B t c 29 60 min t s 095 015 080 min t wc 1560 900 min

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(b) T c = ( 29 60 0.95 60 = 0.95 min, T s = 0.95 - 0.15 = 0.80 min T wc = 15(60) = 900 min of direct labor w = Minimum Integer 900 0 90 080 . ( . ) = 1250 workers , and n = 1250 2 5 . = 500 stations 15.7 Production rate for a certain assembled product is 47.5 units per hour. The assembly work content time = 32 min of direct manual labor. The line operates at 95% uptime. Ten workstations have two workers on opposite sides of the line so that both sides of the product can be worked on simultaneously. The remaining stations have one worker. Repositioning time lost by each worker is 0.2 min/cycle. It is known that the number of workers on the line is two more than the number required for perfect balance. Determine (a) number of workers, (b) number of workstations, (c) balance efficiency, and (d) average manning level. Solution : (a) T c = 60 0 95 47 5 ( . ) . = 1.2 min, T s = 1.2 - 0.2 = 1.0 min For perfect balance, E b = 1.0. w = Minimum Integer 32 0 10 10 . . ( . ) = 32 workers. With 2 more workers than required for perfect balance, w = 32 + 2 = 34 workers . (b) n = 20/2 + (34 - 20) = 10 + 14 = 24 stations . (c) E b = 32 0 34 10 . ( . ) = 0.941 = 94.1% (d) M = 34/24 = 1.417 15.8 The work content for a product assembled on a manual production line is 48 min. The work is transported using a continuous overhead conveyor that operates at a speed of 5 ft/min. There are 24 workstations on the line, one-third of which have two workers; the remaining stations each have one worker. Repositioning time per worker is 9 sec, and uptime efficiency of the line is 95%. (a) What is the maximum possible hourly 104
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Assembly Lines-3e-S 07-05/06, 06/04/07 production rate if the line is assumed to be perfectly balanced? (b) If the actual production rate is only 92% of the maximum possible rate determined in part (a), what is the balance delay on the line? Solution : (a) w = 2(24/3) + 1(24 x 2/3) = 2(8) + 1(16) = 32 workers w = wc b s T E T , therefore, T s = wc b T E w If the line is perfectly balanced, the E b = 1.0. T s = 48 0 10 32 . . ( ) = 1.5 min, T c = 1.5 + 0.15 = 1.65 min R p = 60 0 95 165 ( . ) . = 34.55 pc/hr (at E = 0.95 and E b = 1.0) (b) Actual R p = 0.92(34.55) = 31.78 pc/hr T c = 60 0 95 3178 ( . ) . = 1.7935, T s = 1.7935 - 0.15 = 1.6435 min d = 32 16435 48 0 32 16435 ( . ) . ( . ) - = 0.087 = 8.7% 15.9 Work content time for a product assembled on a manual production line is 45.0 min. Production rate of the line must be 40 units/hr. Work units are attached to a moving conveyor whose speed = 8 ft/min. Repositioning time per worker is 8 sec, line efficiency is 93%, and manning level = 1.25. Owing to imperfect line balancing, it is expected that the number of workers needed on the line will be about 10% more workers than the number required for perfect balance. If the workstations are arranged in a line, and the length of each station is 12 ft, (a) how long is the entire production line, and (b) what is the elapsed time a work unit spends on the line? Solution : (a) T c = 60 0 93 40 ( . ) = 1.395 min T s = 1.395 - 0.133 = 1.262 min For perfect balance, E b = 1.0. w = Minimum Integer 450 10 1262 . . ( . ) = 35.7 With 10% more workers, w = 1.1(35.7) = 39.2 40 workers. n = 40 125 . = 32 stations L = (32 stations)(12 ft/station) = 384 ft . (b) Given L = 384 ft and v c = 8 ft/min, ET = 384 8 = 48.0 min Line Balancing (Single Model Lines) 15.10 Show that the two statements of the objective function in single model line balancing in Eq. (15.20) are equivalent.
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