(a) Picking up of six components (b) Picking up of three simultaneously. components simultaneously. Fig. 2 An example of the simultaneous pickup. 6 /

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*1 *1 *1 *2 *2 Optimization of Printed Circuit Board Assembly Prioritizing Simultaneous Pickup in a Placement Machine Toru TSUCHIYA *3, Atsushi YAMASHITA, Toru KANEKO, Yasuhiro KANEKO and Hirokatsu MURAMATSU *3 Department of Mechanical Engineering, Graduate School of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, Shizuoka 432-8561, Japan In this paper, we propose a new method for reducing assembly time in printed circuit board (PCB) assembly by prioritizing efficient simultaneous pickup operation of placement machines. There are three major problems of the scheduling: (1) component feeder location (affects efficiency of pickup operation), (2) mounting sequencing (affects total distance of the mounting tour), and (3) simultaneous pickup (affects efficiency of pickup operation). To solve these problems, this paper proposes the following approaches. We solve (1) and (3) in a heuristic way by using a random multi-start local search. We solve (2) greedily with putting the result of the feeder array to effective use. The effectiveness of the proposed method was shown through simulations. Key Words : Optimization, Scheduling, Printed Circuit Board Assembly 1. Printed Circuit Board: PCB PCB?? (? : : : *1 ( 432-8561 3 5 1) *2 E-mail: f0730066@ipc.shizuoka.ac.jp Rotary Head Feeders PCB z x y Feeders Multiple Head PCB z y (b) Non-rotary type. (a) Rotary type. Fig. 1 An example of the two different types of the placement machines. PCB PCB PCB 8? NP?,?,?,??? x

(a) Picking up of six components (b) Picking up of three simultaneously. components simultaneously. Fig. 2 An example of the simultaneous pickup. 6 / (6) NP Multi-start Local Search: MLS? PCB 1. 2. 3. 4 1 4. PCB 1 4 3. PCB?? p max : 2.?? 1 1 Fig. 4 The structure of our model with the notations (h max = 6, f max = 9, s max = 18, D h /D f = 2). Fig. 3 The structure of the placement machine.

t : (t = 1,..., t max ) j t : t ( j t = 1,..., j maxt ) C t, jt (x, y) : j t f : ( f = 1,..., f max ) s : (s = 1,..., s max ) S f : f T f : f Q f : f r f : f l f : f D h : D f : h : (h = 1,..., h max ) 4. 2 MLS MLS 5. 5 1 MLS x x x x x x x x MLS 5 2 1 1. 0 2. f max 3. 2. f ( f = 1,..., f max ) 2 2 3 3 V 1 V 2 V 3 (1) V V = αv 1 + βv 2 + γv 3 (1) α β γ MLS 3 a V 1?? 1 3 5 6 7 2 5 1 3 4 1 3 A(1) A(3) A( f ) f (2) f max V 1 = A( f ) (2) f =1 3 b V 2 PCB Fig. 5 An example of the overlapping.

(3) f max V 2 = Q f S Gt f S f (3) f =1 G T f (4) T f S Gt f G T f G T f = j maxt f n=1 C T f,n(x, y) (4) 3 c V 3 h max n n h max h max n n??(a)??(b) n D h D f D h /D f D h /D f = 2?? (c) 5??(b)??(c) 1. 2. 3. h = 1 2. 4. 1 5. 2. 0 4. 6. 6. 2. (5) (6) h max V 3 = (h max n + 1)B(n) (5) n=1 (p max C n ) if n = h max B(n) = otherwise C n (6) C n 1. 6. n 4 V 2 2 1 MLS 5 3 MLS 1. 6.?? (a) n h max?? (b) h max 1 Rank 1 6 Rnak 2 5 Rank1 (a) The head template. (b) The quantity of each feeder. (c) 5-simultaneous pickup (d) The quantity of each feeder obtained. after (c). Fig. 6 An example of calculating the number of the simultaneous pickups (h max = 6, f max = 8, s max = 11, D h /D f = 2). (a) n-simultaneous pickup patterns obtained through the MLS. (b) Combined pickup patterns with (a). Fig. 7 An example of pickup patterns before combination and after combination (h max = 6).

