Problem 6-1 An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day. a. What are the minimum and maximum cycle times? (Round your answers to 1 decimal place.) b. What range of daily output is theoretically possible for the line? (Round your answers to 1 decimal place. Enter the smaller value in the first box and the larger value in the second box.) Range of output Correct to units/day c. What is the minimum number of workstations needed if the maximum output rate is to be sought? (Round up your answer to the next whole number.) Minimum number of workstations d. What cycle time will provide an output rate of 125 units per day? (Round your answer to 1 decimal place.) Cycle time e. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes? Cycle Time Potential Output Problem 6-5 As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows: Task Duration (minutes) Immediate Predecessor a 0.2 – b 0.4 a c 0.2 b d 0.4 – e 1.2 d f 1.2 c g 1.0 e, f ________________________________________ Do each of the following: b. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.) The minimum cycle time Correct minutes per unit The maximum cycle time Correct minutes per unit Calculated cycle time minutes per unit ________________________________________ c. Determine the minimum number of stations needed. (Round your answer to the next whole number.) Minimum number of stations d. Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice. Work stations Following Tasks I A, B, D, C Correct II E Correct III F Correct IV G Correct ________________________________________ e. Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 2 decimal places. Omit the “%” sign in your response.) Percentage of idle time Problem 6-7 For the set of tasks given below, do the following: Task Task Time(seconds) Immediate Predecessor A 45 – B 11 A C 9 B D 50 – E 26 D F 11 E G 12 C H 10 C I 9 F, G, H J 10 I 193 ________________________________________ b. Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a seven-hour day. (Round your answers to 1 decimal place.) c. Determine the minimum number of workstations for output of 500 units per day. (Round up your answer to the next whole number.) Minimum number of workstations d. Balance the line using the greatest positional weight heuristic. Break ties with the most following tasks heuristic. Use a cycle time of 50 seconds. e. Calculate the percentage idle time for the line using the 50 second cycle time. (Round your answer to 1 decimal place. Omit the “%” sign in your response.) Percentage of idle time Problem 6-3 A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 4 units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. b. In order of greatest positional weight. c. What is the efficiency? (Round your answer to 2 decimal places. Omit the “%” sign in your response.) Efficiency