108 min t s 108 008 100 min c t wc σ t ek 849 min w

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= 1.08 min , T s = 1.08 - 0.08 = 1.00 min (c) T wc = Σ T ek = 8.49 min, w = Minimum Integer 8 49 100 . . = 8.49 9 workers 110
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Assembly Lines-3e-S 07-05/06, 06/04/07 (d) Line balancing solution using ranked positional weights method ( T e expressed in min): Elements by RPW Allocation of elements to stations Element T e (min) RPW Station Element T e (min) T si (min) 1 0.15 7.29 1 1 0.15 2 0.37 6.56 2 0.37 5 0.58 6.19 4 0.21 4 0.21 4.42 3 0.21 0.94 3 0.21 4.41 2 5 0.58 10 0.45 4.41 11 0.18 11 0.18 4.34 12 0.20 0.96 12 0.20 4.16 3 10 0.45 9 0.30 4.09 9 0.30 7 0.29 4.08 6 0.12 14 0.72 3.96 8 0.12 0.99 6 0.12 3.91 4 7 0.29 8 0.12 3.91 13 0.65 0.94 13 0.65 3.79 5 14 0.72 16 0.35 3.24 15 0.25 0.97 15 0.25 3.14 6 16 0.35 18 0.12 3.08 18 0.12 19 0.10 3.06 19 0.10 20 0.23 2.96 20 0.23 17 0.16 2.89 17 0.16 0.96 21 0.40 2.73 7 21 0.40 22 0.33 2.33 22 0.33 23 0.25 2.00 23 0.25 0.98 24 1.75/2 1.75 8, 9* 24 1.75/2 0.875 total = 8.490 * Stations 8 and 9 are arranged in parallel to divide the time of element 24 in half. (e) Use T s = 0.99 min (station 3). Balance delay d = 9 0 99 8 49 9 0 99 ( . ) . ( . ) - = 0.0471 = 4.71% (f) E = 0.96 (given), E b = 1 - 0.0471 = 0.9529, E r = 1.00/1.08 = 0.9259. Overall labor efficiency = E E b E r = 0.96(0.9529)(0.9259) = 0.8470 = 84.7% Mixed Model Assembly Lines 15.18 Two product models, A and B, are to be produced on a mixed model assembly line. Hourly production rate and work content time for model A are 12 units/hr and 32.0 min, respectively; and for model B are 20 units/hr and 21.0 min. Line efficiency = 0.95, balance efficiency = 0.93, repositioning time = 0.10 min, and manning level = 1. Determine how many workers and workstations must be on the production line in order to produce this workload. Solution : WL = 12(32) + 20(21) = 384 + 420 = 804 min/hr R p = 12 + 20 = 32 units/hr, T c = 60 0 95 32 ( . ) = 1.78125 min, T s = 1.78125 - 0.1 = 1.68125 min, E r = 168125 178125 . . = 0.94386 AT = 60(0.95)(0.93)(0.94386) = 50.03 min/hr. per worker w = 804 50 03 . = 16.07 17 workers . Since M = 1, n = w = 17 stations . 15.19 Three models, A, B, and C, will be produced on a mixed model assembly line. Hourly production rate and work content time for model A are 10 units/hr and 45.0 min; for model B are 20 units/hr and 35.0 min; and for model C are 30 units/hr and 25.0 min. Line efficiency is 95%, balance efficiency is 0.94, repositioning efficiency = 0.93, and manning level = 1.3. Determine how many workers and workstations must be on the production line in order to produce this workload. Solution : WL = 10(45) + 20(35) + 30(25) = 450 + 700 + 750 = 1900 min/hr 111
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Assembly Lines-3e-S 07-05/06, 06/04/07 AT = 60(0.95)(0.94)(0.93) = 49.83 min/hr per worker w = 1900 49 83 . = 38.1 39 workers . Since M = 1.3, n = w / M = 39/1.3 = 30 stations 15.20 For Problem 15.18, determine the variable rate launching intervals for models A and B. Solution : For product A, T cv (A) = 32 17 0 94386 0 93 ( . )( . ) = 2.144 min For product B, T cv (B) = 21 17 0 94386 0 93 ( . )( . ) = 1.407 min 15.21 For Problem 15.19, determine the variable rate launching intervals for models A, B, and C. Solution : For product A, T cv (A) = 45 39 0 94 0 93 ( . )( . ) = 1.320 min For product B, T cv (B) = 35 39 0 94 0 93 ( . )( . ) = 1.027 min For product C, T cv (C) = 25 39 0 94 0 93 ( . )( . ) = 0.733 min 15.22 For Problem 15.18, determine (a) the fixed rate launching interval, and (b) the launch sequence of models A and B during one hour of production. Solution : R p = 12 + 20 = 32/hr. T cf = 1 32 12 32 20 21 17 0 94386 0 93 ( ) ( . )( . ) x x + = 1.684 min If product A launched, T cjh = T c A h = 32 17 0 94386 0 93 ( . )( . ) = 2.144 min If product B launched, T cjh = T c B h = 21 17 0 94386 0 93 ( . )( . ) = 1.407 min Note that the hourly production rates of the two models (12/hr for A and 20/hr for B) are both divisible by 4 (3 per 15 min for A and 5 per 15 min for B). Thus the sequence repeats every 8 launches. The following table indicates the solution for two cycles (16 launches): ( Σ T c A h -mT cf ) 2 ( Σ T c B h -mT cf ) 2
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