Iii 8 9 min 56 min 8 9 min iii 3 6 21 min 9 6 min iii

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III 8 9 min 56 min 8 9 min III 3 6 21 min 9 6 min III 9 6 min 10 24 min IV 10 24 min 51 min 167.0 min 167.0 min (d) Balance efficiency E b = 167 3 60 ( ) = 0.928 = 92.8% 15.27 For the data given in previous Problem 15.26, (a) solve the mixed model line balancing problem except that line efficiency = 0.96 and repositioning efficiency = 0.95. (b) Determine the balance efficiency for your solution. Solution : (a) Available time per station = 60(0.96)(0.95) = 54.72 min. Use same list of elements by column as in Problem 15.26. List of elements by column Allocation of elements to workstations Element TT k Column Station Element TT k TT si 1 18 min I 1 1 18 min 3 27 min II 3 27 min 2 15 min II 4 5 min 5 5 min II 5 3 min 53 min 4 3 min II 2 2 15 min 7 39 min III 7 39 min 54 min 6 21 min III 3 6 21 min 8 9 min III 8 9 min 9 6 min III 9 6 min 36 min 10 24 min IV 4 10 24 min 24 min 167.0 min 167.0 min (b) Balance efficiency E b = 167 4 54 ( ) = 0.773 = 77.3% 15.28 For Problem 15.26, determine (a) the fixed rate launching interval and (b) the launch sequence of models A, B, and C during one hour of production. Solution : (a) R p = 15 + 10 + 5 = 30 units/hr T cf = ( 29 1 30 15 4 8 10 6 2 5 6 6 3 10 0 928 x x x . . . ) ( . )( . ) + + = 2.000 min If model A launched, T cAh = 4 8 3 0 928 . ( . ) = 1.724 min R pA = 3 If model B launched, T cBh = 6 2 3 0 928 . ( . ) = 2.227 min R pB = 2 If model C launched, T cCh = 6 6 3 0 928 . ( . ) = 2.371 min R pB = 1 117
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Assembly Lines-3e-S 07-05/06, 06/04/07 We note that the hourly production rates of the three models (15/hr for A and 10/hr for B and 5/hr for C) are all divisible by 5 (3 per 12 min for A, 2 per 12 min for B, and 1 per 12 min for C). Thus the sequence should repeat every 6 launches, 5 times each hour. The following table indicates the solution for one cycle (see equations for first three columns following launching sequence): Eq. A Eq. B Eq. C A,B,or C Σ T cjh Σ T cf T cAh T cBh T cCh T cf 1.076 1.052 1.138 B 2.23 2.00 1.724 2.227 2.371 2.000 1.002 2.206 1.358 A 3.95 4.00 1.724 2.227 2.371 2.000 1.606 2.032 1.104 C 6.32 6.00 1.724 2.227 2.371 2.000 1.502 2.301 100.48 A 8.05 8.00 1.724 2.227 2.371 2.000 3.053 2.075 100.17 B 10.27 10.00 1.724 2.227 2.371 2.000 3.000 100.25 100.41 A 12.00 12.00 1.724 2.227 2.371 2.000 Eq. A: ( 29 pA cAh cf Am R T mT Q Σ - + Eq. B: ( 29 pB cBh cf Bm R T mT Q Σ - + Eq. C: ( 29 pC cCh cf Cm R T mT Q Σ - + 15.29 Two similar models, A and B, are to be produced on a mixed model assembly line. There are four workers and four stations on the line ( M i = 1 for i = 1, 2, 3, 4). Hourly production rates for the two models are: for A, 7 units/hr; and for B, 5 units/hr. The work elements, element times, and precedence requirements for the two models are given in the table below. As the table indicates, most elements are common to both models. Element 5 is unique to model A, while elements 8 and 9 are unique to model B. Assume E = 1.0 and E r = 1.0. (a) Develop the mixed model precedence diagram for the two models and for both models combined. (b) Determine a line balancing solution that allows the two models to be produced on the four stations at the specified rates. (c) Using your solution from (b), solve the fixed rate model launching problem by determining the fixed rate launching interval and constructing a table to show the sequence of model launchings during the hour.
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