Table 1 The combination list (h max = 6) Number of pickup times Rank 1 2 3 4 5 6 1 6 2 5 1 3 4 2 4 3 3 5 4 1 1 6 3 2 1 7 2 2 2 8 3 1 1 1 9 2 2 1 1 10 2 1 1 1 1 11 1 1 1 1 1 1 Rank 1. h max 2. 1. 3. 1 5 4 D h /D f = 1?? 1 10 1 10 n G n 1 2 3 4 5 1. C init 2. C init G n n 3. 2. G n 4. 3. 5. 1. C init 4. 6. 498 p max = 498 20 f max = 20 2 60 s max = 60 30mm D h = 30 15mm D f = 15 6 1 (1) α = 0.5 1.5 β = 0.5 1.5 γ = 0.5 1.5 0.25 5 5 5 125 1000 MLS 125 125 α = 1.5 β = 5 γ = 7.5 6 2 1000 MLS 5 n MLS n 9 6 40% Fig. 8 The overview of the pickup and placement sequencing (D h /D f = 1). Rate of n -multiple pickup (%) 100% 80% 60% 40% 20% n = 6 n = 5 n = 4 n = 3 n = 2 0% n = 1 0 200 400 600 800 Number of generating initial solutions Fig. 9 Rate of n-simultaneous pickup.

Table 2 Parameters of the feeder Feeder number ( f ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Component type (T f ) 1 1 1 2 2 2 3 3 4 4 5 6 7 8 9 10 11 12 13 14 Quantity of feeder (Q f ) 30 30 30 40 40 40 29 29 19 19 22 13 32 44 17 7 36 6 10 5 Left half of width (r f ) 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 11.0 11.0 11.0 13.0 13.0 8.5 8.5 16.0 16.0 22.8 23.5 36.3 Right half of width (l f ) 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 12.0 12.0 12.0 14.0 14.0 10.8 10.8 12.2 12.2 18.0 19.9 32.8 AD1 AD5 10 AD1: AD2: AD1 AD3: MLS 1 AD4: AD5: MLS β = 50 MLS γ = 75 10 AD2 AD4 AD5 AD3 12% MLS AD1 2 4 5 PC CPU: Pentium D 2.8GHz, : 1GB, OS: Windows XP 5 AD3 10 5 Assembly time (unit time) 195 185 175 165 155 145 135 125 0 200 400 600 800 1000 Number of generating initial solutions Fig. 10 Assembly time of AD1-AD5. AD1 AD2 AD3 AD4 AD5 7. PCB MLS GA (1) Ayob, M., Cowling, P. and Kendall, G., Optimisation for Surface Mount Placement Machines, Proceedings of the 2002 IEEE International Conference on Industrial Technology (ICIT2002), Vol. 1 (2002), pp. 498 503. (2) Crama, Y., van de Klundert, J. and Spieksma, F., Production Planning Problems in Printed Circuit Board Assembly, Discrete Applied Mathematics, Vol. 123, No. 1 3 (2002), pp. 339 361. (3) Burke, E., Cowling, P. and Keuthen, R., The Printed Circuit Board Assembly Problem: Heuristic Approaches for Multi-Headed Placement Machinery, Proceedings of the 2001 International Conference on Artificial Inteligence (IC-AI2001), (2001), pp. 1456 1462. (4) Ayob, M. and Kendall, G., A Nozzle Selection Heuristic to Optimise the Hybrid Pick and Place Machine, Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent System, Vol. 2 (2004), pp. 1259 1264. (5) Csaszar, P., Tirpak, T. and Nelson, P., Optimization of a High-Speed Placement Machine Using Tabu Search Algorithms, Annals of Operations Research, Vol. 96, No. 1 (2000), pp. 125 147. (6) Lee, W., Lee, S., Lee, B. and Lee, Y., Genetic Optimization Approach to Operation of a Multi-Head Surface Mounting Machine, IEICE Transactions on Fundamentals of Electronics, Vol. E83 A, No. 9 (2000), pp. 1748 1756. (7) Tsuchiya, T., Yamashita, A., Kaneko, T., Kaneko, Y. and Muramatsu, H., Scheduling Optimization of Component Mounting in Printed Circuit Board Assembly by Prioritizing Simultaneous Pickup, Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS2007), (2007), pp. 2913 2918.

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