homework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30…

homework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30 pieces and (b) a shift output of 24 pieces. assume an 6 - hour shift, and use the rule: choose the assignable task with the longest processing time. compute the line efficiency for each case.\na. fill in the table below for a shift output of 30 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation\ttasks\ttotal time\tidle time\n1\t-select-\t\t\n2\t-select-\t\t\n3\t-select-\t\t\n4\t-select-\t\t\ntotal\t\t\nwhat is the assembly - line efficiency? round your answer to one decimal place.\n%\nb. fill in the table below for a shift output of 24 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation\ttasks\ttotal time\tidle time\n1\t-select-\t\t\n2\t-select-\t\t\n3\t-select-\t\t\ntotal\t\t\nwhat is the assembly - line efficiency? round your answer to one decimal place.

homework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30 pieces and (b) a shift output of 24 pieces. assume an 6 - hour shift, and use the rule: choose the assignable task with the longest processing time. compute the line efficiency for each case.\na. fill in the table below for a shift output of 30 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation\ttasks\ttotal time\tidle time\n1\t-select-\t\t\n2\t-select-\t\t\n3\t-select-\t\t\n4\t-select-\t\t\ntotal\t\t\nwhat is the assembly - line efficiency? round your answer to one decimal place.\n%\nb. fill in the table below for a shift output of 24 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation\ttasks\ttotal time\tidle time\n1\t-select-\t\t\n2\t-select-\t\t\n3\t-select-\t\t\ntotal\t\t\nwhat is the assembly - line efficiency? round your answer to one decimal place.

Answer

Explanation:

Step1: Calculate cycle time for each case

For a 6 - hour shift (6×60 = 360 minutes). For output of 30 pieces, cycle time (C_1=\frac{360}{30}=12) minutes. For output of 24 pieces, cycle time (C_2=\frac{360}{24}=15) minutes.

Step2: Determine task times and precedence

Sum of all task times: (5 + 4+2+3 + 4+5+4+2+3+3+2=37) minutes.

Step3: Assign tasks to work - stations for 30 - piece output

Using the rule of choosing the assignable task with the longest processing time and breaking ties by lowest task number:

  • Workstation 1: Tasks A (5 minutes) and B (4 minutes), total time = 5 + 4=9 minutes, idle time = 12 - 9 = 3 minutes.
  • Workstation 2: Tasks D (3 minutes), E (4 minutes), total time = 3+4 = 7 minutes, idle time = 12 - 7 = 5 minutes.
  • Workstation 3: Tasks F (5 minutes), G (4 minutes), total time = 5 + 4=9 minutes, idle time = 12 - 9 = 3 minutes.
  • Workstation 4: Tasks I (3 minutes), H (2 minutes), J (3 minutes), K (2 minutes), total time = 3+2+3+2 = 10 minutes, idle time = 12 - 10 = 2 minutes. Total idle time = 3 + 5+3 + 2=13 minutes, total time across all workstations = 360 minutes. Assembly - line efficiency (E_1=\frac{37}{4\times12}\times100%\approx77.1%)

Step4: Assign tasks to work - stations for 24 - piece output

  • Workstation 1: Tasks A (5 minutes), B (4 minutes), total time = 5 + 4=9 minutes, idle time = 15 - 9 = 6 minutes.
  • Workstation 2: Tasks D (3 minutes), E (4 minutes), F(5 minutes), total time = 3+4 + 5=12 minutes, idle time = 15 - 12 = 3 minutes.
  • Workstation 3: Tasks G (4 minutes), I (3 minutes), H (2 minutes), J (3 minutes), K (2 minutes), total time = 4+3+2+3+2 = 14 minutes, idle time = 15 - 14 = 1 minute. Total idle time = 6+3 + 1=10 minutes, total time across all workstations = 360 minutes. Assembly - line efficiency (E_2=\frac{37}{3\times15}\times100%\approx82.2%)

For 30 - piece output:

Workstation Tasks Total Time Idle Time
1 A, B 9 3
2 D, E 7 5
3 F, G 9 3
4 I, H, J, K 10 2
Total - 35 13
Assembly - line efficiency: 77.1%

For 24 - piece output:

Workstation Tasks Total Time Idle Time
1 A, B 9 6
2 D, E, F 12 3
3 G, I, H, J, K 14 1
Total - 35 10
Assembly - line efficiency: 82.2%

Answer:

For 30 - piece output: Workstation 1: Tasks A, B; Total Time: 9; Idle Time: 3 Workstation 2: Tasks D, E; Total Time: 7; Idle Time: 5 Workstation 3: Tasks F, G; Total Time: 9; Idle Time: 3 Workstation 4: Tasks I, H, J, K; Total Time: 10; Idle Time: 2 Total Total Time: 35; Total Idle Time: 13 Efficiency: 77.1%

For 24 - piece output: Workstation 1: Tasks A, B; Total Time: 9; Idle Time: 6 Workstation 2: Tasks D, E, F; Total Time: 12; Idle Time: 3 Workstation 3: Tasks G, I, H, J, K; Total Time: 14; Idle Time: 1 Total Total Time: 35; Total Idle Time: 10 Efficiency: 82.2%