetic algorithm for a facility layout problem in QAP form. International Journal of Advanced Logistics, 4(3):170-179. [8] Vitayasak, S. , Pongcharoen, P. , & Hicks, C. . (2016). A tool for solving stochastic dynamic facility layout problems with stochastic demand using either a genetic algorithm or modified backtracking search algorithm. International Journal of Production Economics, 190: 146-157. [9] Wang, Z., Zhang, M., Sun, H., & Zhu, G. 2016. Effects of standardization and innovation on mass customization: an empirical investigation. Technovation, 48-49, 79-86. [10] Shaik, A. M., Rao, V. V. S. K., & Rao, C. S. 2015. Development of modular manufacturing systems—a review. International Journal of Advanced Manufacturing Technology, 76(5-8), 789-802. [11] Rogers, G. G., & Bottaci, L. 1997. Modular production systems: a new manufacturing paradigm. Journal of Intelligent Manufacturing, 8(2), 147156. [12] Ren W, Wen J, Guan Y, Hu Y. 2018. Research on assembly module partition for flexible production in mass customization. Procedia CIRP, v 72, p 744-749.